Transcript An application of FLUENT in Design & Optimization

Aerodynamic Design
Optimization Studies at CASDE
Amitay Isaacs, D Ghate, A G Marathe,
Nikhil Nigam, Vijay Mali,
K Sudhakar, P M Mujumdar
Centre for Aerospace Systems Design and Engineering
Department of Aerospace Engineering, IIT Bombay
http://www.casde.iitb.ac.in
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About CASDE
5 years old
Master’s program in Systems Design &
Engineering
MDO
MAV
Modeling & Simulation
Workshops/CEPs/Conferences
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Optimization Studies –Overview
Concurrent aerodynamic shape &
structural sizing of wing
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FEM based aeroelastic design
MDO architectures
WingOpt software
Propulsion system
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Engine sizing & cycle design
Intake duct design using CFD
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Intake Design - Background
Duct design practice of late 80s –
based on empirical rules
Problem Revisited – using formal
optimization and high fidelity analysis
Study evolved with active participation
of ADA (Dr. T.G. Pai & R.K.Jolly)
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Problem Formulation
Objective/Constraints
Entry
Exit
Location and shape (Given)
• Pressure Recovery
• Distortion
• Swirl
Optimum geometry of duct from Entry to Exit ?
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Design Using CFD - Issues
Simulation Time
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CFD takes huge amounts of time for real life problems
Design requires repetitive runs of disciplinary analyses
Integration & Automation
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Parametric geometry modeling
Grid generation
CFD solution
Objective/Constraint function evaluation
Optimization
Gradient Information
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Finite difference – step size (??), (NDV + 1) analyses required
Exact formulations – Automatic differentiation (ADIFOR),
Adjoint method, Complex step method – All require source
code
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Flow Solver
Distortion & Swirl calculation requires NS solution
In-house NS Solver
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Analytical gradients possible
Easy to integrate
Commercial Solvers (STAR-CD, FLUENT…)
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Gradients using finite difference only
Difficult to integrate
FLUENT Inc.
 S-shaped non-diffusing duct
 Results validated with a NASA test case (Devaki Ravi
Kumar & Sujata Bandyopadhyay)
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Strategies
Reducing Time
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Parameterization
Variable fidelity to shrink the search space
Surrogate modeling
Meshing
Parallel computing
Continuation
Integration & Automation
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Wrapping executables and user interfaces
Offline analysis (Surrogate models) – semiautomatic
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Our Strategy
Variable fidelity Response Surface based
design using FLUENT
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Our Methodology
CFD analysis
at DOE points
DOE in
reduced space
Low fidelity
Analysis
Constraints
RS for
PR & DC60
Optimization
Parametrization
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Parametrization
Y
Z
X
Duct Centerline
X
Control / Design Variables
A
• Ym, Zm
• AL/3, A2L/3
Cross Sectional Area
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X
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Parametrization
Y
Z
X
Duct Centerline
X
Control / Design Variables
A
• Ym, Zm
• AL/3, A2L/3
Cross Sectional Area
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X
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Typical 3D-Ducts
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Duct Design - Low Fidelity
Low Fidelity Design Rules
(Constraints)
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Wall angle < 6°
Diffusion angle < 3°
6 * Equivalent Radius
< ROC of Centerline
X2-MAX
X2-MIN
X1-MIN
X1-MAX
Objective function:
pressure recovery
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No low fidelity analysis
for distortion or swirl
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Optimization Process – Low Fidelity
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Automation for CFD
Duct Parameters
(β1, β2, αy, αz)
Clustering
Parameters
Generation of structured volume
grid using parametrization
Generation of entry and exit
sections using GAMBIT
Entry & Exit
sections
Mesh file
Conversion of structured grid
to unstructured format
Conversion of file format to
CGNS using FLUENT
Continuation
Solution
End-to-end (Parameters to DC60)
automated CFD Cycle.
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DC60
Unstructured
CGNS file
CFD Solution using FLUENT
CFD
Solution
Objective/Constraints evaluation
Using UDFs (FLUENT)
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Automation for Design
Duct Parameters
(β1, β2, αy, αz)
Entry & Exit
sections
Conversion of structured grid
to unstructured format
Optimization
Continuation
Solution
DC60
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Generation of structured volume
grid using parametrization
Unstructured
CGNS file
CFD Solution using FLUENT
CFD
Solution
Objective/Constraints evaluation
Using UDFs (FLUENT)
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Results: Total Pressure Profile
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Design Space Reduction
Optimized duct
from low fidelity
Infeasible duct
Poor duct
P
(0.61, 0.31,
1.0, 1.0)
(0.1, 0.31,
0.2, 0.6)
(-0.4, 1.5,
0.3, 0.6)
PLOSS
1.42
2.0
3.53
DC60
6.19
16.28
24.21
P – Parameters; PLOSS – Total Pressure Loss
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Optimization Post-processing
Distortion Analysis
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DC60 = (PA0 – P60min) /q
where,
PA0
- average total pressure at the section,
P60min - minimum total pressure in a 600 sector,
q
- dynamic pressure at the cross section.
