A novel approach is presented to perform nonlinear aeroelastic steady-state simulations of highly flexible structures such as fix wings and rotating blades. The methodology has been developed in a specific OpenFSI service available in MSC Nastran SOL 400 that
includes follower forces and incremental loads features to allow for accurate nonlinear steady Fluid-Structure Interaction analysis. The new service, called HSA.OpenFSI, based on the HSA Toolkit, has been implemented to couple MSC Nastran to a CFD solver. Six DOF spline technology is used to interpolate data between the aerodynamic and structural grids. A new approach has been designed to improve the efficiency of this technology that allows to considerably reduce the time needed to create the interpolation spline matrix and the disk space to store it. A Nastran-based FEM algorithm has been developed to take care of the fluid domain deformation. The proposed approach has been validated on a flap in a duct model, where transient steady-state results are available from other approaches, and then preliminary results on a proprotor two-blade model of Micro Air Vehicles MAV from ISAE will be presented.
UNIT-V FMM.HYDRAULIC TURBINE - Construction and working
Nonlinear Aeroelastic Steady Simulation Applied to Highly Flexible Blades for MAV
1. Nonlinear aeroelastic steady simulation applied to
highly flexible blades for MAV
Presented by: Fausto Gill Di Vincenzo
F. G. Di Vincenzo 1, M. Linari 1, Dr. F. Mohdzawawi 2, and Dr. J. Morlier 3
1 MSC Software, 2 Universiti Teknologi Malaysi, 3 Institut Clément Ader
International Forum on Aeroelasticity and Structural Dynamics
IFASD 2017 25-28 June 2017, Como - Italy
2. 2MSC Software Confidential
Agenda
• Motivation and objective
• Proposed approach
• Steady-state nonlinear FSI workflow
• Sub-cycIing coupling strategy - incremental loads and follower forces
• Aero-structure grid interpolation - performance improvement
• Fluid domain deformation
• Validation case
• Flap in a duct
• Application case
• Graupner 8” × 6” propeller MAV model
• Concluding remarks
4. 4MSC Software Confidential
Motivation and objective
• High-fidelity transient FSI simulations are computationally highly intensive and time
consuming
• Third tools needed to perform the data interpolation between CFD and FEM solvers
and fluid domain deformation
• Important disk space and memory requirements to create and store the aero-structure
interpolation matrices
• Aeroelastic models are often simplified FEM model
• Account for geometric and material nonlinearities
Accurate and efficient nonlinear steady-state FSI simulation for highly flexible structures
• Nastran-based grid interpolation between CFD and FEM solvers
• FEM-based algorithm to deform the fluid domain
Improve the performances and reduce memory requirements
Use any FEM element type: beam, shell, solid, bunch of grids, SE
Follower forces and incremental loads
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Proposed approach – Steady-state coupling
The proposed HSA.OpenFSI service provides an API interface between MSC Nastran SOL 400 and the SC/Tetra solver
to allow for steady-state nonlinear fluid-structure interaction simulations (transient is also available)
• Fluid domain deformation performed by the FEM solver
• Data interpolation is done on nodes that belong to the so-called wetted surfaces. FEM and CFD wetted surfaces are defined
independently and can differ both in shape and discretization. Any FEM element type is supported
• The FEM and CFD codes execute simultaneously (staggered coupling) and exchange information through the interface during the
simulation, providing a tight coupling between the two codes
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Steady-state FSI workflow
Staggered transient FSI coupling Staggered steady-state FSI coupling
• FEM and CFD solvers exchange data at each time step (and within every
time step)
• Computationally highly intensive
• Time consuming
FEM and CFD solvers exchange data at a specific number of main exchanges here called number of loads
• A few CFD-FEM exchanges are needed to for an aeroelastic system to
converge to the steady-state configuration
• Transient simulations can be concatenated to the nonlinear static analysis:
flutter, gust, normal modes..
