Numerical Simulation of Counter-Current Dump

Combustor for Efficient Flame Stabilization

K. Sengupta, ∗ K. Russell, ∗ and F. Mashayek †

University of Illinois at Chicago

842 West Taylor Street, Chicago, IL 60607

In this paper, we report numerical studies of non-reacting and reacting flows in abackward-facing step combustor by employing a novel counter-current shear (or coun-terflow) concept. Counterflow is used to manipulate the turbulent shear layer created bythe step in order to increase turbulent burning velocities, and thereby, reduce ignitiondelay time. Unfortunately, this concept also leads to a smaller residence time because ofa shorter recirculation vortex. These competing challenges of achieving higher burningvelocities and longer residence time demands modification of the step geometry. Changesin the step extension geometry will alter the size and characteristics of the recirculationvortex, affecting both the turbulent energy production and flame anchoring performance.

For the simulations, Reynolds-averaged Navier-Stokes equations are solved in the frame-work of the realizable k-ε turbulence model. A two-layer approach is used for the near walltreatment, whereas, a one-equation model is employed for the viscous sublayer. The clo-sure for the reaction source term is based on the eddy dissipation method (EDM) andthe eddy dissipation concept (EDC). This paper includes a detailed account of the costbenefits of counter-current shear technology, a parametric study based on step geometrymodifications, and an aerodynamic performance evaluation.

Nomenclature

Cp Coefficient of pressure drag acting normal to the step wall, P−P012 ρ0U2

0

Cf Coefficient of skin friction drag on the bottom wall, τ012 ρ0U2

0

G Suction gap heightH Step height of the combustork Turbulent kinetic energyL Combustor lengthLr Length of the recirculation zoneP Static pressureP0 Reference pressureT Splitter plate thicknessU0 Mean axial velocity at the inletU2 Maximum velocity of primary streamU1 Maximum velocity of secondary streamyα Cross-stream locationδ Boundary-layer thicknessρ0 Reference densityτ0 Wall shear stress

∗Graduate students, Department of Mechanical and Industrial Engineering, 842 W. Taylor Street, Chicago, IL 60607.†Professor, Department of Mechanical and Industrial Engineering, 842 W. Taylor Street, Chicago, IL 60607, AIAA Associate

Fellow.

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AIAA 2006-174

Copyright © 2006 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

9H

H

H

G=0.25HSUCTION

T=0.05H

X

Y

U =12.5m/s 0

Figure 1. Schematic of the baseline combustor (not to scale) considered in this study.

I. Introduction

Dump combustors are widely used in modern air breathing propulsion devices as an energy conversioncomponent. A typical characteristic of dump combustors is the sudden expansion of the flow downstream of astep or bluff-body. The sudden expansion causes the flow to separate, leading to a low velocity recirculationzone that contains reacting mixture and serves as a continuous ignition source. Under ideal conditions,the incoming reactants should have sufficient residence time within the recirculation vortex to fully react.This reaction is needed to create hot combustion products, which would subsequently ignite fresh reactants.Counter-current shear flow that is applied to asymmetric step combustors have been studied in Forliti.1 Coldflow results have indicated that high turbulence at a controlled strain rate could be generated by augmentingthe naturally present counterflow within the combustor with additional suction. The overall benefits of awell designed counter-current dump combustor are a large increase in volumetric heat release rate and anextended stable operating condition.

Although the application of counter-current shear technology to traditional step combustors has enormouscost benefits with regards to control of the turbulent flow field, this method may fail to provide adequateflame anchoring. Counterflow through the manipulation of the turbulent shear layer created by the stepincreases turbulent burning velocities, and thereby, reduces ignition delay time. But at the same time, itleads to a smaller residence time because of a shorter recirculation vortex. These competing challenges ofachieving higher burning velocities and longer residence time demands modification of the step geometry.Changes in geometry will alter the size and characteristics of the recirculation vortex, affecting both turbulentenergy production and flame anchoring performance.

In the following sections, we will first briefly describe our computational tools and modeling approach.Then we will present model comparisons and validation results for cold flow with and without counterflow forthe basic step combustor. The effects of counter-current shear on flow quantities relevant to flame dynamics,stabilization, and aerodynamic drag is briefly discussed. Then the impact of step wall geometry modificationson the flow characteristics is addressed. Finally, we will present some results from reacting flow simulationsfocussing on combustion models and flame stabilization.

