Post on 26-Dec-2015
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High-dimensional FSI system and Low-Dimensional Modelling
Marek Morzyński Witold Stankiewicz
Robert Roszak Bernd R. Noack Gilead Tadmor
Overview
Elements and of High- Dimensional Aeroelastic System
Loosely coupled aeroelastic system Computational aspects Elements of the system Solutions
ROM with moving boundaries and ALE ROM in design and flow control ROM for AE – sketch of challenges and
ideas
ROM AE model - motivationNeed of ROM in design
AIAA 2008, Rossow, Kroll Aero Data Production A380
wing
50 flight points 100 mass cases
10 a/c configurations 5 maneuvers
20 gusts (gradient lengths) 4 control laws
~20,000,000 simulations
Engineering experience for current configurations
and technologies
~100,000 simulations
Need of online capable ROMs in feedback flow control
Aeroservoelasticity
Aeroelastic control (Piezo-control of flutter, wing morphing, smart structures)
MicroAerialVehicles (maneuverability)
High- Dimensional Aeroelastic System – ROM testbed
Tau Code
MF3 (in-house),Calculix, Nastran
In-house and AE tools
Spring analogy
Flow code
Structural code
Interpolation
Fluid forces
Forces
Structure displacements and velocities
Deformed CFD mesh, velocities
CFD mesh deformation
Interpolation
t=t+t
convergence
yes
no
Computational aspects – Euler code
Flow code
Structural code
Interpolation
Fluid forces
Forces
Structure displacements and velocities
Deformed CFD mesh, velocities
CFD mesh deformation
Interpolation
t=t+t
convergence
yes
not=80s
t=10s
t=10s
t=4s / 50s
t=30s
One iteration time: 134s (full CSM) / 180s (modal CSM)
Mesh:10 mio elements
CPU Power:16 cores
Computational aspects - RANSRANS
Flow code
Structural code
Interpolation
Fluidforces
Forces
Structure displacements and velocities
Deformed CFD mesh, velocities
CFD mesh deformation
Interpolation
t=t+t
convergence
yes
not=400s
t=90s
t=90s
t=4s / 50s
t=220s
One iteration time: 850s (full CSM) / 804s (modal CSM)
Mesh:30 mio elements(1 mio: surfaces)
CPU Power:32 cores
High-fidelity CFD and CSM High-fidelity CFD and CSM solverssolvers
CFD - TAU CODE
• Finite volume method solving the Euler and Navier-Stokes equations
• hybrid grids (tetrahedrons, hexahedrons, prisms and pyramids)
• Central or upwind-discretisation of inviscid fluxes
• Runge-Kutta time integration• accelerated by multi-grid on
agglomerated dual-grids• miscellaneous turbulence models• Parallelized with MPI• Parallel Chimera grids
CSM MF3: in-house CSM Tool
• Finite Element-based• Rods, beams, triangles (1st / 2nd order), membranes, shells, tetrahedrons (1st / 2nd order), masses and rigid elements
• Static analysis• Transient (Newmark scheme)• Modal analysis• MpCCI and EADS AE interfaces
From DLR TAU-code manual
ALE - Motion of boundary and mesh ALE - Motion of boundary and mesh canonical domaincanonical domain
With boundary conditions:
Arbitrary Lagrangian-Eulerian (ALE) binds the velocity of the flow u and the velocity of the (deforming) mesh ugrid.
For incompressible Navier-Stokes equations the mesh velocity modifies the convective term:
The fluid mesh can move independently of the fluid particles.
0Re
1 =upuuu ),,,( txxxFxKxCxM Eulerian approach Lagrangian approach
Coupling requirementsCoupling requirements
Alenia SMJ FEM model with
2,815 nodes
Alenia SMJ CFD N-S hybrid grid with 1.3 mio
nodes and 4.7 mio elements (cells)
XY
Z
Aerodynamic mesh12437 nodes
Structural mesh212 nodes
Pressure forces interpolation
Coupling toolsCoupling toolsThe meshes are non-conforming•different discretization•different shape (whole wing/torsion box only
Non-conservative interpolation
Conservative interpolation
Coupling toolsCoupling tools
• MpCCi (Mesh-based parallel Code Coupling Interface), developed at the Fraunhofer Institute SCAI
• AE Modules, developed in the framework of TAURUS
• In-house tools, based on bucket search algorithm
AE Modules by EADS and in-house modules perform better in the cases, when only torsion box of the wing was modelled on the structural side.
