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A Coupled Aero−Structural OptimizationMethod for Complete Aircraft Configurations

AIAA 37th Aerospace Sciences Meeting & ExhibitReno, NV

January 11th, 1999

James J. ReutherMCAT Institute

Juan J. Alonso and Joaquim R. R. A. MartinsStanford University

Stephen C. SmithNASA Ames Research Center

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OBJECTIVESOBJECTIVES

❑ Develop a high−fidelity environment for aero−structural analysis and design of complex aircraft configurations.

❑ Create a full aircraft geometry outer mold line (OML) database for the exchange of information between disciplines.

❑ Couple a Reynolds Averaged Navier−Stokes (RANS) flow solver with linear finite element CSM solvers for aero−structural analysis and design.

❑ Establish a basic framework for future use in coupled sensitivity analysis.

❑ Demonstrate aeroelastic analysis and simplified aero−structural design problems.

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OUTLINEOUTLINE

❑ Introduction and Motivation

❑ CSM Models: wind−tunnel model and aircraft wing structures

❑ Aero−Structural Coupling: consistency and conservativeness

❑ Sensitivity Analysis: aerodynamics, structures, coupled

❑ Results: analysis and design cases

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rsity ❑ Dr. James J. Reuther, MCAT Institute, NASA Ames Research Center

❑ Joaquim R. R. A. Martins, Stanford University

❑ Dr. Stephen C. Smith, NASA Ames Research Center

RESEARCH TEAMRESEARCH TEAM

❑ Prof. Juan J. Alonso, Stanford University

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❑ Use of high−fidelity discipline models in the Multi−Disciplinary Optimization (MDO) arena

❑ Advanced aerodynamic shape optimization methods have facilitated great improvements, but they require artificial constraints

❑ Iterative application of single−discipline design methods can miss the true optimum of a coupled system

❑ Single−discipline optmization methods may produce infeasible designs

MOTIVATIONMOTIVATION

❑ Ability to account for trade−offs between various disciplines is the key to generate improved designs

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❑ Aeroelastic wing design

❑ Interaction between aerodynamics and structures

❑ Induced drag vs. structural performance

❑ Compressibility drag vs. structural performance

❑ Variety of off−design constraints (loads, pitch−up, etc.)

DEMONSTRATION PROBLEMDEMONSTRATION PROBLEM

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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HIGH−FIDELITY AERODYNAMICSHIGH−FIDELITY AERODYNAMICS

❑ FLO107−MB: parallel multiblock RANS flow solver

❑ 5−stage Runge−Kutta algorithm

❑ Multigrid

❑ MPI parallel implementation

❑ Residual averaging

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SAMPLE BUSINESS JETSAMPLE BUSINESS JET

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SAMPLE COMMERCIAL JETSAMPLE COMMERCIAL JET

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SAMPLE SUPERSONIC AIRCRAFTSAMPLE SUPERSONIC AIRCRAFT

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MULTIBLOCK SOLVER: TFLO98MULTIBLOCK SOLVER: TFLO98TYPICAL COMPRESSOR STAGETYPICAL COMPRESSOR STAGE

❑ Rotor 37 Compressor Stage❑ 36 Blades❑ 288 Blocks❑ 27,000,000 cells

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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WIND TUNNEL MODELSWIND TUNNEL MODELS❑ Aeroelastic analysis of complete configurations

❑ Comparison with experimental data

❑ 8−node isoparmetric elements

❑ Cholesky factorization

❑ 2−point Gauss quadrature

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❑ Triangular plates and truss elements

❑ Skins modeled with plates

❑ Spars and ribs modeled with plates and trusses

❑ Simplified but realistic and accurate

WING STRUCTURE MODELWING STRUCTURE MODEL

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❑ States the exact form of the functions and arguments provided by the programmer.

❑ Designed for ease of interchangeability of different structural solvers.

❍ CSM_Init(...) memory allocation and initialization of model

STRUCTURAL MODEL APISTRUCTURAL MODEL API

❍ CSM_Solve(...) returns structural deflections

❑ Will establish couplings for NASTRAN, ANSYS.

❍ CSM_Stresses(...) returns element stresses

❍ CSM_GetPoint(...) returns CSM surface information

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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❑ Intent is to maintain accuracy of disciplines.

❑ Accomplished via Aerosurf database.

❑ Aero−structural coupling used here is both consistent and conservative.

−Consistent: resultant forces and moments are preserved. −Conservative: total work/energy is preserved.

AERO−STRUCTURAL COUPLINGAERO−STRUCTURAL COUPLING

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TRANSFER EQUATIONSTRANSFER EQUATIONS

❑ Transfer of CSM nodal displacements to AeroSurf database.

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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OML DATABASEOML DATABASE

❑ Un−intersected set of aircraft components❑ Parametric patches from intersection of surfaces

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OML DATABASE

❑ Parametric location of CFD mesh points is identified by a triad (n, u, v), where n is the patch number.

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PRE−PROCESSING STEPSPRE−PROCESSING STEPS

❑ Aerosurf point "association" procedure

❑ "Association" with parametric location within a given element on the surface of the CSM model

❑ Computation of basis functions values

❑ Calculation of weights, [η]

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❑ In a preprocessing step, all points on Aerosurf are "associated" with a "donor" cell and location inside that cell in CFD mesh.

