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Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluc

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. Outline . Introduction

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Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluc

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  1. Rapidly Sheared Compressible Turbulence: Characterization of Different Pressure Regimes and Effect of Thermodynamic Fluctuations Rebecca Bertsch Advisor: Dr. SharathGirimajiMarch 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. Navier-Stokes Sub-grid Modeling RANS Modeling Bousinessq approach ARSM reduction DNS LES Application Background Second moment closure Decreasing Fidelity of Approach

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

  7. Objectives • Verify 3-stage evolution of turbulent kinetic energy (Cambon et. al, Livescu et al.) • Explain physics of three stage evolution of flow parameters • Investigate role of pressure in each stage of turbulence evolution • 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

  11. Decomposition of variables Substitutions:

  12. Mean field Governing Eqns. 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. 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. Homogeneous shear flow eqns.

  17. Final moment equations

  18. Important Parameters

  19. Validation- b12 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 1st regime, constant Mg value. Mg(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 1st 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 2nd 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 Mg value.

  35. Three Regime Physics: Regime 3 • Energy growth rates nearly independent of Mg. • 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-RDT F-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 Mt 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 Mt value

  44. Regime 1-2 Transition Initial Temperature fluctuation Initial Turbulent Mach number 1st 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. Conclusions • 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 • Explains the physics of three-stages. • Role of initial thermodynamic fluctuations quantified. • Aided in improving to compressible turbulence modeling.

  50. References • S. B. Pope. Turbulent Flows. Cambridge University Press, 2000. • 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. • 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. • 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. • P.A. Durbin and O. Zeman. "Rapid distortion theory for homogeneous compressed turbulence with application to modeling." J. Fluid Mech., 242:349-370, 1992. • 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. • 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

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