research article numerical simulation of reactive flows...
TRANSCRIPT
Research ArticleNumerical Simulation of Reactive Flows in OverexpandedSupersonic Nozzle with Film Cooling
Mohamed Sellam and Amer Chpoun
Laboratoire de Mecanique et drsquoEnergetique drsquoEvry (LMEE) 40 rue du Pelvoux 91020 Evry Cedex France
Correspondence should be addressed to Mohamed Sellam sellamufrstuniv-evryfr
Received 9 October 2014 Revised 4 March 2015 Accepted 4 March 2015
Academic Editor Joseph Majdalani
Copyright copy 2015 M Sellam and A Chpoun This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Reignition phenomena occurring in a supersonic nozzle flow may present a crucial safety issue for rocket propulsion systemsThese phenomena concern mainly rocket engines which use H
2gas (GH
2) in the film cooling device particularly when the nozzle
operates under over expanded flow conditions at sea level or at low altitudes Consequently the induced wall thermal loads canlead to the nozzle geometry alteration which in turn leads to the appearance of strong side loads that may be detrimental to therocket engine structural integrity It is therefore necessary to understand both aerodynamic and chemical mechanisms that areat the origin of these processes This paper is a numerical contribution which reports results from CFD analysis carried out forsupersonic reactive flows in a planar nozzle cooled with GH
2film Like the experimental observations CFD simulations showed
their ability to highlight these phenomena for the same nozzle flow conditions Induced thermal load are also analyzed in termsof cooling efficiency and the results already give an idea on their magnitude It was also shown that slightly increasing the filminjection pressure can avoid the reignition phenomena by moving the separation shock towards the nozzle exit section
1 Introduction
One of the major challenges that the aerospace industrycontinues to face is the continued increase in launcherspayload For example the latest version of the Vulcain-IIengine of the European Ariane 5 ECA launcher is able to putinto geostationary orbit a payload of about 10 tons The goalis however to reach 12 tons in the near future There are twochallenges here the increase in payload and the performanceconsolidation in terms of reliability
These challenges promote development of nozzles withhigher performances which are substantially achieved byincreasing the nozzle expansion area ratio or by developingnew innovative nozzle concepts The rocket engine nozzleswith high expansion area ratio are generally optimized foroperating at high altitudes At sea level and at low altitudesthe nozzle operates in overexpanded flow conditions thatis the ambient pressure is higher than the nozzle exitpressure The resulting adaptation shock may lead to flow
separation unsteadiness and shock interaction The ensuingside loads may be detrimental for both nozzle and otherengine components In addition these nozzles are designed toexpand and accelerate combustion gases at high temperatureTo avoid thermal loads designers adopt several nozzlecoolingmethodsThemost effective one uses the film coolingtechnique For example for Vulcain-II rocket engine thecooling system is designed in two parts a dump cooling forthe first expansion part of the nozzle and GH
2film cooling
for the second part [1 2]The present study is a contribution to the works initiated
by the CNES during the last ten years in the field of innovativenozzle researchesThemain goal is to develop new supersonicnozzle concepts for cryogenic rocket engines One issue thatattracted the interest of scientists is that related to the riskof reignition that can occur in the main flow resulting fromcombustion of GH
2used as film cooling This phenomenon
may happenwhen theGH2film ismixedwith the air engulfed
into the separated region along the mixing shear layer at high
Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2015 Article ID 252404 15 pageshttpdxdoiorg1011552015252404
2 International Journal of Aerospace Engineering
Cylindricalcombustion
chamber
Outlet caisson
C-D planarnozzle
2 injectorGH
(a) From [22]
Wall with pressuretransducers
Gas combustionInjector
Separation shock
Thermal loads due to reignition
Nozzle inlet
Recirculation zone
h = 002818 m
H2 injection
l = 00551mL = 0122m
= 0002myth
(b)
Figure 1 Mascotte test bench assembly (a) and sketch of longitudinal section of the planar nozzle (b)
P0 = 259bar of = 185 P0 = 365bar of = 187
Figure 2 PLIF images of OH radicals from [3]
temperature In this occurrence the film cooling efficiencyis altered and the induced thermal loads may be critical forthese nozzles
To understand these phenomena a campaign of experi-mental measurements was conducted at the cryogenic LH
2-
LO2ONERAMascotte test bench facility [3] The results yet
obtained for low oxidizerfuel ratios (119900119891) on the basis ofPLIF and Kulite pressure measurements already constitute avery useful database for understanding the involved physico-chemical phenomena The first series of measurements wereperformed under 119900119891 ratios of up to 3 and combustionchamber pressure up to 40 bars The first results obtainedduring this measurements campaign highlighted a reignitionphenomenon occurring in the nozzle main flow inside theseparation area
Given the complexity of these phenomena numericalsimulations performed by different computing codes cangive a better interpretation of the experimental results Thepresent numerical work is a further contribution in thisregard and consists in simulating the turbulent reactiveflows in the same operating conditions as those performedexperimentally
This work was carried out within the framework andwith the support of the French research group ATAC(Aerodynamique des Tuyeres et Arrieres Corps (Nozzles andAfterbodies Aerodynamics))
2 Objectives
The aim of this paper is to perform 2D RANS turbulentreacting flows simulations for three test cases carried outexperimentally in the ONERAMascotte test bench For thispurpose two chemical kinetic schemes and two turbulencemodels were tested to investigate their relevance in thereignition process inside the nozzle
Basically the test bench consists of a subscale planarnozzle connected to a cylindrical combustion chamber fedwith a cryogenic mixture LOx-LH2
(Figure 1(a)) This hard-ware version has been developed especially to investigate theflow separation in overexpanded regimes The combustionchamber operates under controlled total pressure and oxi-dizerfuel ratios (119900119891) The main geometrical characteristicsof the nozzle are given in Figure 1(b) Pure hydrogen gas(GH
2) serving as film cooling is injected tangentially into
the upper wall of the nozzle through a slightly supersonicinjector Five Kulite pressure transducers are taped along thiswall A schematic longitudinal cross section of the nozzle isshown in Figure 1(b)
The first results [3] obtained by PLIF visualizationsperformed in this test bench show an increase in concen-trations of OH radical near the upper wall of the nozzlersquosdivergent in the separation zoneThis suggests a reactivationof the combustion inside this area (Figure 2) During these
International Journal of Aerospace Engineering 3
experiments it was also revealed that there is unsteadinessin the radical OH emission inside the separation zone Theauthors related this phenomenon to the pressure fluctuationsobserved in the combustion chamber An example of PLIFimages obtained by this technique is depicted in Figure 2[3] However no detailed explanations have been given so farabout the occurrence of this phenomenon
Parallel to these experiments steady RANS calculationshave been carried out at ONERADEFA using the CEDRECode In these calculations the reduced chemical kineticmodel of Eklund et al [4] was used for chemical ratesHowever no process of reignition in the flowhas been pointedout from the numerical results [3]
From these experimental and numerical conclusionsfurther calculations using new chemical kinetics based onthe well-known Evans and Schexnayder model [5] were rec-ommended This last model was slightly modified by addingtwo additional reactions without excessively penalizing thecomputation time Furthermore two RANS turbulencemod-els have also been tested in these calculations The mainobjective of this studywas to investigate relevance of chemicalkinetics and turbulence models in the context of reignitionphenomenon
3 Numerical Code and Equation Formulation
31 Numerical Code The calculations presented in thispaper were performed using the FASTRAN code This codewas specifically designed for compressible flow studies athigh Mach numbers and based on solving the multispeciesReynolds-Averaged Navier-Stokes (RANS) equations witha finite volume formulation The code offers two upwinddifferencing schemes with a variety of high order slopelimiters to calculate the convective terms in the transportequations Both explicit and implicit iterative and noniter-ative time integration schemes are available for steady-stateand time accurate flow simulationsThe convective fluxes arecalculated by means of either flux difference splitting scheme(Roe) or flux vector splitting scheme (van Leer) The codealso offers a choice of several turbulence models (119896-120576 119896-120596119896-120596-SST-Menter Spalart Allmaras and Baldwin Lomax)Thefollowing sections recall the main fluid physical modellingand the flow field numerical formulations methodology usedin this code for solving reactive Navier-Stokes equations
32 Thermodynamics Gas Properties The thermal equationof state for a mixing or reacting gas is given by Daltonrsquos Lawof partial pressures such that
119901 = sum119904
120588119904
119872119908119904
119877119906119879 (1)
where 119901 is the static pressure 120588119904is the species or mixture
density 119877119906is the universal gas constant 119879 is the static
temperature and119872119908119904
is the molecular weight of the species119904
The caloric equation of state relates the total energyto other gas dynamic variables and gas properties Forcalorically perfect gas
119864119905= 120588119888V119879 +
1
2120588119906
119895119906119895 (2)
where 119864119905is the total energy per unit volume and 120588 119888V 119879 and
119906119895are the gas density the heat capacity of the gas mixture
at constant volume the static temperature and the massaveraged velocity respectively
The form of the caloric equation of state for a mixingor reacting gas depends on the database used for describingthe molecular properties of the species Two databases areavailable the first is based on molecular (or spectroscopic)data for chemical species and the second is based on fifth-order polynomial curve fits for each chemical species [6]Using molecular properties (2) can be written as
