Coupled Adjoint Optimisation for a

Flexible Wing with Fluid-Structure

Interaction

A. Stannard, PhD studentN. Qin, Academic SupervisorDepartment of Mechanical EngineeringUniversity of Sheffield

Funded by EPSRC DTG and Airbus

29/11/2019 © The University of Sheffield

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Motivation: To enable coupled adjoint optimization for fluid-structure interaction simulations of aircraft

• Minimize optimization run time

• Unconstrained gradient-based algorithms

• Adjoint-based gradients for efficiency

• Trim in the loop

• Direct mesh deformation methods

• High-fidelity modelling

• RANS-based CFD

• FEM-based CSM

29/11/2019 © The University of Sheffield

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Use of FlowSimulator for aeroelastic coupling• Parallel environment for solving

multi-physics simulations

• The Data Manager holds data in memory to reduce time consuming I/O

• High fidelity CFD and CSM solvers TAU and Nastran

FSI in FlowSimulator• Sequentially solve the Fluid

and Structural problems

• Interpolate the forces between the TAU and Nastran

• Inner loop for FSI convergence and outer loop for Trim convergence

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Fluid Structure Coupling• Multiple interpolation options

• RBF interpolation

• Beam spline interpolation

• Rigid body splines

• Couple each section of the aircraft separately• RBF performs inversion on matrix the size

of the section’s CSM nodes

• Cut section further to speed up inversion

CFD Nodes

CSM Nodes

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Create Control Surfaces• Define arbitrary control surface

locations with cutting method

• Control surface deflections on CSM mesh nodes added to CSM displacements• These are interpolated to the CFD

surface

• Ensures smooth continuous surface

• Potential to create active camber trailing edge device

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Two Strategies for Mesh Deformation• RBF Mesh Deformation

• Handles large deformations well

• Fast: Calculates mesh sensitivity on the fly

• Uses subset of surface points: Sacrificing

surface resolution

• Delaunay Mesh Deformation

• Very fast: Explicitly stores mesh sensitivity

• Uses all surface points

• Can’t handle very large deformations

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Optimisation overview• Optimisation algorithm

• Minimise !"• Gradient-based

• Unconstrained BFGS method

• Shape Parameterisation

• Surrogate CATIA v5 model

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PODShaper: CATIA Surrogate Model

How to Create PODShaper Model - Holger Barnewitz

PODShaper

Sampler

Decomposer

• CATIA V5• DesignTable• CATScript

POD Database File

PODShaperSynthesizer

DeformationVectors

+ Sensitivities

CFD SurfaceMesh Deformation

+ Gradients

Generate on Local WorkstationCATIA-PC

Use in HPC Environment,FlowSimulator without CATIA

DoEDesign of

Experiments

POD Database File

PODProper

OrthogonalDecomposition

Design Variable Values

RBFRadialBasis

FunctionInterpolation

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Aeroelastic coupled adjoint

29/11/2019 © The University of Sheffield

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for(k=0;k≤ N;k++)

./0

.12304 = − .6

.12− .70

.12 .78.70

23849:

3∆4 = − .6.<=

+ 3042 ./0.<=

+ 3849:2 .78.<=

.<=.>8?@A

2

./8

.>823B4 =

.>8

.>03∆4

CFD-Solver:

CSM-Solver:

Mesh-Defo:

• Solve system using Gauss-Seidel method

• Use converged solution to solve jig mesh adjoint for the full gradient

Trim Correction!"#$!% = '()#$

(% *,,+ .#$

!/!% + 0#$

!1!% = 0

!"3!% = '()3

(% *,,+ .3

!/!% + 03

!1!% = 0

!"4!% = '()4

(% *,,+ .4

!/!% + 04

!1!%

29/11/2019 © The University of Sheffield

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• All values are known except 5*54 and 5,54

• These are found by solving a simultaneous equation

• Successful validation for both Delaunay and RBF mesh deformation approaches at low Mach numbers

Coupled Adjoint Validation

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• The coupled adjoint suffers convergence problems with the RBF approach at higher Mach numbers

• Use RBF in FSI simulation and use Delaunay in coupled adjoint

Non-Consistent mesh deformation

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Test Case Description: LANN-WingAircraft configuration

• Wing Only

Objective

• Minimise Drag

Optimization point

• Cruise Mach: 0.73

• Cruise Cl: 0.4

Parameterization

• 8 PODShaper Parameters

• 2 Twist parameters

• 3 separate camber locations

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• Optimiser performed well with steepest descent

• BFGS moved with step sizes that were too small (despite scaling the gradient)

Optimisation History

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Optimisation Results: !" Contours

Original Pressure Contours Optimised Pressure Contours

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Optimisation Results: Shape Changes

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Summary• Presented trimmed aeroelastic gradient-based optimization

process

• Adjoint-based gradients

• High-fidelity CFD & CSM coupling

• Efficient in-memory and HPC-based Workflow

• Surrogate CAD model parameterization

• Demonstration on a simple wing test case

Future Work• Trim optimisation on XRF1

• Use control surface interpolation to represent a morphing

wing mechanism

• Run coupled adjoint trim optimization on full aircraft

configuration with morphing wing parameters

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Dr J. Pattinson, PhDFor showing me the ropes with FlowSimulator and consistent help

M. CrossFor help in moving the project forward

A. MerleFor helping to debug some tricky problems

Acknowledgments

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