LateTime Turbulent Mixing

1
MAE614 Term Project Presentation Instructed By
Professor R. Pelz
Late-Time Turbulent Mixing in Shock-Accelerated
Inhomogeneous Flows A Quantitative Approach via
Optimization
By SHUANG ZHANG
Laboratory of Visiometrics and Modeling Dept. of
MAE Rutgers University 12/03/2001
2
Motivations
1. CFD and optimization

• Fluid Mechanics analysis beyond the ability of
  solving complex problems and predict flowfields
• Optimal design solutions by integrating the
  Fluid solver hierarchy together with advanced
  optimization methodologies
• Reduce product development time and improve
  performance.

Computational Fluid Dynamics (CFD)-based Turbine
Blade Optimization System at Boeing.
3
Motivation cont.
2. Shock accelerated inhomogeneous flow (aifs)
environment Rayleigh-Taylor (RT)
Richtmyer-Meshkov (RM) instability
Originations

• RT interface between fluids of different
  densities is unstable when subjected to an
  acceleration directed from the heavy fluid to the
  light fluid.

• RM the impulsive acceleration were specified as
  a shock

• aifs RTRM initiated late time complex
  (always vortex dominated) flows

4
Motivation cont.
Applications

• There are many density-stratified classical and
  contemporary high-energy fluid environments where
  accelerated flows are paramount, including
• Combustion (Curran et al 1996)
• Inertial confinement (laser) fusion, or ICF
  (Lindl 1995) and
• Astrophysics, particularly supernova remnants
  (Wang Robertson 1985, Muller et al 1991,
  Chevalier et al 1992, Klein et al 1994, Stone
  Norman 1994, Chevalier Blondin 1995, Xu Stone
  1995, Dohm-Palmer Jones 1996).

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Turbulent contact discontinuity of the
circumstellar region and the bumpy ring of SN
1987A a more realistic situation
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2D Simulation of turbulent contact
discontinuity/blast wave SN 1987 A ring
interaction prediction of upstream erosion
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Motivation cont.
3. Late time turbulent behavior of aifs flows

• Highly inhomogeneity needs more detailed
  description of the flow other than well developed
  Homogeneous Isotropic Turbulent descriptions
• Vortex dominating flow a big help in modeling
  and understanding physics

Moving Frame Uf
Upper Reflecting Boundary
At t0
p1 ,?1, ?1, a1
shock M
p2 , ?2, ?2, a2
H
p1 ,?1, ?1, a1
30
y
Outflow
Inflow
2
3
x
Lower Reflecting Boundary
5
0.427H Gas Layer
2
2.9906
3
5
6
0.4740
8
Motivation cont.
3. Flow optimization challenges and difficulties

• Pure flow field no body/structures involved
• ---- difficult to identify objective functions
• Design variables high complexity
• ---- state of the art

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Approaches
1. Identify Objective functions
func(M, ?ini , initial geometry)

• Turbulent State func(?),a statistical
  description
• ? func(??) ? ? ?1/ ?2
• ?? func(?) lt---- Governed by vorticity
  evolution equation Baroclinic vorticity
• ? func(t, M, ?ini , numerical resolution,
  boundary condition, frame scheme and initial
  geometry)
• Where

• - density ratio,
• ?ini initial density ratio
• ?- vorticity
• t time
• M Mach number

Baroclinic Term
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Approaches cont.
2. Statistical description of the turbulent
state a working direction
Density distribution
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1
6
2
8
5
3
?background1.862
4

• Initial Density Ratio 0.14

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Approaches cont.
3. Geometrical related design variables
Common geometries for studying accelerated
inhomogeneous flows (aifs)
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Approaches cont.
Focus Curtain Geometry
Moving Frame Uf
?3
?4
Upper Reflecting Boundary
At t0
?1
?2
p1 ,?1, ?1, a1
shock M
p2 , ?2, ?2, a2
H
p1 ,?1, ?1, a1
30
y
Outflow
Inflow
x
Lower Reflecting Boundary
kH Gas Layer
Geometrical Design Variables

• Width of the shock tube H
• Width of the curtain kH
• Angles of inclined curtain ?
• Symmetry of the curtains two interface ?1, ?2
• Symmetry of the saw tooth shock tube ?1, ?2, ?3,
  ?4
• Thickness of the transition layer n

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M 2.0
Geometrical design variable Influence of
turbulent state Mach number scaling

• Early Simulation snapshots

1.9657
0.3337
t0
M 5.0, Rapid turbulization
M 1.5
density
vorticity
1
VP1
VDL
14

• Global circulation

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• Simulation Late time snapshots

1.9657
(e)
0.3337
M 1.5 t 23.76 eIV
0.2868
-0.3572
M1.5
2
2.9906
3
5
M 2.0 t 21.88 eIV
6
0.4740
4.10?10-3
VP2
VP3-
VP4
VP5
-2.76?10-3
VP6
(colormap)
M2.0
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Summary

• The optimization idea in CFD is very helpful to
  understand underlying physical processes
• It is difficult but possible to model the flow
  as objective function via certain statistical
  approach
• It is important to carefully identify the design
  variables to simplify the problem.