119864119905= sum
119904
120588119904(119888Vtr119904119879 + Δℎ
0
119891119879119903119904) + 119864V +
1
2120588119906
119895119906119895 (3)
where 120588119904is the species density 119862Vtr119904 is the translational-
rotational heat capacity for species 119904 at constant volumeΔℎ0
119891119879119903119904is the heat of formation at reference temperature 119879
119903
and pressure for species 119904 and 119864V is the molecular vibrationalenergy per volume
Using of polynomial curve fits for properties gives twoforms of caloric equation of state
For thermal equilibrium
119864119905= sum
119904
120588119904(ℎ
119904minus119877119906119879
119872119908119904
) +1
2120588119906
119895119906119895 (4)
For thermal nonequilibrium
119864119905= sum
119904
120588119904[119888Vtr119904119879 + Δℎ
0
119891119879119903119904minus 119879
119903(119888Vtr119904 minus
119877119906
119872119908119904
)]
+ 119864int +1
2120588119906
119895119906119895
(5)
where ℎ119904is the sensible enthalpy per unit mass for species 119904
defined as
ℎ119904= int
119879
119879119903
119888119901119904119889119879 + Δℎ
0
119891119879119903119904 (6)
where 119888119901119904is calculated from fifth-order polynomial curve fits
for each chemical species from Gordon database [6]The viscosity of each fluid species 119904 in the case of reactive
flows is calculated by the relationship of Bird et al [7]
120583119904= 266693sdot10
minus6radic119872119908119904
119879
120590Ω120583
(7)
where 120590 is the characteristic molecular diameter and Ω120583is
the viscosity collision integral The characteristic moleculardiameter is based on Lennard-Jones potentials [8] For the
4 International Journal of Aerospace Engineering
mixture the viscosity is calculated by the semiempiricalrelationship of Wilke [9]
120583 = sum119904
119883119904120583119904
Φ119904
(8)
where119883119904is the mole fraction of specie 119904 and Φ
119904is given by
Φ119904= sum
119903
119883119903[1 + radic
120583119904
120583119903
(119872
119908119903
119872119908119904
)
14
]
2
[radic8(1 +119872
119908119904
119872119908119903
)]
minus1
(9)
For the diffusivity vector 119869119904 the mass diffusivity can be
represented by either Fickrsquos law [10] or a binary diffusionmodel [11] Consider
119869119904= minus120588119863
119904nabla119884
119904 (10)
where119863119904is the diffusion coefficient and119884
119904is the speciesmass
fraction119863119904is given by
119863119904=120583
120588Sc (11)
where Sc is the Schmidt number
33 Chemical Production The reactive flow calculation isobtained by solving the flow conservation equations in whichone integrates a source term120596
119904expressing themixture chem-
ical composition variation resulting from chemical reactionsIn the approach used for reacting flows the general finite
rate reaction is written as119899119904
sum119904=1
]1015840119904119903119872
119904lArrrArr
119899119904
sum119904=1
]10158401015840119904119903119872
119904 (12)
where ]1015840119904119903and ]10158401015840
119904119903are the stoichiometric coefficients of the
reaction and 119872119904represents an arbitrary molecule in the
reaction According to Kuo [11] the source term for species119904 is given by
120596119904= 119872
119908119904(]10158401015840
119904119903minus ]1015840
119904119903) [
119899119904
sum119904=1
120573119904119903119862119904]
sdot 119870119891119903
119899119904
prod119904=1
[119862119904]1205721015840
119904119903 minus 119870119887119903
119899119904
prod119904=1
[119862119904]12057210158401015840
119904119903
(13)
where 120573119904119903is the coefficient of efficiency of the third body for
the reaction 119903 119862119904is the species concentration and 119870
119891119903and
119870119887119903
are forward and backward reaction rates of a reaction119903 respectively The concentration powers 1205721015840
119904119903and 12057210158401015840
119904119903are
identical to ]1015840119904119903and ]10158401015840
119904119903 respectively for most applications
particularly for chemical kinetic reaction governed by Arrhe-nius rates of reaction
119870119891119903= 120572
119891119903119879120573119891119903 sdot 119890
(minus119864119886119903(119877sdot119879))
(14)
where 120572119891119903 120573
119891119903 and 119864
119886119903119877must be specified for each reaction
under investigation
34 Flow Field Numerical Method Basically the conserva-tion equations with appropriate closure models are expressedin vector form as
120597119876
120597119905+ nabla sdot
997888119865
119862minus (nabla sdot
997888119865
119863) = 119878 (15)
In this expression 119865119862and 119865
119863represent the convective and
diffusive fluxes respectively such as
119876 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int
1205881
1205882
120588119899119904
120588119906
120588V
120588119908
119864119905
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119862=
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int119906
1205881119906
1205882119906
120588119899119904119906
1205881199062 + 119901
120588119906V
120588119906119908
(119864119905+ 119901) 119906
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119878 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
int
1
2
119899119904
0
0
0
0
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119863=
[[[[[[[[[[[[[[[[[[[[[[[
[
119899119904
sum
119904=1
119890V119904120588119904119880119904 + 119896int120597119879int120597119909
minus12058811198801
minus12058821198802
minus120588119899119904119880119904
120591119909119909 minus2
3120588119896
120591119909119910
120591119909119911
[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879
120597119909+ 119896int
120597119879int120597119909
+sumℎ119904120588119904119880119904]
]]]]]]]]]]]]]]]]]]]]]]]
]
(16)In this system of equations 119906 V and 119908 are the velocitycomponents (119908 = 0 for 2D calculations) 120588 is the mixturedensity and 120591
119894119895is the shear stress tensor 120588
119904and 119880
119904are
respectively the species density and species velocity One cannote that for calorically perfect gas only one ldquospeciesrdquo istracked such that 119899119904 = 1 120588
119904= 120588 and 119880
119904= 0 Note that
for thermal equilibrium calculation all terms relating thecontribution of vibrational internal energy (119864int 119879int 119890V119904 )are no longer required
4 Chemical Kinetic Models
To investigate the pertinence of the chemical reactions asso-ciated with the reacting mixture issued from the combustionchamber it was expedient to test the most suitable kineticschemes for reactive H
2-O
2flow Two kinetic schemes were
selected for this study the modified Evans-Schexnaydermodel and Eklundrsquos kinetic model commonly used byONERA and CNES
International Journal of Aerospace Engineering 5
Table 1 Modified Evans-Schexnayder reaction model 119896119891
incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579
119894= 119864
119886119877
Number Reaction 120572119894
120573119894
120579119894(K)
1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950
41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O
2 H
2 OH H
2O N
2 and O] and 8
chemical reactionsrsquo scheme [12] In this system N2operates
as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO
2) in this scheme Indeed studies have shown that fast
three body recombination reactions involving the radicalHO
2 have been identified as major contributor in the heat
release process during the combustion of hydrogen with air[16]
To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time
H +O2+MlArrrArr HO
2+M (17)
H +HO2lArrrArr OH +OH (18)
Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H
2O
2) in the model
Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model
O2+HlArrrArr OH +O (19)
Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]
119896119891= 22 sdot 10
14 exp(minus8455119879) (20)
This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903
by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1
Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H
2-O
2combustion The results
are presented in terms of pressure and temperature riseH
2consumption and OH and H
2O formation from one-
dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]
42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O
2 H
2 OH
H2O O and H] As can be seen in Table 2 this scheme does
not involve any third body reaction which can present anadvantage in terms of computing time
5 Results and Discussions
51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries
Combustion temperature and species mass fractions forthe cryogenic LH
2-LO
2combustion products at desired
operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]
In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =
0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
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International Journal of
2 International Journal of Aerospace Engineering
Cylindricalcombustion
chamber
Outlet caisson
C-D planarnozzle
2 injectorGH
(a) From [22]
Wall with pressuretransducers
Gas combustionInjector
Separation shock
Thermal loads due to reignition
Nozzle inlet
Recirculation zone
h = 002818 m
H2 injection
l = 00551mL = 0122m
= 0002myth
(b)
Figure 1 Mascotte test bench assembly (a) and sketch of longitudinal section of the planar nozzle (b)
P0 = 259bar of = 185 P0 = 365bar of = 187
Figure 2 PLIF images of OH radicals from [3]
temperature In this occurrence the film cooling efficiencyis altered and the induced thermal loads may be critical forthese nozzles
To understand these phenomena a campaign of experi-mental measurements was conducted at the cryogenic LH
2-
LO2ONERAMascotte test bench facility [3] The results yet
obtained for low oxidizerfuel ratios (119900119891) on the basis ofPLIF and Kulite pressure measurements already constitute avery useful database for understanding the involved physico-chemical phenomena The first series of measurements wereperformed under 119900119891 ratios of up to 3 and combustionchamber pressure up to 40 bars The first results obtainedduring this measurements campaign highlighted a reignitionphenomenon occurring in the nozzle main flow inside theseparation area
Given the complexity of these phenomena numericalsimulations performed by different computing codes cangive a better interpretation of the experimental results Thepresent numerical work is a further contribution in thisregard and consists in simulating the turbulent reactiveflows in the same operating conditions as those performedexperimentally