Newmark direct integration method
[M] x’’ (t) + [D] x’ (t) + [K] x (t) = f (x, x’, x’’, t)
xi+1 = xi + t xi‘ + t2/2 xi‘‘
xi+1‘‘ = ( [M] + t/2 [D] ) -1 { f i+1 - [K] x i+1 - [D] ( xi‘ + t/2 xi‘‘ ) }
xi+1‘ = xi‘ + t/2 ( xi‘‘ + xi+1‘‘ )
NEWMARK explicit scheme
with = 0 and = 0.5
Inertial Damping Elastic Aerodynamic forces forces forces forces
Structural forces
Integration in time in CFD (or CSM) codexi+1 = xi + t xi‘ + t2 [ ( 1/2 - ) xi‘‘ + xi+1‘‘ ]
xi+1‘ = xi ‘ + t [ ( 1 - ) xi‘‘ + xi+1‘‘ ]
Dynamic Coupling: time integrationDynamic Coupling: time integration
General aeroelastic equations of motion :
Fluid mesh deformationFluid mesh deformation
• All edges of tetrahedra are replaced with springs (torsional, semi-torsional, ortho-semi-torsional, ball-vertex, etc.)
• The stiffness km of each spring may be constant, or related to element size or distance from boundary
• Another possibilities:Elastic material analogy, Volume Splines
(Radial Basis Functions), Transfinite Interpolation
• Spring analogy
• Shephard interpolation(Inverse Distance Weighting) Based on the distances di between a given mesh node and boundary nodes:
I22 and I23 airplanesfrom: wikimedia
Flutter analysis for I-23 airplaneFlutter analysis for I-23 airplaneMach number: M = 0.166, 0.2, 0.3, 044Atmospheric pressure: P = 0.1 MPa Reynolds number: Re = 2e+6Angle of attack: α = 0.026Time step: dt = 0.01 sSingular input function: Fz = 2000 N in time t = 0.01 s
Flutter analysis for I-23 airplaneFlutter analysis for I-23 airplane
Simulation: flutter at Ma=0.44
Experiment: flutter at Ma=0.41
Time history for displacement and rotation Time history for displacement and rotation in control node on wingin control node on wing
Flutter Laboratory IoA and PUT
experiment and computations
• Scale :
• Length - 1:4
• Strouhal number 1:1
Experimentalconfigurations
• 5 cases – mass added
- 50 grams on the wing's tip
- 20 grams in the middle of ailerons
- 30 grams on vertical stabilizer + 20 grams on tail plane aileron
- 20 grams on horizontal stabilizer
- configuration
FSI - test case 1
#1 - 50 grams on the wing's tip
Results of test case 1
#1 - 50 grams on the wing's tip
Low-Dimensional FSI algorithmLow-Dimensional FSI algorithm
Flow ROM
Structural code
Interpolation
Pressure
Forces on structure
Structure displacements and velocities
Deformed CFD mesh, velocities
CFD mesh deformation
Interpolation
t=t+t
convergence
yes
no
Amplitudes of „mesh” modes
Reduced Order Model of the flowReduced Order Model of the flow
N
iii
N uauu1
0][
kj
N
j
N
kijkj
N
jiji aaqala
0 00Re
1
0Re
1 =upuuu
1. GALERKIN APROXIMATION
2. GALERKIN PROJECTION
3. GALERKIN SYSTEM
0, ][ N
i uu
Navier-Stokes Equations
Projection of convective termProjection of convective term
G
ii
N
i
GGgrid uau
1
kGji
G uuuqijk
,
0)(Re
1 =upuuuu grid
1. DECOMPOSITION
2. GALERKIN PROJECTION
GN
jk
Gj
N
k
Gijk
N
jkj
N
kijk
gridiigridi
aaqaaq
uuuuuuuuuu
1 00 0
,,)(,
Arbitrary Lagrangian-Eulerian Approach
ROM for a moving boundaryROM for a moving boundaryDNS with ALE
2-D, viscous, incompressible flow = 15˚, Re = 100 (related to chord length)displacement of the boundary andmesh velocity:
