Proceedings of Turbo Expo 2007 ASME Turbo Expo 2007: Power

Proceedings of Turbo Expo 2007ASME Turbo Expo 2007: Power for Land, Sea and Air

May 14-17, 2007, Montreal, Canada

GT2007-27096

ON COUPLING OF RANS AND LES FOR INTEGRATEDCOMPUTATIONS OF JET ENGINES

Gorazd MedicCenter for Integrated Turbulence

SimulationsStanford University

Stanford, CA 94305-3030Email: [email protected]

Donghyun YouCenter for Integrated Turbulence



Georgi KalitzinCenter for Integrated Turbulence



ABSTRACTLarge scale integrated computations of jet engines can be

performed by using the unsteady RANS framework to computethe flow in turbomachinery components while using the LESframework to compute the flow in the combustor. This requires aproper coupling of the flow variables at the interfaces betweenthe RANS and LES solvers. In this paper, a novel approachto turbulence coupling is proposed. It is based on the observa-tion that in full operating conditions the mean flow at the in-terfaces is highly non-uniform and local turbulence productiondominates convection effects in regions of large velocity gradi-ents. This observation has lead to the concept of using auxilliaryducts to compute turbulence based on the mean velocity at theinterface. In the case of the RANS/LES interface, turbulent fluc-tuations are reconstructed from an LES computation in an aux-iliary three-dimensional duct using a recycling technique. Forthe LES/RANS interface, the turbulence variables for the RANSmodel are computed from an auxilliary solution of the RANSturbulence model in a quasi-2D duct. We have demonstrated thefeasibility of this approach for the integrated flow simulation ofa 20o sector of an entire jet engine.

NOMENCLATUREui velocity vector′ fluctuation¯ averageD duct

xi coordinate vectort timeT time-window for averagingδ wake thicknessν kinematic viscosityk turbulent kinetic energyε dissipation of turbulent kinetic energyω specific dissipation rateνt eddy-viscosityCµ = 0.09

INTRODUCTIONLarge scale computations of the flow in an entire jet engine

can be carried out by using different simulation techniques foreach component of the engine. The flow in the combustor ischaracterized by multiphase flow, intense mixing and chemicalreactions and the prediction of turbulent combustion is greatlyimproved by using LES [1]. The flow in the compressor and tur-bine is computed using the unsteady RANS framework since thehigh Reynolds numbers make the cost of resolving the boundarylayers with LES prohibitive [2]. For the success of such inte-grated computations a proper coupling of the flow variables isneeded at the interfaces between the RANS and LES solvers.

For a fully coupled solution all flow variables have to beexchanged at the interface. When some engine components arecomputed with LES and others with RANS, approximations willhave to be made to couple instantaneous and averaged variables.

1 Copyright c© 2007 by ASME

Figure 1. Compressor and combustor: RANS and LES axial velocity,mid-passage.

For subsonic interfaces, information is passed downstream aswell as upstream. The body force method by [3] has been de-signed to pass information upstream. Here we focus on the oneway coupling of the velocity and turbulence variables. One waycoupling means that information is passed only downstream; thevariables at the inlet of the downstream domain are computedfrom the variables at the outlet of the upstream domain. In afurther simplification, it is assumed that the unsteadiness of theRANS and LES mean flow is considered to be moderate, so thata time-average of the flow variables is still meaningful.

For the RANS/LES interface turbulent fluctuations need tobe added to the velocity from an upstream RANS computation.This was previously investigated in [4]. It has been argued thatthe LES flow solver has to reconstruct the resolved turbulence ac-cording to the statistical data delivered by the RANS flow solver,in particular, according to the turbulent kinetic energy k whenRANS is computed with a two equation turbulence model thatincludes a transport equation for k. It is further argued, that onecould use fluctuations computed from an auxilliary, a priori LESof a periodic channel and scale them with the turbulent kineticenergy from the upstream RANS computation assuming that tur-bulence fluctuations are isotropic. Virtual body forces were usedinside the channel to drive the flow to the desired mean flow ve-locity [5].

