3d duct design

8/14/2019 3D Duct Design

1/19

Scientific Programmes Committee

Centre for Aerospace Systems Design & Engineering

K. SudhakarDepartment of Aerospace Engineering

Indian Institute of Technology, Mumbai

http://www.casde.iitb.ac.in/MDO/3d-duct/

July 5, 2003

3D-Duct Design


2/19

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


3/19

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.


4/19

Optimization

n

k

m

n

SdesignsFeasible

g0)x(g

h0)x(h

;toSubjectx)x(fMinimise

=

=

How to reduce CFD analysis requirements? If gradient based optimization is used; how to

evaluate derivatives?


5/19

Gradient Based

X1

X2

Gradient of

functions

Required!

=

n

2

1

x

f

x

f

xf

)x(f


6/19

3-D Duct DesignDesign Problem in Brief

Entry ExitLocation and shape known

Geometry of duct from Entry to Exit ?

PressureRecovery?

Distortion? Swirl?


7/19

Parametrization of 3D-Ducts


8/19

3D-Duct Design UsingHigh Fidelity Analysis

?

X1-MIN X1-MAX

X2-MAX

X2-MIN

Domain for search using high fidelity code is large


9/19

3D-Duct Design UsingHigh Fidelity Analysis

Low Fidelity Design Criteria Wall angle < 6

Diffusion angle < 3

6 * REQ < ROC

Fluent for CFD

RSM / DOE

DACEX1-MIN X1-MAX

X2-MAX

X2-MIN


10/19

Surrogate Modeling

DOE / RSM modeling in physical experiments.

experimental point

RSM. Least Square Fit.

y = a0 + a1 x + a2 x2 . . .

Fitted model is smooth and easily differentiable.

Curse of dimensionality! 2k function evaluations

Sequential RSM.

x

y


11/19

Sequential RSM

Reported @ICIWIM


12/19

Design & Analysis of Computer Experiments

Regression fit + Stochastic process Single global fit

Variability in prediction known and exploitable

xx

xx

x

Estimates of

Predictive error

x = Computer exp

DACE Fit


13/19

Building Models Using DACE

xx

xx

x

5% predictive

error

x = Computer exp

DACE Fit

xx

x

Use multi-modal GA to identify n highest peaks.

Test if they are higher than 5%

Add computer experiments at those spots


14/19

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


15/19

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

?2x

f;?

1x

f=

=


16/19

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


17/19

Problem with Finite Differencing?

Only (n+1) CFD runs?

Correct step size for FDM is important!

Will demand more CFD runs!

b

CLIterative

Convergence

Criteria


18/19

Complex Variable Approach

Evaluate f{x + i e} ; e


19/19

Gradients by ADIFOR

Complex Analysis

Code in FORTARN

FORTRAN

source code

that can evaluate

gradients

Automated

Differentiation

Package

Euler code is

being put through

ADIFOR

(Not for 3D-Duct)

3d duct design

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