where: T = 5s and Y1 = 1/4 of chord length
NACA-0012 AIRFOIL
Inverse Distance Weighted
First 8 POD modes: 99.96% of TKE
ROM for a moving boundaryROM for a moving boundary
ALE ROM vs DNSEulerian ROM vs ref. DNS
Dumping of oscillationtypical for sub-critical Re
The first two modes
AE mode basisAE mode basis
• Test-case: bending and pitching LANN wing
• Fluid answer to separated, modal deformations (varying amplitudes)
• Fluid answer to combined deformation
LANN wing structure
Pressure field and structure deformation
(high-dimensional AE)
for a flow induced by structure deformations
ROM AE: ROM AE: CFD → CSM CouplingCFD → CSM Coupling
• High-dimensional fluid forces retrived from the Galerkin Approximation
Neighbour search:ae_modules f_cfd2csd
Pressure interpolation: ae_modules b_cfd2csd
where si (i=1..15) is a distance from CFD node to closest CSM elements
• We preserve full-dimensional CSM and existing AE coupling tools to interpolate fluid forces on coupling - “wet” - surface;
(similarly to Demasi 2008 AIAA)
ROM AE: ROM AE: CSM → CFDCSM → CFDCoupling and CFD mesh deformationCoupling and CFD mesh deformation
• Linear CSM: deformation decomposed onto mesh modes; Galerkin Projection of ALE term is performed during the construction of GM
• Solution of resulting Galerkin System requires only the input of mesh mode amplitudes
• Time stepping: the mesh deformation/velocity calculated for next time step with the Newmark scheme
G
ii
N
i
GGgrid uau
1
kGji
G uuuqijk
,
ui+1 = ui + t ui‘ + t2 [ ( 1/2 - ) ui‘‘ + ui+1‘‘ ]
ui+1‘ = ui ‘ + t [ ( 1 - ) ui‘‘ + ui+1‘‘ ]
Mode interpolation Mode interpolation Parametrized Mode Basis (Reynolds number here)
steady solution
time-avg. solution
shift-mode
OPERATING CONDITIONS II
=0.50
=0.25
=0.75
POD modes
Eigen-modes
OPERATING CONDITIONS I
M. Morzynski & al.. Notes on Numerical Fluid Mechanics 2007
Tadmor & al. CISM Book 2011 -fast transients
Results and Conclusions Advanced platform for FSI ROMs testing open for common
research Computations ongoing
Treatment of CSM - evolution Linear CSM model Non-linear CSM model Tadmor & al. CISM Book 2011 – control capable AE model
Mode parametrization
CFD/CSMCFD/CSM
Coupling Canonical computational domain
Coupling in Low-Dimensional Coupling in Low-Dimensional AEAE
• Full-dimensional CSM
• Modal CSM
• The algorithm essentially the same as the high-dimensional one
• Interpolation of pressures/forces required• Interpolation of boundary displacements and mesh
deformation required: dependent on the chosen approach of boundary motion modelling (acceleration forces / actuation modes / Lagrangian-Eulerian / …) – Tadmor et al., CISM book
• The aerodynamic forces on the surface of structure might be related to the POD (or any other) decomposition of pressure field
• Thus: interpolation of pressures/forces not required• Mesh deformation (velocity) modes / actuation modes
calculated in relation to the eigenmodes of the structure• The amplitudes of „mesh” modes calculated from the
amplitudes of eigenmodes of structure (time integration?)
• Thus: interpolation of boundary displacements and mesh deformation not required