Although an accurate turbulence description needs to takeinto account the convection from upstream, in this paper it issuggested that at full operating conditions of the engine, turbu-lence at the compressor/combustor and combustor/turbine inter-faces is sufficiently well approximated by the local turbulencegeneration. The wakes of the upstream compressor blades cre-ate significant mean shear and the local production of turbulencedominates. Thus, only the mean velocity is passed to the LES in-let from RANS and turbulence fluctuations equilibrated with themean velocity profile are computed using a recycling techniquefrom an LES of an auxiliary annular duct. This avoids the need

for the use of virtual body forces.

For the LES/RANS interface, such as the combustor/turbineinterface, a simple time-average of the velocity provides a meanvelocity at the inlet of the RANS domain. This velocity distri-bution is again highly non-uniform which allows to describe tur-bulence at the inlet with the local turbulence generation from themean velocity. In analogy to the treatment for RANS/LES in-terface, we propose here to use an auxiliary duct in which theRANS turbulence model equations are solved for the transferredmean velocity.

The generation of turbulence equilibrated with the meanvelocity has an important advantage over directly transferringturbulence information from upstream LES. Lower order statis-tics like mean velocity will converge over a much smaller time-window than the higher order statistics required to reconstructRANS turbulence variables. This is in particular important whenthe LES mean flow or RANS is unsteady and the time average isto be computed over the smallest possible time window.

Figure 2. Compressor/combustor interface: axial velocity from RANS.

Figure 3. Compressor/combustor interface: turbulent kinetic energyfrom RANS.


Figure 4. Compressor/combustor interface: RANS→ LES.

RANS/LES INTERFACEThe region of the compressor exit and combustor inlet is

shown in Figure 1. The flow in the compressor is computedwith unsteady RANS using the k-ω model [6] and the flow inthe combustor is computed with LES. The last blade row of thecompressor is a row of stators and does not rotate. The blade rowupstream is a row of rotors that rotate anti-clockwise.

The axial velocity and turbulent kinetic energy in a cross-section at the exit of the compressor are shown in Figures 2 and3, respectively. The mean flow is highly complex, with the wakesoriginating from the last stage of the compressor. These wakesare unsteady due to the rotation of the rotors in the compressor.Larger values of turbulent kinetic energy are in the regions withstrong velocity gradients. The large values of k near the hubare not physical, they are highly dependent on the quality of thegrid. They originate at further upstream blade rows and convectdownstream.

The flowfield in the downstream LES domain is highly de-pendent on the conditions at the inlet. To generate an inflow pro-file for the LES in the combustor the mean velocity at the com-bustor inlet is set equal to the RANS velocity at the exit of thecompressor and appropriate fluctuations are added. The meanvelocity differs significantly from the mean velocity in a peri-odic channel. Thus simply adding fluctuations from a periodicchannel is inadequate. Adding random fluctuations is also un-desirable, as the transient process is non-physical and it affectsthe evolutions of skin-friction, momentum thickness, and otherintegral quantities.

Here we propose to compute the fluctuations in an auxiliaryannular duct with a cross-section that corresponds to the com-bustor inlet in parallel with the compressor and combustor com-putations. The length of the duct is chosen to correspond to thedistance between last compressor blade row and combustor inlet.Convective boundary conditions are imposed at the exit of theduct and no-slip condition is applied at the top and bottom cylin-drical walls. When the integrated computations are performed

Figure 5. Auxilliary duct: the instantaneous (left) and mean (right) axialvelocity, mid-plane, top-view.

Figure 6. Compressor/combustor interface: instantaneous axial velocity.

Figure 7. Compressor/combustor interface: mean axial velocity.

for a 20o sector of the engine, periodicity is assumed in the cir-cumferential direction for the duct as well. At the duct inlet themean velocity from the compressor/combustor interface is im-posed. By using the viscosity of the flow in the combustor, theReynolds number of the duct LES corresponds to the Reynoldsnumber at the combustor inlet.

The fluctuations are computed with a recycling technique


(e.g., [7]). A cross-section a bit upstream of the duct exit is cho-sen, as shown schematically in Figure 4. The mean velocity atthis cross-section is computed by time-averaging the velocity:ui,D = 1/T

Rui,D(t)dt. The fluctuations u′i,D = ui,D− ui,D are then

added to the mean flow at the inlet of the duct. The LES in theduct is computed until converged rms values at the inlet are ob-tained.

