studies of injection of jet fuel at supercritical conditions

Studies of Injection of Jet Fuel at Supercritical Conditions

Thammarat Doungthip, Jamie S. Ervin,* Theodore F. Williams, and Jarrod Bento

University of Dayton Research Institute, 300 College Park, Dayton, Ohio 45469-0210

At temperatures above 400 °C and at fuel system pressures, JP-8 and Jet A jet fuels exist assupercritical fluids. Fuel nozzles operating under conventional aircraft (subcritical) conditionsatomize liquid fuel streams into droplets. The physical injection and mixing mechanismsassociated with a nozzle operating under supercritical conditions are very different from thoseoccurring under subcritical conditions. The current research examines the flow of fuel atsupercritical conditions through a simple nozzle into a region that is also at supercriticalconditions. Schlieren images of supercritical jet fuel exiting a simple nozzle into an opticalchamber are presented. Computational fluid dynamics simulations of the flow were performedusing n-decane as a surrogate fuel because it has a critical temperature and pressure similar tothe pseudo critical temperature and pressure of the jet fuel sample used in the experiments.The results of the computational fluid dynamics simulations and the measurements obtainedfrom the recorded images show that n-decane is a reasonable surrogate for Jet A fuel forpredictions of the spreading angle and jet penetration length. Measurements and computationshow that jet penetration and spreading angle are dependent on the fuel exit temperature andmass flow rate. In addition, it was found that the penetration depth of a supercritical jet intothe optical chamber is less than that for a subcritical jet with the same fuel mass flow rate andpressure conditions.

Introduction

Fuel is the primary cooling medium in high-perfor-mance aircraft. Advanced aircraft are expected to havecooling demands which require jet fuel to exist attemperatures above the critical temperature beforeinjection into the combustor. Thus, future gas turbineengines will require the injection of fuel existing at asupercritical thermodynamic state into an environmentthat is also above the critical point of the fuel. Attemperatures above approximately 400 °C and at fuelsystem pressures, the primary fuel of the U.S. Air Force,JP-8, or jet fuels such as Jet A-1 and Jet A exist as asupercritical fluid with gaslike diffusivity and viscosity.1Under supercritical temperature conditions, pyrolyticreactions within heated jet fuel become dominant.Chemical changes, such as fuel pyrolysis, are controlledby physical characteristics of the fuel and the fuelsystem. The involved fluid dynamics and heat transfervary during flight and change the location of maximumthermal gradients and maximum chemistry. Thus, it isimportant to understand the fundamental physical andchemical processes which occur for hydrocarbon fuelsexisting under supercritical conditions.

For purposes of combustion, fuel nozzles operatingunder conventional aircraft (subcritical) conditions at-omize liquid fuel streams into small, uniformly sizeddroplets with the desired spray angle. Under supercriti-cal conditions, the fuel exits the nozzle as a gaslike fluidrather than as a multitude of droplets, and there canbe large variations in fuel density, specific heat, speedof sound, viscosity, and thermal conductivity.2 Thus, thephysical injection and mixing mechanisms associatedwith a nozzle operating under supercritical conditionsare very different from those occurring under subcritical

conditions. Previous research considered the injectionof ethylene which was initially at supercritical condi-tions into a large chamber filled with nitrogen atconstant temperature and subcritical pressures.3,4 Thegoal was to examine the effects of transport propertiesnear the critical point on shock structure, jet appear-ance, and flow choking. Others have studied the injec-tion of liquid jets injected into supercritical conditions.2,5-8

It is also desirable to conduct experiments in which asupercritical fluid is injected into surroundings undersupercritical conditions. Knowledge of injection pro-cesses into surroundings at supercritical conditions isimportant because supercritical conditions will exist inthe combustion chamber of advanced aircraft.1 In someof their experiments, Chehroudi et al.2 and Chen andSui8 injected fluids initially at supercritical conditionsinto surroundings that were also at supercritical pres-sures and temperatures (relative to the injected fluid).Chehroudi et al.2 injected pure N2, He, and O2 into ahigh-pressure chamber containing either N2, He, ormixtures of CO and N2. Chen and Sui8 studied theinjection of SF6 injected into a chamber filled withstagnant N2 or CO2 at high pressure. Much of their workfocused on subcritical injection very near the criticalpoint of SF6. Unfortunately, there is little available inthe literature concerning the injection of an initiallysupercritical hydrocarbon fuel into supercritical condi-tions.9 The relatively high critical temperatures andpressures associated with common hydrocarbon fuelsnecessarily make injection studies at supercritical con-ditions difficult. Previous studies involving supercriticalfluid injection largely consider studies of droplets andsprays. Studies involving jets of supercritical fluids arerelatively rare and, thus, more research involvinginjection of supercritical fluids is needed.2,9

In the current work, Jet A fuel initially at supercriti-cal conditions is injected into an environment withpressures and temperatures above the critical pressure

* To whom correspondence should be addressed. E-mail:[email protected]. Phone: 937-229-2998. Fax: 937-252-9917.

