Scientific Programmes Committee Centre for Aerospace Systems Design

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Scientific Programmes Committee Centre for
Aerospace Systems Design Engineering
3D-Duct Design

• K. Sudhakar
• Department of Aerospace Engineering
• Indian Institute of Technology, Mumbai
• http//www.casde.iitb.ac.in/MDO/3d-duct/
• July 5, 2003

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Design Optimization / MDO So far . . .

• Airborne Early Warning System (M Tech)
• Complex system, simple models.
• Maneuver Load Control (M Tech)
• Existing system, database driven
• Hypersonic Launch Vehicle (Ph D)
• New system, simple models, system analysis
• WingOpt Wing Design (4 x M Tech)
• Simple models
• Intermediate level models
• FEM VLM

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3D-Duct Optimization

• Joint exercise - CASDE ADA
• First attempt at CFD based optimization
• Literature
• Techniques to inject CFD into optimization
• About the design Problem
• Capturing of design problem
• Parametrization
• Capturing designers thumb rules heuristics to
  trim design space.

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Optimization

• How to reduce CFD analysis requirements?
• If gradient based optimization is used how to
• evaluate derivatives?

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Gradient Based
Gradient of functions Required!
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3-D Duct DesignDesign Problem in Brief
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Parametrization of 3D-Ducts
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3D-Duct Design Using High Fidelity Analysis
X2-MAX
?
X2-MIN
X1-MAX
X1-MIN
Domain for search using high fidelity code is
large
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3D-Duct Design Using High Fidelity Analysis

• Low Fidelity Design Criteria
• Wall angle lt 6
• Diffusion angle lt 3
• 6 REQ lt ROC
• Fluent for CFD
• RSM / DOE
• DACE

X2-MAX
X2-MIN
X1-MAX
X1-MIN
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Surrogate Modeling

• DOE / RSM modeling in physical experiments.

Fitted model is smooth and easily
differentiable. Curse of dimensionality! 2k
function evaluations Sequential RSM.
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Sequential RSM
Reported _at_ICIWIM
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Design Analysis of Computer Experiments

• Regression fit Stochastic process
• Single global fit
• Variability in prediction known and exploitable

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Building Models Using DACE
5 predictive error
Use multi-modal GA to identify n highest
peaks. Test if they are higher than 5 Add
computer experiments at those spots
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Homotopy / Continuation

• If you seek f(x) 0
• Create a parametric problem
• g(x, ?) ( 1 - ?) h(x) ? f(x)
• Solution to h(x) 0 is known
• ie. g(x,0) 0 is known
• Vary ? slowly from 0 to 1
• g(x, 1) 0 f(x)
• Solution for duct-1 (? 0) is known
• Solve for duct-2 (? 1) by slowly varying ?

? 0
? 1
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How to evaluate gradients?

• Consider design of wings
• Design variables, x x1, x2
• Objective function, f(x)
• Analysis is CFD
• Give values to x x1, x2 ? duct ? mesh
• Run a CFD code and generate solution
• Generate f(x) based on solution.
• How to evaluate

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Methods to Evaluate Gradients?

• Finite difference method. Easy to implement, but
  problematic?
• Complex variables approach, requires source
• ADIFOR Automatic DIfferentation in FORtran
  requires source. Analytical accuracy
• Surrogate Modeling Surface fits
• Response Surface Method (RSM / DOE)
• Design Analysis of Computer Experiments

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Problem with Finite Differencing?

• Only (n1) CFD runs?
  
• Correct step size for FDM is important!
• Will demand more CFD runs!

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Complex Variable Approach
subroutine func (x, f) real x, f
subroutine func(x, f) complex x, f

• Evaluate fx i e e ltlt 1
• f(x) Real Part f(x i e) -
  f(x) e2 / 2
• df/dx Imag Part f(x i e) / e - f
  (x) e2 / 6
• CPU time up by 3, RAM up by 2

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Gradients by ADIFOR
Euler code is being put through ADIFOR (Not for
3D-Duct)