Optimisationfor CFD. ANSYS R14 Fluids Update Seminar. Milton Park, February 16 th, 2012 Sheffield, February 29 th, 2012 Aberdeen, March 8 th, 2012

Transcription

1 Optimisationfor CFD ANSYS R14 Fluids Update Seminar David Mann, ANSYS UK Ltd. Milton Park, February 16 th, 2012 Sheffield, February 29 th, 2012 Aberdeen, March 8 th,

2 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 2

3 Introduction I have run my analysis, but.. What happens if I increase/reduce the flow rate? What do I need to adjust to unify the flow distribution? How should the geometry change to maximise heat rejection? What can be to done to mix out the species earlier? Which parameters have greatest effect on the pressure drop? What actions can I take to prevent the coolant from boiling? How do I optimisemy design. 3

4 Introduction Optimisationrefers to seeking the best possible design point within the design space Optimisation is a three-fold problem Formulation of appropriate parameterisation Parametric geometry using CAD tool or Design Modeler Mesh morpher to define parametric mesh deformations Selection of objective function What are we seeking to maximiseor minimise Selection of robust optimiser Gradient based optimisation method (Adjoint Solver) Direct search based optimisation method (e.g. Simplex Method) Statistical Optimisation method (ANSYS DesignXplorer) 4

5 ANSYS provides a comprehensive set of tools for optimisation Manual part mesh replacement Design of Experiments Response Surfaces Goal Seek Mesh Morphing Introduction Adjoint Solutions Optimisation can be based around parametric geometry, arbitrary freeform mesh deformation, or precise geometrical mesh deformation 5

6 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 6

7 Manual Optimisation Replace sub zones effectively as parameter for design points. New in R14. Allows automatic first order interpolation of face and cell data Allows automatic grid manipulations (face slitting, node merging, zone fusing, recreation of mesh interfaces etc) Can use apriorigrid preparation/decomposition but also works well with cavity re-meshing tool in TGrid for conformal interfaces Only requires re-meshing of sub zones (replaced part) and larger mesh can be re-used across design points Able to cope with large design changes and topology changes (with consistent zone names) 7

8 Manual Optimisation Part Swapping : Six Each Cavity different wing remesh has wing slightly zone configurations for different conformal rotation, to sub-grid be compared position transplant and AoA 8

9 Manual Optimisation Transplant of meshes using script Design 2 Design 1 Design 3 Design 4 Design 5 Design 6 9

10 Manual Optimisation Example Script for the case Replace sub grid command Path to new sub grid Repeat for N designs New fluid zone name and zone to be replaced (need not be the same as here) Interpolate face/cell data? 10

11 Manual Optimisation Design1 Design 2 Design 3 Design 4 Design 5 Design 6 11

12 Manual Optimisation Design 1 Drag=97N Design 4 Drag=141N Design 2 Drag=137N Design 5 Drag=139N Design 3 Drag=131N Design 6 Drag=173N 12

13 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 13

14 Gain Deeper Product Insights ANSYS simulation software can give you more clarity into your products and development processes Move from a single point solution to understanding the design space so simulation can guide design.??? 14 Single Point What If? Response Surface

15 Design Xplorer(DX) Workbench based optimisation tool Input and output parameters from all types of analysis can be shared with DX via WorkBench Works with all ANSYS products from ANSYS structural to EMAG to CFD, making it beneficial for multiphysics analysis 15

16 Example of DX usage Simple Diffuser To illustrate how Design Xplorercan be used to optimise a simple geometry consider the simple diffuser below:- The diffuser geometry is characterised by four input parameters This allows the diffuser s shape to be controlled by WorkBenchand Design Xplorer 16

17 Initial setup and run Current Design Point The initial run is setup and run as normal with CFD post then being used to provide output parameters This forms the current design point which can then be rerun with a different geometry simply by changing the input parameters, and the new results viewed via the output parameters 17

