Phoenix > Manfred Imiela High Fidelity Optimization Framework for Helicopter Rotors

Phoenix > Slide 2/25 > High-Fidelity Optimization Framework for Helicopter Rotors Results Optimization in Hover (2 Testcases) Optimization in Forward Flight (1 Testcase) Multipoint Optimization (1 Testcase) Outline Framework Overview Design Variables Mesh Generation Case Study: Optimization Algorithms Results Optimization in Hover (2 Testcases) Optimization in Forward Flight (1 Testcase) Multipoint Optimization (1 Testcase)

Phoenix > Slide 3/25 > High-Fidelity Optimization Framework for Helicopter Rotors Framework Overview Design Variables Geometry Mesh Partitioning Preprocessor Mesh Deformation Flow Solution Force Integration Aerodynamic Interpolation Trim Deformation Structure Forces Moments Controls Deformation Aerodynamic Coefficients Optimizer Algorithms Design Variables Objective Function

Phoenix > Slide 4/25 > High-Fidelity Optimization Framework for Helicopter Rotors Design Variables Chord/TaperTwistAnhedralSweepProfile Transition OA213TransitionOA209 Blade Tip Start Blade Tip

Phoenix > Slide 5/25 > High-Fidelity Optimization Framework for Helicopter Rotors Mesh Generation Hover Optimization Type:NS Topo:C-H Size:88x36x32 ~ st Space:10e-6*c Blocks:6*3 Verification Type:NS Topo:C-H Size:256x84x64 ~1.4 Mill. 1 st Space:1e-6*c Blocks:7*4

Phoenix > Slide 6/25 > High-Fidelity Optimization Framework for Helicopter Rotors Mesh Generation Forward Flight Optimization Type:NS Topo:C-H Size:128x48x40 ~ 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.

Phoenix > Slide 7/25 > High-Fidelity Optimization Framework for Helicopter Rotors Case Study: Algorithms Congra/SubPlex/EGO Conjugate GradientSubPlex (=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

Phoenix > Slide 8/25 > High-Fidelity Optimization Framework for Helicopter Rotors Case Study: Algorithms Parameter scan of the design variables Design Variables Theta Twist Chord Specifications 7A-Modelrotor Rigid blades Hover DV Lower - Upper StepBest Theta25.5 – Twist18.5 – Chord0.2 –

Phoenix > Slide 9/25 > High-Fidelity Optimization Framework for Helicopter Rotors Case Study: Algorithms Optimization CongraSubPlexEGO Commentwrong stepsizerestart necessaryoptimum found # CFD~ 65~ 8652

Phoenix > Slide 10/25 > High-Fidelity Optimization Framework for Helicopter Rotors Results Optimization in Hover (2 Testcase) Optimization in Forward Flight (1 Testcase) Multipoint Optimization (1 Testcase) Outline Framework Overview Design Variables Mesh Generation Case Study: Optimization Algorithms

Phoenix > Slide 11/25 > High-Fidelity Optimization Framework for Helicopter Rotors Trim and Objective Function in Hover Objective Function Max F(x) = Figure of Merit x i min <= x i <= x i max Specifications Rotor ModelArticulated, Soft Blade Number of Blades4 Radius2.1m Flight Speedμ = 0,0 Tip Mach numberMatip = 0,646 Free Controls DTC DTS Prescribed Values FXA = 0 FYA = 0 HOST

Phoenix > Slide 12/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Development of the surrogate model Exploration Move = Untwisted Expected Improvement Function Objective, Predicted Objective (FM_hat) Six initial Samples are spread over the parameter space as far as possible The surrogate model gets refined with each new training point Predicted values approach real values as the optimization proceeds. Only for untwisted blades prediction stays poor. Eif decreases with increasing number of CFD- Evaluations. Kinks signify exploration of undiscovered design space.

Phoenix > Slide 13/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Twist/Thrust distribution Both rotors have geometric nonlinear twist because of different zero incidence angle. Optimized blade has much higher twist than baseline rotor. Maximal loading at blade tip is decreased. Loading is shifted inboard.

Phoenix > Slide 14/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Comparison of Polars on Coarse and Fine Mesh Figure of Merit is improved over whole range of thrust coefficients. Maximal improvement of 6.7 points on the coarse mesh is achieved. Figure of Merit is improved by 6.1 points on the fine mesh. Coarse and fine meshes show the same trend.

Phoenix > Slide 15/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization with all Parameters Theta,Twist, Chord, Anhedral, Sweep, Tipstart, Protrans Theta29.98 Twist Chord0.5*c Anhedral0.08*c Sweep0.87*c Tipstart0.96*r Protrans0.56*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.

Phoenix > Slide 16/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of all Parameters Thrust/Power distribution Maximal loading at blade tip is decreased. Loading is shifted inboard. Power consumption at blade tip is decreased.

Phoenix > Slide 17/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of all Parameters Comparison of Polars on Coarse and Fine Mesh Figure of Merit is improved over whole range of thrust coefficients. Maximal improvement of 7.7 points on the coarse mesh is achieved. Figure of Merit is improved by 7.9 points on the fine mesh. Coarse and fine meshes show the same trend.

Phoenix > Slide 18/25 > High-Fidelity Optimization Framework for Helicopter Rotors Trim and Objective Function in Forward Flight Rotor is trimed according to the Modane Law (4-Component Trim) HOST Prescribed Values β 1S = 0 β 1C + θ 1S = 0 XB = 1,6 ZB = 12,5 Free Controls DT0 DTC DTS α q Objective Function Min F(x) = Performance G(x) = Thrust = const. H(x) = Propulsive = const. x i min <= x i <= x i max Specifications Rotor ModelArticulated, Soft Blade Number of Blades4 Radius2.1m Flight Speedμ = 0,4 Tip Mach numberMa tip = 0,646

Phoenix > Slide 19/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Objective on Coarse and Fine Mesh 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 Twist [°]Power [kW] Power of Rotors with differentTwist on Fine Mesh (Chimera)

Phoenix > Slide 20/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Comparison 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

Phoenix > Slide 21/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist Comparison 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°

Phoenix > Slide 22/25 > High-Fidelity Optimization Framework for Helicopter Rotors Optimization of Twist in Hover and Forward Flight Weighing 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) Set λ Hov λ FF Set1 Set4 Set7

Phoenix > Slide 23/25 > High-Fidelity Optimization Framework for Helicopter Rotors 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

Phoenix > Slide 24/25 > High-Fidelity Optimization Framework for Helicopter Rotors Thank you for your attention