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Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations Rebecca Bertsch Advisor:

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Presentation on theme: "Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations Rebecca Bertsch Advisor:"— Presentation transcript:

1 Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations Rebecca Bertsch Advisor: Dr. Sharath Girimaji March 29, 2010 Supported by: NASA MURI and Hypersonic Center

2 Outline Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

3 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

4 Motivation Compressible stability, transition, and turbulence plays a key role in hypersonic flight application. Hypersonic is the only type of flight involving flow-thermodynamic interactions. Crucial need for understanding the physics of flow-thermodynamic interactions.

5 Application Background Navier-Stokes Bousinessq approach ARSM reduction Second moment closure LES Sub-grid ModelingRANS Modeling DNS Decreasing Fidelity of Approach

6 ARSM reduction 2-eqn. ARSM Averaging Invariance Application 7-eqn. SMC Transport Processes Linear Pressure Effects: RDT Nonlinear pressure effects Spectral and dissipative processes 2-eqn. PANS Navier-Stokes Equations

7 Objectives 1.Verify 3-stage evolution of turbulent kinetic energy (Cambon et. al, Livescu et al.) 2.Explain physics of three stage evolution of flow parameters 3.Investigate role of pressure in each stage of turbulence evolution 4.Investigate dependence of regime transitions *Previous studies utilized Reynolds-RDT, current study uses more appropriate Favre-RDT.

8 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

9 Inviscid Conservation Equations (Mass) (Momentum) (Energy)

10 Reynolds vs. Favre-averaging Approach R-RDT(Previous work) Easier F-RDT(Current Study) More appropriate for compressible flow AveragingUnweighted:Weighted: Moments2 nd order:3 rd order: # of PDEs2564

11 Decomposition of variables Mass ` Momentum Energy

12 Mean field Governing Eqns. Mass Mom. Energy Apply averaging principle and decompose density

13 Path to Fluctuating Field Eqns. Subtract mean from instantaneous Apply homogeneity condition(shear flow only) Apply linear approximations.

14 Mass Mom. Energy Linear F-RDT Eqns. for Fluctuations

15 Physical to Fourier Space Easier to solve in Fourier space Apply Fourier transform to variables PDEs become ODEs

16 Mass Momentum Energy Evolution of Homogeneous shear flow eqns.

17 Final moment equations

18 Important Parameters InputGradient Mach number Turbulent Mach Number Temperature Fluctuation Intensity OutputTurbulent Kinetic Energy Turbulent Polytropic Coefficient Equi-partition Function TimescalesShear time Acoustic time Mixed time

19 Validation- b 12 Anisotropy Component DNS R-RDT F-RDT Good overall agreement

20 Validation- KE Growth Rate DNS R-RDT F-RDT

21 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

22 Three-stage Behavior: Shear Time Peel-off from burger’s limit clear; shows regime transition. * Verification of behavior found in Cambon et. al.

23 Status Before Current Work Validation of method and verification of previous results complete. New investigations of three-stage physics follows.

24 Three-stage Behavior: Acoustic Time Three-stages clearly defined; final regime begins within 2-3 acoustic times. *Acoustic timescale first presented in Lavin et al.

25 Three-stage Behavior: Mixed Time Three-stages clearly defined; onset of second regime align.

26 Regimes of Evolution Regime 1: Regime 2: Regime 3:

27 Evolution of Gradient Mach Number Shear time aligns 1 st regime, constant M g value. M g (t) reaches 1 by 1 acoustic time regardless of initial value.

28 Evolution of Turbulent Mach Number First regime over by 4 shear times. Second regime aligns in mixed time.

29 Three Regime Physics: Regime 1 Pressure plays an insignificant role in 1 st regime.

30 Three Regime Physics: Regime 1 Zero pressure fluctuations. Dilatational and internal energy stay at initial values. No flow-thermodynamic interactions.

31 Three Regime Physics: Regime 2 Pressure works to nullify production in 2 nd regime.

32 Three Regime Physics: Regime 2 Pressure fluctuations build up. Dilatational K. E. and I. E. build up. Equi-partition is achieved as will be seen later.

33 Three Regime Physics: Regime 3 Rapid pressure strain correlation settles to a constant value

34 Three Regime Physics: Regime 3 Production nearly insensitive to initial M g value.

35 Three Regime Physics: Regime 3 Energy growth rates nearly independent of M g. p’(total) =p’(poisson) + p’(acoustic wave).