This work was carried out within the framework andwith the support of the French research group ATAC(Aerodynamique des Tuyeres et Arrieres Corps (Nozzles andAfterbodies Aerodynamics))
2 Objectives
The aim of this paper is to perform 2D RANS turbulentreacting flows simulations for three test cases carried outexperimentally in the ONERAMascotte test bench For thispurpose two chemical kinetic schemes and two turbulencemodels were tested to investigate their relevance in thereignition process inside the nozzle
Basically the test bench consists of a subscale planarnozzle connected to a cylindrical combustion chamber fedwith a cryogenic mixture LOx-LH2
(Figure 1(a)) This hard-ware version has been developed especially to investigate theflow separation in overexpanded regimes The combustionchamber operates under controlled total pressure and oxi-dizerfuel ratios (119900119891) The main geometrical characteristicsof the nozzle are given in Figure 1(b) Pure hydrogen gas(GH
2) serving as film cooling is injected tangentially into
the upper wall of the nozzle through a slightly supersonicinjector Five Kulite pressure transducers are taped along thiswall A schematic longitudinal cross section of the nozzle isshown in Figure 1(b)
The first results [3] obtained by PLIF visualizationsperformed in this test bench show an increase in concen-trations of OH radical near the upper wall of the nozzlersquosdivergent in the separation zoneThis suggests a reactivationof the combustion inside this area (Figure 2) During these
International Journal of Aerospace Engineering 3
experiments it was also revealed that there is unsteadinessin the radical OH emission inside the separation zone Theauthors related this phenomenon to the pressure fluctuationsobserved in the combustion chamber An example of PLIFimages obtained by this technique is depicted in Figure 2[3] However no detailed explanations have been given so farabout the occurrence of this phenomenon
Parallel to these experiments steady RANS calculationshave been carried out at ONERADEFA using the CEDRECode In these calculations the reduced chemical kineticmodel of Eklund et al [4] was used for chemical ratesHowever no process of reignition in the flowhas been pointedout from the numerical results [3]
From these experimental and numerical conclusionsfurther calculations using new chemical kinetics based onthe well-known Evans and Schexnayder model [5] were rec-ommended This last model was slightly modified by addingtwo additional reactions without excessively penalizing thecomputation time Furthermore two RANS turbulencemod-els have also been tested in these calculations The mainobjective of this studywas to investigate relevance of chemicalkinetics and turbulence models in the context of reignitionphenomenon
3 Numerical Code and Equation Formulation
31 Numerical Code The calculations presented in thispaper were performed using the FASTRAN code This codewas specifically designed for compressible flow studies athigh Mach numbers and based on solving the multispeciesReynolds-Averaged Navier-Stokes (RANS) equations witha finite volume formulation The code offers two upwinddifferencing schemes with a variety of high order slopelimiters to calculate the convective terms in the transportequations Both explicit and implicit iterative and noniter-ative time integration schemes are available for steady-stateand time accurate flow simulationsThe convective fluxes arecalculated by means of either flux difference splitting scheme(Roe) or flux vector splitting scheme (van Leer) The codealso offers a choice of several turbulence models (119896-120576 119896-120596119896-120596-SST-Menter Spalart Allmaras and Baldwin Lomax)Thefollowing sections recall the main fluid physical modellingand the flow field numerical formulations methodology usedin this code for solving reactive Navier-Stokes equations
32 Thermodynamics Gas Properties The thermal equationof state for a mixing or reacting gas is given by Daltonrsquos Lawof partial pressures such that
119901 = sum119904
120588119904
119872119908119904
119877119906119879 (1)
where 119901 is the static pressure 120588119904is the species or mixture
density 119877119906is the universal gas constant 119879 is the static
temperature and119872119908119904
is the molecular weight of the species119904
The caloric equation of state relates the total energyto other gas dynamic variables and gas properties Forcalorically perfect gas
119864119905= 120588119888V119879 +
1
2120588119906
119895119906119895 (2)
where 119864119905is the total energy per unit volume and 120588 119888V 119879 and
119906119895are the gas density the heat capacity of the gas mixture
at constant volume the static temperature and the massaveraged velocity respectively
The form of the caloric equation of state for a mixingor reacting gas depends on the database used for describingthe molecular properties of the species Two databases areavailable the first is based on molecular (or spectroscopic)data for chemical species and the second is based on fifth-order polynomial curve fits for each chemical species [6]Using molecular properties (2) can be written as
119864119905= sum
119904
120588119904(119888Vtr119904119879 + Δℎ
0
119891119879119903119904) + 119864V +
1
2120588119906
119895119906119895 (3)
where 120588119904is the species density 119862Vtr119904 is the translational-
rotational heat capacity for species 119904 at constant volumeΔℎ0
119891119879119903119904is the heat of formation at reference temperature 119879
119903
and pressure for species 119904 and 119864V is the molecular vibrationalenergy per volume
Using of polynomial curve fits for properties gives twoforms of caloric equation of state
For thermal equilibrium
119864119905= sum
119904
120588119904(ℎ
119904minus119877119906119879
119872119908119904
) +1
2120588119906
119895119906119895 (4)
For thermal nonequilibrium
119864119905= sum
119904
120588119904[119888Vtr119904119879 + Δℎ
0
119891119879119903119904minus 119879
119903(119888Vtr119904 minus
119877119906
119872119908119904
)]
+ 119864int +1
2120588119906
119895119906119895
(5)
where ℎ119904is the sensible enthalpy per unit mass for species 119904
defined as
ℎ119904= int
119879
119879119903
119888119901119904119889119879 + Δℎ
0
119891119879119903119904 (6)
where 119888119901119904is calculated from fifth-order polynomial curve fits
for each chemical species from Gordon database [6]The viscosity of each fluid species 119904 in the case of reactive
flows is calculated by the relationship of Bird et al [7]
120583119904= 266693sdot10
minus6radic119872119908119904
119879
120590Ω120583
(7)
where 120590 is the characteristic molecular diameter and Ω120583is
the viscosity collision integral The characteristic moleculardiameter is based on Lennard-Jones potentials [8] For the
4 International Journal of Aerospace Engineering
mixture the viscosity is calculated by the semiempiricalrelationship of Wilke [9]
120583 = sum119904
119883119904120583119904
Φ119904
(8)
where119883119904is the mole fraction of specie 119904 and Φ
119904is given by
Φ119904= sum
119903
119883119903[1 + radic
120583119904
120583119903
(119872
119908119903
119872119908119904
)
14
]
2
[radic8(1 +119872
119908119904
119872119908119903
)]
minus1
(9)
For the diffusivity vector 119869119904 the mass diffusivity can be
represented by either Fickrsquos law [10] or a binary diffusionmodel [11] Consider
119869119904= minus120588119863
119904nabla119884
119904 (10)
where119863119904is the diffusion coefficient and119884
119904is the speciesmass
fraction119863119904is given by
119863119904=120583
120588Sc (11)
where Sc is the Schmidt number
33 Chemical Production The reactive flow calculation isobtained by solving the flow conservation equations in whichone integrates a source term120596
119904expressing themixture chem-
ical composition variation resulting from chemical reactionsIn the approach used for reacting flows the general finite
rate reaction is written as119899119904
sum119904=1
]1015840119904119903119872
119904lArrrArr
119899119904
sum119904=1
]10158401015840119904119903119872
119904 (12)
where ]1015840119904119903and ]10158401015840
119904119903are the stoichiometric coefficients of the
reaction and 119872119904represents an arbitrary molecule in the
reaction According to Kuo [11] the source term for species119904 is given by
120596119904= 119872
119908119904(]10158401015840
119904119903minus ]1015840
119904119903) [
119899119904
sum119904=1
120573119904119903119862119904]
sdot 119870119891119903
119899119904
prod119904=1
[119862119904]1205721015840
119904119903 minus 119870119887119903
119899119904
prod119904=1
[119862119904]12057210158401015840
119904119903
(13)
where 120573119904119903is the coefficient of efficiency of the third body for
the reaction 119903 119862119904is the species concentration and 119870
119891119903and
119870119887119903
are forward and backward reaction rates of a reaction119903 respectively The concentration powers 1205721015840
119904119903and 12057210158401015840
119904119903are
identical to ]1015840119904119903and ]10158401015840
119904119903 respectively for most applications
particularly for chemical kinetic reaction governed by Arrhe-nius rates of reaction
119870119891119903= 120572
119891119903119879120573119891119903 sdot 119890
(minus119864119886119903(119877sdot119879))
(14)
where 120572119891119903 120573
119891119903 and 119864
119886119903119877must be specified for each reaction
under investigation
34 Flow Field Numerical Method Basically the conserva-tion equations with appropriate closure models are expressedin vector form as
120597119876
120597119905+ nabla sdot
997888119865
119862minus (nabla sdot
997888119865
119863) = 119878 (15)
In this expression 119865119862and 119865
119863represent the convective and
diffusive fluxes respectively such as
119876 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int
1205881
1205882
120588119899119904
120588119906
120588V
120588119908
119864119905
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119862=
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int119906
1205881119906
1205882119906
120588119899119904119906
1205881199062 + 119901
120588119906V
120588119906119908
(119864119905+ 119901) 119906
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119878 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
int
1
2
119899119904
0
0
0
0
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119863=
[[[[[[[[[[[[[[[[[[[[[[[
[
119899119904
sum
119904=1
119890V119904120588119904119880119904 + 119896int120597119879int120597119909
minus12058811198801
minus12058821198802
minus120588119899119904119880119904
120591119909119909 minus2