The recycling technique can be refined to account for pres-sure gradients, curvature, and flow structures in the duct. Con-tour plots of the axial velocity in a mid-plane between the bottomand top walls are shown in Figure 5. As shown, the mean velocitydiffuses when propagating downstream. In the recycling proce-dure, this evolution of the wakes in the streamwise direction canbe accounted for with a scaling of the circumferential spreadingof the wakes. A similarity analysis in the far wake implies thatthe thickness of the wake spreads proportional to the square-rootof streamwise coordinate (δ∼ x1/2). With such a scaling the re-cycled fluctuations correspond better to the mean velocity at theinflow of the LES domain. Otherwise, the thickness of the wakeincreases as the recycling progresses.

Contour plots for the instantaneous axial velocity and themean axial velocity are shown for the duct inlet in Figures 6 and7, respectively. The corresponding uRMS velocity and turbulentkinetic energy from the LES are shown in Figures 8 and 9. Bothturbulent quantities have larger values in the shear regions. Thelarge values of turbulent kinetic energy, observed with the RANSturbulent kinetic energy near the hub (Figure 3), are not presentas convection from upstream is neglected.

As mentioned above, the LES in the auxiliary duct is com-puted in parallel with the computations in the compressor and thecombustor. This allows to take into account the unsteadiness ofthe mean flow. Finally, after the fluctuations are generated in theauxiliary duct, they are superimposed with the mean velocity atthe compressor/combustor interface as presented in Figure 4.

Validation: recycling for plane channel flowThe recycling technique used here has been validated for

plane channel flow at Reτ = 180. The Reynolds number isbased on channel half height and friction velocity. A mesh of64× 64× 64 grid points in the streamwise, wall-normal, andspanwise directions, respectively, is employed in the computa-tional domain size of 4πδ×2δ× 4

3 πδ. Periodic boundary condi-tions are imposed in the spanwise direction and a no-slip condi-tion is applied at the top and bottom walls. The dynamic subgrid-scale (SGS) model [8] is employed.

First, periodic channel flow is computed by also imposingperiodic boundary conditions in the streamwise direction. Themean velocity profile is in good agreement with the DNS [9], asshown in Figure 10.

In the recycled channel case, convective outlet boundaryconditions are employed at the outlet of the channel. The ve-

Figure 8. Compressor/combustor interface: uRMS.

Figure 9. Compressor/combustor interface: turbulent kinetic energy.

locity at the inflow is computed every time-step by superposingthe mean velocity profile (from the periodic channel case) withthe fluctuations computed at the exit of the channel. The simula-tion is initiated with the mean velocity profile superimposed withrandom fluctuations and the simulation is continued until con-verged rms velocities are obtained. As shown in Figure 11, therms velocity fluctuations obtained from the recycled simulationcompare well with those from the periodic channel simulationand DNS [9].

LES/RANS INTERFACE

At the combustor/turbine interface (from LES to RANS, seeFigure 12), inflow conditions are needed for the RANS turbu-lence variables. Here we use the k-ω turbulence model in theturbine; k and ω need to be specified at the turbine inflow. Anobvious suggestion would be to compute k and ω directly fromthe instantaneous velocity field at the exit of the combustor.


Periodic channel flowIn order to examine in detail how well the RANS turbulence

variables can be reconstructed from LES, we return to the peri-odic channel flow at Reτ = 180 we discussed earlier. The LEShas a sufficient near-wall resolution and it was run for approx-imately 100 flow-through times. This permits a long-time inte-gration of the equation resulting in a statistically well convergedsolution.

The Reynolds number is somewhat low for a RANS compu-tation, but the inconsistencies between the LES statistics and theRANS turbulence variables are representative. Figure 13 com-pares k from the k-ω model with k from LES computed usingk = 1/2u′iu

′i. The near wall peak is practically absent for the k-ω

turbulent kinetic energy.The specific dissipation rate ω = ε/(Cµk) is compared to ω

from the LES, computed using two different approaches. A firstapproach consists in computing the turbulence dissipation using

100 101 1020

5

10

15

20

y+

U+

Figure 10. Mean streamwise velocity profiles in wall units at Reτ = 180., periodic LES; ◦ , DNS [9].