5856 Ind. Eng. Chem. Res. 2002, 41, 5856-5866

10.1021/ie0109915 CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 10/17/2002

and temperature of the fuel. In addition, the Jet A fuelis in coflow with N2 gas. (In this work, supercriticalrefers to the critical condition of the fuel.) To betterunderstand the mixing and injection processes, schlierenimaging is used. It is believed that these are the firstimages of supercritical jet fuel exiting a nozzle into achamber which is also at supercritical conditions.Computational fluid dynamics simulations are per-formed using a simple surrogate fuel for purposes ofcomparison with the images of Jet A. The results of thiswork can be used to assist further development ofcomputational models for engine designers to simulatefuel flowing through nozzles at supercritical conditions.

Experimental Section

Jet A fuel is similar to both JP-8 and Jet A-1 jet fuels,but Jet A has a higher freeze point temperaturespecification.10 JP-8 is essentially Jet A-1 with threeadditives: a lubricity improver/corrosion inhibitor, anantistatic additive, and an icing inhibitor. In addition,Jet A and Jet A-1 are used as commercial aviation fuels.In this study, a Jet A fuel sample (designated as F3219in Table 1) was additized and then injected into anoptical chamber for purposes of flow visualization.

Additives combined with the neat fuel include thosegiven by MIL-T-83133D (JP-8 fuel specification) and aproprietary thermal stability additive (Betz Dearborn8Q462) used in the JP-8+100 Program. This additivewas found to reduce thermal-oxidative surface deposi-tion significantly below that of the neat fuel in most fueltest devices.11 Dissolved O2 within heated jet fuel isresponsible for thermal-oxidative fuel degradation andsurface deposit formation. Because it was desired toeliminate surface deposition, gaseous N2 was bubbledthrough the fuel to reduce the dissolved O2 concentra-tion within the fuel. A gas chromatograph verified thatthe dissolved O2 concentration of the fuel before heatingwas less than 1 ppm (w/w) and, thus, ensured thatminimal thermal-oxidative surface deposition wouldoccur.

The fuel was heated in a flow rig (Figure 1) whichuses two different types of heaters.12 The first consistsof a heated copper block. The block is comprised of twocylindrical halves which have a 7.62-cm diameter anda 45.7-cm length. The cylindrical pieces, when clampedtogether, form a near-interference fit about the stain-less-steel tubing through which the fuel passes. Eachhalf contains a 1500-W cartridge heater, and a thermo-couple embedded within one of the halves provides atemperature signal to the controller for the cartridgeheaters. The second kind of heater is a split-tube furnace(7980 W) that is mounted vertically and employs radiantheating. It has an active length of 61.0 cm and a 12.7-cm interior diameter. In addition, the furnace employsK-type thermocouples for control purposes. The pressurein the copper block and furnace was held near 2.7 MPa

Figure 1. Schematic of the flow rig used to heat fuel.

Table 1. Characteristics of Jet A Fuel F3219

specific gravity at 15.6 °C 0.8109 flash point, °C 55sulfur total, wt % 0.0321 aromatics, vol % 16.6copper, ppb <5 ( 5 smoke point, mm 20iron, ppb <10 ( 5 copper strip corrosion 1azinc, ppb <10 ( 5 JFTOT breakpoint, °C 285freeze point, °C -46

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5857

by the use of a pump and flow control valves such thatthe fuel entered the copper blocks as a liquid andtransitioned to a supercritical fluid within the furnace.After passing through the heated block and furnace, thefuel flowed through a nozzle. The nozzle (Figure 2)consists of a (316) stainless-steel tube (12.7 mm length× 1.6 mm o.d. × 0.3 mm i.d.) welded to a larger tube.(The 3.2 mm o.d. × 1.4 mm i.d. fuel line tube was drilledto an i.d. of 1.6 mm and a depth of 6.35 mm toaccommodate the smaller tube.) Fuel passed from thenozzle into the optical chamber (Figure 3) in (verticaldownward) coaxial flow with heated N2. The flowing N2(3.6 g/s) was heated by another furnace to produce ahigh nozzle wall temperature. In addition, for safetypurposes the N2 served to reduce the probability ofignition. Moreover, injected fuel in actual aircraft isoften in coaxial flow with an air stream. The opticalchamber has quartz windows (5.08 cm × 10.16 cm) ontwo sides for optical access and allows a maximumpressure of 3.45 MPa. Feed-throughs permit insertionof two type K thermocouples (1.5 mm diameter), andthe pressure was measured using a pressure transducer.Thermocouples (20 gauge) welded to the outer surfaceof the chamber provided outer wall temperatures withan uncertainty of (2 °C. The fuel mass flow rate wasfixed at either 0.2 or 0.4 g/s. In these experiments, fueland N2 temperatures upstream of the nozzle, fuel andN2 mixture temperatures below the nozzle, the chamberwall temperature, and fuel and N2 flow rates weremeasured. Individual experiments were run for shorttimes (∼15 min) to minimize surface deposition.