User Defined Functions (UDF) and scheme files were
used to generate this information from the FLUENT
case and data file.
Iterations may be stopped when the distortion values
stabilize at the exit section with reasonable
convergence levels.
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Continuation Method
Methodology
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Store the solution in
case & data files
Open the new case (new grid)
with the old data file
Setup the problem
Solution of (0.61 0.31 1 1) duct slapped on (0.1 0.31 0.1 0.1)
3-decade-fall
6-decade-fall
Without continuation
4996
9462
With continuation
1493
6588
Percentage time
saving
70%
30%
Journal
file
Old
Data file
Duct
Parameters
Generate new
case file
FLUENT Solution
Huge benefits as compared to the efforts involved!!!
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Simulation Time
Strategies
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Continuation Method
Parallel execution of FLUENT on a 4-noded
Linux cluster
Time per CFD Run
Time for simulation has
been reduced to around
20%.
Serial
Parallel
Slapping
0
20
40
60
80
100
Time (hrs)
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Sequential (Multipoint)
Response Surface Approximations
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Sequential (multipoint)
Response Surface Methodology
Response Surfaces generated in sub-domains
around multiple points
Surfaces used to march to optimum
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Wing aerodynamic design problem
Planform fixed
2 spanwise
stations
4 variables for
camber
3 variables for
geometric pretwist
Maximize cruise
L/D
Lift constraint
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Design Problem Statement
Maximize
Sub. to
L/D
CL = .312
-5  r + m  5
-5  r + m + t  5
with side constraints,
.05  x1  .33;
.05  x2  .33;
.001  h1  .1
.001  h2  .1
-2  r  5
-2  m  5
-2  t  5
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Design Tools
Lift Calculation: CL from VLM
Drag Calculation: CD0 from a/c data
CDi from VLM
DOE: Design Expert
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D-optimality Criterion
Response Surfaces: Design Expert
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quadratic/cubic
Optimizers : FFSQP
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Overall Design Procedure
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Results - Arbitrary Starting Point 1
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Results - Arbitrary Starting Point 2
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Observations
Quadratic model found better than cubic model
in subspaces.
Global model inadequate.
Cost of D-optimality significant
SRSA seems to work well!
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GRADIENT INFORMATION
BY
AUTOMATIC DIFFERENTIATION
OF
CFD CODES
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User Supplied Analytical Gradients
Analysis
Code in Fortran
Manually extract
sequence of
mathematical
operations
Manually differentiate
mathematical
functions - chain rule
FORTRAN
source code
that can evaluate
gradients
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Code the complex
derivative evaluator
in Fortran
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Automatic Differentiation for
Analytical Gradients
Analysis
Code in FORTARN
Automatically parse and
extract the sequence
of mathematical
operations
Use symbolic math
packages to automate
derivative evaluation
FORTRAN
source code
that can evaluate
gradients
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Automatically
code the complex
derivative evaluator
in Fortran
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Automatic Differentiation for
Analytical Gradients
Complex Analysis
Code in FORTARN
Euler
FORTRAN
source code
that can evaluate
gradients
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Automated
Differentiation
Package
eg. ADIFOR
&
ADIC
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Comparison of Derivative Calculation
Finite Difference vs ADIFOR

1.12
3.06
4.11
5.48
-0.38
-1.20
Value
5.09
-0.52
-1.23
% Error
7.17
38.10
2.46
Value
5.44
-0.40
-1.18
% Error
0.70
4.44
1.73
Value
5.45
-0.41
-1.18
% Error
0.61
7.08
1.56
Value
5.56
-0.67
-1.02
% Error
1.54
77.25
15.09
d(L/D) / d using ADIFOR
=0.2
=0.02
d(L/D) / d
using Finite
Difference
=0.002
=0.0002
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Optimization - ADIFOR vs FD
Single design variable unconstrained
optimization problem
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Find  for max. L/D for Onera M6 wing
Same starting point; FD step size 0.002
init
opt
L/Dopt
Calls
ADIFOR
1.060
2.810
11.99
15
424
FD
1.060
2.810
11.99
17
111
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Time
(min.)
