An advanced RBF Morph application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model and Comparison to Experimental Data

Transcription

1 An advanced RBF Morph application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model and Comparison to Experimental Data Dr. Marco Evangelos Biancolini Tor Vergata University, Rome, Italy Dr. Ubaldo Cella Piaggio Aero Industries, Naples, Italy

2 Introduction Research partners Problem definition Goals Research path RBF Morph tool presentation Morphing & Smoothing The Aim of RBF Morph RBF Morph Features Background How It Works Outline Industrial Application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model and Comparison to Experimental Data MathCAD feasibility study General algorithm for deforming CFD model according to FEM solution Strategy used for loading the FEM model according to CFD solution Problem definition Morphing Set Up Results

3 Research Partners PHT Research Department Flight Technologies and Aerodynamics Structures and advanced materials Preliminary Design Mechanical Engineering Department Structural Mechanics Machines, fluids and combustion Fluid Structure Interaction

4 Problem definition CFD calculations are currently performed considering the undeformed aircraft configuration A procedure for evaluating the extent of structural deformation mapping CFD results onto FEM model allows to evaluate in advance the extent of such deformation When important effect are observed (wing tip deformation and rotation) the CFD model should be updated to the deformed configuration A tool for CFD model updating is currently missing

5 Goals Define a mesh updating procedure that allows to perform CFD calculation on the deformed model Automate information exchanging between FEM and CFD models Preserve the baseline model (i.e. FEM and CFD models has to be generated starting from the same CAD model of the undeformed design) Integrate the procedure in the design loop

6 Research Path A partnership was born to transfer the expertise on FSI and mesh morphing on a industrial application A specific industrial case has been defined to evaluate if the FSI method tested in different fields was suitable for aircraft design The tools has been defined CFD++ for flow solution MSC/Nastran for structural calulations MSC/Patran to map flow solution onto FEM model RBF Morph for update CFD mesh The problem has been successfully solved (less than one month!)

7 RBF Morph tool presentation Morphing & Smoothing The Aim of RBF Morph RBF Morph Features Background How It Works

8 Morphing & Smoothing A mesh morpher is a tool capable to perform mesh modifications, in order to achieve arbitrary shape changes and related volume smoothing, without changing the mesh topology. In general a morphing operation can introduce a reduction of the mesh quality A good morpher has to minimize this effect, and maximize the possible shape modifications. If mesh quality is well preserved, then using the same mesh structure it s a clear benefit.

9 The Aim of RBF Morph The aim of RBF Morph is to perform fast mesh morphing using a mesh-independent approach based on state-of-the-art RBF (Radial Basis Functions) techniques. The use of RBF Morph allows the CFD user to perform shape modifications, compatible with the mesh topology, directly in the solving stage, just adding a single command line in the input file The final goal is to perform parametric studies of component shapes and positions typical of the fluid-dynamic design like: Design Developments Multi-configuration studies Sensitivity Studies DOE (Design Of Experiment) Optimization (rbf-morph (("sol-1" amp-1) ("sol-2" amp-2)...("sol-n" amp-n)))

10 RBF Morph Features Add on fully integrated within Fluent (GUI, TUI & solving stage) Mesh-independent RBF fit used for surface mesh morphing and volume mesh smoothing Parallel calculation allows to morph large size models (many millions of cells) in a short time Management of every kind of mesh element type (tetrahedral, hexahedral, polyhedral, etc.) Support of the CAD re-design of the morphed surfaces Multi fit makes the Fluent case truly parametric (only 1 mesh is stored) Precision: exact nodal movement and exact feature preservation.

11 New upcoming RBF Morph features RBF allows to exactly prescribe surfaces movements, this opens several opportunities, among them: Target surfaces (STL). The new shape can be directly defined in the CAD, meshed and used as a morphing target thanks to the RBF algorithm that allows to project a mesh onto another (non conformal) one. FEM deformed shape (static, modal). The structural solution obtained on the (usually) non conformal FEM mesh is used to generate the morphing field applied to the CFD mesh. For complex shapes an advanced two steps approach is available for mapping FEM property IDs onto CFD threads IDs.