A water-cooled heat exchanger reduces the temper-ature of the fuel to near ambient conditions after thefuel exits the test section. Cooling the fuel allows safesample collection and extends the life of the tubedownstream of the heat exchanger. Near the exit of thesystem, fuel is diverted to a gas/liquid separator.Separation allows gas product samples to be analyzedoffline using a GC-FID/TCD system. The liquid portionof the stressed fuel is analyzed by conventional GC-MS techniques. Beyond the gas/liquid separator, the fuelexits to a scrap tank. In the experiments performedhere, products of thermal cracking reactions were es-sentially immeasurable. Thus, it can be reasonablyassumed that there was little pyrolysis of the fuel.

At supercritical conditions, fuel exiting the nozzle isvisible neither to the naked eye nor to white lightphotography. For this reason, a schlieren optics ar-rangement (Figure 4) was used for flow visualization.13

Light emanating from a xenon flash lamp passesthrough a condenser and focusing lens and is thenredirected by a 45° flat mirror to a parabolic mirror(152.4-cm focal length × 15.2-cm diameter). The para-bolic mirror then directs the parallel light rays throughthe test section. Other mirrors direct the detected lightsuch that a knife edge blocks a portion of the lightentering the camera. An image of the flow pattern isrecorded using a CCD camera (Panasonic GPUS502,three interline transfer CCDs with 768 × 494 pixels)connected to a (Mitsubishi HSU770 SVHS) VCR. Animage is captured using a frame grabber (Matrox

Figure 2. Nozzle used in flow visualization studies.Figure 3. Optical chamber used in flow visualization experi-ments.

5858 Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002

Marvel G400) connected in series with the VCR. Twosequential images are averaged for each conditionreported.

Numerical Model

Computational fluid dynamics simulations assist theinterpretation of flow visualization studies and extendthe study of phenomena for which experimental tech-niques are either unavailable or limited. To simulatethe injection of supercritical fuel into a supercriticalenvironment, the species, temperature, and velocitydistributions were obtained by the finite volume solutionof the species, enthalpy, Navier-Stokes, and turbulentenergy equations. The time-dependent governing equa-tions written in the cylindrical (z, r) coordinate systemfor axisymmetric flow are

Equation 1 is the continuity equation, and eq 2 repre-sents the momentum, species, or energy equation de-pending on the variable represented by Φ. Table 2 liststhe transport coefficients ΓΦ and the source terms SΦ

of the governing equations. Buoyancy forces were in-cluded in the simulations, and the gravity vector is inthe same direction as the flow from the nozzle. The fuelexiting the nozzle has Reynolds numbers (from 12 000to 23 000) that are characteristic of turbulent jet flows(Re is defined as FUD/µ). In contrast, the Reynoldsnumber at the fuel nozzle exit of the nitrogen in coflowwith the jet fuel was relatively low (on the order of2000). The standard k-ε turbulence model14 has beenused previously in supercritical and transcritical studiesto provide reasonable predictions of the evolution of an

O2 jet.15 In preliminary work here, there were negligibledifferences between calculations of the spreading angle,jet length, and velocities which used the standard k-εturbulence model and those which employed the lowReynolds number k-ε model of Chien.16 In addition, itwas found that calculations which used the low Rey-nolds number k-ε turbulence model required only halfthe computational time used by the standard k-ε model.Thus, in this physical arrangement which involvedsimultaneously occurring high and low Reynolds num-ber flows, a low Reynolds number k-ε model was usedin all of the calculations presented. Because the fuel (Reof 12 000-23 000 at the location where the fuel isinjected into the optical chamber) and N2 flows areturbulent, the rate of turbulent mass transport isseveral orders of magnitude greater than that of theconcentration-driven (molecular-diffusive) mass trans-port. Thus, a constant Schmidt number of unity wasused for simplicity. Values of the constants used in themodel of turbulent species transport are listed in Table2 and in the Nomenclature section.

Figure 4. Schlieren optical arrangement.

