numerical analysis of the cambridge strati ed ame series ... · the ltered progress variable...
TRANSCRIPT
NOTICE: this is the authors version of a work that was accepted for publication in Combustion and Flame. Changesresulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other qualitycontrol mechanisms may not be reflected in this document. Changes may have been made to this work since it wassubmitted for publication. A definitive version was subsequently published in Combustion and Flame,http://dx.doi.org/10.1016/j.combustflame.2014.04.010
Numerical analysis of the Cambridge stratified flame series using artificial thickenedflame LES with tabulated premixed flame chemistry
F. Procha,∗, A.M. Kempfa,b
aInstitute for Combustion and Gasdynamics (IVG), Chair for Fluid Dynamics, University of Duisburg-Essen, 47048 Duisburg, GermanybCenter for Computational Sciences and Simulation (CCSS), University of Duisburg-Essen, 47048 Duisburg, Germany
Abstract
Detailed comparisons of LES results against measurement data are presented for the turbulent lean and rich stratifiedCambridge flame series. The co-annular methane/air burner with a central bluff body for flame stabilization has beeninvestigated experimentally by Sweeney et al. [1, 2]. Three cases with varying levels of stratification in the lean and richcombustion regime are taken into account. Turbulent combustion is modeled by using the artificial thickened flame (ATF)approach in combination with flamelet generated manifolds (FGM) lookup tables. The model is adapted for stratifiedcombustion and an alternative formulation for the flame sensor is presented. Three different grids are used to investigatethe influence of the filter width and the sub-filter modeling on the overall results. Velocities, temperatures, equivalenceratios, and major species mass fractions predictions are compared with measurements for three different stratificationrates and an overall good overall agreement was found between simulation and experiment. Some deviations occur nearthe bluff body, which are analyzed further by evaluation of atomic and species mass fractions. The stratified combustionprocess was further investigated and characterized by probability density functions extracted from the simulation results.
Keywords: Turbulent combustion, Stratified combustion, Co-annular jet burner, Large Eddy Simulation, Tabulatedchemistry, Cambridge stratified burner
1. Introduction
Premixed combustion plays an important role in mod-ern concepts for gas-turbines and IC-engines because ofthe reduced pollutant formation. However, to make thesesystems operable under the lean conditions desired, strat-ification of the mixture is often required. To predict andoptimize the complex interaction between mixing and com-bustion occuring within these systems, large eddy simula-tion (LES) has proven to be a suitable and convenientapproach.
In contrast to non-premixed combustion, the flame thick-ness in premixed and stratified combustion processes isnormally too small to resolve it properly on a typicallyLES grid. Different approaches have been developed toovercome this difficulty. One possibility is tracking of theflame front by means of a level-set method. This ap-proach was originally introduced as the G-equation modelfor Reynolds-averaged Navier-Stokes (RANS) simulationsby Peters [3], and later has been adapted to extend itsvalidity to the LES context [4–6].
A second group of models is based on computing theflame structure on the LES grid. In order to properly per-form this computation on the too coarse grid, the flame
∗Corresponding authorEmail address: [email protected] (F. Proch)
needs to be spatially thickened in the flame normal direc-tion. This can be achieved by reducing the source term andincreasing the diffusion term in the transport equations forthe chemical species. This technique is referred to as theartificially thickened flame (ATF) [7] approach, which hasbeen successfully applied first in the RANS and later inthe LES context [8, 9]. Another possibility is to solve atransport equation for the progress variable and filter itwith a filter size larger than the computational mesh, asintroduced by Boger et al. [10]. The sum of molecular dif-fusion and chemical source term for the progress variableis evaluated as a function of the laminar flame speed, sim-ilar to the Bray-Moss-Libby model in the RANS context[11]. This method, usually referred to as the flame surfacedensity (FSD) approach, needs modeling of the additionalflame surface caused by flame wrinkling on the sub-filterscale level. A wide range of algebraic [12–14] as well as dy-namic models have been developed for that purpose, Maet al. recently presented a detailed study on the subject[15, 16].
A further approach for modeling premixed flames isbased on the tabulation of precomputed detailed-chemistryflames. There are two simultaneously developed flamelet-type tabulation strategies for premixed flames, these arethe FPI (flame propagation of ILDM) [17–19] and thePFGM (premixed flamelet generated manifolds) [20, 21].Vreman et al. [22] and later Kuenne et al. [23] combinedATF with PFGM, whereas Galpin et al. [24] extended
Preprint submitted to Elsevier April 14, 2014
the filtered progress variable approach into FPI-PCM (pre-sumed conditional moment), which was further modifiedby Fiorina et al. [25] resulting in the F-TACLES model.
Recently, these models have been further extended toaccount for stratified conditions. Different groups haveadapted their combustion models for varying mixture frac-tions inside the lean combustion regime [26–28] to simu-late the Darmstadt stratified flame series [29]. Auzillonet al. [30] modified the F-TACLES model for lean strat-ified combustion and investigated the Darmstadt MOLE-CULES combustion chamber [31]. Nambully et al. [32, 33]performed LES computations of the Cambridge stratifiedflame series with the filtered laminar flame (FLF) - PDFmodel.
The present work aims to continue the investigations onthe LES of turbulent stratified flames in the lean and richcombustion regime. The investigated turbulent methane/airburner has recently been developed and investigated at theUniversity of Cambridge and the Sandia National Labora-tories by Sweeney, Hochgreb, Dunn and Barlow [1]. Ourmodeling of turbulent combustion is done by the ATF ap-proach, which is combined with a PFGM tabulation ofprecomputed premixed flames. Three cases with differentlevels of stratification are taken into account within thiswork.
In the first part of the paper, the combustion and sub-filter model and the LES-solver are described, pointing atthe necessary adaptions to make the approach suitable forstratified combustion over the whole flammability range.A brief description of the experimental setup is also in-cluded here. The presentation and discussion of the resultsstarts with a description of the global flame behavior forthe different cases investigated. Subsequently, results ondifferent grids are compared to measurements by analyzingradial profiles of mean and rms at different heights abovethe burner for velocities, equivalence ratio, temperatureand species mass fractions. The behavior in the weaklyturbulent zone near the bluff body is discussed. After thevalidity of the approach has been demonstrated, the sim-ulation data is analyzed further to gain a clearer under-standing of the influence of different levels of stratificationon the flame behavior. For that purpose, probability dis-tributions of relevant quantities are analyzed.
2. Modeling approach
2.1. Generation and accessing of the FGM
In the flamelet generated manifolds (FGM) approach,the chemical state and reaction progress space is tabu-lated over just a small subset of control variables. Thisis described only briefly here, the detailed derivation waspresented by van Oijen et al. [20, 21]. The basis for theFGM is a set of one-dimensional freely propagating pre-mixed flames, which are computed using a detailed chem-ical mechanism.
In the present work, these computations are performedusing the reaction kinetics library Cantera [34] with the
GRI-3.0 [35] mechanism for methane-air flames. The re-sulting chemical state is tabulated over a progress variable,which is chosen as the sum YC = YCO2
+ YCO + YH2O ofthe major product species mass fractions. We found thatthis progress variable definition works well for the casesinvestigated, although more complete formulations surelyexist [36, 37].
To make the tabulation suitable for stratified com-bustion, multiple flames with varying initial gas compo-sition are computed. This assumes that stratified com-bustion can be described by an ensemble of perfectly pre-mixed flames with different initial compositions. UnityLewis number assumption for all species is used which re-sults in constant atomic mass fractions over the flame. Asthe Cantera library normally does not support such unityLewis number computations, it was modified to computethe transport coefficients for that purpose. It is knownthat this assumption has a notable influence on the lami-nar flame speed of methane/air flames for equivalence ra-tios bigger than approximately 0.8 [38]. Nevertheless, thisassumption has turned out to work well in the contextof turbulent combustion, and therefore has been and isused by numerous groups in different combustion modelswith good success [10, 23, 25, 26, 30, 39–41]. The advan-tage of this assumption is that it is consistent with theapplied model for the sub-filter treatment as introducedbelow, which has been derived based on single-step chem-istry with constant Lewis number [9]. Furthermore, themixture fraction remains constant along the flame, whichsimplifies the tabulation and avoids an additional sourceterm in the respective transport equation. In the presentwork, the mixture fraction formulation by Bilger [42] hasbeen used, which is related to the fresh gas equivalenceratio in the following manner:
φ =Z
1− Z1− ZsZs
(1)
The stoichometric mixture fraction takes a value of Zs =0.054. The flammability limits of methane are set to Zfl =0.026 or φfl = 0.45 and (Zfr = 0.093 or φfr = 1.8) on thelean (rich) side [43, 44]. Outside the flammability lim-its, a linear interpolation of the species mass fractions andthe enthalpy is applied, assuming ideal mixing towards thestate of pure air (YO2
= 0.23, YN2= 0.77) and pure fuel
(YCH4= 1) at ambient conditions. The remaining quan-
tities like temperature, density and transport coefficientscan be determined consistently with the thermophysicalmodels used within the flammability limits.