3120588119896
120591119909119910
120591119909119911
[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879
120597119909+ 119896int
120597119879int120597119909
+sumℎ119904120588119904119880119904]
]]]]]]]]]]]]]]]]]]]]]]]
]
(16)In this system of equations 119906 V and 119908 are the velocitycomponents (119908 = 0 for 2D calculations) 120588 is the mixturedensity and 120591
119894119895is the shear stress tensor 120588
119904and 119880
119904are
respectively the species density and species velocity One cannote that for calorically perfect gas only one ldquospeciesrdquo istracked such that 119899119904 = 1 120588
119904= 120588 and 119880
119904= 0 Note that
for thermal equilibrium calculation all terms relating thecontribution of vibrational internal energy (119864int 119879int 119890V119904 )are no longer required
4 Chemical Kinetic Models
To investigate the pertinence of the chemical reactions asso-ciated with the reacting mixture issued from the combustionchamber it was expedient to test the most suitable kineticschemes for reactive H
2-O
2flow Two kinetic schemes were
selected for this study the modified Evans-Schexnaydermodel and Eklundrsquos kinetic model commonly used byONERA and CNES
International Journal of Aerospace Engineering 5
Table 1 Modified Evans-Schexnayder reaction model 119896119891
incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579
119894= 119864
119886119877
Number Reaction 120572119894
120573119894
120579119894(K)
1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950
41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O
2 H
2 OH H
2O N
2 and O] and 8
chemical reactionsrsquo scheme [12] In this system N2operates
as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO
2) in this scheme Indeed studies have shown that fast
three body recombination reactions involving the radicalHO
2 have been identified as major contributor in the heat
release process during the combustion of hydrogen with air[16]
To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time
H +O2+MlArrrArr HO
2+M (17)
H +HO2lArrrArr OH +OH (18)
Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H
2O
2) in the model
Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model
O2+HlArrrArr OH +O (19)
Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]
119896119891= 22 sdot 10
14 exp(minus8455119879) (20)
This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903
by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1
Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H
2-O
2combustion The results
are presented in terms of pressure and temperature riseH
2consumption and OH and H
2O formation from one-
dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]
42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O
2 H
2 OH
H2O O and H] As can be seen in Table 2 this scheme does
not involve any third body reaction which can present anadvantage in terms of computing time
5 Results and Discussions
51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries
Combustion temperature and species mass fractions forthe cryogenic LH
2-LO
2combustion products at desired
operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]
In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =
0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
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International Journal of
International Journal of Aerospace Engineering 3
experiments it was also revealed that there is unsteadinessin the radical OH emission inside the separation zone Theauthors related this phenomenon to the pressure fluctuationsobserved in the combustion chamber An example of PLIFimages obtained by this technique is depicted in Figure 2[3] However no detailed explanations have been given so farabout the occurrence of this phenomenon
Parallel to these experiments steady RANS calculationshave been carried out at ONERADEFA using the CEDRECode In these calculations the reduced chemical kineticmodel of Eklund et al [4] was used for chemical ratesHowever no process of reignition in the flowhas been pointedout from the numerical results [3]
From these experimental and numerical conclusionsfurther calculations using new chemical kinetics based onthe well-known Evans and Schexnayder model [5] were rec-ommended This last model was slightly modified by addingtwo additional reactions without excessively penalizing thecomputation time Furthermore two RANS turbulencemod-els have also been tested in these calculations The mainobjective of this studywas to investigate relevance of chemicalkinetics and turbulence models in the context of reignitionphenomenon
3 Numerical Code and Equation Formulation
31 Numerical Code The calculations presented in thispaper were performed using the FASTRAN code This codewas specifically designed for compressible flow studies athigh Mach numbers and based on solving the multispeciesReynolds-Averaged Navier-Stokes (RANS) equations witha finite volume formulation The code offers two upwinddifferencing schemes with a variety of high order slopelimiters to calculate the convective terms in the transportequations Both explicit and implicit iterative and noniter-ative time integration schemes are available for steady-stateand time accurate flow simulationsThe convective fluxes arecalculated by means of either flux difference splitting scheme(Roe) or flux vector splitting scheme (van Leer) The codealso offers a choice of several turbulence models (119896-120576 119896-120596119896-120596-SST-Menter Spalart Allmaras and Baldwin Lomax)Thefollowing sections recall the main fluid physical modellingand the flow field numerical formulations methodology usedin this code for solving reactive Navier-Stokes equations
32 Thermodynamics Gas Properties The thermal equationof state for a mixing or reacting gas is given by Daltonrsquos Lawof partial pressures such that
119901 = sum119904
120588119904
119872119908119904
119877119906119879 (1)
where 119901 is the static pressure 120588119904is the species or mixture
density 119877119906is the universal gas constant 119879 is the static
temperature and119872119908119904
is the molecular weight of the species119904
The caloric equation of state relates the total energyto other gas dynamic variables and gas properties Forcalorically perfect gas
119864119905= 120588119888V119879 +
1
2120588119906
119895119906119895 (2)
where 119864119905is the total energy per unit volume and 120588 119888V 119879 and
119906119895are the gas density the heat capacity of the gas mixture
at constant volume the static temperature and the massaveraged velocity respectively
The form of the caloric equation of state for a mixingor reacting gas depends on the database used for describingthe molecular properties of the species Two databases areavailable the first is based on molecular (or spectroscopic)data for chemical species and the second is based on fifth-order polynomial curve fits for each chemical species [6]Using molecular properties (2) can be written as
119864119905= sum
119904
120588119904(119888Vtr119904119879 + Δℎ
0
119891119879119903119904) + 119864V +
1
2120588119906
119895119906119895 (3)
where 120588119904is the species density 119862Vtr119904 is the translational-
rotational heat capacity for species 119904 at constant volumeΔℎ0
119891119879119903119904is the heat of formation at reference temperature 119879
119903
and pressure for species 119904 and 119864V is the molecular vibrationalenergy per volume
Using of polynomial curve fits for properties gives twoforms of caloric equation of state
For thermal equilibrium
119864119905= sum
119904
120588119904(ℎ
119904minus119877119906119879
119872119908119904
) +1
2120588119906
119895119906119895 (4)
For thermal nonequilibrium
119864119905= sum
119904
120588119904[119888Vtr119904119879 + Δℎ
0
119891119879119903119904minus 119879
119903(119888Vtr119904 minus
119877119906
119872119908119904
)]
+ 119864int +1
2120588119906
119895119906119895
(5)
where ℎ119904is the sensible enthalpy per unit mass for species 119904
defined as
ℎ119904= int
119879
119879119903
119888119901119904119889119879 + Δℎ
0
119891119879119903119904 (6)
where 119888119901119904is calculated from fifth-order polynomial curve fits
for each chemical species from Gordon database [6]The viscosity of each fluid species 119904 in the case of reactive
flows is calculated by the relationship of Bird et al [7]
120583119904= 266693sdot10
minus6radic119872119908119904
119879
120590Ω120583
(7)
where 120590 is the characteristic molecular diameter and Ω120583is
the viscosity collision integral The characteristic moleculardiameter is based on Lennard-Jones potentials [8] For the
4 International Journal of Aerospace Engineering
mixture the viscosity is calculated by the semiempiricalrelationship of Wilke [9]
120583 = sum119904
119883119904120583119904
Φ119904
(8)
where119883119904is the mole fraction of specie 119904 and Φ
119904is given by
Φ119904= sum
119903
119883119903[1 + radic
120583119904
120583119903
(119872
119908119903
119872119908119904
)
14
]
2
[radic8(1 +119872
119908119904
119872119908119903
)]
minus1
(9)
For the diffusivity vector 119869119904 the mass diffusivity can be
represented by either Fickrsquos law [10] or a binary diffusionmodel [11] Consider
119869119904= minus120588119863
119904nabla119884
119904 (10)
where119863119904is the diffusion coefficient and119884
119904is the speciesmass
fraction119863119904is given by
119863119904=120583
120588Sc (11)
where Sc is the Schmidt number
33 Chemical Production The reactive flow calculation isobtained by solving the flow conservation equations in whichone integrates a source term120596
119904expressing themixture chem-
ical composition variation resulting from chemical reactionsIn the approach used for reacting flows the general finite
rate reaction is written as119899119904
sum119904=1
]1015840119904119903119872
119904lArrrArr
119899119904
sum119904=1
]10158401015840119904119903119872
119904 (12)
where ]1015840119904119903and ]10158401015840
119904119903are the stoichiometric coefficients of the
reaction and 119872119904represents an arbitrary molecule in the
reaction According to Kuo [11] the source term for species119904 is given by
120596119904= 119872
119908119904(]10158401015840
119904119903minus ]1015840
119904119903) [
119899119904
sum119904=1
120573119904119903119862119904]
sdot 119870119891119903
119899119904
prod119904=1
[119862119904]1205721015840
119904119903 minus 119870119887119903
119899119904
prod119904=1
[119862119904]12057210158401015840
119904119903
(13)
where 120573119904119903is the coefficient of efficiency of the third body for
the reaction 119903 119862119904is the species concentration and 119870