II. Numerical Modeling Approach

In our previous works2–4 we have shown that Reynolds-average Navier-Stokes (RANS) modeling is asuitable technique for simulating two-phase reacting flow in practical configurations at an affordable com-putational time. Therefore, in this work we adopt the RANS approach for our analysis and design. TheFLUENT software is used for all of the simulations conducted in this paper. A survey of existing literature5,6

revealed that both two-equation based models and Reynolds stress closures have been used to simulate flowsin back-step configurations. Thus, in order to asses the viability of these models for the present problem,we tested the standard k-ε model, realizable k-ε model, and Reynolds stress model (RSM) against the ex-perimental data of Forliti.1 The results (which are discussed in the following section) demonstrate that therealizable k-ε model predicts the flow features fairly well. Thus, there is no need to resort to the arguablymore accurate but, computationally expensive, full Reynolds stress closures.

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-0.2 0 0.2 0.4 0.6 0.8 1U/U

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X/H=2X/H=5X/H=7

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Realizable k-ε ModelStandard k-ε Model

Reynolds Stress Model

(a) (b)

(c)

Figure 2. Comparisons of turbulence models against experimental data for the baseline combustor. Continuouslines with markers indicate numerical model results, while markers without lines indicate experimental data:(a) standard k-ε, (b) realizable k-ε, and (c) Reynolds stress models.

Modeling the reaction source term in turbulent flow is very challenging. Turbulent combustion involvesvarious length, velocity, and time scales describing turbulent flow fields and chemical reactions. The physicalanalysis and models employed for a specific situation is based on the comparison between these scales.Broadly speaking, these models can be classified into two categories, one based on fast chemistry assumptionand the other which includes finite rate chemistry effects. In this paper, we test both groups of models. Theeddy dissipation model7 (EDM) is based on the assumption that the reaction zone is composed of a collectionof fresh and burnt gas pockets. Turbulence leads to the breakdown of fresh gas structures. Accordingly, themean reaction rate is controlled by turbulent mixing rather than chemistry. The eddy dissipation concept(EDC) model is an extension of the eddy dissipation model to incorporate detailed chemistry.8 It assumesthat reaction occurs in small turbulent structures, called the fine scales. Combustion at the fine scales isassumed to occur as a constant pressure reactor, with initial conditions taken as the current species andtemperature in the cell. Reactions proceed over the time scale, governed by the Arrhenius rates, and areintegrated numerically using the In-Situ Adaptive Tablulation (ISAT) algorithm.9

0 2 4 6 8X/H

0

0.01

0.02

0.03

0.04

0.05

0.06

k/(U

0*U0)

ExperimentalNumerical

Figure 3. Cross-stream averaged turbulent kinetic energy distributions.

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Figure 4. Comparisons of axial velocity profiles at selected axial stations for the baseline combustor with 10.7%counter-current shear flow: (a) x/H=2, (b) x/H=5, and (c) x/H=7.

III. Results: Non Reacting Flow

A. Turbulence Model Comparison

For the assessment of turbulence models we simulate the basic back-step combustor without counter-currentflow and without an added step extension, which will henceforth be referred to as the baseline case. Aschematic of the baseline combustor is shown in figure 1. Figure 2 shows the axial velocity profiles atthree different axial stations for the baseline case. The axial velocities have been normalized with the meaninlet velocity (U0). We find that both the realizable k-ε and Reynolds stress models compare well with theexperimental data, especially in the shear layer, with RSM doing marginally better near the reattachmentpoint. However, Reynolds stress models have a high relative computational overhead. Therefore, in all thesubsequent simulations, the realizable k-ε model is used because of its good accuracy and low computationalcost. The standard k-ε results were shown to fare poorly, especially away from the step.

At the combustor exit, we employed a pressure outlet (flow exhausting to the atmosphere) boundarycondition. Whereas, in the experimental setup, the flow exits to a rectangular duct and finally up anexhaust pipe to the atmosphere. Thus, we attribute the differences between the numerical and experimentalresults to insufficient modeling of the outlet boundary condition.