18 Design of Experiments (DoE) A Design of Experiments can then be used to automatically generate a set of runs which cover the design space specified by the parameters 18

19 Response Surface Results The data from the Design of Experiments runs is then used to generate a response surface from which the performance of other designs can be predicted A clear maximum pressure rise is visible in the results beyond which additional diffusion causes separation 19

20 Goal Driven Optimisation The response surface is used to predict the parameters that give the optimum design The objective function can be multi-variate, but in this case is simply chosen to maximise the pressure rise through the diffuser. Once determined the optimum design can be run to confirm the predicted results or to improve the resolution of the response surface 20

21 Confirmation Run Pressure Rise = Pa ( Pa predicted) 21

22 Design Xplorer(DX) DesignXplorer features the following studies: Design point analysis (default) -examines how the input parameters affect the output parameters by creating designs in a spreadsheet like view. Response Surface -Goal-Driven Optimization or GDO automatically change design parameters to find optimal design. -Six Sigma incorporates uncertainties of input parameters. Min-Max Search examines the entire output parameter space from a Response Surface to approximate the minimum and maximum of each output parameter. You can perform this search at any time. Parameter Correlation gives correlation data that has been used to derive sensitivities and decide if individual sensitivity values are significant or not. 22

23 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 23

24 Introduction The mesh morphing technology introduced to ANSYS FLUENT at R13 allows a single mesh to be deformed in a freeform way to achieve new designs without the need to create new geometries or meshes. Thisgives us a platform on which we can carry out design optimisation studies without the need to build a parametric model on a topologically identical mesh. 24

25 Mesh Morpher Introduction The FLUENT Mesh Morpherutilizes Bernstein Polynomials to allow smooth mesh deformations based upon movement of predefined control points. The Morpheris hooked up to some basic optimization algorithms allowing shape optimization to be carried out within FLUENT with the following benefits: Shape modification carried out quickly in parallel solver Zero file I/O requirement Quick convergence -data from previous design point can be used for subsequent design points so initial data field is close to final solution Scriptable by Text User Interface journals Works on all mesh types, i.e. hex, tet, cutcell, hybrid, poly etc. 25

26 Mesh Morpher Case Study Manual Morphing Generic F1 car (Hexcore) nose extension before 26 Two control points moved in -x

27 Mesh Morpher Case Study Manual Morphing Generic F1 car (Hexcore) nose extension after 27 Two control points moved in -x

28 The morpher deformation modes In FLUENT the user specifies a deformation region inside which the mesh is morphed and an array of control points to define the deformation Modes of deformation are specified by describing how all the control points move together, for example the sine wave deformation shown Multiple deformation modes can be specified and the relative weighting of each controlled by parameters (three deformation modes = 3 parameters) 28 A sufficient number of deformation modes will allow arbitrary shapes to be formed

29 Mesh Morpher Interface Deformation Setup In R14 we now have the ability to constrain boundaries within deformation regions! 29

30 Optimisation methods Design Xplorer Design of Experiments Internal FLUENT Simplex Optimiser Two different optimisation techniques are available when using the FLUENT morpher: Optimisation using Design of Experiments (DoE) in Design Xplorer(DX) requires script 2. Optimisation using one of the internal FLUENT Mesh MorpherOptimiser (MMO) methods such as the Simplex optimiser

31 Mesh Morpher Optimiser 31

32 Mesh Morpher Objective Functions and Definition The Objective Function is a single scalar value that the chosen optimizer method will drive towards a minimum. Typical Objective Functions Lift & drag Mass flow-rate for inlets and outlets Surface average pressures for walls/inlets/outlets Min-max absolute pressure/temperature etc. Objective Function can be defined by: User defined functions Scheme Function NEW IN R14 GUI Driven Objective Function Definition that can call FLUENT exposed parameters 32