36 Three-regime conclusions Regime 1: Turbulence evolves as Burger’s limit; pressure insignificant. Regime 2: Pressure works to nullify production; turbulence growth nearly zero. Regime 3: Turbulence evolves similar to the incompressible limit.

37 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

38 Polytropic Coefficient R-RDTF-RDT n≈γ according to DNS with no heat loss (Blaisdell and Ristorcelli) F-RDT preserves entropy, R-RDT does not

39 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

40 KE: Initial Temperature Fluctuation Initial temperature fluctuations delay onset of second regime.

41 KE: Initial Turbulent Mach Number KE evolution influenced by initial M t only weakly

42 Equi-Partition Function: Initial Temperature Fluctuation Dilatational energy maintains dominant role longer.

43 Equi-Partition Function: Initial Turbulent Mach Number Balance of energies nearly independent of initial M t value

44 Regime 1-2 Transition Initial Temperature fluctuation Initial Turbulent Mach number 1 st transition heavily dependent on temperature fluctuations

45 Regime 2-3 Transition Initial Temperature fluctuation Initial Turbulent Mach number 2nd transition occurs within 4 acoustic times regardless of initial conditions

46 Initial fluctuations conclusions Turbulence evolution heavily influenced by temperature fluctuations. Velocity fluctuations weakly influence flow. Regime 1-2 transition delayed by temperature fluctuations. Regime 2-3 transition occurs before 4 acoustic times.

47 Progress Introduction RDT Linear Analysis of Compressible Turbulence –Method –3-Stage Evolution of Flow Variables –Evolution of Thermodynamic Variables –Effect of Initial Thermodynamic Fluctuations Conclusions

48 F-RDT approach achieves more accurate results than R- RDT. Flow field statistics exhibit a three-regime evolution verification. Role of pressure in each role is examined: –Regime 1: pressure insignificant –Regime 2: pressure nullifies production –Regime 3: pressure behaves as in incompressible limit. Initial thermodynamic fluctuations have a major influence on evolution of flow field. Initial velocity fluctuations weakly affect turbulence evolution.

49 Contributions of Present Work 1.Explains the physics of three-stages. 2.Role of initial thermodynamic fluctuations quantified. 3.Aided in improving to compressible turbulence modeling.

50 References 1.S. B. Pope. Turbulent Flows. Cambridge University Press, 2000. 2.G. K. Batchelor and I. Proudman. "The effect of rapid distortion of a fluid in turbulent motion." Q. J. Mech. Appl. Math. 7:121-152, 1954. 3.C. Cambon, G. N. Coleman and D. N. N. Mansour. "Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number." J. Fluid Mech., 257:641-665, 1993. 4.G. Brethouwer. "The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport, linear theory and direct numerical simulations." J. Fluid Mech., 542:305-342, 2005. 5.P.A. Durbin and O. Zeman. "Rapid distortion theory for homogeneous compressed turbulence with application to modeling." J. Fluid Mech., 242:349- 370, 1992. 6.G. A. Blaisdell, G. N. Coleman and N. N. Mansour. "Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain." Phys. Fluids, 8:2692-2705, 1996. 7.G. N. Coleman and N. N. Mansour. "Simulation and modeling of homogeneous compressible turbulence under isotropic mean compression." in Turbulent Shear Flows 8, pgs. 269-282, Berlin:Springer-Verlag, 1993

51 References cont. 8.L. Jacquin, C. Cambon and E. Blin. "Turbulence amplification by a shock wave and rapid distortion theory." Phys. Fluids A, 5:2539, 1993. 9.A. Simone, G. N. Coleman and C. Cambon. "The effect of compressibility on turbulent shear flow: a rapid distortion theory and direct numerical simulation study." J. Fluid Mech., 330:307-338, 1997. 10.H. Yu and S. S. Girimaji. "Extension of compressible ideal-gas RDT to general mean velocity gradients." Phys. Fluids 19, 2007. 11.S. Suman, S. S. Girimaji, H. Yu and T. Lavin. "Rapid distortion of Favre-averaged Navier- Stokes equations." Submitted for publication in J. FLuid Mech., 2009. 12.S. Suman, S. S. Girimaji and R. L. Bertsch. "Homogeneously-sheared compressible turbulence at rapid distortion limit: Interaction between velocity and thermodynamic fluctuations." 13.T. Lavin. Reynolds and Favre-Averaged Rapid Distortion Theory for Compressible, Ideal Gas Turbulence}. A Master's Thesis. Department of Aerospace Engineering. Texas A \& M University. 2007.

52 Questions…


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