Comparisons for the reattachment length, Lr, shows that the realizable k-ε model over-predicts the ex-perimental value of 7.1 by 19.71%. Interestingly, the standard k-ε model predicted a reattachment lengthof 7.5. We also compared the cross-stream averaged normalized turbulent kinetic energy in figure 3. Themaximum deviation from the experimental data is approximately 30%, which can be considered reasonable.The cross-stream averaged turbulent kinetic energy gives us an indication of the volume of energetic turbu-lence that exists across the combustor. The results indicate that the quantity increases monotonically withaxial distance and eventually flattens out towards the end of the combustor.

B. Effects of Counter-current Shear

Having validated our modeling approach, we will now examine the effects of counter-current shear on theflow characteristics for the basic step combustor of figure 1. We employ a suction level of 10.7% of theprimary mass flow in our calculations, since most of the experimental data for comparison was available forthis case.1 Figure 4 shows comparisons of velocity profiles for numerical and experimental data for 10.7%counterflow at different axial locations. A comparison of figures 2 and 4 reveals that suction leads to rapidmixing and enhanced cross-stream transport of the streamwise momentum, resulting in much flatter velocity

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Figure 5. Mean streamline contours for (a) 0% counter-current flow with Lr = 8.5H and (b) 10.7% counterflowwith Lr = 7.5H.

profiles. The increased mixing with counter-current shear should lead to a better pattern factor, which is ameasure of the spatial distribution of mean temperature and velocity at the exit of the combustor. Figure 5shows the streamlines for cases without and with counter-current. The most obvious change is the reductionof the streamwise length of the recirculation bubble. This shortening will lead to compact burning withinthe combustor but, at the same time has potential detrimental effects to flame anchoring.

Figure 6 shows the shear layer growth along the baseline combustor length. The flow past a backwardfacing step could be viewed as a counter-flowing mixing layer. The characteristic width of a mixing layercan be defined in a number of ways based on the mean axial velocity profile. The velocity, U(x, yα(x)), atthe cross-stream location, yα, has been outlined in the works of Pope10 and is defined as,

U(x, yα(x)) = U1 + α(U2 − U1), (1)

where U2 and U1 are the maximum velocity of the primary and the secondary streams, respectively. Thethickness, δ(x), is defined by,

δ(x) = y0.9(x)− y0.1(x). (2)

We observe in figure 6 that the spreading rate is very similar for the cases with and without counter-current flow, except near the step wall where counter-current results in a slower growth rate.

The wall pressure coefficient is an important parameter for engineering applications. Figure 7 showsthe pressure coefficient at the bottom wall of the baseline combustor for the 0% and 10.7% counterflow.Counter-current flow leads to a greater pressure loss in the immediate vicinity of the step, but at the sametime it results in a faster pressure recovery.

Analysis of turbulent quantities is essential because they directly impact the physics of the reactingflow within the combustor. Counterflow increases the overall shear within the combustor, and higher sheargenerates more turbulence. This is evident in figure 8 where the turbulent kinetic energies for the baseline casewith 0% and 10.7% counter-current flow are compared. This figure also shows that the cross-stream widthof the high turbulence region increases with the application of suction. A thicker region of high turbulenceresults in higher flame surface areas (more convoluted flames). Interestingly, turbulent kinetic energy nearthe end of the combustor is similar for both cases. This occurs because suction increases the dissipation ofturbulent energy in the upstream region where the fluctuations are high. The other important flow featurethat should be analyzed in order to determine the combustor performance under counter-current shear is thestrain rate. Strain rates influence combustion through flame stretch mechanisms. Excessive strain rate leadsto local extinction of the flame. For the conventional dump combustor, turbulent energy and strain ratesscale with the inlet velocity, U0.1 Therefore, in order to increase the burning rate for the conventional dumpcombustor, one must increase the turbulence by increasing the inlet velocity, which also increases the strainrate. Figure 9 shows that with counter-current flow, the strain rates remain nominally invariant compared tothe baseline case. Therefore, one of the main advantages of the counter-current shear control is the increaseof turbulence levels without the penalty of augmenting the strain rate to a great extent.