12 Some investigated applications F1 car aerodynamics shape optimisation of wings and deflectors wheel steering including tyre deformation effect of adjustable surfaces Tuning of a motorbike windshield deflector shape and set-up driver size and position Shape optimisation of an air-box air flow balancing max volumetric efficiency More examples on the web:

13 Background: RBF Theory A system of radial functions is used to fit a solution for the mesh movement/morphing, from a list of source points and their displacements. This approach is valid for both surface shape changes and volume mesh smoothing. The RBF problem definition does not depend on the mesh Radial Basis Function interpolation is used to derive the displacement in any location in the space, so it is also available in every grid node. An interpolation function composed by a radial basis and a polynomial is defined. s N x x x hx i1 i i x h 1x 3 y 4z

14 Background: RBF Theory A radial basis fit exists if desired values are matched at source points with a null poly contribution The fit problem is associated with the solution of a linear system M is the interpolation matrix P is the constraint matrix g are the scalar values prescribed at source points and are the fitting coefficients N i k i k k i i i q N i g s x x x 0 g β γ 0 P P M T N j i M j k i k ij 1 x x N N N k k k k k k k k k z y x z y x z y x P

15 Background: RBF Theory The radial function can be fully or compactly supported. The biharmonic kernel fully supported gives the best results for smoothing. For the smoothing problem each component of the displacement prescribed at the source points is interpolated as a single scalar field. Radial Basis Function (r) Spline type (R n ) n r, n odd Thin plate spline (TPS n ) Multiquadric(MQ) 2 1 r Inverse multiquadric (IMQ) 1 v v v Inverse quadratic (IQ) r n log r, n even 1 r r Gaussian (GS) 2 e r x y z s s y s x z N x x x x i1 N y x x x i1 N z x x x i1 i i i k k k i i i x 1 y 1 z 1 2 x x x x y z 2 y y x 2 y y z z z z x y z

16 Background: accelerating the solver The evaluation of RBF at a point has a cost of order N The fit has a cost of order N 3 for a direct fit (full populated matrix); this limit to ~ the number of source points that can be used in a practical problem Using an iterative solver (with a good pre-conditioner) the fit has a cost of order N 2 ; the number of points can be increased up to ~ Using also space partitioning to accelerate fit and evaluation the number of points can be increased up to ~ The method can be further accelerated using fast preconditioner building and FMM RBF evaluation

17 Background: solver performances escalation RBF centers FIT 120 minutes Jan seconds Jan 2010 Largest fit minutes Largest model morphed cells Fit and Morph a cells model using RBF centers within 15 minutes Front wing flap rotation up to +/-6 (+/-8 enabling Fluent remeshing) #points 2010 (Minutes) 2008 (Minutes) (1s) (5s) (44s) Not registered Not registered Not registered Not registered

18 How it Works: the work-flow RBF Morph basically requires three different steps: Step 1 [SERIAL] setup and definition of the problem (source points and displacements). Step 2 [SERIAL] fitting of the RBF system. Step 3 [SERIAL or PARALLEL] morphing of the surface and volume mesh (available also in the CFD solution stage).

19 How it Works: the problem setup The problem must describe correctly the desired changes and must preserve exactly the fixed part of the mesh. The prescription of the source points and their displacements fully defines the RBF Morph problem. The problem is mesh-independent, and could be defined using grid nodes as well as arbitrary point locations. Each problem and its fit define a mesh modifier or a shape parameter.

