Developments towards fluid-structure interaction …Title Developments towards fluid-structure interaction simulations in BAE Systems’ corporate CFD suite, SOLAR/Flare Author Forster,

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Dr. Matthew Forster Research Scientist, Computational Engineering, BAE Systems 15th October 2019

Developments towards fluid-structure interaction simulations in BAE Systems’ corporate CFD suite Aerodynamics Tools and Methods in Aircraft Design, Royal Aeronautical Society


Towards FSI simulations in BAE Systems’ Computational Fluid Dynamics suite Overview

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• A need to incorporate higher fidelity aerodynamics into flutter and structural coupling toolsets was identified within BAE Systems. We want:

• Capability to predict transonic flutter

• Ability to simulate complex geometries, e.g. unconventional planforms, inlaid controls (spoilers)

• Accommodate structural models in multiple formats

• Tool to fit into existing flutter and structural processes

• Interchangeable results between CFD and DLM (Doublet Lattice Method)

• Two approaches being developed for unsteady aeroelastic predictions:

• Linearised Frequency Domain CFD

• Coupled CFD-CSM

• Preliminary LFD results presented here

• Dr. Sebastian Timme from the University of Liverpool, via the Royal Academy of Engineering Industrial Secondment Scheme, helped materialise part of this work


Towards FSI simulations in BAE Systems CFD suite Outline

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• Overview of BAE Systems Corporate CFD suite

• Summary of FSI approaches ongoing development

• Coupled CFD-CSM


• Advantages/disadvantages of approaches

• Fluid-Structure Interaction challenges

• LFD Validation results

• Pitching NACA64A010 at M=0.8

• 3D Goland Wing at M=0.8

• Conclusions/further work


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Suite of tools commonly referred to as “SOLAR and Flare”

• The SOLAR toolset has been developed over 20+ years, in collaboration with Airbus and ARA

• Flare has been in development for 10+ years at Computational Engineering, Filton

• SolCAD was originally developed at MA&I Warton, now maintained by Computational Engineering

BAE Systems Corporate CFD Suite Toolset Overview

BAE S

yst

em

s Corp

ora

te C

FD

Suite

SO

LAR

SolCAD

Mercury

Venus

Io

Flare

Prospero Pluto

Geometry Generation & Pre-Processing

Mesh Generation

Mesh Pre-Processing

Flow Solver

Post-Processing


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SOLAR/Flare Core Capabilities Mesh Generation

• Fast response mesh generation for complex configurations – “bottom up” approach using an unstructured, quadrilateral-dominant surface mesh (generated in Mercury) and a grown boundary layer mesh interfaced to a Cartesian farfield mesh via cut-cells (generated by Venus)

• Surface meshing:

• Iso/Anisotropic quad-dominant, triangular or structured surface meshes

• User-defined spacing fields, or automatic spacing fields based on model characteristics such as curvature

• Volume meshing:

• Wake plane and “multiple normal” capabilities for better treatment of sharp trailing edges

• Tetrahedral meshing for acoustic simulation

SolCAD

Mercury

Venus

Io

Flare

Pluto/ Prospero


• 2nd order, unstructured finite volume solver, supporting arbitrary polyhedral meshes

• Fully parallel, using MPI, with both implicit and explicit solvers

• Capable of performing single phase simulations in air or water, over a large speed range – including incompressible flows using the Artificial Compressibility Method (ACM) and Low-Mach-Number preconditioning

• RANS simulation using a range of turbulence models – including Spalart-Allmaras, Menter SST and Reynolds Stress Transport (RST) models

• Unsteady simulation using scale-resolving methods – including DES and wall modelled LES

• Range of boundary conditions including jets, intakes and propellers/rotors

• Adaptive mesh refinement

• Overset method

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SOLAR/Flare Core Capabilities Flow Solver SolCAD

Mercury

Venus

Io

Flare

Pluto/ Prospero


SolCAD Mercury Venus Io Flare

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SOLAR/Flare Core Capabilities Development Strategy

Structural Modelling

Aero and hydro

acoustics

SOLAR/Flare



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• Coupled CFD-CSM




• LFD Validation results





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Aeroelastics/Fluid Structure Interaction prediction CFD-CSM Approaches

Coupled CFD-CSM approach using OpenFSI with MSC Nastran. Figure modified from MSC Nastran 2017.1 User Defined Services Guide.

• Development ongoing for two CFD-CSM approaches: • Multi-physics code-coupling using MSC Nastran’s OpenFSI

interface • Data transfer between Flare and Nastran (see right) • Forces from CFD applied to wetted nodes of CSM • Displacements from CSM applied to CFD surface

• Modal-based aeroelastics solver contained within Flare

• Approximates deflected shape as a superposition of mode shapes

• Aeroelastic equations are solved to determine modal amplitudes

Flare


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Aeroelastics/Fluid Structure Interaction prediction Linearised Frequency Domain Approach

Mesh transformers: update 𝒖 and 𝒖 for

this mode shape

Get 𝜕𝑹

𝜕𝒘 solve for 𝒘

𝜕𝑹

𝜕𝒖,

𝜕𝑉

𝜕𝒖 and

𝜕𝑹

𝜕𝒖 for 𝒃

Steady mean state -> 𝑹 𝒘,𝒖, 𝒖 = 𝟎

• LFD is a time-linearised approximation of the unsteady Navier-Stokes

equations 𝑑(𝑉𝒘)

𝑑𝑡+ 𝑹 𝒘,𝒖, 𝒖 = 𝟎 about a steady mean state (

𝑑(𝑉𝒘)

𝑑𝑡= 0).