Transient approach - main disadvantages Steady-state approach - main advantages
VS
• The FSI simulation ends after N exchanges or earlier when one of the displacement/load convergence criterions is satisfied
• Load convergence criterion: Displacement convergence criterion:
• The first load typically causes the most deformation of the structure
• The load that does not change within each load
Limitations
Acceptable for linear (or slightly nonlinear) structures
The structure could stretch
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• The CFD solution is recomputed at each increment
• The FEM solver receives the CFD load incrementally as an increasing
percentage of the updated aero load recomputed at each
increment
•
!"#$%&#
'
∗
Sub-cycling coupling strategy
• Nk iterations are computed within every load exchange K
• The FEM solver receives the CFD load incrementally as an
increasing percentage of the aero load calculated at
the beginning of the exchange
•
'
∗
• The fluid domain is updated at every increment
Incremental loads Follower forces
Sub-cycling strategy Incremental loads Follower forces
Help and speed up the convergence of the aeroelastic system and improve the accuracy
Applied to highly nonlinear structures
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Aero-structure grid interpolation
6DOF Spline technology, SPLINE6 (3D finite surface spline) and SPLINE7 (3D finite beam spline), for structure to
structure load mapping and for aero to structure load/displacement mapping (SOL 144)
CFD wetted surface (K-SET) FEM wetted surface (G-SET)
SPLINE
• )* +* )
+*
, -
+*
, -
+*
Moments
Forces
Aero load - .* Structural load - .
SOL 144
.*
.
• . +*
, -
.*
Transformation displacement spline matrix FEM -> CFD
Transformation load spline matrix CFD -> FEM
+*
) )*
Ensure energy equilibrium
Regular and smooth aero deformation
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Aero-structure grid interpolation - performances
SOL 144 is called at the beginning of the FSI simulation to create the spline interpolation matrices and +*
, -
-
+* are put in memory in the service
SOL 144 performances are really important
Reduce disk space and memory requirement as much as possible
New spline approach :
• Multiple smaller splines that ensure the continuity over the boundaries
• Drastically reduces the simulation run time of SOL 144
• Drastically reduces the memory requirement
• Improve the accuracy of the load transfer while enhancing the performances
• CPU time was reduced to
40 seconds – 48X speed up
• Spline matrix from 2.2 Gb
to 0.48 Gb. From a full
dense to a sparse matrix
40 s
32 m
• The aerodynamic load
pattern is accurately
reproduced on the
structural model
+*
, -.* .
1 2 4 8 17 39 1 2 4 8 17 39
0.48
2.2
• 60000 CFD wet nodes
• 40 FEM wet nodes
SOL 144
+*
, - +*
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Fluid domain deformation
SC/Tetra does not have a dynamic mesh tool to perform a fluid domain deformation during a fluid-structure
interaction simulation
A linear Nastran-Based Interpolation Tool (NBIT) has been designed and incorporated in the service to carry out this task
SC/Terta CFD domain
./012
1. The fluid domain or a subdomain of it that encapsulates the deformable walls is transformed into a linear Nastran FEM model ./012
UDF
(CTRIAR)
34 (SPC1/SPCD)
• Boundary nodes not allowed to
move out-of-plane
• Dummy enforced displacement
34 conditions are applied on
the nodes of the wetted surfaces
Boundary constraints (SPC1)
Normal
rotational
(drilling)
DOF
Nastran format
(SOLID)
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34 (SPC1/SPCD)
Fluid domain deformation
2. A linear static solution SOL 101 is performed with a DMAP alter
Boundary constraints (SPC1)
SOL 101
DMAP ALTER
567
• 86 567 34 567 --> Partitioned stiffness matrix to reduce the static load vector 86 on free nodes (where no SPC1 and SPCD
condition are applied) from the enforced displacement vector 34
5''
Stiffness matrix in g-set 5
Stiffness matrix in n-set after
mpc reduction
5Stiffness matrix in l-set
“left over” after the r-set is removed
34 )* +* )
• 5 9 86 --> Sparse lower triangular factor/diagonal from 5
86 567 +* )
9 --> Displacement of free nodes of the fluid domian
9
The problem can be rewritten -
9 86
Efficient way to store the matrix
Solved with a Forward Backward Substitution
1. 3 567 +* ) 2. -
9 3 9
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Fluid domain deformation
Looking at one CFD-FEM exchange..