∂F∂t

+ ∂Fu∂z

+ ∂Fv∂r

+ Fvr

) 0 (1)

∂FΦ∂t

+ ∂FuΦ∂z

+ ∂FvΦ∂r

)

∂

∂z (ΓΦ ∂Φ∂z ) + ∂

∂r (ΓΦ ∂Φ∂r ) - FvΦ

r+ ΓΦ

r∂Φ∂r

+ SΦ (2)

Table 2. Source Terms and Transport CoefficientsAppearing in Equations 1 and 2a

Φ ΓΦ SΦ

u µ + µt - ∂p∂z

+ ∂

∂z (Γu ∂u∂z) + ∂

∂r (Γu ∂v∂z) + Γu

r∂v∂z

+ Fg

v µ + µt - ∂p∂r

+ ∂

∂z (Γv ∂u∂r) + ∂

∂r (Γv ∂v∂r) + Γv

r∂v∂r

- 2Γv vr2

k µ +µt

σkG - Fε

ε µ +µt

σε

C1Gε

k- C2Fε

2

k

hkcp

+µt

σε

0

Yi FDi +µt

σYi

ω̆i

a Here G ) µt[2{(∂u/∂z)2 + (∂v/∂r)2 + (v/r)2} + (∂v/∂z + ∂u/∂r)2],where µt ) CµFk2/ε, C1 ) 1.47, C2 ) 1.92, Cµ ) 0.09, σk ) 1.0,σε ) 1.3, σh ) 1.0, and σYi ) 1.0.


The governing equations were solved sequentiallyusing the commercially available CFD-ACE computa-tional fluid dynamics code.17 Convective terms wererepresented by a second-order accurate upwind scheme,and a version of the SIMPLEC algorithm was used inthe solution procedure.17 The grid system of Figure 5which contains 89 cells in the radial direction and 200cells in the axial direction is used in most simulations.Because the nozzle i.d. (0.3 mm) is significantly smallerthan either the chamber width (50.8 mm) or length(101.6 mm), it was assumed that the flow near thechamber walls does not significantly affect the flow nearthe nozzle outlet. Thus, the rectangular shape of theactual chamber was (as a first-order approximation)adequately represented by a two-dimensional axisym-metric (structured) grid. Because the behavior of the fueljet near the nozzle exit is of primary interest, the lengthof the computational grid is one-fourth of the chamberlength (25.4 mm). The length in the radial direction ofthe computational grid is 25.4 mm. Computational cellsare clustered within the shear layer between the N2 andfuel. In other regions, the orthogonal grid system hasexpanding cell sizes in both z and r directions. Near thewalls, the first cell was located at a y+ distance of lessthan 5.

Large gradients in temperature, velocity, or speciesare not expected in the far field away from the fuel andN2 jets under the present flow conditions. From thephysical arrangement, the greatest changes in the flowvariables are expected to be near the co-annular passage(Figure 5). Thus, a grid study was performed in whichthe grid density was increased in the fuel nozzle (from6 to 12 cells), the region where the n-decane and N2 aremixed (from 19 to 38 cells), and the N2 inlet (from 20 to40 cells). In addition, the total number of cells in theaxial (main flow direction) direction was increased (from200 to 300 cells). The computational grid of Figure 5was refined differently in different regions because ofthe grid nonuniformity. Solutions for species, temper-ature, and velocities changed little (less than 2%) withthe use of the fine grid. In addition, the differences

between the calculated spreading angles and penetra-tion depths resulting from use of the coarse and finegrids were immeasurable. Thus, to have a more practi-cal computational time, the coarse grid was used for thecalculations presented in this work.

With regard to boundary conditions, the flow has zerovelocity at solid surfaces. At the upper boundary of thegrid (Figure 5), the velocity profiles of the enteringnitrogen and fuel are assumed to be uniform forsimplicity. Entering fuel and nitrogen temperatures, aswell as the wall temperatures, were obtained from theexperiments and are used as boundary conditions. Inaddition, the measured pressure level at the inlet wasknown. Along the bottom of the grid (Figure 5), anoutflow boundary condition which employs a simpleextrapolation procedure17 is used to determine theunknown variables there. The calculations were initi-ated with a uniform flow of N2 everywhere, and thenthe fuel flow is switched on. After the residuals werereduced below 4 orders of magnitude from their maxi-mum value, the solution was considered to be converged.