100 101 1020.0

0.5

1.0

1.5

2.0

2.5

3.0

y+

urm

s,v

rm

s,w

rm

s

urms

wrms

vrms

Figure 11. Profiles of rms velocity fluctuations in wall units at Reτ =180. , recycling LES; , periodic LES; ◦ , DNS [9].

Figure 12. Combustor and turbine: LES and RANS axial velocity, mid-passage.

its definition (for DNS): ε = ν∂u′i∂xk

∂u′i∂xk

. The resulting ω is com-pared to the one from the k-ω model in Figure 14. The trend ofincreasing ω when approaching the wall is relatively well cap-tured, but there are significant discrepancies in the buffer andthe logarithmic layer. Therefore, we also examined a second ap-proach where ε is computed using the assumption that the dissi-pation rate equals production: ε = −u′iu

′k∂ui/∂xk. The resulting

ω is compared to the one from k-ω model in Figure 15. As ex-pected, the agreement is best in the logarithmic layer where theused assumption holds. However, below y+ = 20 this approachfor computing ε yields a bad prediction for ω; the near-wall in-crease is completely missed. Such near-wall behavior may leadto numerical instabilities in the near-wall region.

The convergence of the statistics for ε is presented for thelogarithmic layer in Figure 16, where ω for both approachesare plotted for computations with averaging over different time-windows (from one flow through time to only 15 % of one flowthrough-time). It becomes apparent that for short time-windows,the values of ω are strongly oscillating, thus further reducing thenumerical stability when used with the k-ω model. This is es-pecially important as the mean flow in jet engines has unsteadyfeatures with relatively small time-scales (up to one flow-throughtime). Thus, the use of weakly averaged statistics of ε is ques-tionable; our experience with the engine computations showedthat these approaches for computing ω lead to severe numericalinstabilities. Note that in the jet engine computations we couldnot afford the grid resolution for both LES and RANS compara-ble to the one used for this simple flow.

Furthermore, to complicate matters, if one is to employ amore complex RANS turbulence model, such as the four equa-tion v2- f model [10], it becomes practically impossible to recon-struct turbulence variables from the LES; i.e. the variables f orv2 have no clear physical counterpart. This discussion makes itclear that reconstructing the RANS turbulence variables directlyfrom the LES is unfeasible in a general case.


Combustor/turbine interfaceThe aforementioned arguments lead to a conclusion that k

and ω at the inlet of the turbine should rather be computed fromthe mean flow velocity field, shown for the combustor/turbineinterface in Figure 17. The mean velocity is a first order mo-ment that converges significantly faster than the rms velocities(second order moment) and a smaller averaging windows can beemployed. As before for the compressor/combustor interface,convection of turbulence will be ignored.

In analogy to the proposed auxiliary annular duct used tocompute the inflow fluctuations for the LES domain, we pro-pose here to use an auxiliary duct in which the RANS turbulencemodel equations are solved for the mean velocity field trans-ferred at the turbine inflow (see Figure 19). The duct is quasi

y+

k+

10-1 100 101 1020

1

2

3

4

5RANS k-!LES

Figure 13. Channel flow at Reτ = 180, LES vs. RANS k-ω model,turbulent kinetic energy k.

y+

!+

10-1 100 101 10210-2

10-1

100

101

102

103

104

RANS / k-!LES

Figure 14. Channel flow at Reτ = 180, LES vs. RANS k-ω model,

specific dissipation rate ω computed using ε = ν∂u′i∂xk

∂u′i∂xk

.

y+

!+

10-1 100 101 10210-2

10-1

100

101

102

103

104

RANS / k-!LES ("=P)

Figure 15. Channel flow at Reτ = 180, LES vs. RANS k-ω model,specific dissipation rate ω computed using ε = P.

y+

!+

50 100 15010-2

10-1

100

LES (" = P), one flow-through timeLES (" = P), 30% flow-through timeLES (" = P), 15% flow-through timeLES, one flow-through timeLES, 30% flow-through timeLES, 15% flow-through time

Figure 16. Channel flow at Reτ = 180, LES vs. RANS k-ω model,specific dissipation rate in the logarithmic layer, computed using statisticsfor ε and k over a very short time-window.

two-dimensional with a cross-section identical to the combus-tor/turbine interface and with a single cell in the streamwise di-rection. The mean velocity from the combustor outlet is passedto the duct and the equations for k and ω are iterated till conver-gence for a frozen mean flow. Finally, the mean velocity from thecombustor and k and ω from the duct are passed to the turbineinlet. This produces an inflow boundary condition for the RANSdomain that is consistent with the RANS turbulence model used.Most importantly, the turbulent eddy-viscosity remains consis-tent with the transferred mean velocity, as shown in Figures 17and 18.