Table 1 summarizes the above findings. We conclude that a counter-current combustor is characterized byhigher turbulence levels, limited strain rate penalty, and compact burning. All of these translate to a moreefficient energy conversion under reacting conditions. Unfortunately, comparisons of the drag coefficientsreveals that both form and skin friction drags increase with the application of counterflow. Thus, increasing

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0 1 2 3 4 5 6 7X/H

0

0.005

0.01

0.015

0.02

0.025

0.03

Shea

r L

ayer

Thi

ckne

ss

No counter-currentCounter-current

Figure 6. Comparisons of the shear layer growth of the baseline combustor for 0% and 10.7% counter-currentflow.

0 2 4 6 8 10

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-0.4

-0.3

-0.2

-0.1

0

Pres

sure

Coe

ffic

ient

(C

p)

No Counter-currentCounter-current

Figure 7. Comparisons of pressure coefficient, Cp, along the bottom wall of the baseline combustor for 0% and10.7% counter-current flow.

drag penalty can potentially restrict the applicability of counter-current combustors in actual ramjet systems.The drag penalty could be limited by employing lower levels of suction and reducing the combustor length.

C. Step-geometry Modification

Previous studies on counter-current shear layers have demonstrated that turbulence can be increased bymaintaining the negative velocity ratios over larger streamwise distances.11 In a step combustor configura-tion, this could be readily achieved by implementing a step extension as illustrated in figure 10(a). The stepextension serves the dual purpose of providing a streamwise domain to enhance the counter-current shear,and as a bluff-body flame anchor. The success of any geometry in flame anchoring depends on the locationand length of the recirculation zone. Figure 10(a) shows two distinct recirculation regions. Reacting flowexperiments for this geometry shows that the flame could not find a stable anchor in this configuration.11

The upstream recirculation zone, being too compact, has an insufficient residence time for flame holding.For the downstream vortex, the burnt products failed to reach the fresh reactants due to the presence of athick shear layer. A possible alternative to this step extension is to modify the extension surface to be slopedat different angles. The target design is to enhance the counterflow effects by reducing the available cross-

Table 1. Metric study for counter-current combustor.

Cases Compact (Lr) Turbulence Strain rate Cp Cf × 104

No counter-current No ∝ U0 Limits operability -0.356 9.36Counter-current Yes ∝ suction level Lower strain rate -0.466 21.74

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Figure 8. Turbulent kinetic energy distributions for the baseline combustor: (a) 0% and (b) 10.7% counter-current flow.

sectional area for the secondary stream, and by maintaining negative velocity ratios over large streamwisedistances. At the same time, we want to provide a suitable recirculation vortex for anchoring the flame.

We consider four cases with different step angles. The geometries were selected on the recommendationof the experimental group at the University of Minnesota. Figure 10 depicts the streamlines for the stepextension at angles of 0◦, 45◦, 60◦, and 70◦. We observed that a secondary recirculation zone still exists forthe 45◦ case in figure 10(b). But, the secondary recirculation zone eventually combines with the downstreambubble (main recirculation zone) as the extension angle is increased to 60◦, as shown in figure 10(c) toproduce a single zone. This single large vortex will provide greater residence time for the fresh reactants toachieve complete combustion. The streamline pattern for the 70◦ case shown in figure 10(d) is similar to the60◦ case.

Distribution of turbulent kinetic energy within the recirculation vortex determines the burning velocityof the fresh reactants. Thus, it is necessary to compare the turbulent kinetic energy profiles in order to judgethe relative merit of each geometry. Figure 11 shows that close to the step (up until x/H = 3), the 60◦

configuration has more energetic turbulence. But at x/H = 4, the 70◦ case has greater turbulence. Figure12 shows the turbulent kinetic energy distribution throughout the combustor for step extension angles of 0◦,45◦, 60◦, and 70◦. As discussed previously, the 60◦ and 70◦ extensions yield greater turbulent kinetic energyin the shear layer.

Figure 13 shows comparisons of strain rates. Figure 13(c) shows that the 60◦ case produces the loweststrain rate in the shear layer. Results of the pressure coefficient along the bottom wall for different geometryconfigurations are shown in figure 14. We observe that pressure loss increases as the angle of the stepextension increases. The recovery rate is essentially the same.