33 Case Study 1 -Generic Sedan Drag Optimization Study effect of various vehicle shape parameters on drag force Shape parameters are defined using mesh morphing technology in ANSYS Fluent ANSYS WB is used to drive the shape parameters, create DOE & perform goal driven optimization ANSYS WB makes the process automatic Three Shape Parameters 1. Backlight angle (θ 1 ) 2. Tumble home angle (θ 2 ) 3. Windshield angle (θ 3 ) 33 Generic Sedan Model

34 Generic Sedan Baseline Design 34

35 Generic Sedan Worst Design 35

36 Generic Sedan Optimal Design 36

37 Case Study 2 Optimisation of NACA0012 The initial geometry to be optimised is the NACA0012 symmetrical 2D aerofoil section. A grid of 5 rows of 18 control points is superimposed over the mesh to facilitate the mesh morphing Moving these control points causes the mesh to morph A course tetmesh and a finer quad pave mesh were used Seek to maximise Lift to Drag ratio 37

38 Sine deformation modes applied to NACA 0012 section Mode n = sin(n.pi.x) where x is normalised between 0 and 1 from leading edge to trailing edge Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode o Mode o Mode o 38 Mode o Mode o Mode o

39 Workbench MorpherOptimisation Project Workflow Workbench and Design Xplorer are used to drive the six morpher parameters to optimise the design for lift/drag The workflow is shown below 39

40 Output parameters from CFD Post CFD Post is used to return the lift and drag from the aerofoil as Workbench output parameters A new workbench output parameter of Lift/Drag can then be derived in WB parameter manager for use in the DoE optimisation 40

41 Optimisation using Design Xplorer Data points using six morpherparameters are very noisy in their fit to the response surface, as there are always four other parameters not involved in the surface fit The response surface fit can be poor if the search area is wide, so the limits on parameters were tightened around the then best point and the DoE rerun several times to get a better fit 41

42 Optimisation using sine modes and inbuilt Simplex optimiser Convergence history using Simplex optimiser 42

43 Comparison of optimised aerofoil shapes with different optimisers Sine modes using DoE in Design Xplorer Sine modes using internal MMO simplex optimiser Parameters { , , , , , } C L /C D = , C L = , C D = Parameters { , , , , , } C L /C D = , C L = , C D = Interestingly two completely different sets of parameters were obtained giving very similar but laterally displaced aerofoil shapes with the same morpher modes The number of design points required were 3x 45 design points with DX and 148 with the MMO running the Simplex optimiser. DX required some manual refinement points. For the same C L /C D DX would have needed less. DX can spawn runs to multiple machines/cores via RSM 43

44 Comparison of DX and MMO results The two optimisation methods ended up with very similar aerofoil sections, but in each case the geometry ended up in a different y location The DX route is less prone to get stuck in a local minimum, but requires more manual fine tuning of limits Sine Modes DX Sine Modes MMO Sine Modes DX Sine Modes MMO Optimised designs translated and overlaid Optimised designs untranslated 44

45 Case Study 3 -Optimisation of a UAV wing A generic (representative, but not accurate) model of the Global Hawk UAV was downloaded from The non realistic wing was replaced with one with a realistic section and the correct planform view derived from open literature relating to this aircraft The Mesh MorpherOptimiser (MMO) tool in ANSYS Fluent was used to deform the wing section to optimise the Lift-Drag ratio 45

46 Deformation Modes Mode 1 Decrease/Increase Aft Thickness Mode 2 Decrease/Increase Stagger Mode 3 Redistribute Camber 46 Mode 4 Increase/Decrease Camber

47 The Optimised Wing Section The simplexoptimiser was used to find the combination of the four deformation modes that gave the maximum lift/drag ratio º 6º The resultant wing section has a C L /C D ratio 24.8% higher than the originalat the datum 3 degree Angle of Attack (AoA), and a wider range of AoA capability The optimised section is more aft loaded C L º 3º 3º 2º 2º 1º 1º 0º 0º -1º -1º 4º 5º 6 Optimised Section -2º -2º 0.2 Original Section C D Original PS Original SS Optimised Baseline Optimised C P Chord Baseline Optimum