• Following Taylor expansion of unsteady Navier-Stokes, and retaining only first

harmonics we get a complex-valued linear system of the form: 𝑨𝒘 = 𝒃

where

𝑨 = 𝑖𝜔𝑉𝑰 +𝜕𝑹

𝜕𝒘 𝒘 ,𝒖 ,𝒖 𝒈

𝒃 = −𝜕𝑹

𝜕𝒖 𝒘 ,𝒖 ,𝒖

+ 𝑖𝜔𝒘 𝜕𝑉

𝜕𝒖 𝒖

+ 𝑖𝜔𝜕𝑹

𝜕𝒖 𝒘 ,𝒖 ,𝒖

𝒖 𝑛

with 𝜔 the frequency of oscillation.

• Aeroelastic equations in modal form:

𝜆𝑗2𝑴𝒖 + 𝜆𝑗𝑪𝒖 + 𝑲𝒖 𝒖 𝑗 = 𝑸𝒖 𝒋 = 𝝓𝑇

𝜕𝒇

𝜕𝒖𝒖 𝑗 + 𝝓𝑇

𝜕𝒇

𝜕𝒘𝒘 𝑗

𝑸 matrix output

LFD DLM


Aeroelastics/Fluid Structure Interaction prediction Choosing the right tool for the job

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Method Pros Cons

Nastran with DLM

+ Fast + Linear/Nonlinear structural models

− Simple aerodynamics, unsuitable in transonic regime − Unable to deal with complex geometries (e.g. non-streamwise

tips, inlaid controls)

LFD CFD + High fidelity aerodynamics, applicable in transonic range

+ Capable of modelling complex geometries

− Increased computational cost compared to DLM (similar cost to few timesteps of unsteady CFD)

− Requires high-fidelity aerodynamic model to be generated − Linearisation about a steady state o Linear structural model

Modal CFD-CSM

+ High fidelity aerodynamics and capable of modelling complex geometries

+ Unsteady aerodynamics + No communication between solvers needed

− Significantly increased computational cost compared to LFD (Unsteady CFD + structural solver)

− Requires high-fidelity aerodynamic model to be generated o Linear structural model

OpenFSI CFD-CSM

+ High fidelity aerodynamics and capable of modelling complex geometries

+ Unsteady aerodynamics + Linear/Nonlinear structural models

− Significantly increased computational cost compared to LFD (Unsteady CFD + structural solver + data transfer)

− Requires high-fidelity aerodynamic model to be generated


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Aeroelastics/Fluid Structure Interaction prediction Choosing the right tool for the job

LIFECYCLE

DLM

LFD

CFD-CSM

Conceptual design • Quick turnaround • CFD fidelity not be

needed • CFD model not available

Preliminary design • Support wind tunnel

testing • CFD and higher fidelity

structural models

Detailed design • Targeted simulations • Support flight testing

FID

ELIT

Y/C

OST



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• Coupled CFD-CSM




• Validation results





Aeroelastics/Fluid Structure Interaction challenges RBF interpolation

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• For both LFD and CFD-CSM a method is needed to transfer information between structural and fluid domains.

• CFD mesh and structural mesh points often not co-located, need to transfer mode shape deflections, structural displacements and forces

• Radial Basis Functions (RBF) are used as an interpolation for:

• Interpolation between structural grid and CFD surface grid

• Efficient CFD volume mesh deformation

• Algorithm used from: Kedward, et al, “Efficient and exact mesh deformation using multiscale RBF interpolation”, J. Comp. Phys., 2017.

• Allen showed that same RBF matrix can also be used to interpolate forces back to structure for CFD-CSD, in “Unified Approach to CFD-CSD Interpolation and Mesh Motion using Radial Basis Functions”, 2007 AIAA Applied Aerodynamics conference.


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Aeroelastics/Fluid Structure Interaction challenges Interpolation of structural mode-shapes/deflections

Structural grid with deflections

Baseline CFD surface geometry

RBF MATRIX


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Aeroelastics/Fluid Structure Interaction challenges Interpolation of forces to structural grid

RBF MATRIX

Forces on CFD surface

Forces interpolated onto structural grid

Keep matrix built for deformations and invert

-1



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• Coupled CFD-CSM









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Validation Results NACA 64A010 AGARD CT8

NACA 64A010 CFD grid with centre of rotation at 0.25 chord

CFD results comparing LFD and URANS from Thormann and Widhalm 2013: DOI:10.2514/1.J051896

• Validation of the unsteady aerodynamics prediction capabilities of the LFD.