❑ During the calculation process, the current pressure distribution is transferred directly to the Aerosurf database.

❑ Using appropriate weights a conservative and consistent load vector is created and passed to the CSM solver.

❑ CSM_Solve is called to obtain structural displacements.

CFD PRESSURE TRANSFERCFD PRESSURE TRANSFER

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❑ Result of CSM_Solve is the vector of displacements at the CSM nodes.

❑ Using the CSM model displacement basis functions and pre−computed [η] matrix, new locations of Aerosurf points are found.

❑ Aerosurf database is used to deform the CFD mesh on the solid boundaries.

❑ Warp−MB is used to perturb the interior of the CFD mesh.

DISPLACEMENT TRANSFERDISPLACEMENT TRANSFER

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INGREDIENTS OF THE FRAMEWORKINGREDIENTS OF THE FRAMEWORK

❑ High−fidelity modeling in the component disciplines:

− Euler and Navier−Stokes equations for aerodynamics.− Detailed Finite Element Model for structures.

❑ High−fidelity coupling between participating disciplines:

− Consistency: force and moment resultant preserved.− Conservativeness: total work/energy preserved.

❑ OML geometry database for information exchanges (shape, pressure distributions, displacements).

❑ Sensitivity analysis.

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AERODYNAMIC SENSITIVITIESAERODYNAMIC SENSITIVITIES

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AERODYNAMIC SENSITIVITIESAERODYNAMIC SENSITIVITIES

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STRUCTURAL SENSITIVITIESSTRUCTURAL SENSITIVITIES

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COUPLED SENSITIVITIESCOUPLED SENSITIVITIES

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COUPLED SENSITIVITIESCOUPLED SENSITIVITIES

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COUPLED SENSITIVITIESCOUPLED SENSITIVITIES

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❑ Navier−Stokes aeroelastic analysis of complete configuration wind tunnel models

− Rigid model− Flexible model

❑ Aerodynamic shape optimization of a flight wing−alone geometry

− Aerodynamics only− With aeroelastic deformation

RESULTSRESULTS

❑ ✳❉❍❐●❉❆❉❅❄ aero−structural shape optimization

−Wing−alone−Complete configuration

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CONCLUSIONSCONCLUSIONS

❑ High−fidelity modeling in aerodynamics and structures

❑ Centralized OML geometry database as reference for different disciplines

❑ Force and work preserving coupling algorithm

❑ Framework for computation of coupled sensitivities

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KEY ENABLING TECHNOLOGIESKEY ENABLING TECHNOLOGIES

❑ Development of adjoint−based, gradient calculation techniques for systems governed by partial differential equations.

❑ Portable, scalable, parallel implementations for efficient computing platforms such as the SGI Origin2000.

❑ Advances in automatic multiblock mesh generation techniques.

❑ Recent development of direct interfaces to CAD geometry kernels.

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❑ SPMD (Single Program Multiple Data) layout.

❑ MPI (Message Passing Interface) Library for message passing.

❑ Using block boundaries in the multiblock domain, natural parallelization is achieved.

❑ Domain decomposition strategy.

❑ MPI is used to update the "halo" quantities at every stage of the time−stepping.

❑ Computational cost of optimization is negligible compared to flow and adjoint solutions.

PARALLEL IMPLEMENTATIONPARALLEL IMPLEMENTATION

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LOAD BALANCING AND COMMUNICATIONLOAD BALANCING AND COMMUNICATION

❑ Needed communication:

−Multiblock decomposition, multigrid acceleration.

−CFD stencil.

−Multistage time−stepping:✔ Convective fluxes at all stages and levels.✔ 1st order dissipation on odd stages at all levels.✔ 3rd order dissipation only on fine mesh at odd stages.

1st Level Halo 2nd Level Halo

Convective Stencil Dissipative Stencil

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LOAD BALANCING AND COMMUNICATIONLOAD BALANCING AND COMMUNICATION

❑ Load balancing and communication:

−CPU time:

✔ Balance the number of computational cells in each processor.

−Bandwidth:✔ Place adjacent blocks on same processor.

−Latency:✔ Gather all communication between an two processors into a single message regardless of the number of blocks in each processor.

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PARALLEL PERFORMANCEPARALLEL PERFORMANCE

240 Blocks

4,157,440 Cells

Maximum Speedup 28.0 / 32.0

Maximum Possible29.5 / 32.0

Load Balance Effects

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CONCLUSIONSCONCLUSIONS

❑ Feasible and Efficient Parallel Environment Developed and Demonstratedfor the Inviscid Design of Complete Aircraft Configurations

❑ Portable, Scalable Parallel Implementations Necessary for Continuityand Fast Turnaround

❑ Final Objective is to Make Use of These Techniques During thePreliminary Design Stage

❑ Performance of Computing Platform is Essential for Accomplishing Task

❑ Origin2000 Has Delivered Expected Performance for These Calculations

❑ Navier−Stokes Based Methods are Needed and Currently in Development