48 Mesh Morpher- Conclusions The inbuilt freeform mesh morpherin Fluent provides a powerful tool for arbitrary changes in the geometry without being limited by a constrained parameterised geometry If sufficient well designed deformation modes are used with the mesh morpher, any arbitrary shape change can be achieved and true optima can be approached This mesh morpheris less suitable for cases where a high degree of control is needed, for example part of the geometry is a given shape. 48

49 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 49

50 RBF-Morph RBF Morph tool 3 rd Party Add-on 50

51 RBF-Morph Tool Objective The aim of RBF Morph is to perform fast mesh morphing using a meshindependent 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: (rbf-morph (("sol-1" amp-1) ("sol-2" amp-2)...("sol-n" amp-n))) 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 51

52 RBF-Morph Features Fully integrated within Fluent (GUI, TUI & solving stage) and Workbench Mesh-independent RBF fit used for surface mesh morphing and volume mesh smoothing Parallel support allows morphing of large grids in a short time Support for all mesh types (tetrahedral, hexahedral, hexcore, polyhedral, etc.) Ability to generate modified CAD file from morphed surface mesh Multi fit makes the Fluent case truly parametric (only 1 mesh is stored) High precision morphing : exact nodal movement and exact feature preservation. 52

53 s 53 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. N ( x ) = γ i φ ( x x i ) + h ( x ) i =1 RBF-Morph Background and Theory ( x ) = β + β x + β y + v z h 1 3 β 4 Radial Basis Function φ (r) Spline type (R n ) n r, n odd Thin plate spline (TPS n ) Multiquadric(MQ) 2 1+ r Inverse multiquadric (IMQ) 1 Inverse quadratic (IQ) r n log r, n even 1+r r Gaussian (GS) 2 e r x = s vy = s vz = s x y z N x ( x) = γ φ( x x ) i= 1 N y ( x) = γ φ( x x ) i= 1 N z ( x) = γ φ( x x ) i= 1 i i i k k k i i i x + β 1 y + β 1 2 x x x + β x+ β y+ β z y y y + β x+ β y+ β z z z z z + β + β x+ β y+ β z

54 RBF-Morph How it Works : 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. 54

55 RBF-Morph Solid body motion and exact deformation The main differentiator between RBF-Morph and the inbuilt morpheris that RBF-Morph allows the mesh to be deformed to give precise geometry changes, such as solid body motion. The inbuilt morpheris designed for arbitrary shape change with little constraint. RBF-Morph is a useful alternative to parameterising the geometry as the mesh does not need to be recreated. 55

56 RBF-Morph Industrial Applications 56

57 Motorbike driver height and position The original motorbike model is parameterized to investigate the effect of driver height and position: 1. Changing of driver height [-5 cm, 0 cm, 5 cm]; 2. Changing of driver position acting on the hunching angle [0,7.5,15 ]; 57

58 Set up of RBF Morph The morphed action is limited in the box region domain 1. The motion of the surfaces inside the encapsulation domain is imposed to the points on the windshield (fixed), the fairing (fixed) and the helmet (moving). Driver height is changed moving the helmet Driver position is changed rotating the helmet around the ankle 58

59 Motorbike Windshield (Bricomoto, MRA) 59

60 60 Formula 1 Front Wing

61 Sails Trim (Ignazio Maria Viola, University of Newcastle) 61

62 Generic Formula 1 Front End 62

63 Generic Formula 1 Front End 63

64 Fluid Structure Interaction 64

65 Turbine Blade 65

66 MIRA Reference car (MIRA ltd) 66

67 Conclusions A shape parametric CFD model can be defined using ANSYS Fluent and RBF Morph. Such parametric CFD model can be easily coupled with preferred optimization tools to steer the solution to an optimal design that can be imported in the preferred CAD platform (using STEP) Proposed approach dramatically reduces the man time required for set-up widening the CFD calculation capability M.E. Biancolini, Mesh morphing and smoothing by means of Radial Basis Functions (RBF): a practical example using Fluent and RBF Morph in Handbook of Research on Computational Science and Engineering: Theory and Practice ( 67