119891119903and
119870119887119903
are forward and backward reaction rates of a reaction119903 respectively The concentration powers 1205721015840
119904119903and 12057210158401015840
119904119903are
identical to ]1015840119904119903and ]10158401015840
119904119903 respectively for most applications
particularly for chemical kinetic reaction governed by Arrhe-nius rates of reaction
119870119891119903= 120572
119891119903119879120573119891119903 sdot 119890
(minus119864119886119903(119877sdot119879))
(14)
where 120572119891119903 120573
119891119903 and 119864
119886119903119877must be specified for each reaction
under investigation
34 Flow Field Numerical Method Basically the conserva-tion equations with appropriate closure models are expressedin vector form as
120597119876
120597119905+ nabla sdot
997888119865
119862minus (nabla sdot
997888119865
119863) = 119878 (15)
In this expression 119865119862and 119865
119863represent the convective and
diffusive fluxes respectively such as
119876 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int
1205881
1205882
120588119899119904
120588119906
120588V
120588119908
119864119905
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119862=
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int119906
1205881119906
1205882119906
120588119899119904119906
1205881199062 + 119901
120588119906V
120588119906119908
(119864119905+ 119901) 119906
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119878 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
int
1
2
119899119904
0
0
0
0
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119863=
[[[[[[[[[[[[[[[[[[[[[[[
[
119899119904
sum
119904=1
119890V119904120588119904119880119904 + 119896int120597119879int120597119909
minus12058811198801
minus12058821198802
minus120588119899119904119880119904
120591119909119909 minus2
3120588119896
120591119909119910
120591119909119911
[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879
120597119909+ 119896int
120597119879int120597119909
+sumℎ119904120588119904119880119904]
]]]]]]]]]]]]]]]]]]]]]]]
]
(16)In this system of equations 119906 V and 119908 are the velocitycomponents (119908 = 0 for 2D calculations) 120588 is the mixturedensity and 120591
119894119895is the shear stress tensor 120588
119904and 119880
119904are
respectively the species density and species velocity One cannote that for calorically perfect gas only one ldquospeciesrdquo istracked such that 119899119904 = 1 120588
119904= 120588 and 119880
119904= 0 Note that
for thermal equilibrium calculation all terms relating thecontribution of vibrational internal energy (119864int 119879int 119890V119904 )are no longer required
4 Chemical Kinetic Models
To investigate the pertinence of the chemical reactions asso-ciated with the reacting mixture issued from the combustionchamber it was expedient to test the most suitable kineticschemes for reactive H
2-O
2flow Two kinetic schemes were
selected for this study the modified Evans-Schexnaydermodel and Eklundrsquos kinetic model commonly used byONERA and CNES
International Journal of Aerospace Engineering 5
Table 1 Modified Evans-Schexnayder reaction model 119896119891
incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579
119894= 119864
119886119877
Number Reaction 120572119894
120573119894
120579119894(K)
1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950
41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O
2 H
2 OH H
2O N
2 and O] and 8
chemical reactionsrsquo scheme [12] In this system N2operates
as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO
2) in this scheme Indeed studies have shown that fast
three body recombination reactions involving the radicalHO
2 have been identified as major contributor in the heat
release process during the combustion of hydrogen with air[16]
To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time
H +O2+MlArrrArr HO
2+M (17)
H +HO2lArrrArr OH +OH (18)
Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H
2O
2) in the model
Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model
O2+HlArrrArr OH +O (19)
Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]
119896119891= 22 sdot 10
14 exp(minus8455119879) (20)
This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903
by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1
Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H
2-O
2combustion The results
are presented in terms of pressure and temperature riseH
2consumption and OH and H
2O formation from one-
dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]
42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O
2 H
2 OH
H2O O and H] As can be seen in Table 2 this scheme does
not involve any third body reaction which can present anadvantage in terms of computing time
5 Results and Discussions
51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries
Combustion temperature and species mass fractions forthe cryogenic LH
2-LO
2combustion products at desired
operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]
In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =
0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
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DistributedSensor Networks
International Journal of
4 International Journal of Aerospace Engineering
mixture the viscosity is calculated by the semiempiricalrelationship of Wilke [9]
120583 = sum119904
119883119904120583119904
Φ119904
(8)
where119883119904is the mole fraction of specie 119904 and Φ
119904is given by
Φ119904= sum
119903
119883119903[1 + radic
120583119904
120583119903
(119872
119908119903
119872119908119904
)
14
]
2
[radic8(1 +119872
119908119904
119872119908119903
)]
minus1
(9)
For the diffusivity vector 119869119904 the mass diffusivity can be
represented by either Fickrsquos law [10] or a binary diffusionmodel [11] Consider
119869119904= minus120588119863
119904nabla119884
119904 (10)
where119863119904is the diffusion coefficient and119884
119904is the speciesmass
fraction119863119904is given by
119863119904=120583
120588Sc (11)
where Sc is the Schmidt number
33 Chemical Production The reactive flow calculation isobtained by solving the flow conservation equations in whichone integrates a source term120596
119904expressing themixture chem-
ical composition variation resulting from chemical reactionsIn the approach used for reacting flows the general finite
rate reaction is written as119899119904
sum119904=1
]1015840119904119903119872
119904lArrrArr
119899119904
sum119904=1
]10158401015840119904119903119872
119904 (12)
where ]1015840119904119903and ]10158401015840
119904119903are the stoichiometric coefficients of the
reaction and 119872119904represents an arbitrary molecule in the
reaction According to Kuo [11] the source term for species119904 is given by
120596119904= 119872
119908119904(]10158401015840
119904119903minus ]1015840
119904119903) [
119899119904
sum119904=1
120573119904119903119862119904]
sdot 119870119891119903
119899119904
prod119904=1
[119862119904]1205721015840
119904119903 minus 119870119887119903
119899119904
prod119904=1
[119862119904]12057210158401015840
119904119903
(13)
where 120573119904119903is the coefficient of efficiency of the third body for
the reaction 119903 119862119904is the species concentration and 119870
119891119903and
119870119887119903
are forward and backward reaction rates of a reaction119903 respectively The concentration powers 1205721015840
119904119903and 12057210158401015840
119904119903are
identical to ]1015840119904119903and ]10158401015840
119904119903 respectively for most applications
particularly for chemical kinetic reaction governed by Arrhe-nius rates of reaction
119870119891119903= 120572
119891119903119879120573119891119903 sdot 119890
(minus119864119886119903(119877sdot119879))
(14)
where 120572119891119903 120573
119891119903 and 119864
119886119903119877must be specified for each reaction
under investigation
34 Flow Field Numerical Method Basically the conserva-tion equations with appropriate closure models are expressedin vector form as
120597119876
120597119905+ nabla sdot
997888119865
119862minus (nabla sdot
997888119865
119863) = 119878 (15)
In this expression 119865119862and 119865
119863represent the convective and
diffusive fluxes respectively such as
119876 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int
1205881
1205882
120588119899119904
120588119906
120588V
120588119908
119864119905
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119862=
[[[[[[[[[[[[[[[[[[[[[[[[[
[
119864int119906
1205881119906
1205882119906
120588119899119904119906
1205881199062 + 119901
120588119906V
120588119906119908
(119864119905+ 119901) 119906
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119878 =
[[[[[[[[[[[[[[[[[[[[[[[[[
[
int
1
2
119899119904
0
0
0
0
]]]]]]]]]]]]]]]]]]]]]]]]]
]
119865119863=
[[[[[[[[[[[[[[[[[[[[[[[
[
119899119904
sum
119904=1
119890V119904120588119904119880119904 + 119896int120597119879int120597119909
minus12058811198801
minus12058821198802
minus120588119899119904119880119904
120591119909119909 minus2
3120588119896
120591119909119910
120591119909119911
[119906120591119909119909 + V120591119909119910 + 119908120591119909119911 + (119896 + 119896119905)120597119879
120597119909+ 119896int
120597119879int120597119909
+sumℎ119904120588119904119880119904]
]]]]]]]]]]]]]]]]]]]]]]]
]
(16)In this system of equations 119906 V and 119908 are the velocitycomponents (119908 = 0 for 2D calculations) 120588 is the mixturedensity and 120591
119894119895is the shear stress tensor 120588
119904and 119880
119904are
respectively the species density and species velocity One cannote that for calorically perfect gas only one ldquospeciesrdquo istracked such that 119899119904 = 1 120588
119904= 120588 and 119880
119904= 0 Note that
for thermal equilibrium calculation all terms relating thecontribution of vibrational internal energy (119864int 119879int 119890V119904 )are no longer required
4 Chemical Kinetic Models
To investigate the pertinence of the chemical reactions asso-ciated with the reacting mixture issued from the combustionchamber it was expedient to test the most suitable kineticschemes for reactive H
2-O
2flow Two kinetic schemes were
selected for this study the modified Evans-Schexnaydermodel and Eklundrsquos kinetic model commonly used byONERA and CNES
International Journal of Aerospace Engineering 5
Table 1 Modified Evans-Schexnayder reaction model 119896119891
incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579
119894= 119864
119886119877
Number Reaction 120572119894
120573119894
120579119894(K)
1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950
41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O
