This viewgraph presentation discusses project description, turbulence models, and computational engine and results for second-order closures for compressible turbulence

Lumley, J. L.

Savarese, S.

Volte, C. C.

English

NASA Technical Reports Server

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SECOND-ORDER CLOSURES FOR COMPRESSIBLE TURBULENCE
J.L. Lumley, S. Savarese, and C.C. Volte
Mechanical and Aerospace Engineering Department
Comell University
Ithaca, New York
N95-27898
l OUTLINEi
• II. Project Descriptionl
• ill. Turbulence Modeling t
•tlII. Computational Engine / Results I
I FUTURE WORKj
IIlo PROJECT DESCRIPTION I
1. Flows of Interest
2. Motivation
3. Method
203
https://ntrs.nasa.gov/search.jsp?R=19950021477 2020-06-16T08:04:05+00:00Z
Schlieren photograph of a shock-wave turbulent boundary-layer interaction
M--0.90 Re=1,750,000 [Liepmann]
1.2.MOTIVATION
204
• Pliysics
- Boundary Layer Separation & Wall Heat Transfer
- Spreading rate
• Modeling
Account for Compressibility Effects
on Turbulence
• Numerics
Compare 1-point Closures on Identical Solver
1.3. METHOD
• 1-Point Closures: from EVM to Second-Order Closures
• Dynamical Compressibility Effects
• 3D / Finite Volume Approach
205
I It TURBULENCE MODELING I
1. Closure Levels
2. Compressibility EfFects
3. Shock Wave Interactions
206
II.1. Closure Levels
1. EVM Mixing-Length
(Baldwin-Lomax)
2. EVM Multi-Equation
(k-E-S)
3. Second-Order Closure
(Shih and Lumley)
II.2. Compressibility Effects
1. New Physics & Averaging
2. Models
207
II.2.1. New Physics
(Turbulent Kinetic Energy Sink)
-- < TijUi,j )-'- Rd -- Cd -- Cs
4 d 2
• _=(uB+_u)< >
• Fld=<pd>
II.2.3. Turbulence Modeling
(Zeman, Sarkar et al., Yoshizawa)
• dilatation dissipation:
4 d2
_d=(UB+2U)< >
- Sarkar et al. (asymptotic analysis)
- Zeman
(Shocklet model)
208
• pressure-dilatation correlation:
_d --< pd >
- Zeman (acoustic model)'
- Sarkar et al.
(DNS & asymptotic analysis)
1.6
r Lm_D
1.4 DNS
[2
q_ ..........
0.8 _
0.8 , I , 1 r ' ,_'"
2.5 5 7,5 10 l_._ ]5 17.5 2D _-5 2.5
x_lk_o
Response of turbuJence kinetic energy" to the passage through shock
209
II.3. Shock Wave Interactions
i. Experimental Observations
2. Physics
3. Modeling
11.3.1. Experimental Results
• Oscillation increases with Shock Strength
(Dolling)
• Oscillation increases with Separation Region
• Normal Stresses Preferentially Amplified
(D_lery et al.)
210
II.3.2. Physics
Oscillation Caused by (?):
• "Breathing" of Separation Region
• Vortex Bursting
in Incoming Boundary Layer
(Dolling)
II.3.3. Shock Oscillation Modeling
• Parametrized Source Terms
in Normal RS Evolution Equation
(gradient activated)
• Separation region Extend
211
fill. COMPUTATIONAL ENGINE!
1. Numerical Method
2. Turbulence Models
3. Validation Procedure / Results
Initi I Code: flo103
[A.Jameson L.Martinelli,
Princeton)
1. Geometry
C-mesh
2D
2. PDE Solver
spatial discretization: FV
time integration: RK
3. Convergence
Acceleration:
variable time step
residual smoothing
artificial dissipation
multigrid preconditioning
4. I/O
PLOT3D format
5. Turbulence Models
Baldwin-Lomax
II1.1. Numerical Method
Current Code: cvste
1. Geometry
O- R-meshes
(EAGLEView MSU)
2. PDE Solver
vadable number of PDE's
consistent gradient comp.
3. Convergence Acceleration
Enhanced multigrid sequencing
4. I/O
Restart option
Post-processing (DX,Tecplot,...)
convergence histories
5. Turbulence Models
k-epsilon (-S)
6. Software Engineering
Dynamical mem. allocation (C)
Vectorized data structure
Unix Integration
Future
1. Geometry
30
2. Turbulence Models
SOC
212
III.2.Turbulence Models:
Incompressible / Compressible: an additive approach
• Baldwin-Lomax
• k-Epsilon / k-Epsilon-S: B.C's
• Second-Order Closures
Boundary Conditions: Wall-Functions
III.3. Validation Procedure / Results
• Calibration against simple well-documented
flows (flat plate, jet )
• Results and Comparison of models
213
0.5
3.0
).5
_n fl_ IN lq
/ //
,/ ,/
\
\\ _\
[FUTURE WORK]
• Numerics
- 2D _ 3D
- More Complex Wall Functions
- Realizability Conditions (SOC)
• Modeling
- Refinement of Existing Models (_d , < pd >)
- Shock Oscillation Model
214
O_INAL PAGE IS
OF POOR QUAI.I'T_
Homogeneous Turbulence (R) / k-eps / Mach=O.045 Re=24357
Downstream Evolution
-[0 .5
t0"
10 _ [
: <--_q TKE :
_--_-7 epsiion
E
t
Do-':nctream Location
I
y= 2e-5 x"(+1.29)
!
!
y= (2e-51 . _( .....
215
Homogeneous Turbulence (R) / k-eps-S / Mach=0.045 Re=24357
Downstream Evolution
10-s
10 .7
10.9
_ITKE
epsilon
E)----> S
y= (2e-4) x^(-1.24)
n
y= (2¢-5)x^(-2.41)
Dc'.'.'.".ctre="m Lcc=+Jen
Homogeneous Turbulence (R) / RSC / Mach=0.5
Downstream Evolution
10s
10.7
10.9
_----_ epsilon
_Z_uu
D-----> w
-t-----i- ww
y= (0.3c-3) x"(-128)
y= (0.2e--4) x^(-2.33)
Dcw.-.c,tre-"-mLccat!on
216
ORIGINAL PAGE IS
OF POOR QUALITY
217



Second-order closures for compressible turbulence

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