Automated High Fidelity Simulation

David Darmofal, Bob HaimesGarrett Barter, Laslo Diosady, Krzysztof Fidkowski

James Modisette, Todd Oliver, Mike Park

Massachusetts Institute of TechnologyDepartment of Aeronautics and Astronautics

October 28, 2008

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Computational Fluid Dynamics (CFD)

CFD in aerospace engineeringNumerous codes in private and public sectorActively used in design and analysisSupplements or replaces expensive wind-tunnel testsReduces design cycle timeMeshing relies on expert judgment

Typical Design ProcessError

Estimate,AdaptiveIndicator

SolutionFlow

MeshComputational

Discrete

Geometry(CAD)

Aided DesignComputer-

Weeks Hours/Days

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Drag Prediction Workshops I & II

DescriptionGeometries: DLR-F4 WB andDLR-F6 WB / WBNPCase: M! = 0.75, CL = 0.5,Re = 3! 106, fully turbulentGrids: " 3! 106 (DPW I)," 1# 10! 106 nodes (DPW II)" 25 participants, " 20 codes

http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/

Results [Levy et al , 2003; Hemsch and Morrison, 2004]Code-to-code scatter very large: $ 40 drag counts ignoringoutliers (DPW I)No discernible reduction in scatter with grid refinement (DPW II)Asymptotic rates not achieved with grid refinement (DPW II)Project X (MIT) AHFS October 28, 2008 3 / 14

Further Results

Mavriplis demonstrated uniformrefinement of different meshtopologies (UW versus CESSNAtopology) apparently convergingto different lift (CL) estimateseven with meshes having manymore elements (N) than typicallyused in practice.

Mavriplis, 2007“The range of scales inherent in computational aerodynamicsproblems... make it unfeasible to fully resolve all regions of thecomputational domain through successive global refinements of anarbitrarily constructed initial grid...”

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Next-Generation CFD

Project XResearch initiative at Aerospace Computational Design Laboratoryaimed at developing the next generation CFD capability.Goal:

Engineering accuracy in a reasonable amount of time and in anautomated manner.

Outcome:Desired outcome: let engineers be engineers not meshingexperts.

Enabling Features:Solution-based adaptivityHigher-order discretizationDirect interface to Computer-Aided Design (CAD) modelsProject X (MIT) AHFS October 28, 2008 5 / 14

Enabling Feature: Output-Based Adaptation

CD = 565.7 countsHow accurate is this value?Where is more resolution necessary to improve the accuracy?

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Output Error Estimation: The Adjoint

Given a governing equation with a source term (g), a solution (u)and a functional output, (J ),

% · F(u) = g(x), J (u(g))

The adjoint, !, is a Green’s function relating the output sensitivityto the source term,

J (u(g)) # J (u(0)) =

!!

!g(x)

For error estimation and adaptation, g is the truncation error.For gradient-based design optimization, g is the residualperturbation due to design variable perturbation.

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Output Error Estimation: The Adjoint

The adjoint, !, is a Green’s function relating the output sensitivityto the source term,

J (u(g)) # J (u(0)) =

!!

!g(x)

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Adaptive Algorithm

Idea: refine elements with high error; coarsen elements with low error

Iteration 0

Iteration 2

Iteration 4

Solve primal and dual equations oncurrent mesh.Estimate output error and elementcontributions.Find desired mesh size in eachexisting element using an a priorioutput error estimate to relateelement error to size request:h! = h!("!)

Adapt mesh

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Examples of Output-based Adaptation

High-lift, multi-element airfoilSonic boom applicationNozzle Guide Vane missile (NASA Ames)

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RANS drag adaptation example: EET Airfoil

Initial Mesh (11063 elements)

Final Mesh (11620 elements), p = 3 solution

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EET Airfoil Results (p = 3)

Mach Number

Eddy Viscosity

Pressure Distribution

−0.2 0 0.2 0.4 0.6 0.8 1 1.2

−1

0

1

2

3

4

5

6

x/c

−cp

Outputs on final meshc! = 3.51—agrees well with experiment and other computationscd = 436 counts—error estimate = 3 counts

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Supersonic flowFarfield pressure adaptation

NACA 0012, M! = 2, Re = 104, # = 0"

Adaptation on" x1x0

(p# p!)dx ona line location 20 chords aboveairfoilInterpolation orders p = 1–3.

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Supersonic flowFarfield pressure adaptation

Initial (all p) Final p = 1 Final p = 3

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Supersonic flowFarfield pressure adaptation

Pressure signal convergence for p = 2

10 15 20 25 30 35 40−0.1

−0.05

0

0.05

0.1

0.15

0.2

x

Δ p

/ p ∞

Adapt Iter 1Adapt Iter 2Adapt Iter 3Adapt Iter 7

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NGV Missile

Functional: Axial force

• Initial mesh: ~5k cells

• Supersonic flow: M! = 2, !"="0°

• Power boundary conditions applied at

plenum face

Nozzle cutaway

Near-body view of initial mesh

Fins and nozzle guide vanes

NGV Missile

Nozzle cutaway (6 adaptations, Mach contours)

Future Work

Applications in other areas in particular internal flowsExtensions to unsteady flows

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