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Thank You
Please visit
www.casde.iitb.ac.in
for details and other information
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Thank You
http://www.casde.iitb.ac.in/mdo/3d-duct/
Problem Statement
•Ambient conditions: 11Km altitude
• Inlet Boundary Conditions
• Total Pressure:
34500 Pa
• Total Temperature: 261.4o K
• Hydraulic Diameter: 0.394m
• Turbulence Intensity: 5%
• Outlet Boundary Conditions
• Static Pressure: 31051 Pa (Calculated for the desired mass flow rate)
• Hydraulic Diameter: 0.4702m
• Turbulence Intensity: 5%
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Duct Parameterization
Geometry of the duct is derived from
the Mean Flow Line (MFL)
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MFL is the line joining centroids of crosssections along the duct
Any cross-section along length of the duct
is normal to MFL
Cross-section area is varied
parametrically
Cross-section shape in merging area is
same as the exit section
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MFL Design Variables - 1
Mean flow line (MFL) is considered as a
piecewise cubic curve along the length of
the duct between the entry section and
merging section
y(Lm/2), z(Lm/2) specified
y2, z2
y(x), z(x)
Cmerge
r
y1, z1
Centry
0
Lm/2
Lm
x
Lm : x-distance between the entry and merger section
y1, y2, z1, z2 : cubic polynomials for y(x) and z(x)
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MFL Design Variables - 2
• y1(x) = A0 + A1x + A2x2 + A3x3, y2(x) = B0 + B1x + B2x2 + B3x3
• z1(x) = C0 + C1x + C2x2 + C3x3, z2(x) = D0 + D1x + D2x2 + D3x3
• y1(Lm) = y2 (Lm), y1’(Lm) = y2’(Lm), y1” (Lm) = y2” (Lm)
• z1(Lm) = z2 (Lm), z1’(Lm) = z2’(Lm), z1” (Lm) = z2” (Lm)
• y1’(Centry) = y2’(Cmerger) = z1’ (Centry) = z2’(Cmerger) = 0
• The shape of the MFL is controlled by 2 parameters which
control the y and z coordinate of centroid at Lm/2
• y(Lm/2) = y(0) + (y(L) – y(0)) αy
0 < αy < 1
• z(Lm/2) = z(0) + (z(L) – z(0)) αz
0 < αz < 1
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Area Design Variables – 1
Cross-section area at any station is
interpolated from the entry and exit crosssections
•A(x) = A(0) + (A(Lm) – A(0)) * β(x)
• corresponding points on entry and
exit sections are linearly interpolated
to obtain the shape of the intermediate
sections and scaled appropriately
• Psection = Pentry + (Pexit - Pentry) * β
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Area Design Variables - 2
β variation is given by piecewise cubic curve as function of x
β(Lm/3) and β(2Lm/3) is specified
β(x)
β2
1
β1
0
0
β=
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Lm/3
2Lm/3
A0 + A1x + A2x2 + A 3x3
B0 + B1x + B2x2 + B3x3
C0 + C1x + C2x2 + C3x3
Lm
x
0  β < β1
β1  β  β2
β2< β  1
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Turbulence Modeling
Relevance: Time per Solution
Following aspects of the flow were of interest:
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Boundary layer development
Flow Separation (if any)
Turbulence Development
Literature Survey
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S-shaped duct
Circular cross-section
Doyle Knight, Smith, Harloff, Loeffer
 Baldwin-Lomax model (Algebraic model)
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Computationally inexpensive than more sophisticated models
Known to give non-accurate results for boundary layer separation etc.
Devaki Ravi Kumar & Sujata Bandyopadhyay (FLUENT Inc.)
 k- realizable turbulence model
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Two equation model
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Turbulence Modeling
(contd.)
Standard k- model
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Turbulence Viscosity Ratio
exceeding 1,00,000 in 2/3
cells
Realizable k- model
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Shih et. al. (1994)
Cμ is not assumed to be
constant
A formulation suggested for
calculating values of C1 & Cμ
Computationally little more
expensive than the standard
k- model
Total Pressure profile at the
exit section (Standard k- 
model)
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Results
Mass imbalance:
0.17%
Energy imbalance: 0.06%
Total pressure drop: 1.42%
Various turbulence related quantities of interest at entry and exit
sections:
Entry
Exit
Turbulent Kinetic Energy (m2/s2)
124.24
45.65
Turbulent Viscosity Ratio
5201.54
3288.45
y+ at the cell center of the cells adjacent to boundary
throughout the domain is around 18.
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Flow Separation
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Flow Separation
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