+*
, -
.* .:
CFD simulation SC/Tetra
UDF
): )*
SOL 400
NBIT 9
SOL 400
+*
86 567 )*
3 86
-
9 3
CFD
UDF
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Validation case
Elastic flap in a duct
Static pressure on internal domain and flap
Aerodynamic load .* Structural load .
+*
, -
SOL 144
• A SOL 144 is performed to check at the quality of the spline matrix
• Converged CFD steady-state before the FSI
Residuals
• Hexa solid elements
• Clamped on the top
• Inlet ;< 8>/
• Pressure outlet = 0
• No slip walls
Aerodynamic load .* Structural load .
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Validation case
5 CFD-FEM exchanges, 5 increments per load, incremental loads and follower forces
Displacement convergence - Node 1282
L1
L2 L3 L4 L5
Sub-cycling within the first load
Load convergence - Node 641
Steady-state and aerodynamic load
At the end of the first exchange the aeroelastic system has almost converged
The aerodynamic load stabilizes after a
few iterations as the displacement does
-0.494030E-1
The simulation takes about 11 minutes to
get the steady-state configuration
Steady-state FSI
4 min 11 min
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Validation case
Follower forces effect on the load exchange
With follower forces
Without follower forces
• The aerodynamic load follows the structure as it deforms
• The structural load updates both magnitude and direction because the fluid domain is updated and solution recomputed at every
iteration
Contrary, the aerodynamic load on the structure would keep the same direction without employing follower forces
20. 20MSC Software Confidential
Validation case – Steady-state vs transient
Time step of 0.00025s fixed for both FEM and CFD solvers
Simulation time of 0.2s
CFD static pressureTip displacement - Node 1282
Explicit tranisnet FSI simulations
• CSS zero displacement predictor order scheme
• CSS first displacement predictor order scheme )@ A
)@ B 0.5ΔG ∗ ;̅
• CSS second displacement predictor order scheme )@ A
)@ B 1.0ΔG ∗ ;̅ B 0.5ΔGJ;̅ ;̅ K ;̅ +̿* ;̅
Transient FSI
The steady-state approach is in good agreement with the transient simulation
Simulation run time reduced by a factor of 7 (factor of 19)
Tip displacement - Node 1282
The steady-state approach is in good agreement with other approaches Tip displacement between-0.46E-2m and -0.49E-2m
22. 22MSC Software Confidential
Application case
Graupner 8” × 6” propeller MAV model
• 3D to 1D beam coupling – lagrangian
formulation
• Ensure the energy equilibrium
Aerodynamic load .* Structural load .
+*
, -
Main challenges:
• 232855 CFD wet points • 102 FEM wet points
~ 8.7 cm
• Highly flexible blades
23. 23MSC Software Confidential
Application case
Steady-state FSI simulation
20 splines 80 splines
FEM Steady-state deformation CFD Steady-state deformation and aero load
-0.0193m
1 20 80 200 308 1 20 80 200 308
Both spanwise and spinewise/chordwise patches have been tested
At the end of the 3rd exchange the aeroelastic system has
already converged to the steady-state
308 splines
+ static loading condition due to angular velocity
• ~ 150X speed up • ~ 98 % space saved
25. 25MSC Software Confidential
Concluding remarks
• A high-fidelity nonlinear steady-state FSI coupling has been developed
• Applied to higly flexible structures – fix wings and rotating blades
• Incremental loads and follower forces features
• FEM-based fluid domain deformation tool
• Aero-structure grid interpolation efficiency has been improved
• The proposed approached has been validated on a canonical model
• The proposed approached has been applied to a prototor MAV from ISAE
Application to a full scale model is being investigated (NASA CRM)
Use of HPC configuration
Extend the coupling to CFD polymesh
Step forward