68 Using CFX moving mesh for optimisation The preceding mesh morphing sections have been on Fluent, but the moving mesh model in CFX can also be used as the basis of an optimisation Solid body motion and deflections can be applied and the mesh will morph to accommodate the movement Multiple scenarios can then be run with one mesh 68

69 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 69

70 The Adjoint Solver The Adjointsolver is anadditional solver within Fluent that is run after the conventional solution is converged The Adjointsolver is used to assess the sensitivity of output parameters such as lift, drag or pressure drop to inputparameters such as the geometrical shape without the need for additional runs The output from the Adjoint solver is typically a surface vector field that illustrates how the geometry would need to change to increase or decrease the output parameter of interest Assuch it forms a very useful tool in an optimisation study and can be linked to the mesh morpher Drag sensitivity for NACA

71 Adjoint Solver Key Ideas - Fundamentals High-level system view of a conventional flow solver Inputs Boundary mesh Interior mesh Material properties Boundary condition 1 Flow angle Inlet velocity FLOW SOLVER Outputs Field data Contour plots Vector plots xy-plots Scalar values Lift Drag Total pressure drop 71

72 Adjoint Solver Fundamentals HOW ARE CHANGES TO KEY OUTPUTS DEPENDENT ON CHANGES TO THE INPUTS? Inputs Boundary mesh Interior mesh Material properties Boundary condition 1 Flow angle Inlet velocity? ADJOINT SOLVER Outputs Field data Contour plots Vector plots xy-plots Scalar values Lift Drag Total pressure drop 72

73 Adjoint Solver Key Ideas The Adjointsolver can be used to compute the derivative of a chosen observation of engineering interest with respect to all the input data for the system. Solving an adjointproblem is not trivial about as much effort as a flow solution. The adjointsolution provides guidance on the optimal adjustment that will improve a system s performance. An adjointsolution can be used to estimate the effect of a change prior to actually making the change. Shape sensitivity data can be combined with mesh morphing to guide smooth mesh deformations. An adjointsolution can be used as part of a gradient-based optimization algorithm. 73

74 Adjoint Solver Mesh Morphing Completing the design cycle Mesh Morphing Sensitivity of lift to surface shape Use Bernstein polynomial-based morphing scheme Adjoint to deformation operation Surface shape sensitivity becomes control point sensitivity Benefit of this approach is two-fold Smoothsthe surfacesensitivity field Provides a smooth interior mesh deformation Select portions of the geometry to be modified Flow 74

75 Adjoint Solver Mesh Morphing Constrained motion Some walls within the control volume may be constrained not to move. A minimal adjustment is made to the control-point sensitivity field so that deformation of the wall is eliminated. Cast as a least-squares problem. Actual change 3.1 P = Total improvement of 8% 75

76 Adjoint Solver Current Functionality ANSYS-Fluent flow solver has very broad scope Adjoint is configured to compute solutions based on some assumptions Steady, incompressible, laminar flow. Steady, incompressible, turbulent flow with standard wall functions. First-order discretization in space. Frozen turbulence. The primary flow solution does NOT need to be run with these restrictions Strong evidence that these assumptions do not undermine the utility of the adjoint solution data for engineering purposes. Fully parallelized. Gradient algorithm for shape modification Mesh morphing using control points. Adjoint-based solution adaption 76

77 Adjoint Solver Example Test Cases S809 HAWT Blade Objective Maximise Lift/Drag Ratio 77

78 Adjoint Solver Example Test Cases S809 HAWT Blade The best lift/drag ratio is observed when setting observable for lift, and using a scale factor of 2.5. The new shape provides about 30% more lift than the original geometry Highest lift/drag ratio achieved 78