Jet fuel is a complex mixture of a multitude ofhydrocarbon species. For purposes of simulating thefluid dynamics involving a jet fuel, it is reasonable touse a simple representative fuel. Here, n-decane wasselected as a surrogate fuel because it has a criticaltemperature and pressure (Tc ) 344.55 ( 0.6 °C andPc ) 2.11 ( 0.05 MPa)18 similar to the pseudo criticaltemperature and pressure of the selected Jet A sample.The pseudo critical temperature and pressure for thisfuel sample were estimated (Tc ) 368 °C and Pc ) 1.96MPa) using correlations described elsewhere.19 Edwardsand Maurice suggest that a single-component surrogatefuel that has a critical temperature near the pseudocritical temperature of a selected jet fuel can be used toadequately represent the actual jet fuel in simulationsof nonreacting flows (which do not have liquid-to-vaporphase changes).10 The commercial solver was modifiedto calculate supercritical thermodynamic and transportproperties of mixtures of n-decane and N2 as a functionof the local pressure and temperature within the

Figure 5. Computational grid.


computational cells using SUPERTRAPP FORTRANsubroutines. With SUPERTRAPP, the phase composi-tions were calculated using the Peng-Robinson equa-tion of state,20 and the properties were determined bya NIST extended corresponding states model which usespropane as a reference fluid.21 SUPERTRAPP is knownto provide well-behaved thermodynamic properties nearthe critical point.21 Table 3 shows representative valuesof thermodynamic and transport properties for mixturesof N2 and n-decane for temperatures and pressures forwhich n-decane is a supercritical fluid.

Results and Discussion

Effects of Varying the Nozzle Exit Temperature.For a constant supercritical pressure, as the tempera-

ture of the fuel is increased above the effective criticaltemperature, the fuel transitions from liquid to super-critical fluid. From a fundamental perspective, it isimportant to study the effects of varying the nozzle exittemperature on the resulting flow. Figure 6 shows jetimages under conditions of a fuel mass flow rate of 0.2g/s and a chamber pressure of 2.65 MPa. In addition,Figure 6 shows the fuel jet in coflow with heated N2 forthree different fuel-nozzle exit temperatures. The fueljet appears as a dark region emanating from the fueltube, and the nitrogen jet is the larger structure aboutthe fuel jet. The dark solid object that protrudes intothe flow from the right side of each image is a thermo-couple (1.5-mm diameter). In Figure 6a, the tempera-ture of the fuel at the nozzle exit is 266 °C, and later it

Table 3. Properties of n-Decane/Nitrogen Mixtures for Different Temperatures, Pressures, and Mole FractionsCalculated Using SUPERTRAPP

temperature(K)

pressure(MPa)

C10H22mole fraction

N2mole fraction

density(kg/m3)

cp(kJ/kg K)

µ(×10-6 N‚s/m2)

k(×10-2 W/m‚K)

713 3.08 1 0 107.20 3.52 16.74 5.33725 2.65 0.75 0.25 55.10 3.14 16.34 4.30735 2.65 0.5 0.5 37.50 2.90 18.66 3.63745 2.65 0.25 0.75 23.90 2.47 23.16 3.49

Figure 6. Effect of different jet fuel injection temperatures (fuel mass flow rate ) 0.2 g/s and Pch ) 2.65 MPa): (a) 266 °C; (b) 325 °C;(c) 441 °C.


is increased to 441 °C (Figure 6c). Figure 6a shows theinjection of fuel (Re of 12 800) initially at 266 °C as itflows into the chamber and field of view. In addition,the N2 (Re of 2000) that heats the nozzle is at atemperature of 500 °C. At a temperature of 266 °C anda pressure of 2.65 MPa (Pr ) 1.35 and Tr ) 0.84), themajor components of the fuel exist as a compressedliquid mixture (subcritical condition).22 Figure 6a showsthat the length of the fuel jet, measured from the nozzleexit to a location where the fuel is visually indistin-guishable from the N2, is 5.7 cm. With the nozzle exitfuel temperature increased to 325 °C (Pr ) 1.35 andTr ) 0.93) and an exit N2 temperature of 502 °C (Re of2000), Figure 6b shows the injection of subcritical fuelinto the chamber (Re of 16 400). From Figure 6b, thelength of the fuel jet measured from the nozzle exit toa location where the fuel is visually indistinguishablefrom the N2 is 3.5 cm. For the same pressure conditionsas in Figure 6a but at a greater temperature of 325 °C(Figure 6b), both the surface tension and heat ofvaporization of the fuel are diminished below values at266 °C. In addition, the evaporation rate increases withdecreasing surface tension and heat of vaporization.Thus, because of greater evaporation rates and morerapid entrainment of N2, the fuel jet of Figure 6b(spreading angle of 4.5 ( 0.5° and nozzle exit temper-ature of 325 °C) widens more rapidly than that of Figure6a (spreading angle of 3.0 ( 0.5° and nozzle exittemperature of 266 °C) for a given axial location alongthe centerline of the fuel jet. Moreover, the more rapidevaporation and enhanced mixing of the fuel in Figure6b prevent the fuel from penetrating as far into thechamber as in Figure 6a. The nozzle exit temperatureis 441 °C in Figure 6c, and the temperature (506 °C) ofthe flowing N2 is similar to that of Figure 6a,b. At 2.65MPa and 441 °C (Pr ) 1.35 and Tr ) 1.11), the fuel is asupercritical fluid upon entering the nozzle and theoptical chamber.