The resulting manifold is stored in a two-dimensionalequidistant lookup-table with the mixture fraction Z andthe dimensionless progress variable
C =YC − Y minC (Z)
Y maxC (Z)− Y minC (Z)(2)
as independent variables, permitting fast non-searching ac-cess within the CFD-solver. The FGM includes quanti-ties required by the CFD-solver such as laminar viscosity,
2
Figure 1: Progress variable reaction rate ωC and temperature T asfunction of mixture fraction Z and dimensionless progress variableC. The temperature plot shows the entire mixture fraction range,whereas the illustration of the source term only shows the flamma-bility range, as it vanishes outside.
density or progress variable reaction rate, but also postprocessing quantities like temperature and species massfractions. Figure 1 shows the corresponding entries of thetable for progress variable reaction rate and temperature.The table is based on 68 premixed one-dimensional flamecomputations to cover the whole range of flammable mix-ture fractions, and it has 201 entries in progress variableand 1001 entries in mixture fraction direction.
2.2. ATF approach
In the ATF approach, the flame (typical thickness of0.1−0.5 mm) is artificial thickened with the goal of resolv-ing it on a practically affordable LES grid with typical cellsizes bigger than 0.5 mm. This is achieved by introduc-ing a thickening factor F into the Favre-filtered transportequation of the progress variable mass fraction:
∂ρYC∂t
+∂
∂xi
(ρuiYC
)=
∂
∂xi
([FEρDC + (1− Ω)
µtSct
]∂YC∂xi
)+E
FωC
(3)
In Eq. 3, ρ, ui, µt and Sct denote the fluid density, flowvelocity, turbulent viscosity and turbulent Schmidt num-ber respectively. The progress variable diffusion coefficientDC and reaction rate ωC are obtained from the FGM ta-ble. The flame sensor Ω and the efficiency function E arediscussed below. The choice of an un-normalized progress
variable, also applied in other works (e.g. [26, 30]), avoidscross terms which would occur for a normalized progressvariable, e.g. the cross-scalar dissipation rate term.
In contrast to the classical formulation of the ATFmodel [9], the thickening factor F is only applied insidethe flame region, which is characterized by a high gradi-ent of the progress variable, as suggested by Legier et al.[45]. The thickening factor is reduced smoothly to unityoutside the flame region to avoid unphysical behavior inregions of pure mixing as well as excessive and unneces-sary thickening of the pre-heat and burnout zones. Thedetection of the flame region is performed by the flamesensor Ω, which takes a value of zero in fully burnt or un-burnt regions and increases up to unity inside the flame.It should be mentioned that the ATF method without aflame sensor is also able to recover the correct flame prop-agation. However, the flame sensor improves the methodby ensuring that the (unphysical) thickening of the flameis limited to the regions where it is numerically necessary.This especially avoids an unphysical spatial extension ofthe burnout zones, which is of particular importance nearthe bluff body of the investigated burner. Our investiga-tions have shown that with the use of a constant thick-ening factor, the burnout zones interfere in this region onthe coarse grid, causing an extinction of the flame (whichdoes not represent the physical behavior). With the flamesensor, simulations on the coarse grid were possible with-out problems. A study of the impact of the flame sensoron the medium grid can be found in Appendix A. A com-mon choice for the flame sensor Ω is based on the progressvariable, as suggested by Durand and Polifke [46]:
Ω(C) = 16 [C (1− C)]2
(4)
In this work, the normalized gradient of the progress vari-able from the one-dimensional Cantera flame computa-tions is used instead. It is mapped over progress variableand mixture fraction and stored as an additional quantityinside the FGM table.
Ω(C,Z) =
dYC(x)dx
max(dYC(x)dx
)
1−D
(5)
The advantage of this choice is that the thickening behav-ior becomes independent of the local mixture fraction, asillustrated in Fig. 2. Shown are the profiles of dimension-less progress variable C and the two flame sensors com-puted with equations 4 and 5 as a function of the flamecoordinate normalized by the laminar flame thickness δ0
l .The laminar flame thickness is based on the temperatureprofile
δ0l =
Tb − Tumax
(dTdx
) , (6)
where the subscripts b and u denote the burnt and un-burnt state, respectively. To compare the flame sensorsfor the whole mixture fraction range, plots are shown for
3
0
0.2
0.4
0.6
0.8
1Z = Zfl = 0.026δl
0 = 2.665e-03 mΩ, Eq. (4) / (-)Ω, Eq. (5) / (-)
C / (-)
0
0.2
0.4
0.6
0.8
1
Z = Zfl = 0.026δl
0 = 2.665e-03 m
Z = Zst = 0.054δl
0 = 5.025e-04 m
0
0.2
0.4
0.6
0.8
1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
x/δl0 / (-)
Z = Zfl = 0.026δl
0 = 2.665e-03 m
Z = Zst = 0.054δl
0 = 5.025e-04 m
Z = Zfr = 0.093δl
0 = 2.8e-03 m
Figure 2: Comparison of profiles of the progress variable C and twodifferent flame sensors Ω over the normalized flame coordinate. Com-pared are plots for stoichometric (Zst) conditions and the lean (rich)flammability limit Zfl (Zfr).
the stoichometric condition, the lean and the rich flamma-bility limit. The gradient based sensor covers the entireC-profile, independent of the mixture fraction value. TheC based sensor also works sufficiently well for stoichomet-ric conditions, but rarely covers the high-temperature partof the flame at both flammability limits. This leads to aninconsistent thickening procedure inside regions of strati-fied combustion, which involves the danger of altering theresults in an unphysical way.
The final formulation of the thickening factor is:
F = 1 + Ω (Fmax − 1) (7)
with
Fmax = max
(n∆mesh
δ0l
, 1
)(8)
Here, ∆mesh denotes the cell size of the computationalgrid and n represents the number of grid-points to resolvethe flame thickness, which was set to 5 as suggested byCharlette et al. [9]. The limitation of Fmax to unity en-sures that the flame is not ’thinned’ when the grid is suffi-ciently fine. As the thermal flame thickness δ0
l depends onthe mixture fraction, it also needs to be tabulated to en-sure a consistent thickening procedure in stratified flames.
The modeling of the effect of turbulent velocity fluctu-ations at the sub-filter level on the progress variable trans-port also depends on the flame sensor. Inside the flame,the efficiency function E, which corrects for the loss offlame wrinkling by the ATF-approach is evaluated fromthe commonly used analytical model of Charlette et al.
[9]. This model has been chosen as it improves the orig-inal formulation by Colin et al. [8] and avoids unphysicalstretching of the flame in regions of low turbulence, asfound next to the bluff body. The model is used in themodified version by Wang et al. [47]:
E =
(1 + min
[Fmax − 1,Γ∆
(Fmax,
u′
∆
s0l
, Re∆
)u
′
∆
s0l
])β(9)
This formulation makes the model suitable for finer gridresolutions, as the original model implicitly assumed thatFmax 1 (Fmax takes values between 2.5 and 10 withinthis work). In Eq. 9, s0
l denotes the laminar flame speed,which is obtained from a table lookup depending on themixture fraction, Fmax is determined with Eq. 8. Themodel constant is set to the common value of β = 0.5,which was proposed by Charlette et al. [9] and is also usedby other groups [26, 30]. The complete formulation of theremaining terms in Eq. 9 can be found in Appendix B.Outside the flame region the sub-filter fluxes are modeledby the eddy diffusivity approach, it is smoothly blendedover by use of the flame sensor as shown in the first termon the RHS of Eq. 3.