79 Adjoint Solver Example Test Cases Internal ducting U bend 100 Base design p tot [Pa] End design Run [-]

80 Adjoint Solver Example Test Cases External Aero (Small car) Surface map of the drag sensitivity to shape changes Surface map of the drag sensitivity to shape changes 80 Surface map of the drag sensitivity to shape changes

81 Adjoint Solver Example Test Cases External Aero (Full Generic Race Car) Increase the downforce on the vehicle Adjoint result shows regions of highest sensitivity of downforce to shape 81

82 Adjoint Solver Example Test Cases External Aero (Full Generic Race Car) Front Wing changes Rear Wing Changes Downforce(N) Geometry Predicted Result Original Modified Downforce(N) Geometry Predicted Result Original Modified

83 Adjoint Solver Summary The Adjoint solution is carried out as an addition to the primary flow solution The Adjointsolver solves the NavierStokes equations recast as derivatives of output flow variables of interest such as drag, lift or pressure drop As the equations are rewritten only a finite number of predefined flow variables of interest are available The output from the Adjointis a field of the sensitivity of inputs such as the geometry and boundary conditions to the output variables of interest. This can form the basis for optimising these inputs. 83

84 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 84

85 The Remote Solve Manager (RSM) RSM has a three tiered architecture Client Solver Manager Compute Server 85

86 A queue can be set up on the solver manager for multiple compute cores which may be available on the network All design points are then submitted to this queue Design points are run as compute cores become available WB session can be detached and reattached Results picked up by WB when complete The Remote Solve Manager (RSM) 86

87 Workbench RSM Terminology There are RSM controls at both the solution level, e.g. FLUENT or CFX, to control how jobs are run, and also at the parameter set (global) level giving good control of resource utilisation Solution Component properties Parameter Set properties 87

88 RSM Summary Optimisation can create a large number of design points that would be slow to run sequentially in serial. In R14 the Remote Solve Manager provides a way of controlling compute resource allocation for CFD design point/ optimisation studies to allow multiple design points to be submitted to a queue of available compute nodes. 88

89 Agenda Optimisation Tools for CFD Introduction Manual Optimisation and Scripting Design Xplorer(DX) Mesh Morpher or Shape Optimiser RBF-Morph AdjointSolver Remote Solve Manager (RSM) Summary 89

90 Summary Where should I use these tools? Manual Optimisation and Scripting I want high level control on the meshes to be generated and I am prepared to script the process Design Xplorer My optimisation may include a wider process or workflow in Workbench with input and output parameters coming from multiple simulations, and/or I am working with parametric geometry. My design spacemayhavelocalminimathatiwish toavoid.ihave agood ideaofnatureandlimitsofthedesignspaceandwanttoenforcestrict control on any changes. MMO I am interested arbitrary shape optimisation where geometry parameterisation may limit finding a true optimum. Constraints and prescribed deformations are secondary concerns. No additional cost. Can interface with Workbench but scripts needed. 90

91 Where should I use these tools? RBF-Morph I want high level control on the morphed geometry shape, for example can do solid body transformations and modify geometry in a manner consistent with using parameterised geometry. Highly beneficial where remeshing a parametric geometry is costly. Morphed modifications can be fed back to CAD. Additional cost. Adjoint Solver Summary I am interested in finding where I could potentially modify my geometry to make small improvements. Which areas are most contributing to lift, drag, pressure drop Limitations on models and objective functions. No additional cost. No interaction with Workbench, solver only. Geometry deformation is free form as with the MMO. 91

92 Conclusions ANSYS can provide tools to drive your design to optimise for chosen parameters This can be done with geometric parameterisation, mesh replacement or morphing technologies Some tools can provide predicted off design performance without running multiple design points The Remote Solve Manager allows the efficient handling of large numbers of design points We are continually developing these new technologies to be more efficient We want to listen to your feedback to improve the usefulness of the tools Increase your ROI using the ANSYS optimisation tools 92