For a given pressure, the density and viscosity of ahydrocarbon fuel may vary strongly with temperature.Thus, for a fixed mass flow rate and pressure, theReynolds numbers of the fuel in Figure 6a-c increaserapidly with temperature. Upon comparison of imagesa-c of Figure 6, it is observed that the length of thefuel jet decreases as the injected fuel transitions fromcompressed liquid to supercritical fluid. The decreasein the jet length implies that the fuel and nitrogen aremixed faster than under subcritical conditions. Undersupercritical conditions, the surface tension of the fuelvanishes, and the mixing process does not involveevaporation. Moreover, a supercritical fluid generallyhas a greater diffusivity and a lower viscosity than aliquid. Together with zero surface tension, these trans-port characteristics contribute to the relatively morerapid mixing of the supercritical fuel. Thus, the mixingprocess between the fuel and nitrogen occurs morerapidly for fuel at supercritical conditions and resultsin less penetration into the chamber than for liquid fuel.The observation that the penetration depth decreaseswith increasing fuel temperature at supercritical condi-tions is important for the design of future combustors.Admittedly, the design of gas turbine combustors iscomplex and depends on many factors. However, areduced penetration depth implies a reduced mixingtime for the fuel jet for otherwise identical circum-stances.

Passing through the nozzle, jet fuel is heated by N2flowing over the nozzle exterior. Upon exiting the nozzleat supercritical conditions, the fuel expands into thechamber, forming a gaslike turbulent jet. Within thefuel jet, the fluctuating transverse velocity componentenhances transport of unmixed fuel from the core regionof the jet to the surrounding fluid. Understanding themixing dynamics of Jet A and N2 is complicated bydifferences in molecular weight, velocity, and temper-ature. Figure 7 shows a schlieren image of Jet A fuel

Figure 7. Jet fuel or n-decane at supercritical conditions in coflow with N2. Fuel mass flow rate of 0.2 g/s, inlet nozzle temperature of441 °C, and pressure of 2.65 MPa (Tr ) 1.11 and Pr ) 1.35). (a) Schlieren image of jet fuel and N2 (scale above image for reference). (b)Predicted density (kg/m3) of n-decane and N2 mixture. (c) Predicted mass fraction of n-decane. (d) Predicted temperature (°C).


and N2 at supercritical conditions (Figure 7a; fuel massflow rate of 0.2 g/s, exit nozzle temperature of 441 °C,and pressure of 2.65 MPa) together with plots ofpredicted density (Figure 7b), mass fraction of n-decane(Figure 7c), and temperature (Figure 7d). Figure 7a(same as Figure 6c) shows that the fuel jet becomesindistinguishable from the N2 at a location 7.5 mm(Z/D ) 30, where Z is the distance along the jetcenterline below the nozzle and D is the nozzle i.d.)below the fuel nozzle. For nonisothermal cold-into-hotjets, similar Z/D have been observed elsewhere.2,23 Inaddition, Figure 7b shows that axial and radial densitygradients have become negligible 7.5 mm below thenozzle. Because schlieren imaging is sensitive to densitygradient, images a and b of Figure 7 support oneanother in defining a value for the jet length (7.5 mm).This agreement also shows that it is reasonable to usea simple fuel such as n-decane in numerical simulationsof the heat transfer and transport phenomena of a morecomplex Jet A fuel. At this location 7.5 mm from thenozzle, Figure 7c shows that the mass fraction is lessthan 0.2. Moreover, Figure 7d shows that the low-temperature (blue) core region of the fuel jet persistsfor 7.5 mm beyond the nozzle exit. Figure 7d also showsthat the temperature of the N2 away from the fuel jetis nearly uniform. This uniformity indicates that heatloss from the chamber walls to the ambient has littleeffect on the temperature distribution near the fuel jet.

Effects of Varying the Mass Flow Rate. Theschlieren images of Figure 8a,b show the effects ofincreasing the jet fuel mass flow rate from 0.2 to 0.4g/s for conditions of similar reduced temperatures.Figure 8a shows that the length of the Jet A jet whichhas the lower mass flow rate of 0.2 g/s (nozzle exittemperature of 441 °C; Tr ) 1.11) is 7.5 mm. Figure 8b

shows that, with a mass flow rate of 0.4 g/s (nozzle exittemperature of 405 °C; Tr ) 1.06), the length of the JetA jet increases to 15 cm. In addition, images a and b ofFigure 8 show that the spreading angle increases from3.5° to 5.0° when the mass flow rate increases from 0.2to 0.4 g/s. However, understanding the influence of massflow rate on the penetration of the fuel jet into thechamber is complicated by the coupled effects of fueltemperature and velocity. The results of numericalsimulations assist the understanding of the influenceof the mass flow rate on jet penetration and jet growthrate and are described below.