2.3. Sub-filter closure
As described above, in the FGM approach for strat-ified combustion the computational quantities are deter-mined from a table lookup depending on mixture fractionand progress variable. However, inside the LES simula-tion only the filtered values of the independent variablesare available. To account for the unknow sub-filter distri-bution, a common approach is to assume an analytic shapefor it and determine the filtered FGM quantities from:
Φ =
∫C
∫Z
Φ(C,Z)P (C,Z) dZdC (10)
The joint sub-filter distribution of progress variable andmixture fraction is represented by the filtered density func-tion (FDF), P (C,Z). A common simplification in model-ing of stratified combustion is the assumption of statisti-cal independence of C and Z, which is motivated by theobservation that C usually varies on significantly smallerlength scales than Z. The consequence is that the localflame front is only exposed at most to a small variationof mixture fraction, in contrast to the high variation ofprogress variable. It is then possible to rewrite Eq. 10 to:
Φ =
∫C
∫Z
Φ(C,Z)P (C)P (Z) dZdC (11)
=
∫C
P (C)
(∫Z
Φ(C,Z)P (Z) dZ
)dC (12)
=
∫Z
P (Z)
(∫C
Φ(C,Z)P (C) dC
)dZ (13)
The FDF of the respective quantity in the outer integra-tion is approximated by a Dirac delta function (the validity
4
of this assumption is discussed below):
Φ ≈∫Z
Φ(C,Z)P (Z) dZ (14)
≈∫C
Φ(C,Z)P (C) dC (15)
In this work, the mixture fraction and progress variableFDF shape is assumed to follow a top-hat distribution assuggested by Floyd et al. [48] and applied with good suc-cess to the simulation of a gas turbine model combustorby Olbricht et al. [49]. Vreman et al. [50] carried outa comparison of LES results with different FDFs againstDNS data, and found a comparable performance of a top-hat function applied in space to the standard β FDF. Thetop-hat FDF then avoids the necessity for adding an addi-tional dimension to the FGM table [48, 49], thus reducingthe memory requirement and improving the performanceof the table lookup. Furthermore, the top-hat FDF isable to represent three-stream mixing in the LES-context,which occurs in the investigated burner between the coflowair and the inner/outer stream, an extensive discussion onthe subject and on the comparison of top-hat FDF and βFDF can be found in [48].
To determine the upper (lower) limit of the top-hatFDF for mixture fraction and (if required) progress vari-able, previous studies [48, 49] computed the value at thecell center plus (minus) the scaled square root of sub-filtervariance evaluated from a gradient model like the one byBranley and Jones [51]. Besides introducing the neces-sity to determine an additional modeling constant, thisalso causes the problem of handling situations in wich thecomputed limit falls outside of the valid mixture fractionand normalized progress variable range between zero andunity.
To avoid this problem, within this work the value ofthe filtered quantities is determined from the average oftwo top-hat distributions, one ranging from the minimumvalue on the cell faces to the value at the cell center andthe second between the cell center value and the maximumvalue on the cell faces. The face values are determined bylinear interpolation between the neighboring cell centers.It is shown in Appendix C that this converges to the gra-dient formulation for the case of a linear one-dimensionalmixture fraction profile over the cell, the same holds forthe normalized progress variable. For cases with curvedmixture fraction (normalized progress variable) profiles theorder of the approximation is improved in comparison tothe gradient formulation.
To investigate the influence of sub-filter modeling, thefollowing coarse grid simulations have been carried out forall three cases: a simulation with a Dirac delta function inC and a top-hat FDF in Z (LES-C-SZ), a simulation with aDirac delta function in Z and a top-hat FDF in C (LES-C-SC), and finally a simulation with Dirac delta functions inboth Z and C (LES-C). As shown in the discussion of theresults below, it turned out that the sub-filter modeling has
Ø38.1
Ø25.4
Ø34.8
Ø12.7
Ø23.6
Ui Uo UcoUiUoUco
Figure 3: Sketch of the burner setup, all dimensions in mm.
Table 1: Operating conditions of the burner for the different cases.Shown are mean axial velocities, ambient temperature and equiva-lence ratios.
Case Ui Uo Uco T φi φo φcom/s m/s m/s K - - -
SwB1 8.31 18.7 0.4 295 0.75 0.75 0SwB5 8.31 18.7 0.4 295 1.0 0.5 0SwB9 8.31 18.7 0.4 295 1.125 0.375 0
only a small influence on the results for the investigatedconfigurations. Therefore, the medium and fine grid com-putations have been performed with the assumption of aDirac distributions for both progress variable and mixturefraction, as the sub-filter contribution can be expected tobe smaller on the finer grids.
3. Experimental and numerical setup
3.1. Experiment
The Cambridge stratified burner [1] consists of two an-nular slots surrounding a central bluff body. Each slotsupplies a perfectly premixed methane/air mixture withvarying composition allowing to investigate different lev-els of stratification. The burner is embedded in a coflowof air. A sketch of the setup is shown in Fig. 3. Threedifferent stratified cases are investigated here. Table 1summarizes the corresponding operating conditions. Theresulting Reynolds numbers are 5,960 in the inner and11,500 in the outer stream. Based on measured values[1] of u′ = 4.37 m/s and Lturb = 1.72 mm for the intensityand length scale of the turbulent fluctuations 45 mm down-stream of the burner exit, the combustion process falls intothe thin reaction zone regime of the modified Borghi dia-gram for the whole range of equivalence ratios. Velocitydata is available from PIV- and LDA-measurements byZhou et al. [52], the latter ones used as reference in thiswork. This choice is based on the availability of LDA dataat all scalar measurement locations, whereas the PIV datais only available up to 60 mm. Radial profiles for tempera-ture and mass fractions of major species are available fromRayleigh respectively Raman scattering measurements bySweeney et al. [1].
3.2. CFD-solver and numerical setup
The numerical simulations have been performed withthe in-house LES-code ’PsiPhi’ [27, 53, 54]. The program
5
solves the low-Mach number Favre-filtered governing equa-tions for mass, momentum, progress species and mixturefraction. Continuity is ensured by a projection method,the resulting Poisson equation for pressure is solved iter-atively by the Gauss-Seidel method with successive over-relaxation (SOR). The equations are discretized with thefinite-volume method (FVM) on an equidistant and or-thogonal cartesian grid. Interpolation of the convectivefluxes on the cells faces is performed by a second ordercentral-difference scheme for momentum and a total vari-ation diminishing (TVD) scheme with non-linear CHARMlimiter [55] for density and other scalars. The solution isadvanced in time with a low-storage third order Runge-Kutta scheme. The code is parallelized with a distributedmemory domain decomposition concept using the messagepassing interface (MPI). The method of immersed bound-aries is applied for a computationally efficient treatmentof the geometric shape.
The effect of the velocity fluctuations at the sub-filterlevel is modeled with the eddy-viscosity approach for mo-mentum and the eddy-diffusivity approach for mixture frac-tion and progress variable, with the turbulent Schmidtnumber set to 0.7. The turbulent viscosity is evaluatedwith the σ-model suggested by Nicoud et al. [56]:
µt = ρ (Cm∆)2Dm (u) (16)
In this model, the differential operator Dm is a functionof the singular values of the velocity gradient:
Dm =σ3 (σ1 − σ2) (σ2 − σ3)
σ21
(17)
withσ1 ≥ σ2 ≥ σ3 ≥ 0 (18)
The singular values σi are identically equal to the squareroot of the eigenvalues of the tensor:
Gij =∂uk∂xi
∂uk∂xj
(19)
The corresponding modeling constant is set to a value ofCm = Cσ = 1.5. The σ model has been chosen as it avoidsthe over-prediction of the turbulent viscosity near wallsand in shear layers typical of the classical Smagorinskymodel without using a computational expensive dynamicprocedure.
The computational domain extends 112 mm in the ax-ial z-direction, and 110 mm in the x- and y-directions. Thelast 12 mm of the burner have been included in the simu-lation to obtain realistic flow conditions at the burner exit.To study the influence of filter width on the results, com-putations have been carried out for three different grid res-olutions, which are summarized with the respective com-putational costs in Table 2. The sampling for statisticalmeans and variances was started after 7 and carried outfor at least 8 flow-trough times based on the inner stream
Table 2: Details of the simulations on three different grids. Thecomputations were run for 15 flow through times at the inner streamvelocity Ui = 8.31 m/s.
Grid ∆mesh nCells tCPU tWall nProcsmm million h h -
Coarse (C) 1.0 1.6 91 2.5 36Medium (M) 0.5 13.4 3,533 10.3 343Fine (F) 0.25 103.2 49,152 96.0 512
velocity, leading to a simulated time of approximately 0.2seconds.
Parabolic velocity profiles with mean values correspond-ing to Table 1 and superimposed pseudo-turbulent fluctu-ations were set at the inflow of the computational domain.The fluctuations were generated with the filtering methodof Klein et al. [57] in an efficient numerical implementa-tion proposed by Kempf et al. [58]. The turbulent lengthscale was set to 1 mm and the rms of the fluctuations to2.5 m/s. A zero gradient condition was imposed at theoutflow for all quantities.
4. Results and discussion
4.1. General flame behavior
Figure 4 shows instantaneous and mean simulated con-tour plots of equivalence ratio in a burner cross section,giving a first impression of the flow. Downstream of theburner exit, mixing occurs between the coflow and theouter stream in all three cases and in addition betweenthe inner and outer stream in the SwB5 and SwB9 cases.The mixing rate is increased by additional turbulent mo-tion developing in the shear layers between the coflow andthe inner and outer stream. The lean flammability limitis denoted by a black isoline, which starts between theouter stream and the coflow at the burner exit and slowlywidens up further downstream for SwB1 and SwB5. ForSwB9 the mixture of the outer stream is leaner than theflammability limit, therefore the isoline starts between theinner and outer stream and widens up to a smaller radiusthan in the other cases. The isolines of the flame sensor(Eq. 5), which border the region where combustion takesplace, are shown in white.
