Loading in 5 sec....

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

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

- By
**zanna** - Follow User

- 126 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Outline' - zanna

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Rebecca Bertsch

Advisor: Dr. SharathGirimajiMarch 29, 2010

Supported by: NASA MURI and Hypersonic Center

Outline Different Pressure Regimes and Effect of Thermodynamic Fluctuations

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

- Conclusions

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

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

- Conclusions

Motivation Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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.

Navier Different Pressure Regimes and Effect of Thermodynamic Fluctuations-Stokes

Sub-grid Modeling

RANS Modeling

Bousinessq approach

ARSM reduction

DNS

LES

Application

Background

Second moment closure

Decreasing Fidelity of Approach

Transport Processes Different Pressure Regimes and Effect of Thermodynamic Fluctuations

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

Objectives Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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.

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

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

- Conclusions

Inviscid Different Pressure Regimes and Effect of Thermodynamic Fluctuations Conservation Equations

(Mass)

(Momentum)

(Energy)

Reynolds vs. Favre-averaging Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Decomposition of variables Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Substitutions:

Mean field Governing Eqns. Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Apply averaging principle and decompose density

Path to Fluctuating Field Eqns. Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Subtract mean from instantaneous
- Apply homogeneity condition(shear flow only)
- Apply linear approximations.

Linear F-RDT Eqns. for Fluctuations Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Physical to Fourier Space Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Easier to solve in Fourier space
- Apply Fourier transform to variables
- PDEs become ODEs

Homogeneous shear flow eqns. Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Final Different Pressure Regimes and Effect of Thermodynamic Fluctuationsmoment equations

Important Parameters Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Validation- b Different Pressure Regimes and Effect of Thermodynamic Fluctuations12 Anisotropy Component

DNS

R-RDT

F-RDT

Good overall agreement

Validation- KE Growth Rate Different Pressure Regimes and Effect of Thermodynamic Fluctuations

DNS

R-RDT

F-RDT

Progress Different Pressure Regimes and Effect of Thermodynamic Fluctuations

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

- Conclusions

Three-stage Behavior: Shear Time Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Peel-off from burger’s limit clear; shows regime transition.

*Verification of behavior found in Cambon et. al.

Status Before Current Work Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Validation of method and verification of previous results complete.
- New investigations of three-stage physics follows.

Three-stage Behavior: Acoustic Time Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Three-stages clearly defined; final regime begins within 2-3 acoustic times.

*Acoustic timescale first presented in Lavin et al.

Three-stage Behavior: Mixed Time Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Three-stages clearly defined; onset of second regime align.

Regimes of Evolution Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Regime 1:
- Regime 2:
- Regime 3:

Evolution of Gradient Mach Number Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Shear time aligns 1st regime, constant Mg value.

Mg(t) reaches 1 by 1 acoustic time regardless of initial value.

Evolution of Turbulent Mach Number Different Pressure Regimes and Effect of Thermodynamic Fluctuations

First regime over by 4 shear times.

Second regime aligns in mixed time.

Three Regime Physics: Regime 1 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Pressure plays an insignificant role in 1st regime.

Three Regime Physics: Regime 1 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Zero pressure fluctuations.

Dilatational and internal energy stay at initial values.

No flow-thermodynamic interactions.

Three Regime Physics: Regime 2 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Pressure works to nullify production in 2nd regime.

Three Regime Physics: Regime 2 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Pressure fluctuations build up.

Dilatational K. E. and I. E. build up.

Equi-partition is achieved as will be seen later.

Three Regime Physics: Regime 3 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Rapid pressure strain correlation settles to a constant value

Three Regime Physics: Regime 3 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Production nearly insensitive to initial Mg value.

Three Regime Physics: Regime 3 Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Energy growth rates nearly independent of Mg.
- p’(total) =p’(poisson) + p’(acoustic wave).

Three-regime conclusions Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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.

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

- Conclusions

Polytropic Different Pressure Regimes and Effect of Thermodynamic Fluctuations 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

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

- Conclusions

KE: Initial Temperature Fluctuation Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Initial temperature fluctuations delay onset of second regime.

KE: Initial Turbulent Mach Number Different Pressure Regimes and Effect of Thermodynamic Fluctuations

KE evolution influenced by initial Mt only weakly

Equi Different Pressure Regimes and Effect of Thermodynamic Fluctuations-Partition Function: Initial Temperature Fluctuation

Dilatational energy maintains dominant role longer.

Equi Different Pressure Regimes and Effect of Thermodynamic Fluctuations-Partition Function: Initial Turbulent Mach Number

Balance of energies nearly independent of initial Mt value

Regime 1-2 Transition Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Initial Temperature fluctuation

Initial Turbulent Mach number

1st transition heavily dependent on temperature fluctuations

Regime 2-3 Transition Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Initial Temperature fluctuation

Initial Turbulent Mach number

2nd transition occurs within 4 acoustic times regardless of initial conditions

Initial fluctuations conclusions Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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.

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

- Conclusions

Conclusions Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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.

Contributions of Present Work Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- Explains the physics of three-stages.
- Role of initial thermodynamic fluctuations quantified.
- Aided in improving to compressible turbulence modeling.

References Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- 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

References cont. Different Pressure Regimes and Effect of Thermodynamic Fluctuations

- L. Jacquin, C. Cambon and E. Blin. "Turbulence amplification by a shock wave and rapid distortion theory." Phys. Fluids A, 5:2539, 1993.
- 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.
- H. Yu and S. S. Girimaji. "Extension of compressible ideal-gas RDT to general mean velocity gradients." Phys. Fluids 19, 2007.
- 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.
- S. Suman, S. S. Girimaji and R. L. Bertsch. "Homogeneously-sheared compressible turbulence at rapid distortion limit: Interaction between velocity and thermodynamic fluctuations."
- 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.

Questions… Different Pressure Regimes and Effect of Thermodynamic Fluctuations

Download Presentation

Connecting to Server..