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
- 6. 6MSC Software Confidential 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
- 7. 7MSC Software Confidential 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
- 8. 8MSC Software Confidential • 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
- 10. 10MSC Software Confidential 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
- 11. 11MSC Software Confidential 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 +* , - +*
- 13. 13MSC Software Confidential 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)
- 14. 14MSC Software Confidential 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
- 15. 15MSC Software Confidential 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
- 16. Validation case
- 17. 17MSC Software Confidential 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 .
- 18. 18MSC Software Confidential 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
- 19. 19MSC Software Confidential 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
- 21. Application case
- 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