Jet Growth Rate. The fluctuating transverse veloc-ity component of the n-decane jet enhances mixing offuel from the jet core region with the surrounding N2within a mixing layer. The mixing layer grows outwardas the heated jet extends further into the chamber. Thegrowth of the mixing layer has been described in termsof an initial jet spreading angle.24 In Figure 9, the jetspreading angle is measured from the nozzle centerlineto a tangent line drawn along the outer portion of thejet mixing layer. The spreading angle of the Jet A jet inthe schlieren image of Figure 9a is 3.5 ( 0.5°, and thespreading angle determined from the calculated densityplot for n-decane in Figure 9b is 3.0 ( 0.5°. Here, thecalculated density field resulting from the use of n-decane (nozzle exit temperature 441 °C and N2 temper-ature of 506 °C) provides a reasonable prediction of thespreading angle of the supercritical Jet A jet. In addi-tion, Table 4 shows that the spreading angles deter-mined from schlieren images at other conditions com-pare well with those obtained by numerical simulation.

To confirm the numerical simulations of the coflowof n-decane and N2 jets, predictions of the mean fuelmass fraction along the jet centerline are compared to

Figure 8. Effect of jet fuel mass flow rate. (a) Mass flow rate of 0.2 g/s, nozzle exit temperature of 441 °C (Tr ) 1.11 and Pr ) 1.35). N2temperature of 508 °C. (b) Mass flow rate of 0.4 g/s, nozzle exit temperature of 405 °C (Tr ) 1.06 and Pr ) 1.35). N2 temperature of588 °C.


values predicted by a semiempirical correlation. Time-averaged concentration measurements along the cen-terlines of variable-density, axisymmetric, turbulent jetsformed by the flow of a faster moving gas into a slowcoflow of a second gas have been performed by Pitts.23

Pitts found that eq 3 described his time-averaged

measurements of the jet mass fraction along the cen-terline, Ym.23,25 In eq 3, Yo is the time-averaged massfraction at the nozzle exit, F∞ is the density of theexternal, slow-moving gas, Fo is the density of the fastermoving jet at the nozzle exit, Z is the distance from thenozzle exit along the jet centerline, and both K andKc are constants. The effective radius, rε, is defined asrε ) ro(Fo/F∞)1/2, and ro is the radius of the jet nozzle. (Inthis discussion, Yo ) 1.) Following Pitts, values ofK ) -0.5 and Kc ) 0.114 have been assumed, and valuesfor the global density ratio are from Figure 7b.23 If ournumerical simulations of Yo/Ym within the n-decane jetare reasonable, they should follow the predictions of eq3. Figure 10 shows predictions of Yo/Ym for severaldifferent jet/coflow pairs as a function of Z/ro using eq3 and values from Pitts.23 The use of several different

jet/coflow pairs demonstrates the wide applicability ofeq 3. In addition, Figure 10 includes predictions of Yo/Ym for the n-decane/N2 coflow pair from both the use ofeq 3 and the present numerical simulations. The solidcircular symbols near the n-decane/N2 curve representYo/Ym values derived from the current numerical simu-lations which involve the Reynolds-averaged turbulenceequations. Figure 10 shows that there is good agreementbetween the empirical correlation (eq 3) and the presentsimulations.

Downstream from the flow development region (>5-10 diameters) one dimensionless length scale will specifytime-averaged concentrations for jet coflow pairs.23 It

Figure 9. Measured (3.5°) and predicted (3.0°) spreading angle for jet fuel and surrogate fuel, n-decane.

Table 4. Predicted and Measured Spreading Angles andJet Lengths (Chamber Pressure of 2.65 MPa)

exit temp(°C)

spreading angle (deg)(uncertainty ( 0.5°)

jet length(mm)mass flow

rate (g/s) jet fuel N2 measd pred measd pred

0.2 393 510 3.5 3.0 12.0 15.00.2 441 506 3.5 3.0 7.5 9.00.2 465 588 3.5 3.0 6.0 7.00.4 405 588 5.0 4.5 15.0 18.00.4 424 590 5.0 4.5 12.0 14.00.4 465 590 5.0 4.5 8.0 9.0

Yo/Ym ) (KcZ)/rε + (F∞/Fo - 1)K (3)Figure 10. Reciprocal of the mass fraction for different gas pairs.The lines represent the correlation given by eq 3. The solid circlesare predictions resulting from the present computational fluiddynamics simulations.