2 H
2 OH H
2O N
2 and O] and 8
chemical reactionsrsquo scheme [12] In this system N2operates
as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO
2) in this scheme Indeed studies have shown that fast
three body recombination reactions involving the radicalHO
2 have been identified as major contributor in the heat
release process during the combustion of hydrogen with air[16]
To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time
H +O2+MlArrrArr HO
2+M (17)
H +HO2lArrrArr OH +OH (18)
Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H
2O
2) in the model
Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model
O2+HlArrrArr OH +O (19)
Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]
119896119891= 22 sdot 10
14 exp(minus8455119879) (20)
This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903
by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1
Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H
2-O
2combustion The results
are presented in terms of pressure and temperature riseH
2consumption and OH and H
2O formation from one-
dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]
42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O
2 H
2 OH
H2O O and H] As can be seen in Table 2 this scheme does
not involve any third body reaction which can present anadvantage in terms of computing time
5 Results and Discussions
51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries
Combustion temperature and species mass fractions forthe cryogenic LH
2-LO
2combustion products at desired
operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]
In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =
0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 5
Table 1 Modified Evans-Schexnayder reaction model 119896119891
incm3molesdots119872 is the third body with an efficiency = 1 for all speciesand 120579
119894= 119864
119886119877
Number Reaction 120572119894
120573119894
120579119894(K)
1 H2 + MhArrH+ H +M 55 times 1018 minus10 519872 O2 + MhArr O + O +M 72 times 1018 minus10 593403 H2O + MhArr OH + H +M 52 times 1021 minus15 593864 OH +MhArr O + H +M 85 times 1018 minus10 508305 H2O +OhArr OH + OH 58 times 1013 00 90596 H2O + HhArr OH + H2 84 times 1013 00 101167 O2 + HhArr OH + O 66 times 1014 00 84558 H2 + OhArr OH + H 55 times 1013 00 55869 H + O2 + MhArrHO2 + M 23 times 1016 00 minus40310 H + HO2 hArr OH + OH 24 times 1014 00 950
41 Modified Evans-Schexnayder This model is initiallybased on 7 species [O
2 H
2 OH H
2O N
2 and O] and 8
chemical reactionsrsquo scheme [12] In this system N2operates
as the third body anddoes not dissociateThismechanismhasbeenwidely used for simulation in supersonic andhypersonicflows particularly in the case of combustion initiation aroundobstacles or in scramjets [13ndash15] This model was proved tobe less expensive in terms of computation time howeverit presents weakness in modeling the self-ignition delay(induction time) and in estimating the reaction heat releaseThis is mainly due to the absence of hydroperoxyl radical(HO
2) in this scheme Indeed studies have shown that fast
three body recombination reactions involving the radicalHO
2 have been identified as major contributor in the heat
release process during the combustion of hydrogen with air[16]
To overcome this deficit two reactions taken from themodel of Rogers and Chinitz [14] involving this radicalhave been added to the original Evans model adding nosubstantial computation time
H +O2+MlArrrArr HO
2+M (17)
H +HO2lArrrArr OH +OH (18)
Another insufficiency attributed to this model is its autoigni-tion delay which is relatively long especially for reactionsat low temperature (asymp1000K) This problem is related to theabsence of hydrogen peroxide (H
2O
2) in the model
Adding more reactions involving this species to correctthis deficiency substantially complicates the model An alter-native solution would be to increase the production rate ofReaction 7 of the original model
O2+HlArrrArr OH +O (19)
Indeed this reaction has been identified as important in thecase of inflammation at low temperatures [14] Initially theforward rate equation for this reaction is expressed as [5]
119896119891= 22 sdot 10
14 exp(minus8455119879) (20)
This valuewas obtainedwith an accuracy of 50 for a temper-ature range of 300 to 2000K By multiplying the coefficient120572119891119903
by 3 the rate of hydroperoxyl radical production OHis increased which leads to reduction in the ignition delay[12] The corresponding ignition delay becomes compara-ble to those obtained by more complex chemical kineticmodels with more reactions Finally the modified Evans-Schexnayder kinetic model with ten chemical reactions isgiven in Table 1
Figure 3 depicts the results obtained for validation of thiskinetic model in the case of H
2-O
2combustion The results
are presented in terms of pressure and temperature riseH
2consumption and OH and H
2O formation from one-
dimensional combustion simulation In Figures 3(a) and 3(b)the initial and themodified Evans-Schexnaydermodel resultsare compared to those from more complex kinetic schemesof Rogers and Chinitz [17] Drummond [18] and Bitker andScullin [19] respectively The results clearly highlight therelevance of the added specific reactions on the ignition timedelay [12]
42 Eklund Model This reaction simplified scheme pro-posed by Eklund et al [4] and implemented on both CEDREand CPS codes has been widely used by ONERA and CNES[3 20] for nozzle reactive flow studies This scheme consistsof 7 reversible reactions and 6 chemical species [O
2 H
2 OH
H2O O and H] As can be seen in Table 2 this scheme does
not involve any third body reaction which can present anadvantage in terms of computing time
5 Results and Discussions
51 Initial Conditions and Implementation of CalculationsThe calculations were performed over a computationaldomain which includes the nozzle the injector and the out-side experimental environmentThe calculation was initiatedat the nozzle inlet using the same initial data as the exper-imental test conditions described below No-slip conditionsalong the nozzlewalls were assumed For the outlet condition1 bar fixed pressure is applied at the downstream exit sectionAdiabatic no-slip conditions are imposed for the rest of thesurrounding block boundaries
Combustion temperature and species mass fractions forthe cryogenic LH
2-LO
2combustion products at desired
operating pressure chamber and 119900119891 ratio are obtained fromseparate calculations using the CEA thermochemical code[21]
In order to perform 2D CFD simulations of the nozzlersquosflow field finite volume grids have been constructed usingalgebraic grid generator software Multiblock structuredgrids have been used in this calculation The computationaldomain includes the convergent-divergent parts of the noz-zle the injector the zone downstream and the area located onboth sides of the nozzle The dimensions of the downstreamblock are more than 70ℎ in both 119909 and 119910 directions ℎ =
0028m being the nozzle height at its exit section A part ofthe meshing used in the computational domain representing
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
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Shock and Vibration
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
6 International Journal of Aerospace Engineering
Table 2 Reduced Eklund reaction model [4] 119896119891in cm3molesdots
Number Reaction 120572119891119894
120573119891119894
120579119891119894(K) 120572
119887119894120573119887119894
120579119887119894(K)
1 H2 + O2 hArr 2OH 17 times 107 0 24240 27810 0363 146202 H + O2 hArr O + OH 142 times 108 0 8258 417 times 105 03905 minus2053 OH + H2 hArrH2O + H 316 times 101 18 1526 8953 1572 93464 O + H2 hArr OH + H 207 times 105 00 6924 1153 times 108 minus002726 57695 OH + OHhArrH2O + O 55 times 1008 00 1511 2797 times 1010 minus22004 104906 H + OHhArrH2O 1105 times 1012 minus20 00 2365 times 106 1313 509107 H + HhArrH2 3265 times 1007 minus10 00 308 times 106 0664 47201
the nozzle and part of the outer domain is illustrated inFigure 4(a)
The right part of Figure 4(b) depicts the mesh systemused for the injection slot and the nearby region It alsodepicts the mesh refinement near the wall To achieve theCFD calculation up to 40000 cells were required The gridrefinement near the wall in the 119910 direction such as the firstcell-height leads to 119910+ = 1 where 119910+ is the dimensionlessdistance defined as
119910+=119910
]radic120591119908
120588119908
(21)
with 120591119908 120588
119908 and ] being the shear stress at the wall the
density and the kinematic viscosity respectively An averageof 25 cells in the normal direction of the nozzle wall wasused to resolve the boundary layer thickness Furthermorea preliminary study of the mesh refinement sensitivity wasbeforehandperformed before achieving the final calculations
The fluid is considered to be an ideal gas mixture inthermal equilibrium The mixture heat capacity at constantpressure 119888
119901(119879) is calculated as a function of temperature from
the calorific capacity of each species expressed in polynomialform The Schmidt number Sc and the turbulent Prandtlnumber are set equal to 09 for all calculations
Boundary conditions for turbulence model are alsoneeded For the 119896-120576 turbulence model the turbulent kineticenergy 119896 and the turbulent dissipation rate 120576 required at theinlets for both nozzle and injector are calculated on the basisof an estimated turbulence intensity of 5 for this nozzle [3]
Moreover the Spalart Allmaras turbulence modelrequires the kinematic turbulence viscosity ]
119905of the mixture
For Reynolds numbers Re gt 105 which is the case here avalue of the turbulent viscosity ratio namely the ratio ofturbulent viscosity to laminar viscosity (120573 = ]
119905]) up to 100
is a reasonable estimateIn this study the fluxes are evaluated at each time step
using the Roe scheme associated with the second-orderspatial accuracy MINMOD flux limiter The time integrationis performed by a fully implicit scheme with a local time stepbased on CFL number ramped from 01 to 05 within thefirst 1000 iteration cycles Convergence to 10minus6 residuals wasusually attained after 20000 to 25000 iterations
Finally the code is based on the finite rate mechanismin calculating the chemical composition Each chemicalreaction obeys the law of mass action hence the backward
rate coefficient is calculated on the basis of the equilibriumconstant for each reversible reaction