Tables 2 and 3 list the results of the detailed performance metric study for the four cases with 0%and 5% counterflow, respectively. The turbulent kinetic energy (TKE) and strain rate values representthe area-weighted averages over the entire combustor. Application of counter-current shear on any selectedgeometry has the same effects as those observed for the baseline combustor. Comparative analysis of differentconfigurations with counter-current flow shows that the basic step extension, although has minimum drag, isunfavorable with respect to turbulence production and strain rate characteristics. Thus, taking into accountthe higher turbulent recirculation vortex and lower strain rates, we conclude that the 60◦ configurationis expected to be the most effective design. The 60◦ step extension is effective in enhancing the effects

Figure 9. Strain rate distributions for the baseline combustor: (a) 0% and (b) 10.7% counter-current flow..

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Figure 10. Mean streamline contours for 5% counter-current flow, showing the effects of geometry on thestructure of the recirculation vortex: (a) 0◦, (b) 45◦, (c) 60◦, and (d) 70◦ extension angles.

of counterflow, while maintaining a reliable flame anchor. It should be emphasized, however, that thisconclusion may change in the presence of chemical reaction.

Table 2. Geometry metric study for 0% counter-current flow.

Cases Lr/H TKE (m2/s2) Strain rate (1/s) Cp Cf × 104

0◦ 6.9 2.337 1301.1 -0.320 8.5445◦ 7.6 2.729 1011.7 -0.350 8.6460◦ 6.7 3.196 947.6 -0.377 9.2270◦ 8.0 2.667 1049.0 -0.359 9.11

Table 3. Geometry metric study for 5% counter-current flow.

Cases Lr/H TKE (m2/s2) Strain rate (1/s) Cp Cf × 103

0◦ 2.65 1.092 964.3 -0.136 1.6745◦ 6.20 2.336 936.8 -0.322 1.2060◦ 5.70 3.105 926.9 -0.381 1.1270◦ 7.50 2.872 1064.5 -0.428 1.20

IV. Results: Reacting Flow

A. Combustion Model Evaluation

We have evaluated both of the groups of turbulent combustion models discussed in Section II by simulatingthe combusion of premixed methane-air with an equivalence ratio φ = 0.65 for the baseline combustorwithout counterflow. Figure 15(a) shows the temperature distribution for the flame computed with theeddy dissipation model. Since in this model the reaction rate depends solely on the turbulent quantities (kand ε), chemical reaction is expected wherever ε/k has large values (highly strained regions). This leads

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to un-physical flame structures, as evident in figure 15(a), where the flame propagates into the boundarylayer along the upper wall. Such results do not corroborate with experimental results for reacting flow forthe same configuration. We conclude that the eddy dissipation model (EDM) is not suitable for predictingcombustion in a step dump combustor. This essentially indicates that finite rate chemistry effects must beconsidered. Switching to chemistry-based models demands additional modeling considerations like reactionmechanisms and ignition.

In our simulations with finite rate chemistry, we patched a group of cells (near the top portion of the step)with a high temperature of 1500K to imitate an ignition source. Figure 15(b) shows the temperature contoursfor the eddy dissipation concept (EDC) model with a 5-step global mechanism.12 It must be pointed outthat the flame extinguishes once the hot patch is removed, a phenomenon also observed in the experiment.11

Nevertheless, with the ignitor in place, the flame shape is in agreement with the long exposure shots of theflame taken in the experiment.9 The phenomenon of flame extinction without the ignitor persisted even whenwe simulated the flow with other mechanisms (e.g. a global 2-step mechanism). Thus, we conclude that thephysics of the reacting flow within the baseline combustor is not conducive to anchoring the flame in theabsence of an ignitor. This prompted us to simulate the flame in other step extension geometries that wereinvestigated in the cold flow simulations. Figure 16 demonstrates that it is possible to stabilize the flamewithout a continuous ignition source (hot patch) for the combustor with 60◦ and 70◦ step extensions. Allnumerical simulations for the reacting cases were conducted without the addition of counter-current shearflow.