has been suggested that the reciprocal of the time-averaged mass fraction along a gaseous jet centerlinescales with the following relationship: 23,25

In eq 4, Zo is the virtual origin of the jet. (This is thepoint where the jet centerline intersects a line drawntangent to the jet exterior. Here, Yo is unity, and Zo isnegative.) Several experimental studies (isothermal andnonisothermal) support the scaling representation of eq4 for axisymmetric jets where the coflowing gases havedifferent densities but the downstream density asymp-totically becomes constant.25 Figure 11 shows 1/Ymplotted against (Z - Zo)/rε for the present n-decane andN2 computational fluid dynamics calculations togetherwith measured values for six jet/coflow gas pairs fromPitts.23 Figure 11 shows that the jet/coflow pairs par-tially collapse onto a single curve, and this collapseindicates a degree of similarity. Similarity is useful inthe fundamental understanding of the fluid dynamicsof simple flows. Moreover, the observation that thenumerical predictions for n-decane and N2 tend to fallon a curve common to other coflow pairs providesadditional validation of the present calculations.

Conclusions

Schlieren images of supercritical jet fuel exiting froma simple nozzle into a supercritical environment wereobtained. The jet penetration depth, spreading angle,and phase behavior vary with fuel temperature andmass flow rate, which, in turn, can vary considerablyduring an aircraft mission. The observations that thepenetration depth decreases with increasing fuel tem-perature at supercritical conditions and that the spread-ing angle increases with increasing mass flow rate areimportant for the design of future combustors.

Numerical simulations which used n-decane as asurrogate fuel for purposes of calculating the jet spread-ing angle and length agreed reasonably well with the

measurements. In addition, the numerical predictionsof the jet centerline fuel mass fraction agreed well withestablished correlations. Thus, n-decane or a similarhydrocarbon surrogate fuel can be used for calculationsof the heat transfer and fluid dynamics of nonreactingsupercritical jet fuel which has a similar critical tem-perature and pressure.

Acknowledgment

This work was supported by the U.S. Air Force, FuelsBranch, Propulsion Directorate, Air Force ResearchLaboratory, Wright-Patterson AFB, OH, under ContractNo. F33615-97-C-2719.

Nomenclature

C1 ) constant ) 1.47C2 ) constant ) 1.92Cµ ) constant ) 0.09D ) tube diameter, mDi ) diffusion coefficient of the ith species, m2/sG ) µt[2{(∂u/∂z)2 + (∂v/∂r)2 + (v/r)2} + (∂v/∂z + ∂u/∂r)2]g ) gravitational acceleration, m/s2

h ) enthalpy, kJ/kgk ) thermal conductivity, W/m‚K; turbulent kinetic energy,

kJ/kgK ) constant in eq 3Kc ) constant in eq 4p ) pressure, MPaPch ) chamber pressure, MPar ) radial coordinate, mro ) radius of the jet nozzle, mrε ) effective radius, mSΦ ) source termu ) axial velocity component, m/suτ ) friction velocity, (τω/F)1/2, m/sU ) mean velocity, m/sv ) radial velocity component, m/sω̆ ) rate of production of the ith species, kg/m3‚sy ) normal distance from the wall, mYi ) mass fraction of the ith speciesYo ) time-averaged mass fraction at the nozzle exitYm ) time-averaged mass fraction along the jet centerliney+ ) dimensionless distance from the wall, Fyuτ/µz ) axial coordinate, mZ ) distance from the nozzle exit along the jet centerline,

mZo ) virtual origin of the jet, mΦ ) assigned variable in eqs 1 and 2ΓΦ ) transport coefficientε ) dissipation rate, kJ/kg‚sF ) density, kg/m3

F∞ ) density of external, slow-moving gas, kg/m3

Fo ) density of faster-moving fuel at the nozzle exit, kg/m3

σk ) constant ) 1.0σε ) constant ) 1.3σh ) constant ) 1.0σYi ) constant ) 1.0τw ) wall shear stress, N/m2

µ ) absolute viscosity, N‚s/m2

µt ) turbulent viscosity, CµFk2/ε, N‚s/m

Literature Cited

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Figure 11. Reciprocal of the measured time-averaged massfraction along the gaseous jet centerline for different gas pairs incoflow as a function of dimensionless distance from the virtualorigin of the jet.22 Here, rε ) ro(Fo/F∞)1/2. In addition, values obtainedby computational fluid dynamics simulations for n-decane and N2are shown.

Yo

Ym) Kc(Z - Zo

rε) (4)


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Received for review December 7, 2001Revised manuscript received August 19, 2002

Accepted August 27, 2002

IE0109915


studies of injection of jet fuel at supercritical conditions

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