One can distinguish three characteristic flame regions.The first region is perfectly premixed and characterized bya constant mean flame angle and only moderate broaden-ing of the mean flame brush.
The second region starts where the (instantaneous)flame enters into the region of equivalence ratio gradients,and is exposed to stratification. The curvature decreases(increase) for the isolines of the mean flame sensor at theunburnt (burnt) side of the flame, resulting in a broad-ening of the mean flame brush. This location is found atapproximately 40 mm (SwB1), and 30 mm (SwB5, SwB9).In addition, from about 40 mm onwards the whole flame is
6
Figure 4: Instantaneous and mean contour plots of equivalence ra-tio in a burner cross section for the three investigated cases on themedium grid, the lean flammability limit is marked by a black iso-line, the flame sensor which marks the combustion region is denotedby white isolines. The values in the nozzle give the respective equiv-alence ratio.
Figure 5: Instantaneous and mean contour plots of the flame indexin a burner cross section for SwB9. Values between -0.1 and +0.1are colored in white.
exposed to an equivalence ratio gradient in the two lattercases. The equivalence ratio at the burnt side of the flameconverges then towards a value of 0.6, which is the mean ofthe value at the flammability limit and the average valueat the inlet, which is 0.75 for all cases.
The transition point to the third region is located wherethe instantaneous flame touches the flammability limit line.Here, the motion of the unburnt side of the flame is deter-mined by the mixing behavior and the outer isoline of theflame sensor coincides with the flammability limit. In con-trast to before, the curvature of the isolines of the meanflame sensor increases at the unburnt side of the flameand decreases at the burnt side of the flame resulting ina decrease of the flame angle and a stabilization of theflame brush thickness. This region starts at around 60mm (SwB1), and 50 mm (SwB5, SwB9).
To demonstrate that the premixed mode is dominant,Fig. 5 shows instantaneous and mean contour plots of theflame index evaluated from [19, 59]:
GFO = ∇YCH4 · ∇YO2 (20)
Only the results for the mostly stratified case SwB9 are dis-played as the results are comparable for the other cases.The flame index takes positive (negative) values in pre-mixed (non-premixed) regions and becomes zero outsideof the reaction zone. Overall the combustion process takesplaces in a premixed environment. Only in very small re-gions at the unburnt side of the instantaneous reactionzone the flame index becomes slightly negative locally.
4.2. Velocities
Comparisons of mean and rms radial profiles of ax-ial and radial velocity components from simulations andexperiments for all three cases are shown in Figures 6-9.The LDA measurements from Zhou et al. [52] are denotedby black dots. For the coarse grid two additional datasets are shown (LES-C-SZ and LES-C-SC), which wereobtained with sub-filter modeling using the top-hat FDF,as explained in section 2.3. For all cases the impact of
7
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
10
20
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 6: Radial profiles of the mean axial velocity at different down-stream locations, showing a comparison for three different grids withthe experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
2
4
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 7: Radial profiles of the axial velocity fluctuations at differentdownstream locations, showing a comparison for three different gridswith the experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
the bluff body and the different velocity magnitudes onthe flow field are clearly visible. In the region behind thebluff body a recirculation zone is formed, which disappearsfurther downstream due to momentum exchange with thefaster inner flow and thermal expansion. The latter phe-nomenon is more dominant for SwB5 and SwB9, as thezone of the flame with strong reaction is shorter in thesecases, as can be seen from the isolines of the flame sensorin Fig. 4. In the shear layers between the streams and thecoflow the turbulent fluctuations are amplified.
The simulation results are in good agreement with theexperiments, the basic trends are matched for all casesand grid resolutions. The quality of the predictions im-proves with grid refinement, here the differences betweenthe coarse and medium grid are bigger than between themedium and fine grid, implying good convergence. Theagreement of the fluctuations with the measurements ben-efits substantially from the refinement of the grid. Theinfluence of the top-hat sub-filter model on the coarse gridvelocity results is generally small. Slight deviations oc-cur for the fluctuations of axial velocity at the last twomeasurement positions, where also the agreement with theexperimental results declines for all cases and grids. Thiscan be attributed to the size of the computational domain,which was chosen to be compact so that fine grid simula-tions are computationally affordable. (To investigate theinfluence of the domain size, additional simulations on thecoarse grid with doubled domain size in all directions havebeen performed for all three cases. It was found that theinfluence of the domain size is negligible for the means ofall investigated quantities and the fluctuations of all quan-tities except for axial velocity at the last two measurementpositions. The respective comparisons can be found in Ap-pendix D.)
The strength of the recirculation zone is under pre-dicted by the simulation, most visible for SwB1. This is inagreement with simulation results by Nambully et al. [32],and might be an indicator that the flame is slightly liftedat the bluff body, which can not be reproduced with theapplied adiabatic combustion model. However, this affectsonly a limited area of the flow field and has no significantinfluence on the regions of interest, which are the regionswhere (stratified) combustion occurs.
The radial velocity component shows a considerabledeviation towards the center line where the measurementsshow a negative velocity, whereas the simulations predictzero velocity. This suggests that the experimental data isslightly asymmetric, which on the one hand could be due tomeasurement uncertainties caused by the small magnitudeof the quantity. On the other hand, such burner configura-tions are known to be highly sensitive to small deviationsin the geometrical shape, so that the measured asymmetrymay represent the real flow field. This (unwanted) asym-metry is very hard to take into account within a numericalsimulation, and again the effect on the rest of the flow fieldis small. Overall the flow field is well captured by the sim-ulation, which is a prerequisite for the correct prediction
8
-1
0
1
2
Vmean / (m/s)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
-1
0
1
2
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
-1
0
1
2
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
-1
0
1
2
0 10 20r / (mm)
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Vmean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 8: Radial profiles of the mean radial velocity at differentdownstream locations, showing a comparison for three different gridswith the experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
of scalar quantities.
4.3. Equivalence ratio, temperature and progress variable
The comparisons of mean and rms profiles of equiva-lence ratio and temperature against the measurements bySweeney et al. [1] are shown in Figures 10-13. The profilesof the equivalence ratio mirror the observations made forthe flow field. The steep gradients between the inner andouter streams and the coflow are dissipated downstream,and fluctuations are produced within the shear layers inbetween. The behavior of the temperature profiles cor-relates strongly with the observations made for the meanflame brush in Fig.4, as expected for a unity Lewis numberassumption. The basic trends from the measurements arematched by the simulations, and the effect of grid refine-ment and sub-filter model is comparable to the observa-tions made for velocities.
The mean Favre-filtered normalized progress variableis also shown for completeness in Fig. 14. The progressvariable profiles are comparable to the temperature pro-files, which was to expected for a unity Lewis number as-sumption. The strong effect of the efficiency function isshown in Fig. 14, which also includes profiles that wereobtained from additional simulations with the efficiencyfunction set to unity inside the whole domain. It becomesobvious that, although the Reynolds numbers are smallin the investigated burner, taking into account the loss offlame wrinkling by the thickening procedure is crucial forthe correct flame propagation. This is also reflected by
0
1
2
3
Vrms / (m/s)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
1
2
3
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
1
2
3
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
1
2
3
0 10 20r / (mm)
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Vrms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 9: Radial profiles of the radial velocity fluctuations at differentdownstream locations, showing a comparison for three different gridswith the experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
0
0.25
0.5
0.75
1
Eqmean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.25
0.5
0.75
1
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.25
0.5
0.75
1
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.25
0.5
0.75
1
0 10 20r / (mm)
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Eqmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 10: Radial profiles of the mean equivalence ratio at differentdownstream locations, showing a comparison for three different gridswith the experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
9
0
0.1
0.2
Eqrms / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.1
0.2
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.1
0.2
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.1
0.2
0 10 20r / (mm)
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Eqrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 11: Radial profiles of the equivalence ratio fluctuations atdifferent downstream locations, showing a comparison for three dif-ferent grids with the experiments. LES-C-SZ and LES-C-SC refer toa coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
500
1000
1500
2000
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 12: Radial profiles of the mean temperature at different down-stream locations, showing a comparison for three different grids withthe experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
200
400
600
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure 13: Radial profiles of the temperature fluctuations at differentdownstream locations, showing a comparison for three different gridswith the experiments. LES-C-SZ and LES-C-SC refer to a coarse gridsimulation with additional sub-filter modeling using a top-hat FDFin mixture fraction and progress variable, respectively.
