Robust Design Optimization of an Axial Compressor Johannes Einzinger ANSYS Germany GmbH

Transcription

1 Robust Design Optimization of an Axial Compressor Johannes Einzinger ANSYS Germany GmbH 1

2 Motivation Turbo Machines show: Rotating and stationary Parts Transient Flow Field Choke, Stall Dynamic Blade Loading High Requirement for Optimization 2

3 Primary Design, PCA Engineers 1.5 Stage Axial Compressor IGV(n=37) R1 (n=71, Shroud 2% Span) S1 (n=91, Hub 2% Span) Pressure Ratio Π=1.4 Mass Flow Rate 10.6 [kg/s] Diameter d = [m] Rot. Vel. Ω = 9300 [rpm] Blade Mach Number M u =0.75 Specific Speed n s = 1.3 Specific Diameter d s =2.3 Load Coefficient Ψ=0.45 3

4 Outline Parametric Geometry Automatic Meshing Automatic Solution Fluid Mechanics Structural Dynamics Sensitivity Analysis Design Optimization Robustness Evaluation 4

5 Process Overview 5

6 Process Overview 6

7 Geometry, Aero Dynamic Camber/Thickness for IGV, R1, S1; 2-3 Layers 5 β i per Layer, 3xThk Hub, 8 radii (const. Shroud) 47 CAD Input Parameter 7

8 Geometry, Blade Design CAD Design of Hub/Shroud Solid Casing, Filets DesignModeler CAD-Interface CFD-Mesh FEM-Mesh Blend-Radius 8

9 Meshing, TurboGrid High Quality Meshing Automated for Turbo Machinery Parametric Mesh Sizing 9

10 Meshing, General Hex-Dominant Automatic Size Functions 10

11 CFD Simulation CFD Solver: CFX Nodal based FVM 11 t dv V da da S dv V A A V Coupled Solution + AMG Mass & Momentum, Energy Turbulence Model: Shear Stress Transport One sector by passage, MFR: Profile Transformation Periodic Interface

12 Transient Blade Row Method Profile Transformation Time Transformation Fourier Transformation Harmonic Transformation Mixing Plane Frozen Rotor Time Inclining Shape Correction Phase Shift f(t) F(Ω) R&D unequal pitch ROTOR STATOR Accurate accounts for unsteady interactions Unequal pitch between row passages dictates full or partial wheel modeling Require large computing resource R1 S1 P R V R P S R2 S2 Phase-shifted boundaries a consequence of pitch change 12

13 CFD Post-Processing General Post-Processor Turbo Mode Highly Automated Customize able 13

14 CFD Post-Processing 14

15 Quality Assurance Iteration Error Residuals Variation of Monitor Point <1% Total Pressure Ratio Total Temperature Ratio Goal Residual Efficiency at Iteration

16 Quality Assurance Discretization Error Total Pressure Ratio Total Temperature Ratio Polytrophic Efficiency Convergence study on scalable high quality mesh to minimize numerical error Stator 16 Mesh Min Angle Max Exp. #Nodes ~ ~ ~ ~ Rotor IGV

17 Mechanical Simulation Procedure Mechanical Equation System M u D u K( u) u f f ( t) Linearization Decomposition u( t) u0 u( t) Static System (Pre-Stress) K( u ) u f Modal Analysis 2 M K( u0 ) 0 Linear dynamic System M u D u K( u ) u f ( t) 0 0 f f 0 u 0 Δu(t) u 17

18 Model Order Reduction M u D u K( u0 ) u f ( t) Approximation u( t) q( t) leads to reduced dynamic System T T T T M q D q K ( u ) q f ( t) orthogonality of Φ leads to 2 q 2 q q f ( t) i 0 i 0 i q, i Fourier Transformation Time to Frequency Domain j q f 0 k 0 k i, k q, i, k 0 t = Ω 18

19 Fluid-Structure Coupling Displacements Rot. Velocity CFD-Pressure 19

20 Static Structural (Pre-Stress) Static Solution: Displacement Strain & Stress Numerical Error Pre-Stress for further Analysis 20

21 Modal Analysis Pre-Stressed Modal Analysis: Eigen Frequencies and Vectors Data for further MOR-Analysis 21

22 Forced Response Analysis Harmonic Analysis: Modal Superposition Fluid Load F(Ω) v. Mises Stress σ v.m (Ω) 22

23 Process Summary and Objectives 47 (59) Input Parameter 11 Input Constraints 23 Objective: Efficiency = max Total Pressure = max Stress < Limit No Resonance 24 Output Parameter

24 optislang Integration/Interface Direct Integration Correlation Matrix Coefficient of Prognosis 2D and 3D Plot Anthill Plot Pictures of Design xxxx 24

25 Sensitivity Analysis 25

26 Sensitivity Analysis, Maximal Stress Blade Angle: Hub, Mid Leading Edge CoP=86% Statistic is reliable Detect important Variables Parameter Reduction MoP is plausible β 26

27 Sensitivity Analysis, Eigen Mode 2 CoP=91% Statistic is reliable Detect important Variables Parameter Reduction MoP is plausible 27

28 Sensitivity Analysis, Aero Dynamic CoP=64% and 65% small value Numerical error? Model error? Important Variables Parameter Reduction MoP is plausible 28

29 Trouble Shooting with small CoP Number of Evaluated Designs? no, CoP(80)~CoP(150)! Numerical Error? no, Best-Practice! Model Error? yes, some Designs are transient! Overcome: Full transient Simulation? Transient Blade Row Method!? Use Result carefully! 29

30 Design Optimization Optimization Algorithms: Evolutionary Algorithm Gradient- Based Algorithms Which one is the best? Pareto Optimization 30 Strategy is required! and derived from SA Adaptive Response Surface Generic Algorithm

31 Design Optimization, Strategy Sensitivity Analysis: Shows potential Indicates global optimum Parameter reduction Modify parameter space Initial Design Strategy: Get best Design from SA/MoP Evaluate this Design and get initial for: Optimization in sub space: ARSM Small Number of Parameter Global Optimum 31

32 Design Optimization, Summary Initial Design Best Design SA Best Design Solved (MoP) Best Design ARSM Efficiency [%] (91.0) 88.9 p tot Ratio [-] (1.44) 1.41 Max. Stress [MPa] (230) 239 #Designs (0)

33 Robustness Evaluation X1 X5 X4 CHECK COP/MOP 33

34 Robustness, Maximum Stress Original Robustness decreased Limit = 300 MPa μ=219 MPa σ= 18 MPa Failure ~ 0 % ~4.5 σ Optimized Limit = 300 MPa μ=239 MPa σ= 25 MPa Failure ~ 2 % ~2.5 σ 34

35 Robustness, Efficiency Original Robustness increased Limit = 85.0 [%] μ=87.0 [%] σ= 1.5 [%] Failure ~ 8 % ~2 σ 35 Optimized Limit = 85.0 [%] μ=88.8 [%] σ= 1.5 [%] Failure ~ 5 % ~3 σ

36 Robustness, Total Pressure Ratio Original Robustness approx. equal Limit = 1.38 μ=1.41 σ= 1.2 [%] Failure ~ 2 % ~2.5 σ Optimized Limit = 1.38 μ=1.41 σ= Failure ~ 6 % ~2.0 σ 36

37 Summary Paramterization Fluids Meshing Structural Thermal AUTOMATIZATION OPTIMIZATION MULTIPHYSICS COUPLING CAD Import + - u(t) In-house D(s) Plant Solution y(t) Emag Workflow BREADTH DEPTH Postprocessing 37