V. Conclusions

A numerical study of the counter-current step combustor has been performed. Turbulent model com-parisons demonstrated that the realizable k-ε model results agree within an engineering accuracy with theexperimental data. Application of counterflow is shown to enhance turbulence production within the shearlayer with a minimum strain rate penalty. Counterflow also leads to a compact recirculation zone and in-creases transport of streamwise momentum in the cross-stream direction. Unfortunately, counterflow alsoincreases the aerodynamic drag on the combustor. The effects of counterflow can be augmented by main-taining a large negative velocity ratio over a longer streamwise distance with a suitable extension of thestep. However, the basic step extension fails to guarantee robust flame anchoring. Therefore, modificationsto the geometry of the step extension were investigated to select the best design candidate for increasingcounterflow effects with suitable flame anchoring capabilities. Finally, the reacting flow results showed thatthe flame is unable to stabilize in the baseline combustor without a continuous ignition source. Whereas,the flame was stabilized after alterations to the step extension were performed.

Acknowledgments

The support for this work was provided by the U.S. Office of Naval Research with Dr. G.D. Roy as theProgram Officer.

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145 deg60 deg70 deg

x/H = 1 x/H = 2

x/H = 3 x/H = 4

(a) (b)

(c) (d)

Figure 11. Comparisons of turbulent kinetic energy profiles for 5% counterflow within the recirculation vortexfor different step extension geometries: (a) x/H = 1, (b) x/H = 2, (c) x/H = 3, and (d) x/H = 4.

References

1Forliti, D., PhD thesis, University of Minnesota, Department of Mechanical Engineering, Minneapolis, MN.2Gao, Z. and Mashayek, F., ‘Stochastic model for non-isothermal droplet-laden turbulent flows’, AIAA J., 42, 255, 2004.3Gao, Z., Mashayek, F., Linck, M., and Gupta, A.K., ‘ Experimental results and calculations of two-phase flow in a swirl

burner under isothermal condition ’, AIAA Paper, 2003-0336, 2003.4Sengupta, K., Mashayek, F. and Gao, Z., ‘Numerical study of pulsed injection for control of combustion’, AIAA Paper,

2005-0954, 2005.5Thangam, S. and Speziale, C.G., ‘Turbulent flow past a backward-facing step: a critical evaluation of two-equation models’,

AIAA J., 30(5), 1314-1320, 1992.6Driver, D.M. and Seegmiller, H.L., ‘Features of a reattaching turbulent shear layer in divergent channel flow’, AIAA J.,

23(2), 163-171, 1985.7Magnussen, B.F. and Hjertager, B.H., ‘On mathematical models of turbulent combustion with special emphasis on soot

formation and combustion’, Proceedings of 16th Symp. (Int.) on Combustion, 719-729, The Combustion Institute, Pittsburgh,PA, 1976.

8Magnussen, B.F., ‘On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction inturbulent flow’, AIAA meeting, St Louis, MO, 1981.

9Pope, S.B., ‘Computationally efficient implementation of combustion chemistry using in-situ adaptive tabulation’, Com-bustion Theory and Modeling, 1, 41, 1987.

10Pope, S.B., ‘Turbulent Flows’, Cambridge University Press, Cambridge, 2003.11Behrens, A.A., Anderson, M.J., Forliti, D.J., and Strykowski, P.J., ‘Role of enhanced recirculation in controlling turbulent

combustion and flame anchoring in a step combustor’, Proceedings of 17th ONR Propulsion Meeting , 27-32, MassachusettsInstitute of Technology, MA, 2004.

12Nicaol, D.G., ‘A Chemical and Numerical Study of NOx and Pollutant Formation in Low-Emission Combustion’, PhDDissertation, University of Washington, 1995.

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Figure 12. Turbulent kinetic energy distributions for 5% counter-current flow for different step extensionangles: (a) 0◦, (b) 45◦, (c) 60◦, and (d) 70◦.

Figure 13. Strain rate distributions for 5% counter-current flow for different step extension angles: (a) 0◦, (b)45◦, (c) 60◦, and (d) 70◦.

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0 2 4 6 8 10

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-0.3

-0.2

-0.1

0

Pres

sure

Coe

ffic

ient

0 deg45 deg60 deg70 deg

Figure 14. Comparisons of pressure coefficient, Cp, alon the bottom wall for 5% counterflow for differentgeometry configurations.

Figure 15. Temperature distributions for the baseline combustor with 0% counter-current flow for (a) eddydissipation model (EDM) and (b) eddy dissipation concept (EDC) model.

Figure 16. Temperature distributions for (a) 60◦ and (b)70◦ step extension angles. A flame is stabilized forboth geometries with 0% counter-current flow.

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