00.20.40.60.8
1
Cmean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
00.20.40.60.8
1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
00.20.40.60.8
1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
00.20.40.60.8
1
0 10 20r / (mm)
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
0 10 20r / (mm)
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
0 10 20r / (mm)
Cmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCLES-C-E=1
Figure 14: Radial profiles of the mean Favre-filtered progress variableat different downstream locations. LES-C-SZ and LES-C-SC refer toa coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.LES-C-E=1 shows the results of a computation without efficiencyfunction, i.e. setting E = 1 in Eq. 3.
10
the magnitude of the efficiency function observed in thesimulations, which lies around three for the coarse grid.
To get a better understanding of the reason why theeffect of the mixture fraction sub-filter model is negligi-ble, Fig. 15 shows the instantaneous maximum and min-imum mean Favre-filtered mixture fraction values at thefaces for one time step. In the vast majority of cells, themixture fraction varies by less than 10% of the stoicho-metric value between the cell center and the faces, thecorresponding range is marked by thin dark-red lines inFig. 15. To check the possible influence of this range onthe flame propagation, Fig. 16 shows the laminar flamespeed over the mixture fraction as used in the simulation.The spacing of the mixture fraction grid lines correspondsalso to 10% of the stoichometric value. Assuming an ad-equately resolved (thickened) progress variable field, it isnotable that a piecewise-linear approximation with thismixture fraction sub-filter variance, which corresponds toa computation with the top-hat sub-filter model, is able toreproduce the flame speed correlation with a small error,even around the stoichometric region with high curvaturevalues. At the same time, an approximation by the valueat the center of each interval, which would correspond tothe assumption of a Dirac peak for the sub-filter distri-bution, would lead to an almost identical result. In otherwords, the impact of the sub-filter model is very small.This is in agreement with the findings of Cavallo Marin-cola et al. [27].
However, Fig. 15 shows some distinct features whichcould become important for other cases with higher sub-filter variance. First, the plot is not perfectly symmetric,as would be implicitly assumed by a gradient model for thesub-filter variance. There even exist some points where themixture fraction has a local maximum or minimum at thecell center, which is denoted by minimum (maximum) val-ues of Z at the cell faces above (below) the diagonal (inFig. 15, this is shown by red squares below and yellow tri-angles above the diagonal line). A second notable featureis the presence of a gap between the diagonal and the mix-ture fraction points towards higher values of the mixturefraction. This gap is shifted towards the minimum mixturefraction values. This implies that the corresponding cellis located in a region where the mixture fraction profilechanges mainly towards leaner mixture fractions. Suchcondition occur at the point where the mixture fractionprofiles starts declining from the broad peak at the stoi-chometric value towards higher radii. In the Fig. 10 thiswould correspond to a radial position of approximately 12mm. High mixture fraction variances mainly occur aroundthe burner exit conditions, which correspond to mixturefraction values of 0 for the coflow and 0.0277 (0.054) forthe outer (inner) stream. Although the magnitude of themixture fraction variances at these three locations is com-parable, the distribution among minimum and maximumvalues varies. At Z = 0 (Z = 0.054) high variances mainlyoccur for Zmax (Zmin). A similar behavior is observed forZ = 0.0277, where large Zmax occur for large Z, and small
Zmin for small Z. The reason for that can again be foundin the shape of the equivalence ratio profiles: As shownin Fig. 10, at Z = 0 (Z = 0.054) a steep gradient existsonly towards richer (leaner) conditions. In contrast, thevalue Z = 0.0277 marks an inflection point of the equiva-lence ratio profile and therefore has considerably gradientstowards leaner as well as richer conditions.
The mean temperature profile deviates notably nearthe bluff body for the coarse grid, which can be explainedby the ATF-modeling: The real flame is very thin at theedge of the bluff body due to wall effects, but the ATFapproach thickens the flame also at this position to theadjusted 5 grid points according to Eq. 8. To enforce thethin flame here, the thickening would have to be blockedin the cells near the wall, causing an insufficient resolutionof the flame leading to poor numerical accuracy. The ori-gin of this problem is that modeling approaches based onbroadening of the flame, by thickening or filtering, meana certain loss in spatial accuracy, which can cause devia-tions in the flame position in such situations. However, thefact that the flame position is predicted well further down-stream also for the coarse mesh may be seen as evidencethat the modeling of the overall flame behavior is not de-teriorated significantly by this effect. The rms fluctuationsof the temperature are under predicted on the coarse andmedium grid up to the middle of the computational do-main, which is in agreement with the observations madeby Kuenne et al. [26], and is likely to be caused by theeffect of the thickening procedure on the flame dynamics.
The equivalence ratio (experimental data) plots showa distinct peak in the bluff body region at a radius lowerthan 10 mm. This has been investigated closer experimen-tally by Barlow and coworkers [60, 61] and numerically byKatta and Roquemore [62] and Nambully et al. [33]. Theeffect is explained by preferential diffusion of H2O and H2,which can not be captured with the Lewis number unityassumption applied within this work, but will be analyzedfurther in the next section. Overall, the simulation resultsare in good agreement with the measurements for equiva-lence ratio and temperature.
4.4. Major species
To further access the modeling approach and get deeperinsights into the chemical structure of the flame, mean andrms radial profiles of major species obtained from the sim-ulation are compared to measurements [1]. The trend andobservations made for temperature and mixture fractionin the last section hold for the species, the respective Fig-ures F.29-F.38 have been moved to Appendix F for brevity.
Figure 17 shows a comparison of mean mass fractionprofiles of major species 10 mm above the burner withmeasurements for the fine grid simulation. The relatedatomic mass fractions for carbon, hydrogen, oxygen andnitrogen are displayed in Fig. 18. Noticeable differencesbetween simulation and experiment can be observed forradii smaller than 10 mm, which will be addressed next.
11
Figure 15: Maximum and minimum mean Favre-filtered mixturefractions at the cell faces as a function of the respective value Zat the cell center for the case SwB5 on the coarse grid with top-hatsub-filter model in Z (LES-C-SZ). The diagonal line corresponds tothe values at the cell centers. Enlarged plots are included for regionswith distinct features. The range of 10% mixture fraction deviationbased on the stoichometric value is bordered by thin lines, the innerstream mixture fraction of 0.277 is marked by a vertical line.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.026 0.054 0.093
SL
/ (m
/s)
Z / (-)
ΔZ / (-) = 0.1 Zst = 0.0054
Figure 16: Laminar flame speed vs. mixture fraction for methane/aircomputed with the GRI-3.0 mechanism and unity Lewis number as-sumption for all species. The spacing of the mixture fraction gridlines is 10% of the stoichometric value, corresponding to the rangeindicated in Fig. 15.
For SwB1, the element mass fraction is under predictedfor carbon and over predicted for oxygen relative to theexperiments. Looking at the species profiles, it can beseen that this corresponds to a lack of CO2 and a surplus ofO2. The under predicition of carbon also occurs for SwB5and SwB9, this corresponds to a lack of CO here. Forthe latter case, an additional over prediction of hydrogenand oxygen can be observed, which can be assigned to asurplus of H2O.
The under prediction of H2 mass fraction occurring forall three cases does only have a negligible influence on theatomic mass fraction of hydrogen, as this is dominated bythe contributions of H2O and CH4. It should be consideredthat the experimental profiles are somewhat discontinuousfor oxygen and nitrogen, where nitrogen shows the inversebehavior of oxygen. In accordance with the observationsby Sweeney et al. [1], it is also mentioned here that theagreement of CO2 measurements with predictions based onone-dimensional flame computations (which are the basisfor FGM) is worse than for the other educt and productspecies (CH4, H2O, O2).
The enrichment of CO2 in the recirculation zone forSwB1 can be explained with the effect of preferential dif-fusion suggested by Barlow et al. [60], although the de-pletion of O2 is unexpected in that context. In contrast,the enrichment of CO for SwB5 as well as SwB9 and theadditional depletion of H2O for the latter case may berather due to heat transfer than due to preferential diffu-sion. One indicator for an heat loss effect is that the mea-sured mean temperature profiles have a remaining slopeat the centerline and a lower peak value in comparisonto the adiabatic simulation results. Another indicator isthat the CO and H2O mass fractions in the FGM-tablefor the experimental temperatures at the centerline werefound to be in good agreement with the measured con-centrations of these species. A non-adiabatic extension ofthe ATF/FGM model has been presented and applied byKetelheun et al. [41] with good success, assuming a Diracpeak for the sub-filter distributions.
4.5. Influence of stratification
The effects of stratification on the flame behavior areinvestigated further. As this is rather thought as a deeperanalysis of the combustion process using the capabilities ofthe numerical simulation than as an additional validation,only the fine grid results are taken into account.