Figure 17. Combustor/turbine interface: mean axial velocity.

Figure 18. Combustor/turbine interface: νt from the auxilliary duct.

Figure 19. Combustor/turbine interface: LES→ RANS.

CONCLUSIONSAn approach to couple the LES and RANS computational

frameworks for jet engine computations is proposed. The ap-proach consists in the generation of turbulence inflow conditionsin auxiliary ducts in parallel to the main computation. In the caseof RANS/LES interface, an auxiliary LES computation is carriedout in a three-dimensional duct. Turbulent fluctuations are gen-erated with a recycling technique equilibrated with the complexwakes in the mean velocity. For the LES/RANS interface, anauxiliary RANS computation is carried out in a quasi-2D duct.The turbulence variables for the RANS model, specifically the

k-ω model, are computed from the duct simulation with a frozenmean flow.

Practically, only the mean flow is passed at the interfaceand turbulence convection is neglected. The assumption to ne-glect convection of turbulence is based on the observation thatthe mean velocity at the compressor/combustor and combus-tor/turbine interfaces is unsteady and non-uniform in space andlocal turbulence production dominates convection effects in re-gions of large velocity gradients. We have demonstrated this ap-proach on a simulation of a 20o sector of an entire jet engine [11]

ACKNOWLEDGEMENTSWe thank the US Department of Energy for the support un-

der the ASC program. We also thank Pratt & Whitney for pro-viding the engine geometry, helpful comments and discussions.

REFERENCES[1] H. Pitsch, Large eddy simulation of turbulent combustion,

Annual Review of Fluid Mechanics, Vol. 38, pp. 453–482(2006).

[2] U. Piomelli and E. Balaras, Wall-Layer Models for Large-Eddy Simulations, Annual Review of Fluid Mechanics, Vol.34, pp. 349-374 (2002).

[3] J. U. Schluter, H. Pitsch and P. Moin, Outflow Conditionsfor Integrated Large-Eddy Simulation/Reynolds-AveragedNavier-Stokes Simulations, AIAA Journal, Vol. 43, No. 1,pp. 156–164 (2005).

[4] J. U. Schluter, H. Pitsch and P. Moin, Large Eddy Simulationinflow conditions for coupling with Reynolds-averaged FlowSolvers, AIAA Journal, Vol. 42, No. 3, pp. 478–484 (2004).

[5] C.D. Pierce and P. Moin, Method for generating equilibriumswirling inflow conditions, AIAA Journal, Vol. 36, No. 7,pp. 1325–1327 (1998).

[6] D. C. Wilcox, Turbulence Modeling for CFD, 2nd edition,DCW Industries, Inc., La Canada, CA (1998).

[7] T. S. Lund, X. Wu, K. D. Squires, Generation of turbulent in-flow data for spatially-developing boundary layer simulations,Journal of Computational Physics 140, pp. 233–258 (1998).

[8] M. Germano, U. Piomelli, P. Moin, W. H. Cabot, A dynamicsubgrid-scale eddy-viscosity model, Physics of Fluids A 3,pp. 1760–1765 (1991) .

[9] J. Kim, P. Moin, R. Moser, Turbulence statistics in fullydeveloped channel flow at low Reynolds number, Journal ofFluid Mechanics 177, pp. 133–166 (1987).

[10] P. A. Durbin, Separated flow computations with the k-ε-v2

model, AIAA Journal Vol. 33, pp. 659–664 (1995).[11] G. Medic, D. You, G. Kalitzin, M. Herrmann, F. Ham, E.

van der Weide, H. Pitsch and J.J. Alonso, Integrated Compu-tations of an entire jet engine, ASME Paper GT2007-27094(2007).


Documents

Proceedings of Turbo Expo 2007 ASME Turbo Expo 2007: Power