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High Fidelity Optimization Framework for Helicopter Rotors

High Fidelity Optimization Framework for Helicopter Rotors. Framework. Results. Results. Overview Design Variables Mesh Generation Case Study: Optimization Algorithms. Optimization in Hover (2 Testcases) Optimization in Forward Flight (1 Testcase) Multipoint Optimization

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High Fidelity Optimization Framework for Helicopter Rotors

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  1. High Fidelity Optimization Framework for Helicopter Rotors

  2. Framework Results Results • Overview • Design Variables • Mesh Generation • Case Study: Optimization Algorithms • Optimization in Hover • (2 Testcases) • Optimization in Forward Flight (1 Testcase) • Multipoint Optimization • (1 Testcase) • Optimization in Hover • (2 Testcases) • Optimization in Forward Flight (1 Testcase) • Multipoint Optimization • (1 Testcase) Outline

  3. Optimizer Algorithms Aerodynamic Coefficients Design Variables Design Variables Objective Function Aerodynamic Structure Preprocessor Forces Moments Mesh Deformation Interpolation Geometry Flow Solution Trim Mesh Force Integration Deformation Partitioning Controls Deformation FrameworkOverview

  4. Twist Chord/Taper Anhedral Sweep Profile Transition Blade Tip Start Blade Tip OA213 Transition OA209 Design Variables

  5. Mesh GenerationHover Optimization Type: NS Topo: C-H Size: 88x36x32 ~100.000 1st Space: 10e-6*c Blocks: 6*3 Verification Type: NS Topo: C-H Size: 256x84x64 ~1.4 Mill. 1st Space: 1e-6*c Blocks: 7*4

  6. Mesh GenerationForward Flight Optimization Type: NS Topo: C-H Size: 128x48x40 ~250.000 Space: 1e-6*c Blocks: 6x8 Verification CHGRD: Type: NS Topo: C-H Size: 256x80x80 ~1.6 Mill. Space: 1e-6*c Blocks: 10x5 BGRD: Size: 80x112x120 Blocks: 2x2x4 ~1.1 Mill.

  7. Case Study: AlgorithmsCongra/SubPlex/EGO Conjugate Gradient SubPlex (=Simplex) EGO • Fast convergence for smooth & convex functions • Works partially parallel • No gradients necessary • Robust behaviour • Global approximation of the objective function • Surrogate model is improved based on uncertainty prediction • Very robust behaviour • Poor convergence for noisy functions • Convergence depends on quality of the gradients • Search for local optimum • Poor Convergence to the end of the optimization • Sometimes restart necessary • Works sequentially • Search for local optimum • Works mainly sequential

  8. Case Study: AlgorithmsParameter scan of the design variables Specifications 7A-Modelrotor Rigid blades Hover Design Variables Theta Twist Chord

  9. Case Study: AlgorithmsOptimization

  10. Framework Results • Overview • Design Variables • Mesh Generation • Case Study: Optimization Algorithms • Optimization in Hover • (2 Testcase) • Optimization in Forward Flight (1 Testcase) • Multipoint Optimization • (1 Testcase) Outline

  11. HOST Free Controls DTC DTS Prescribed Values FXA = 0 FYA = 0 Trim and Objective Function in Hover Specifications Rotor Model Articulated, Soft Blade Number of Blades 4 Radius 2.1m Flight Speed μ = 0,0 Tip Mach number Matip = 0,646 Objective Function Max F(x) = Figure of Merit ximin <= xi <= ximax

  12. Expected Improvement Function Exploration Move Objective, Predicted Objective (FM_hat) = Untwisted Optimization of TwistDevelopment of the surrogate model Eif decreases with increasing number of CFD-Evaluations. Kinks signify exploration of undiscovered design space. Six initial Samples are spread over the parameter space as far as possible Predicted values approach real values as the optimization proceeds. The surrogate model gets refined with each new training point Only for untwisted blades prediction stays poor.