To classify the dependency of the combustion processon the equivalence ratio globally, the normalized PDF ofFavre-filtered reaction source term conditional on Favre-filtered equivalence ratio over the entire domain is shownin Fig. 19. To take into account the effects of turbulenceand thickening, the last term on the RHS of Eq. 3 was usedas the source term. This gives a good representation of theinfluence that reaction at the given equivalence ratio hason the global combustion process and heat release. Thesampling was carried out for at least 8 flow-trough timesin accordance with the other flow statistics.
12
0
0.02
0.04
0.06
z = 10 mm
SwB1
YC
H4
mea
n
LES-F EXP
0
0.05
0.1
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
LES-F EXP
0
0.05
0.1
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
n
LES-F EXP
0
0.02
0.04
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
n
LES-F EXP
0
0.0005
0.001
0.0015
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
n
LES-F EXP
00.05
0.10.15
0.2
0 10 20r / (mm)
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
0 10 20r / (mm)
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
0 10 20r / (mm)
z = 10 mm
SwB1
YC
H4
mea
nY
H2
Om
ean
YC
O2
mea
nY
CO
mea
nY
H2
mea
nY
O2
mea
n
SwB5 SwB9
LES-F EXP
Figure 17: Radial profiles of the mean major species mass fractions10 mm downstream of the burner exit.
0
0.02
0.04
z = 10 mm
SwB1
YC
mea
n
LES-F EXP
0
0.005
0.01
0.015
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
LES-F EXP
0.2
0.22
0.24
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
n
LES-F EXP
0.72
0.74
0.76
0 10 20r / (mm)
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5
LES-F EXP
0 10 20r / (mm)
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5 SwB9
LES-F EXP
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5 SwB9
LES-F EXP
0 10 20r / (mm)
z = 10 mm
SwB1
YC
mea
nY
Hm
ean
YO
mea
nY
Nm
ean
SwB5 SwB9
LES-F EXP
Figure 18: Radial profiles of the mean atomic mass fractions 10 mmdownstream of the burner exit
0
0.03
0.06
0.09
0.5 0.6 0.7 0.8 0.9 1 1.1
Σ S
RC
nor
m /
(-)
ϕ / (-)
SwB1SwB5SwB9
Figure 19: Normalized PDFs of Favre-filtered reaction source termconditional on Favre-filtered equivalence ratio over the entire domain.
For all cases, combustion occurs in the whole range ofequivalence ratio between the lean flammability limit andthe respective equivalence ratio in the inner stream. To-wards the lean flammability limit the reaction probabilitydeclines to zero at a comparable rate for all cases.
For SwB1, the PDF is continuously rising until reach-ing an equivalence ratio of 0.7, followed by a broad peaktowards the inner (and outer) stream value of 0.75. Thisshows that already the presence of an air coflow is suf-ficient to trigger combustion over the whole equivalenceratio range down to the flammability limit.
For SwB5 and SwB9 the PDF increases steadily fromthe flammability limit until a value of around 0.6, whichcorresponds to the burnt side of the flame when it is lo-cated completely in a stratified enviroment, as alreadyadressed in section 4.1. From 0.6 onwards, the PDF de-creases constantly until it reaches the respective equiva-lence ratio in the inner stream, here it develops a sharp sec-ond peak. The reason why the first peak is much broaderthan the second one is that the respective samples arefound further downstream, where the flame front has beenwidened by turbulent effects. It is noticeable that theshape of the PDF is very similar for SwB5 and SwB9.The fact that the latter one is partly located within therich equivalence ratio regime does not seem to have a con-siderably influence on the stratified combustion process.
Figure 20 shows the normalized joint PDFs of Favre-filtered equivalence ratio against the Favre-filtered flamesensor, the Favre-filtered normalized progress variable andthe axial distance from the burner exit. This characterizesthe stratified combustion process further taking into ac-count the interaction between the value of equivalence ra-tio and the intensity of reaction, the reaction progress andthe axial position, respectively. Only the points inside theflame region have been considered, the limit has been setat a flame sensor value of 0.01. Therefore the outer streamequivalence ratio does not occur in the axial position plotsfor small distances, as the flame burns only at the innerstream equivalence ratio in this regions.
The shape of the already discussed reaction source termPDFs is basically mirrored in the joint PDFs of the flamesensor for values near zero, which are found in regionswith low reaction rates at the unburnt or burnt side of the
13
Figure 20: Joint PDFs of Favre-filtered equivalence ratio vs. Favre-filtered flame sensor (left), Favre-filtered normalized progress vari-able (middle) and distance from the burner exit (right).
flame. For SwB1 the joint PDF shifts towards the inner(and outer) stream equivalence ratio of 0.75 when proceed-ing to higher flame sensor values. Within the flame zonewith the highest reaction rate corresponding to a flamesensor value of unity, most of the combustion is occur-ring in a broad peak towards the inner (and outer) streamequivalence ratio of 0.75. Nevertheless, contributions ofthe whole equivalence ratio range are found for all flamesensor values. For SwB1 and SwB5 the bimodal shapewith peaks at the respective inner stream equivalence ra-tio of 1.0/1.125 and the already discussed value of 0.6 getsmore and more distinct when proceeding to higher flamesensor values. At a flame sensor value of unity, there isonly a negligible amount of samples found in the equiva-lence ratio range between approximately 0.8 and the innerstream equivalence ratio of 1.0/1.125, which means thatfor the high reactive part of the flame it can be distin-guished between two types of flames which differ about0.2 respectively 0.3 in equivalence ratio.
Within the progress variable joint PDFs, it can be ob-served that for SwB1 most of the combustion at equiva-lence ratios near to the lean flammability limit occurs atlow progress variable values near the unburnt side of theflame. At the burnt side of the flame, which is character-ized by progress variable values near unity, the combustionprocess is only exposed to a narrow range of equivalenceratios between approximately 0.6 and 0.75. In contrastto that, combustion towards the lean flammability limitis found within the whole range of progress variable val-ues for SwB5 and SwB9. Progress variable values close to
unity are not found for equivalence ratio values larger thanapproximately 0.75 for the two latter cases. This impliesthat the respective flames are located further downstreamthan 40 mm above the burner, as this is the position fromwhere the whole flame is located in a stratified environ-ment, as discussed in section 4.1.
Within the axial position PDFs it can be determinedthat these two types of flames for SwB5 and SwB9 arealso separated spatially, combustion at the inner streamequivalence ratio can be found up to approximately 40mm. Above this height the flame is burning betweenthe flammability limit and an equivalence ratio of 0.8.The transition between these two regimes takes place rel-atively rapidly in the region between 25 and 40 mm. Thisbasically correspond to the findings from the analysis ofFig. 4, where three different combustion regimes wherefound. However, the closer analysis with the joint PDFshas shown that the overall flame behavior is dominated bythe contribution of the perfectly premixed combustion (in-ner stream) and the combustion towards the lean flamma-bility limit (mixing layer between air and outer stream).The contribution of the stratified regime away from theflammability limit between 30 mm and 50 mm is small.For SwB1 the combustion towards the flammability limitstarts from around 40 mm onwards, in contrast to the twoother cases flames with the inner stream equivalence ratioare dominating troughout the whole domain.
The equivalence ratio value at a point alone is not suf-ficient to fully characterize the stratified combustion pro-cess, as it yields no information on the interaction of thelocal equivalence ratio gradient with the flame structure.A suitable quantity to investigate this interaction is thealignment angle between the gradients of equivalence ra-tio and progress variable [26, 27, 63]. It is evaluated forevery point in the computational domain according to:
α = arccos
(∇C · ∇φ|∇C||∇φ|
)180
π. (21)
The resulting joint PDFs of α versus flame sensor, progressvariable and axial position are displayed in Fig. 21. Forα < 90, the flame propagates towards lower values ofequivalence ratio, this is denoted as back-supported strat-ification for lean conditions and yields a higher flame prop-agation speed [63]. Front-supported stratification, on theother hand, occurs for lean conditions when α > 90, inthis case the propagation of the flame is directed towardshigher values of equivalence ratio and the flame propaga-tion speed is thought to be lower [63]. Again, only pointswith a flame sensor value greater 0.01 have been takeninto account, which means that a certain progress variablegradient is always ensured. However, the denominator inEq. 21 can still become singular in regions with vanishingequivalence ratio gradients, which corresponds to perfectlypremixed combustion at this point. To consider this con-sistently, all points with |∇φ| < 0.1 have been collected ina separate bin. This bin is plotted above the actual plotsin Fig. 21, its width is scaled to obtain a PDF peak value
14
Figure 21: Joint PDFs of alignment angle between progress variableand equivalence ratio vs. Favre-filtered flame sensor (left), Favre-filtered normalized progress variable (middle) and distance from theburner exit (right).
corresponding to the rest of the plot so that the area belowthe PDFs can be compared.