• LFD and Unsteady RANS simulations in 2D compared using Spalart-Allmaras turbulence model.

• Flow conditions: • Mach = 0.8 • Reynolds number =12.5m per chord • Pitch oscillation frequency = 17.1Hz • Pitch amplitude = 0.5 degrees

• Two 2D CFD grids used for grid convergence analysis:

• Coarse grid: 13234 cell volumes • Finer grid: 26658 cell volumes

Reference solution from DLR Tau solver, see right. Note that the LFD predictions overpredicted the extent of the shock oscillation compared with the URANS.

https://arc.aiaa.org/doi/full/10.2514/1.J051896


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NACA 64A010 AGARD CT8 Steady RANS – Cp

Tau results Thormann and Widhalm 2013: DOI:10.2514/1.J051896

Flare results

https://arc.aiaa.org/doi/full/10.2514/1.J051896


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NACA 64A010 AGARD CT8 Unsteady RANS – time step and grid convergence


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NACA 64A010 AGARD CT8 LFD vs URANS complex Cp


NACA 64A010 AGARD CT8 Summary and cost comparison

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• Pitching oscillation of 2D NACA64A010 at 17.1Hz.

• LFD overpredicted peaks in unsteady Cp, however trend agrees with DLR Tau results.

• URANS 2 seconds (34.2 cycles) of simulation on 20 cores:

• 1/dt = 1kHz on finer grid: 1390 seconds wall clock time. (41 seconds per cycle)



• LFD simulation on 20 cores, finer grid: 67 seconds wall clock time.



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• Coupled CFD-CSM









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Validation Results Goland Wing Flutter

• Cantilever wing with a 20ft span and 6ft chord and tip store.

• Evaluate the capability to produce the Generalised Aerodynamic Force matrices for flutter analysis using existing BAE Systems flutter toolsets.

• This test case is performed at • Mach = 0.8 • Euler CFD

• Comparisons against predictions using Nastran DLM are

also made.


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Goland wing flutter Mode Shapes

Mode 1 Mode 2 Mode 3 Mode 4


Goland wing flutter Flutter solution at Mach = 0.3

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• Frequency – damping plots

• Flutter solution method in existing BAE Systems flutter and structural coupling toolset

• Q matrices generated from

• 2nd order Euler LFD

• Nastran DLM

• Similarities to be expected since DLM is suitable for low subsonic flows


Goland wing flutter Flutter solution at Mach = 0.8

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• Frequency – damping plots

• Flutter solution method in existing BAE Systems flutter and structural coupling toolset

• Q matrices generated from

• 2nd order Euler LFD

• Nastran DLM

• Differences to be expected due to transonic prediction capabilities of DLM


Goland wing flutter Summary and cost comparison

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• LFD solution used in BAE Systems’ flutter and structural coupling toolset

• Direct replacement for DLM Q matrices

• Mode shapes interpolated from Nastran grid to CFD surface using RBF

• CFD volume mesh deformation also using efficient RBF methods

• Low speed M=0.3, flutter solution comparable between LFD and DLM

• Transonic M=0.8, differences in results possibly due to transonic deficiencies of DLM • Nastran SOL145 solution for 10 frequencies, 4 mode shapes: 83 seconds

• LFD simulation on 100 cores for 10 frequencies, 4 mode shapes: 1114 seconds (18.5 minutes)



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• Coupled CFD-CSM









Towards FSI simulations in BAE Systems’ Computational Fluid Dynamics suite LFD conclusions and further work

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• Linearised Frequency Domain CFD capability has been introduced into Flare

• Validation demonstration against academic test cases

• Investigations into more representative test cases ongoing

• Inlaid controls/spoilers (right)

• Overset meshing with LFD

• One- and two-equation turbulence models currently supported in Flare LFD

• Investigations ongoing into choice of linear system solver for LFD

• Currently use GMRES-based algorithm in PETSc, literature suggests others may be stronger

• Investigation ongoing into using automatic differentiation for generation of

Jacobian matrix


Towards FSI simulations in BAE Systems’ Computational Fluid Dynamics suite CFD-CSM progress

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• Early stage in development for CFD-CSM capability

• Modal and code-coupling approaches being developed

• Use cases include:

• Vortex induced vibrations

• Unsteady flows

• Structural nonlinearities

• Freeplay/backlash

• Large deformations


Towards FSI simulations in BAE Systems’ Computational Fluid Dynamics suite Use cases

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Typhoon and Hawk manufacture and capability development

Unmanned and future air system capabilities

• In-house CFD-based aeroelastics capability still relatively early in development

• LFD capability is maturing and is intended to be used in the near future on our products and projects such as • Typhoon • Hawk • Tempest • Future projects

• CFD-CSM capability in early stages of

development


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Developments towards fluid-structure interaction …Title Developments towards fluid-structure interaction simulations in BAE Systems’ corporate CFD suite, SOLAR/Flare Author Forster,