The results obtained by the numerical simulations arepresented in terms of flow Mach number field temperatureand OHmass fraction fields In addition to the PLIF picturesfive experimental wall pressure values are available Thesepressures are measured along the cooled upper nozzle walland will be compared to the calculated values in the sameplots Each test case is simulated using two chemical kineticschemes namely ldquothe modified Evans-Schexnaiyder modelrdquoand ldquothe Eklund modelrdquo Two turbulence models are alsoconsidered in this calculation the standard two-equation 119896-120576and the one-equation Spalart-Allmaras model
The operating conditions of the tested cases and the initialdata for the numerical simulations inputs are summarized inTable 3
52 Aerodynamic Field To understand the flow topology weplotted the aerodynamic flow fields in terms ofMach numberof the different tested cases As depicted in Figure 5 for eachtest case both turbulence models used in the computationpredict a similar flow pattern Indeed in such nozzle regimes(overexpanded conditions) a separation shock is createdinside the nozzle extension to adapt the flow to the outsidepressure This configuration is known as the Free SeparationShock (FSS) As sketched in Figure 5(a) in all configurationsthe separation shock impacts the opposite wall and leads theboundary layer to separate similarly as in the so-called ShockWave Boundary Layer Interaction (SWBLI) The other pointthe flow topology reveals is that relating to the shock positionAs expected this position depends on both nozzle pressureratio NPR for a given turbulence model and turbulencemodel for a given NPR as illustrated in the comparisonsgiven in Figure 5 This point will be emphasized with moredetails in wall pressure discussion below
Moreover it should be noted that an increase in theGH
2injection pressure used in the film cooling as in
the calculated Case 4 pushes back the separation shockdownstream the injection slot towards the nozzle exit sectionThis result is depicted in Figure 6 in terms of calculatedpressure profiles for Case 1 (NPR = 259 119875
0119895= 3 bars) and for
Case 4 (NPR = 259 1198750119895
= 43 bars) As shown the relativedisplacement of shock determined with respect to the length119897 of the nozzle part concerned with the fim cooling (Δ119909119897) isabout 363 A similar trend has been reported in previous
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 7
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
Huber et al
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972Evans and Schexnayder 1980
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
(a) Results from the initial model
Temperature (K)4000
3000
2000
1000
002 04 06 08 10
x (m)
400
300
200
100
002 04 06 08 10
Pressure (kPa)
x (m)
020
010
00002 04 06 08 10
H2O mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
OH mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
003
002
001
00002 04 06 08 10
H2 mass fraction
x (m)
Evans and Schexnayder model
Rogers and Chinitz 1983Drummond 1988Bittker and Scullin 1972
(b) Results from the modified model
Figure 3 Results of one-dimensional combustion tube simulation obtained with some reaction models compared to initial and modifiedEvans-Schexnayder reaction model [12]
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 International Journal of Aerospace Engineering
Caisson Outlet
Nozzle inletP0 T0 Yi
WallWall
Wall
Injector inlet
(a)
(b)
P0j T0j YH2=1
1 2 3 4 5 6 7 8 9
0
001
002
003
004
005
006
007 Y
ZX
005 01 015 02 025 03
0
1
2
3
4
Figure 4 Grids system used for CFD calculation (a) nozzle with part of the surrounding area (b) nozzle with a zoom of the region near theinjection slot
Table 3 Operating test cases conditions and initial inputs for CFD calculation
Test cases 1 2 3 4lowast
Measured quantitiesLO2 mass flow (gs) 449 461 672 xLH2 mass flow (gs) 242 142 359 xof 186 325 187 6
Conditions at the H2cooling injector
1198750119895cooling (H2) (bar) 31 32 43 43
1198790119869cooling (H2) (K) 29135 29425 29565 294
Conditions at the combustion chamber1198750(combustion chamber) (bar) 259 222 365 259
1198790(calculated) (K) 1693 2577 1945 3372
Calculated species mass fractions119884H2O 073229 085903 073366 087603119884OH 0 000190 0 006548119884H2
026771 013840 026634 003777119884O 0 000001 0 000580119884H 0 000065 0 000325119884O2
0 000001 0 001168lowastThis case is performed only numerically
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 9
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
(a) Case 1-119896-120576-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
453Mach
024 026 028 03 032
(b) Case 1-Spal-Evans (NPR = 259)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
149Mach
024 026 028 03 032
(c) Case 2-119896-120576-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
19
Mach
024 026 028 03 032
(d) Case 2-Spal-Evans (NPR = 222)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
654
Mach
024 026 028 03 032
(e) Case 3-119896-120576-Evans (NPR = 365)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 353 3
639
Mach
024 026 028 03 032
(f) Case 3-Spal-Evans (NPR = 365)
Figure 5 Calculated Mach number fields for Cases 1 2 and 3
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
406
Mach
024 026 028 03 032
= 259 P0j = 31barsNPR
(a)
0
001
002
003
004
005
006
007
014 016 018 02 022
00 05 1 15 2 25 3 3
155Mach
024 026 028 03 032
NPR = 259 P0j = 43bars
(b)
Figure 6 Comparison between Case 4 and Case 1 119896-120576 and Evans
works [23] where similar film injection is used to control theflow separation in overexpanded supersonic nozzles
53 Wall Pressure The calculated pressure profiles are com-pared to the experimental pressure measured by means ofKulite transducers Figure 7 depicts the pressure distributionalong the upper wall of the nozzlersquos divergent downstream ofthe injection slot
The results in Figures 7(a) and 7(b) show that the tur-bulence models used in this work were able to predict withgood accuracy the pressure rise in the separation zone forTest Case 1 (NPR = 259) and Test Case 2 (NPR = 222) Thenumerical results also show that the reignition phenomenon
significantly affects the flow field in the separation zone Dueto the combustion process the separation area becomes largerthan the corresponding frozen cases and the separation shockmoves upstreamThis result highlights the chemical reactionsinfluence on the separation shock displacement and thereforeon the pressure rise within the recirculation zone This resultcan be connected to the boundary layer which becomesthicker in reactive flow and easier to detach in response toan adverse pressure gradient This finding is quite consistentwith previous works such as in [24] Note that Test case3 is not represented here in terms of comparison betweenthe calculated and measured pressure profiles Indeed forthis particular test case large pressure fluctuations in the
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
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VLSI Design
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Shock and Vibration
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 International Journal of Aerospace Engineering
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Exp
Pw
all (
Nm
2)
Case 1-Spal-Evans
Case 1-Spal-Frozen
X (m)
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a) Calculated and measured wall pressure (Case 1)
Case 2-Spal-Evans Case 2-Spal-FrozenExp
X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
018 019 02 021 022 02320000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(b) Calculated and measured wall pressure (Case 2)
Case 4-Spal-EvansCase 1-Spal-Evans
X (m)018 019 02 021 022 023
20000
30000
40000
50000
60000
70000
80000
90000
100000
Pw
all (
Nm
2)
(c) Comparison between calculated Cases 1 and 4
Figure 7 Calculated and measured wall pressure in the zone downstream the injection slot
combustion chamber were recorded during the course ofexperiments This led to great separation shock instabilitiesand large discrepancy in measurements
Additional Test Case 4 was carried out only by numericalmeans with an oxidizerfuel ratio (119900119891 = 6) close to that ofreal rocket engines functioning with LO
2-LH
2 The nozzle
pressure ratio NPR is fixed the same way as for Test Case1 that is NPR = 259 while the total pressure of the H
2
film cooling is set to 1198750119895= 43 bars As can be seen in
Figure 7(c) augmenting the film cooling total pressure leads
the separation shock to move downstream as well as thereignition attachment point consequentlyThis possibility canbe used as will be mentioned below as means to avoid thereignition of the mixture inside the nozzle
54 Chemical Production To highlight the reignition phe-nomenon in the separation zone we plotted the flow OHmass fraction The results obtained show that OH radicalconcentrations are at levels high enough to readily suggest
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 11
0001
0002
0003
0004
0005
0006
0007
01
02
03
04
05
06
07
08
09
1
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(a) Case 10001
00015
00005
0 0002
00025
0003
00035
0004
0102030405060708091
OH
H2
0
001
002
003
004
005
006
007
001
002
003
004
005
006
007
014 016 018 02 022 024 026 028 03 032
(b) Case 4
Figure 8 Calculated OH radicals and H2concentrations Evans and 119896-120576 calculations
Separation areaOutside air
Attached flame
Hot gas main flow
Mixing shearlayer
Injected GH2
Figure 9 Flow configuration as deduced from CFD calculations
a reignition of the H2-Air mixture in the separated region
The examples illustrated in Figures 8(a) and 8(b) suggestthat the entrained fresh oxygen from the outside into theseparation zone leads to the inflammation GH
2used in the
film cooling across the mixing shear layer A like-diffusionflame appears and extends downstream along the shear layerA schematic of the flow configuration with an attachedflame to the nozzle upper wall in the separation area isdepicted in Figure 9 It is worth noting that these results wereobserved for both turbulence models with modified Evans-Schexnayder chemical kinetics model but not with Eklundmodel This can be explained by the temperature levels in thenozzle main flow across the shear layer which are not highenough to reactivate the chemical reactions with the abovementioned reaction model On the other hand when thenozzle operates at pressure ratios close to the adaptation as inCase 3 (NPR = 365) no reignition process has been observedin the flow inside the nozzle Indeed as mentioned above theseparation zone size is too small that it does not allow thefull completion of the combustion process within this area Inthis case the combustion takes place in the outer caisson faraway from the nozzle exit sectionThis situation is depicted inFigure 10 for both OH concentrations and temperature plots