For all cases, most of the combustion occurs in the per-fectly premixed regime. Even further downstream, wherethe whole flame region is exposed to equivalence ratio gra-dients as discussed before, a significant amount of perfectlypremixed combustion can be observed. This can be ex-plained by the different magnitude of the length scales onwhich the combustion and the mixing process take place,so that even in a stratified region the equivalence ratio gra-dient inside the flame is still small in comparison to theprogress variable gradient.
For SwB1, back-supported stratification can be foundin the region downstream of 40 mm, mainly for low val-ues of the flame sensor and progress variable values of ei-ther near unity or near zero. A minimal amount of front-supported stratification can also be observed, this can beexplained by turbulent wrinkling, causing the flame topropagate with the equivalence ratio gradient locally.
For SwB5 and SwB9 the basic observations are compa-rable. The region where back-supported and small amountsof front-supported flames are found starts earlier at ap-proximately 30 mm, as it could be expected. The amountof stratified combustion is bigger than for SwB1, especiallyfor flame sensor values near unity. Most of the stratifiedcombustion is found near progress variable values of unityat the burnt side of the flame for these cases.
5. Conclusions
LES computations for three different grid resolutionsand stratification levels have been presented for the Cam-bridge stratified flame series. The ATF approach was usedin combination with the FGM technique in a formula-tion for stratified combustion. The necessary adaptionsto make the model suitable for varying mixture fractionswere investigated carefully. The commonly used flame sen-sor formulation was replaced by a version that makes thethickening behavior independent of the mixture fraction.
Radial profiles from the simulation have been com-pared to measurements for mean value and fluctuationsof axial and radial velocity, equivalence ratio, temperatureand major species concentrations. An overall good agree-ment was found with some deviations occurring within thebluff body region. By analyzing atomic mass fractions andspecies profiles, these deviations could be assigned mostlikely to effects of preferential diffusion for the case SwB1and heat transfer in the cases SwB5 and SwB9. To testthe influence of the assumed sub-filter FDF, the coarse gridsimulations have been carried out with and without usinga top-hat distribution for the FDF in mixture fraction andprogress variable, respectively. It was found that influenceon the results was only small, therefore the simulations onthe medium and fine grid have been performed assuming aDirac-distribution for both mixture fraction and progressvariable. Good convergence of the results with grid refine-ment was observed.
The overall combustion process was analyzed using con-tour plots, conditional PDFs and joint PDFs. It was foundthat combustion occurs over the whole range of equivalenceratios from the value in the respective inner stream downto the lean flammability limit. The combustion proba-bility shows a peak at the inner stream equivalence ratiofor all cases. Three different flame regions could be dis-tinguished, first a perfectly premixed region, followed bya region in which the flame starts to burn in a stratifiedregime and finally a region where the unburnt side of theflames touches the lean flammability limit. The overallcombustion process was found to be dominated by the con-tributions of the first and last region. Also in the stratifiedregions a large amount of the combustion takes place underquasi-premixed conditions due to a negligible equivalenceratio gradient. A significant amount of back-supportedand some front-supported stratification was also found forall three cases, most dominant for SwB5 and SwB9.
Acknowledgements
The authors gratefully acknowledge funding from thestate of Nordrhein-Westfalen, Germany. Computationshave been carried out using the DFG supported HPC re-sources of the Center for Computational Sciences and Sim-ulation (CCSS) of the University of Duisburg-Essen, Ger-many. We also would like to thank Robert S. Barlow, Sar-avanan Balusamy, Matthew J. Dunn, Simone Hochgreb,
15
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
LES-M-DT LES-M-CT EXP
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
LES-M-DT LES-M-CT EXP
500
1000
1500
2000
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-M-DT LES-M-CT EXP
500
1000
1500
2000
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
0 10 20r / (mm)
Tmean / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Figure A.22: Comparison of the radial mean profiles of temperatureobtained with the classical ATF model with constant thickening fac-tor F (LES-M-CT) and the applied version of the model with Fdetermined from Eq. 7 (LES-M-DT) on the medium grid.
Mark S. Sweeney and Ruigang Zhou for providing the ex-perimental data and the TNF-community for many helpfuldiscussions.
Appendix A. Effect of the flame sensor
Figures A.22 and A.23 show comparisons of the meanand rms temperature profiles obtained on the mediumgrid for a simulation with a constant thickening factor(LES-M-CT) and one with the thickening factor deter-mined with the use the flame sensor from Eq. 7 (LES-M-DT). The overall position of the flame is not influenced bythe type of thickening procedures applied. However, thestructure of the burnout zone is affected. The shape ofthe temperature profiles in the burnout zone is in notablebetter agreement with the measurements for LES-M-DT.For the constant thickening factor simulation LES-M-CT,the effect of the excessive thickening of the burnout zonebecomes visible, most obviously for the stratified casesSwB5 and SwB9. The excessive thickening also causes acertain under-prediction of the fluctuation level for LES-M-CT. Figure A.24 compares instantaneous snapshots ofthe resulting temperature field for both methods. Themethod with the flame sensor (LES-M-DT) reduces theflame thickness and thereby avoids excessive damping ofsmaller flame structures in comparison to the classical ATFmodel (LES-M-CT).
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
LES-M-DT LES-M-CT EXP
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
LES-M-DT LES-M-CT EXP
0
200
400
600
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-M-DT LES-M-CT EXP
0
200
400
600
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
0 10 20r / (mm)
Trms / (K)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-M-DT LES-M-CT EXP
Figure A.23: Comparison of the radial fluctuation profiles of temper-ature obtained with the classical ATF model with constant thicken-ing factor F (LES-M-CT) and the applied version of the model withF determined from Eq. 7 (LES-M-DT) on the medium grid.
Appendix B. Velocity fluctuations and fitted effi-ciency function
The velocity fluctuations in Eq. 9 are evaluated fromthe correlation given by Colin et al. [8] and modified byWang et al. [47] to work for other values than 10 for thenumbers of grid points n to resolve the flame thickness:
u′
∆ = 2∆3mesh
∣∣∣∇2(∇× ~u
)∣∣∣ ( n10
) 13
= 2∆3mesh
∣∣∣∇× (∇2~u)∣∣∣ ( n
10
) 13
(B.1)
The Laplace operator is evaluated on a (4∆mesh) stencil,to not consider the highest frequencies (noise) [8]. Theturbulent Reynolds number on the sub-filter scale is eval-uated from [9]:
Re∆ = 4Fmaxu
′
∆
s0l
(B.2)
and the fitted efficiency function from [9]:
Γ∆
(Fmax,
u′
∆
s0l
, Re∆
)=
[(f−au + f−a∆
)− 1a
−b+ f−bRe
]− 1b
(B.3)
16
Figure A.24: Comparison of instantaneous contour plots of tempera-ture obtained with the classical ATF model with constant thickeningfactor F (LES-M-CT) and the applied version of the model with Fdetermined from Eq. 7 (LES-M-DT) on the medium grid. The whiteisolines mark a progress variable value of C = 0.5.
with
fu = 4
(27Ck110
) 12(
18Ck55
)(u
′
∆
s0l
)2
(B.4)
f∆ =
[27Ckπ
43
110
(Fmax)
43 − 1
] 12
(B.5)
fRe =
[9
55exp
(−3
2Ckπ
43Re−1
∆
)] 12
Re12
∆ (B.6)
a = 0.6 + 0.2 exp
(−0.1
u′
∆
s0l
)− 0.2 exp (−0.01 Fmax)
(B.7)
b = 1.4 (B.8)
where Ck = 1.5 is the Kolmogorov constant. It was foundthat the evaluation of this efficiency function became com-putationally expensive in comparison to the rest of theCFD solver, consuming up to 25% of the runtime. Asignificant speedup was achieved by tabulating Eq. 9 atthe beginning of the computation, and then obtaining thevalue of E from an additional table lookup depending onthe local value of the maximum thickening factor and thevelocity ratio.
Appendix C. Variance modeling
For a one-dimensional case, the gradient model for themixture fraction by Branley and Jones [51] reads:
Z ′′2 = C2∆2
(ZN − ZS
2∆
)2
, (C.1)
where ZN and ZS represent the values at the neighboringcell centers. Floyd et al. [48] have shown that in cases ofa linear mixture fraction profile, the resulting value of themodeling constant is:
C2 =1
12, (C.2)
which results in in a upper and lower limit of:
Zu/l = Z ± 0.5
√12Z ′′2 = Z ± 0.25(ZN − ZS) (C.3)
For the approach used within this work, the values at thecell faces are obtained from the mean value of the neigh-boring cells
Zs = 0.5(ZS + ZC) and Zn = 0.5(ZN + ZC) (C.4)
where Zc denotes the value at the cell center. The gradientover the cell is then obtained from
dZ
dx=Zn − Zs
∆=ZN − ZS
2∆(C.5)
This results in an upper and lower limit of :
Zu/l = Z ± 0.5∆dZ
dx= Z ± 0.25(ZN − ZS) (C.6)
which is in agreement with the result for the gradient as-sumption in Eq. C.3.