  13. Optimization of TwistTwist/Thrust distribution Maximal loading at blade tip is decreased. Loading is shifted inboard. Both rotors have geometric nonlinear twist because of different zero incidence angle. Optimized blade has much higher twist than baseline rotor.

  14. Optimization of TwistComparison of Polars on Coarse and Fine Mesh Figure of Merit is improved by 6.1 points on the fine mesh. Coarse and fine meshes show the same trend. Figure of Merit is improved over whole range of thrust coefficients. Maximal improvement of 6.7 points on the coarse mesh is achieved.

  15. Optimization with all ParametersTheta,Twist, Chord, Anhedral, Sweep, Tipstart, Protrans Theta 29.98 Twist -19.95 Chord 0.5*c Anhedral 0.08*c Sweep 0.87*c Tipstart 0.96*r Protrans 0.56*r 36 initial Samples are chosen for the creation of the first surrogate model. Expected Improvement Function decreases drastically after 70 evaluations. Prediction capability improves considerably within the first 70 evaluations.

  16. Optimization of all ParametersThrust/Power distribution Power consumption at blade tip is decreased. Maximal loading at blade tip is decreased. Loading is shifted inboard.

  17. Optimization of all ParametersComparison of Polars on Coarse and Fine Mesh Figure of Merit is improved by 7.9 points on the fine mesh. Coarse and fine meshes show the same trend. Figure of Merit is improved over whole range of thrust coefficients. Maximal improvement of 7.7 points on the coarse mesh is achieved.

  18. HOST Free Controls DT0 DTC DTS αq Prescribed Values β1S = 0 β1C+ θ1S = 0 XB = 1,6 ZB = 12,5 Trim and Objective Function in Forward Flight Objective Function Min F(x) = Performance G(x) = Thrust = const. H(x) = Propulsive = const. ximin <= xi <= ximax Specifications Rotor Model Articulated, Soft Blade Number of Blades 4 Radius 2.1m Flight Speed μ = 0,4 Tip Mach number Matip = 0,646 Rotor is trimed according to the Modane Law (4-Component Trim)

  19. Optimization of TwistObjective on Coarse and Fine Mesh Power of Rotors with different Twist on Fine Mesh (Chimera) On the coarse mesh optimized rotor has a twist of about -6° On the fine mesh the optimal twist is slightly lower at -5.3° Good overall prediction capability of coarse model Clear relationship between torque coefficient and twist

  20. Optimization of TwistComparison of the thrust distribution High twist beneficial fore and aft of the rotor disc but unfavourable on advancing side High twist produces strong negative thrust at outer blade part and more thrust at inner blade part

  21. Optimization of TwistComparison of the power distribution Low twist rotor consumes more power at outer radial sections between 0° and 180° High twist rotor consumes more power at inner blade sections between 0° and 180°

  22. Set1 Set4 Set7 Optimization of Twist in Hover and Forward FlightWeighing of Function Approach (WOF) For pure hover and pure forward flight the reference values of -20° and -6° are reached Slope of „Multipoint-function“ small from Set4 to Set7  increasing twist from -6° to -10° results in only a slight penalty for forward flight For 1 Set 32 computations are needed: each computation takes 20 hours (6 coupling cycles, 24 CPUs)

  23. Conclusion • An optimization framework for helicopter rotors in hover and forward flight including weak fluid-strucutre coupled computations has been presented • Optimizations have demonstrated that the framework is well functioning • Running optimizations on coarse meshes has proven to be a successful optimization strategy • EGO has shown to be a powerful and efficient optimization algorithm • Parameterization is crucial: trade-off between few parameters (efficiency) and multiple parameters (complex geometries = optimization at individual blade sections) • For optimizations in forward flight algorithms which can treat multiple designs in parallel are important • Multipoint optimizations are cumbersome but can give an interesting perspective for trade-off studies between hover and forward flight

  24. Thank you for your attention

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