55 Thermal Loads The film cooling efficiency is evaluatedby a widely used parameter 120578 describing the difference
between the film cooled wall temperature at each point andthe combustion chamber temperature relative to the differ-ence between the coolant temperature and the combustionchamber temperature The cooling efficiency is expressed bythe nondimensional efficiency 120578 defined as
120578 =119879119908minus 119879
119888
119879119891minus 119879
119888
(22)
where 119879119908is the calculated wall temperature119879
119888the calculated
combustion chamber temperature and 119879119891the injected film
temperatureThe cooling efficiency along the wall depends as before
on whether the nozzle flow is fully expanded or overex-panded Figures 11(a) and 11(b) represent an example ofwall temperature calculated in the Case 1 (NPR = 259) andCase 2 (NPR = 222) respectively where the nozzle operatesin overexpanded conditions The combustion of injectedGH
2leads to an increase in wall temperature in the region
where the flame is attached The wall temperature plots arecharacterized by marked peaks up to 1600K compared tofrozen flow calculations These results represent a furtherconfirmation of the hypotheses raised previously about thereignition phenomenon As can be seen these peaks areshifted according to the observations made above about theseparation zone In this case the cooling efficiency falls tovalues close to 005 and 04 respectively for Case 1 and Case
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 International Journal of Aerospace Engineering
0001
0002
0003
0004
0005
0006
0007
0008
0009 0009425OH
4944Eminus022
(a)
2000
1800
1600
1400
1200
100080
060
040
020
0 2113
1539
T (K)
(b)
Figure 10 Calculated OH concentration and flow temperature Case 3 Evans and 119896-120576 calculation The combustion takes place outside thenozzle
018 019 02 021 022 023200
400
600
800
1000
1200
1400
1600
1800
X (m)
Tw
(K)
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-EvansCase 1-k-120576-Frozen
(a)
200
400
600
800
1000
1200
1400
1600
1800
Tw
(K)
Case 2-Spal-Evans Case 2-Spal-Frozen
018 019 02 021 022 023X (m)
Case 2-k-120576-Evans
Case 2-k-120576-Eklund
Case 2-k-120576-Frozen
(b)
260
280
300
320
340
360
380
400
420
440
Tw
(K)
018 019 02 021 022 023X (m)
Case 3-Spal-Evans
Case 3-k-120576-EvansCase 3-k-120576-Evans
(c)Figure 11 Wall temperature profiles with reignition Cases 1 (a) and 2 (b) and without reignition for Case 3 (c)
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 13
0
02
04
06
08
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 1-Spal-EvansCase 1-Spal-Frozen
Case 1-k-120576-Evans
(a)
03
04
05
06
07
08
09
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 2-Spal-Evans Case 2-k-120576-FrozenCase 2-k-120576-Evans Case 2-k-120576-Eklund
(b)
092
094
096
098
1
018 019 02 021 022 023
X (m)
Coo
ling
film
effici
ency
Case 3-Spal-EvansCase 3-k-120576-Evans
(c)
Figure 12 Cooling film efficiency as function of distance from the injection slot for (a) Case 1 (b) Case 2 and (c) Case 3
2 (Figures 12(a) and 12(b)) where the temperature of theattached flame is close to the adiabatic temperature of thecombustion chamber particularly forCase 1MeanwhileCase3 shows a typical behavior of film cooling applications asit was observed in several works [2] In this case the tem-perature of the film cooling grows gradually by mixing withthe hot main flow gas (Figure 11(c)) and the correspondingefficiency (120578 gt 08) is within the range of the expected values(Figure 12(c))
6 Conclusions
This numerical study was conducted with the goal of repro-ducing some experimental tests carried out previously Themain objective was to check to which extent the chemicalkinetics and turbulence models may be relevant to highlightthe reignition phenomenon in the case of a subscale super-sonic nozzle hot flow cooled by H
2film cooling device The
main findings of this study can be summarized as follows
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
14 International Journal of Aerospace Engineering
Even though the real separated flow is naturally unsteadythe steady RANS approach using 119896-120576 and Spalart-Allmarasmodels combined with a modified kinetic model was foundto be able to reproduce the accurate averaged flow field andthe reignition phenomenon observed experimentally
Globally the calculated wall pressures are in good agree-ment with the experimental data for the whole tested casesand the effect of chemical reactions on these quantities hasbeen pointed out
The computed steady reacting regions are slightly dif-ferent from the instantaneous PLIF measurements whichillustrate the complexity of this phenomenon Furthermoreit is demonstrated that the steady attached flame occurs alongthe mixing shear layer and the combustion regime is mostlydiffusion
When reignition occurs the temperature at the nozzlewall is such that the film cooling becomes locally inoperativeand the induced thermal loads is so high that the nozzlersquosaerodynamic properties can be altered up to being detrimen-tal for the nozzle structural integrity
As expected the choice of a turbulence model does notglobally impact the phenomena that depend on the chemicalkinetics as the reignition process however it significantlyaffects the phenomena related to the boundary layer This ishow Spalart-Allmaras model gives a better prediction of theshock position and the pressure rise in the separation zonecompared to the experimental results
Abbreviations
119862 Concentrationℎ Enthalpy119870 Rates of a reaction119872 Mach number119872
119904 Molar mass
NPR Nozzle Pressure Ratio119875 Total pressure119901 Static pressurePr Prandtl number119877119906 Universal gas constant
Re Reynolds numberSc Schmidt number119879 Temperature119906 Flow velocity119881 VolumeV Velocity in 119910 direction119908 Velocity in 119911 direction119883 Mole fraction119884 Masse fraction119909 Axial flow direction119910 Vertical (side) direction
Greek Symbols
120572 Concentration power120574 Ratio of specific heats120583 Molecular dynamic viscosity] Kinematic viscosity120588 Density of fluid
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was part of the ATAC activities and the authorswould like to thank the French Space Agency (CNES) fortheir support
References
[1] L Winterfeldt B Laumert R Tano et al ldquoRedesign ofthe vulcain 2 nozzle extensionrdquo in Proceedings of the 41stIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA-2005-4536 2005
[2] D I Suslov R Arnolds and O J Haiden ldquoExperimentalinvestigation of cooling film efficiency in the nozzle extensionof LOXH2 subscale combustion chamberrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)St Petersburg Russia July 2011
[3] G Ordonneau P Hervat F Grisch L Vingert and P ReijasseldquoPLIF investigation of reactive flows in the separation region ofan over-expanded two-dimensional nozzlerdquo AIAA Paper 2006-5209 2006
[4] D R Eklund J P Drummond and H A Hassan ldquoCalculationof supersonic turbulent reacting coaxial jetsrdquoAIAA journal vol28 no 9 pp 1633ndash1641 1990
[5] J S Evans and C J Schexnayder Jr ldquoInfluence of chemicalkinetics and unmixedness on burning in supersonic hydrogenflamesrdquo AIAA Journal vol 18 no 2 pp 188ndash193 1980
[6] S F Gordon and B J McBride ldquoNASA Glenn coefficients forcalculating thermodynamic properties of individual speciesrdquoTechnical Publication NASATP-2002-211556 NASA Glenn2002
[7] R B Bird W E Stewart and E N Lightfoot TransportPhenomena Wiley New York NY USA 1960
[8] R A Svehla ldquoEstimated viscosities and thermal conductivitiesof gases at high temperaturesrdquo NASA Technical Report R-1321962
[9] C RWilke ldquoA viscosity equation for gas mixturesrdquoThe Journalof Chemical Physics vol 18 no 4 pp 517ndash519 1950
[10] J D Anderson Modern Compressible Flow With HistoricalPerspective McGraw-Hill New York NY USA 2nd edition1990
[11] K K Kuo Principle of Combustion John Wiley amp Sons NewYork NY USA 1986
[12] C S Craddock Computational optimization of scramjets andshock tunnel nozzles [PhD thesis] Department of MechanicalEngineering University of Queensland Brisbane Australia1999
[13] S Yungster S Eberhardt and A P Bruckner ldquoNumericalsimulation of hypervelocity projectiles in detonable gasesrdquoAIAA journal vol 29 no 2 pp 187ndash199 1991
[14] C J Jachimowski ldquoAn analytical study of the hydrogen-airreaction mechanism with application to scramjet combustionrdquoNASA Technical Paper 2791 1988
[15] A P Bruckner C Knowlen and A Hertzberg ldquoApplicationsof the ram accelerator to hypervelocity aerothermodynamic
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Aerospace Engineering 15
testingrdquo in Proceedings of the 28th Joint Propulsion Conferenceand Exhibit AIAA-92-3949 Nashville Tenn USA July 1992
[16] DMHarradine J L Lyman R C Oldenborg G L Schott andH H Watanabe ldquoHydrogenair combustion calculationsmdashthechemical basis of efficiency in hypersonic flowsrdquo AIAA Journalvol 28 no 10 pp 1740ndash1744 1990
[17] R C Rogers and W Chinitz ldquoUsing a global hydrogen-aircombustion model in turbulent reacting flow calculationsrdquoAIAA Journal vol 21 no 4 pp 586ndash592 1983
[18] J P Drummond ldquoA two-dimensional numerical simulation of asupersonic chemically reacting mixing layerrdquo NASA TM-40551988
[19] D A Bittker and V J Scullin ldquoGeneral chemical kineticscomputer program for static and flow reactions with applica-tion to combustion and shock-tube kineticsrdquo NASP TechnicalMemorandum TND-6586 1972
[20] P Durand B Vieille H Lamban et al ldquoCPS a three-dimensionnal CFD numerical code dedicated to space propul-sive flowsrdquo inProceedings of the 36th Joint Propulsion Conferenceamp Exhibit AIAA-2000-36976 July 2000
[21] S F Gordon and B J McBride ldquoComputer program forcalculation of complex chemical equilibrium compositions andapplicationsrdquo NASA RP-1311 NASA Glenn Research Center1996
[22] G Ordonneau P Hervat L Vingert S Pettito and B PouffaryldquoFirst results of heat transfer measurements in a new water-cooled combustor on theMascotte facilityrdquo in Proceedings of the4th European Conference for Aerospace Sciences (EUCASS rsquo11)2011
[23] P Reijasse and L Boccaletto ldquoNozzle flow separation withfilm coolingrdquo in Proceedings of the 38th AIAA Fluid DynamicsConference and Exhibit AIAA 2008-4150 Seattle Wash USAJune 2008
[24] P Gnemmi P Gruhn M Leplat C Nottin and S WallinldquoComputation validation on lateral jet interactions at super-sonic speedsrdquo International Journal of Engineering SystemsModelling and Simulation vol 5 no 1ndash3 pp 68ndash83 2013
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of