17
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
LES-C-small LES-C-large EXP
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-C-small LES-C-large EXP
0
10
20
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-C-small LES-C-large EXP
0
10
20
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
0 10 20r / (mm)
Umean / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Figure D.25: Investigation of the influence of the domain size on theradial mean profiles of axial velocity.
Appendix D. Influence of domain size
To study the influence of the domain size, additionalcomputations were carried out for the coarse grid on adomain that had doubled size in all directions. The influ-ence on the mean values of all quantities was found to benegligible, Fig. D.25 shows the respective comparison foraxial velocity as an example. Some deviations occurredfor the fluctuations of axial velocity further downstream,as displayed in Fig. D.26. For all other quantities the de-viations in the fluctuations were negligible, some exampleprofiles 70 mm above the burner are shown in Fig. D.27.Therefore, it was decided to choose the smaller domain, asthe simulation results benefit significantly from the finerresolution that is computational affordable on the smallerdomain.
Appendix E. Comparison of thickening and filter-ing
The ATF model with flame sensor used in this workis compared to the filtering procedure that forms the ba-sis of approaches like the F-TACLES [30] or the (FLF) -PDF model [32] in this section. For that purpose, a one-dimensional flame computation for stoichiometric condi-tions has been carried out with Cantera. The resultingprofiles for the mass fractions of progress variable (prod-uct species), methane (educt species) and carbon monox-ide (intermediate species) as well as for the temperaturehave been stored over the flame normal coordinate (Orig-inal). Afterwards, these profiles have been filtered with
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
LES-C-small LES-C-large EXP
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
LES-C-small LES-C-large EXP
0
2
4
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-C-small LES-C-large EXP
0
2
4
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
0 10 20r / (mm)
Urms / (m/s)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-C-small LES-C-large EXP
Figure D.26: Investigation of the influence of the domain size on theradial fluctuation profiles of axial velocity.
0
1
2
3
z = 70 mm
SwB1
Vrm
s /
(m/s
)
LES-C-small LES-C-large EXP
0
0.1
0.2
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
LES-C-small LES-C-large EXP
0
200
400
600
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
LES-C-small LES-C-large EXP
0
0.01
0.02
0 10 20r / (mm)
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5
LES-C-small LES-C-large EXP
0 10 20r / (mm)
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5 SwB9
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5 SwB9
LES-C-small LES-C-large EXP
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5 SwB9
LES-C-small LES-C-large EXP
0 10 20r / (mm)
z = 70 mm
SwB1
Vrm
s /
(m/s
)E
qrm
s /
(-)
Trm
s /
(K)
YC
H4
rms
/ (-
)
SwB5 SwB9
LES-C-small LES-C-large EXP
Figure D.27: Investigation of the influence of the domain size onthe radial fluctuation profiles of selected quantities 70 mm above theburner.
18
0 0.05
0.1 0.15
0.2 0.25
YC /
(-)
OriginalATF
ATFomegaATFomegaTH
FilteredGaussFilteredTH
500
1000
1500
2000
YC /
(-)
T /
(K
)
OriginalATF
ATFomegaATFomegaTH
FilteredGaussFilteredTH
0
0.02
0.04
0.06
YC /
(-)
T /
(K
)Y
CH
4 /
(-)
OriginalATF
ATFomegaATFomegaTH
FilteredGaussFilteredTH
0
0.01
0.02
0.03
0.04
0.009 0.0095 0.01 0.0105 0.011 0.0115 0.012x / (m)
YC /
(-)
T /
(K
)Y
CH
4 /
(-)
YC
O /
(-)
OriginalATF
ATFomegaATFomegaTH
FilteredGaussFilteredTH
Figure E.28: Comparison of the influence of thickening and filteringon the structure of a one-dimensional flame.
a top-hat filter (FilteredTH, ∆ = 2.2 mm) and a Gaus-sian filter (FilteredGaussian, ∆ = 6.0 mm), respectively.Afterwards ’PsiPhi’ was used to simulated a laminar one-dimensional flame on a 0.5 mm grid with the classical ATF-model (ATF, constant thickening factor of 5), the ATF-model with flame sensor (ATFomega) and the ATF-modelwith flame sensor and top-hat FDF in C (ATFomegaTH).The respective comparison is shown in Fig. E.28, exceptfor the intermediate species similar results are achievedfor the different approaches. The influence of the thick-ening procedure on the pre-heat and burnout zone for theATF-model without flame sensor becomes obvious. It isnotable that the top-hat FDF improves the agreement withthe filtered results significantly in the burnout zone, andhas negligible influence at the unburnt side of the flame.For the intermediate species carbon monoxide, the filteringprocedure preserves the area below the profile and under-predicts its peak value, whereas the thickening procedurepreserves the peak value and over-predicts the area belowthe profile.
Appendix F. Mean and rms profiles of major speciesmass fractions
The radial profiles of mass fraction means and fluctu-ations for major species are shown in Figures F.29-F.38.
0
0.02
0.04
0.06
YCH4mean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
0 10 20r / (mm)
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCH4mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.29: Radial profiles of the mean methane mass fraction atdifferent downstream locations, showing a comparison for three dif-ferent grids with the experiments. LES-C-SZ and LES-C-SC refer toa coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.05
0.1
YH2Omean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
0 10 20r / (mm)
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2Omean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.30: Radial profiles of the mean water mass fraction at dif-ferent downstream locations, showing a comparison for three differ-ent grids with the experiments. LES-C-SZ and LES-C-SC refer toa coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
19
0
0.05
0.1
YCO2mean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
0 10 20r / (mm)
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.31: Radial profiles of the mean carbon dioxide mass fractionat different downstream locations, showing a comparison for threedifferent grids with the experiments. LES-C-SZ and LES-C-SC referto a coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.05
0.1
0.15
0.2
YO2mean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
0.15
0.2
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
0.15
0.2
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.05
0.1
0.15
0.2
0 10 20r / (mm)
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YO2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.32: Radial profiles of the mean oxygen mass fraction atdifferent downstream locations, showing a comparison for three dif-ferent grids with the experiments. LES-C-SZ and LES-C-SC refer toa coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.0005
0.001
0.0015
YH2mean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.0005
0.001
0.0015
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.0005
0.001
0.0015
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.0005
0.001
0.0015
0 10 20r / (mm)
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2mean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.33: Radial profiles of the mean hydrogen mass fractionat different downstream locations, showing a comparison for threedifferent grids with the experiments. LES-C-SZ and LES-C-SC referto a coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.02
0.04
YCOmean / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0 10 20r / (mm)
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCOmean / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.34: Radial profiles of the mean carbon monoxide mass frac-tion at different downstream locations, showing a comparison forthree different grids with the experiments. LES-C-SZ and LES-C-SC refer to a coarse grid simulation with additional sub-filter mod-eling using a top-hat FDF in mixture fraction and progress variable,respectively.
20
0
0.01
0.02
YCH4rms / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
0 10 20r / (mm)
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCH4rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.35: Radial profiles of the methane mass fraction fluctu-ations at different downstream locations, showing a comparison forthree different grids with the experiments. LES-C-SZ and LES-C-SCrefer to a coarse grid simulation with additional sub-filter modelingusing a top-hat FDF in mixture fraction and progress variable, re-spectively.
0
0.02
0.04
YH2Orms / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0 10 20r / (mm)
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YH2Orms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.36: Radial profiles of the water mass fraction fluctuationsat different downstream locations, showing a comparison for threedifferent grids with the experiments. LES-C-SZ and LES-C-SC referto a coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.02
0.04
0.06
0.08
YO2rms / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
0.08
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
0.08
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.02
0.04
0.06
0.08
0 10 20r / (mm)
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YO2rms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.37: Radial profiles of the oxygen mass fraction fluctuationsat different downstream locations, showing a comparison for threedifferent grids with the experiments. LES-C-SZ and LES-C-SC referto a coarse grid simulation with additional sub-filter modeling using atop-hat FDF in mixture fraction and progress variable, respectively.
0
0.01
0.02
YCOrms / (-)
SwB1
z =
70
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0
0.01
0.02
0 10 20r / (mm)
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
0 10 20r / (mm)
YCOrms / (-)
SwB1
z =
70
mm
z =
50
mm
z =
30
mm
z =
10
mm
SwB5 SwB9
LES-CLES-M
LES-C-SZLES-F
LES-C-SCEXP
Figure F.38: Radial profiles of the carbon monoxide mass fractionfluctuations at different downstream locations, showing a compari-son for three different grids with the experiments. LES-C-SZ andLES-C-SC refer to a coarse grid simulation with additional sub-filtermodeling using a top-hat FDF in mixture fraction and progress vari-able, respectively.
21
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22