20 How it Works: the interface One of the key aspects of RBF Morph, in respect to FLUENT integration, is related to the ability of extracting information from the FLUENT mesh and to the user interface GUI

21 Industrial Application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model Outline MathCAD feasibility study General algorithm for deforming CFD model according to FEM solution Strategy used for loading the FEM model according to CFD solution Problem definition Morphing Set Up Results

22 MathCAD implementation A first MathCAD implementation has been considered using a small CFD model (this is the standard research path we use to add a new algorithm) Tecplot and Nastran file format used to exchange information RBF proven to work properly for CFD mesh updating using FEM results (as expected considering that RBF for mesh smoothing are the core of RBF Morph software) RBF proven to work properly for mapping CFD pressures onto the FEM model PressureQUAD CentroidQUAD for for ie xc for ie 1rows( CQUAD) p s ie RBF CentroidQUAD 1 ie in 14 IG CQUAD iein 2 xc xc xc centroid ie 4 out centroid 1rows( CQUAD) GRID IG2 GRID IG3 GRID IG4 if IsArray ( CQUAD)

23 CFD mesh updating strategy Set-up 1: FEM results written in Nastran format using two files, the Nastran data deck (*.bdf) and the Nastran punch file (*.pch), containing the mesh and nodal displacements Set-up 2: a list of rules is defined each one linking a set of FEM properties (PSHELL only) with a set of deformable threads ID; fixed threads and an (optional) bounding box are specified Step 1: for each rule a local RBF fit is calculated using FEM data (node positions and displacements) Step 2: a new fit is calculated using all the CFD points on deformable threads (with previously extrapolated values as the input), all CFD points on fixed threads limiting the action with the optional box Update: the volume mesh is smoothed using the stored fit.

24 Map CFD results onto FEM model Usually FEM mesh is coarser; the interpolation is not a trivial task. Equilibrium (i.e. resultant loads) has to be globally preserved. Several working tools already available in commercial CFD/FEM software Patran interpolation tool (used in this application) ANSYS Fluent FSI mapping (successfully tested for the simple geometry) A linear FEM model has been considered; this means that current pressure map has to be prescribed on the undeformed model (i.e. solution data obtained on the CFD updated mesh are first imported on the CFD baseline mesh and then interpolated). A new approach based on the RBF interpolation of the pressure field (tested only during the MathCAD feasibility study).

25 Problem definition Wind tunnel model of a business class aircraft in complete configuration Test campaign performed by Piaggio in the ONERA S2MA transonic facility The CFD domain (14 millions hexas) has been generated using ICEM/CFD Deformable wing ( hexas FEM) CFD solver: CFD++ FEM solver: MSC/Nastran

26 Morphing set-up FEM data are used in a first step to generate the input for all the CFD nodes on the wing Method 1 (complexity benchmark, literature approach) the movement of all surface nodes is prescribed (elastic displacements on the wing zero other where, including far field) RBF points 1337s fitting time smoothing in 5445s Method 2 (suggested approach) the action of the morpher is limited using a box RBF points 53s fitting time smoothing in 209s All morphing set-up on a quadcore Intel i Ghz with 8Gb.

27 Results The wing tip of the model, deformed under aerodynamic loads moves about 5 mm from the undeformed geometry. The aerodynamic effect due to the positive sweep angle is a pitching twist increment in the order of half degree.

28 Results (actual deformation)

29 Results Comparison of pressure solutions at different wing sections Wing deformation effect is important (as expected) in sections closer to the tip Sec. 4 Sec. 3 Sec. 2

30 Concluding remarks A quasi static FSI method has been successfully defined: A complete MathCAD implementation, tested on small size models, has proven that RBF are suitable both for pressure mapping and both for mesh updating An industrial implementation able to work on very large models has been defined exploiting the FSI feature of the mesh morphing software RBF Morph The approach has proven to be very useful for the presented industrial application demonstrating that CFD predictions accuracy can be increased accounting for wing flexibility The method is ready to be extended to full-coupled transient problems. The same mesh updating method can be used to to parameterize the CFD model with a basis of FEM computed modal shapes.

31 Thank you for your attention! Dr. Marco Evangelos Biancolini Web: