Robust Design Optimization of an Axial Compressor · 2016. 2. 20. · © 2011 ANSYS, Inc. September...
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© 2011 ANSYS, Inc. September 15, 2011
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Robust Design Optimization of an Axial Compressor
Johannes Einzinger
ANSYS Germany GmbH
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© 2011 ANSYS, Inc. September 15, 2011
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Motivation
• Turbo Machines show:
• Rotating and stationary
Parts
• Transient Flow Field
• Choke, Stall…
• …
• Dynamic Blade Loading
• …
High Requirement
for Optimization
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• 1.5 Stage Axial Compressor
• IGV(n=37)
• R1 (n=71, Gap @ Shroud 2% Span)
• S1 (n=91, Gap @ Hub 2% Span)
• Pressure Ratio Π=1.4
• Mass Flow Rate 10.6 [kg/s]
• Diameter d = 0.525 [m]
• Rot. Vel. Ω = 9300 [rpm]
• Blade Mach Number Mu=0.75
• Specific Speed ns= 1.3
• Specific Diameter ds=2.3
• Load Coefficient Ψ=0.45
Primary Design, PCA Engineers
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Outline
• Parametric Geometry
• Automatic Meshing
• Automatic SolutionFluid Mechanics
Structural Dynamics
• Sensitivity Analysis
• Design Optimization
• Robustness Evaluation
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Process Overview
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Process Overview
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Geometry, Aero Dynamic
• Camber/Thickness for
• IGV, R1, S1; 2-3 Layers
• 5 βi per Layer, 3xThk
• Hub, 8 radii (const. Shroud)
• 47 CAD Input Parameter
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Geometry, Blade Design
• CAD Design of
• Hub/Shroud Solid
• Casing, Filets
• …
• DesignModeler
• CAD-Interface
Blend-Radius
CFD-Mesh
FEM-Mesh
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Meshing, TurboGrid
• High Quality
Meshing
• Automated for
Turbo Machinery
• Parametric Mesh
Sizing
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Meshing, General
• Hex-Dominant
• Automatic Size Functions
• …
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CFD Simulation
• CFD Solver: CFX
• Nodal based FVM
• Coupled Solution + AMG
• Mass & Momentum, Energy…
• Turbulence Model:
• Shear Stress Transport
One sector by passage, MFR:
• Profile Transformation
• Periodic Interface
V A A V
V A AdV d d S dVt
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Transient Blade Row Method
Profile
Transformation
Mixing Plane
Frozen Rotor
Time
Transformation
Time Inclining
Fourier
Transformation
Shape Correction
Phase Shift
Harmonic
Transformation
f(t)→F(Ω)
R&D
S2
S1
R2
R1
ROTOR
STATOR
VRPR PS
unequal pitch • Accurate accounts for unsteady interactions
• Unequal pitch between row passages
dictates full or partial wheel modeling
• Require large computing resource
Phase-shifted boundaries
a consequence of
pitch change
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CFD Post-Processing
• General Post-Processor
• Turbo Mode
• Highly Automated
• Customize able
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CFD Post-Processing
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Quality Assurance Iteration Error
<1%Variation of
Monitor Point
at Iteration 250Goal Residual
Residuals
Total Pressure Ratio
Efficiency
Total Temperature Ratio
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Quality Assurance Discretization Error
Mesh Min Angle Max Exp. #Nodes
1 29.59 15.2 ~50000
2 30.85 6.69 ~100000
3 31.52 4.90 ~150000
4 35.73 4.60 ~250000
Convergence study on
scalable high quality mesh
to minimize numerical error
Rotor
Stator
IGV
Total Pressure Ratio
Total Temperature Ratio
Polytrophic Efficiency
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Mechanical Simulation Procedure
• Mechanical Equation System
Linearization
Decomposition
• Static System (Pre-Stress)
• Modal Analysis
• Linear dynamic System
0( ) ( )M u D u K u u f f t
0 0 0( )K u u f
2
0( ) 0M K u
0( ) ( )M u D u K u u f t
f
u
f0
u0
0( ) ( )u t u u t
Δu(t)
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Model Order Reduction
• Approximation
• leads to reduced dynamic System
• orthogonality of Φ leads to
• Fourier Transformation
• Time to Frequency Domain
( ) ( )u t q t
0( ) ( )
T T T TM q D q K u q f t
2
0 0 ,2 ( )
i i i q iq q q f t
0( ) ( )M u D u K u u f t
2 2
0 0 , , ,2
k k i k q i kj q f
t
Ω
=
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Fluid-Structure Coupling
• Displacements
• Rot. Velocity
• CFD-Pressure
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Static Structural (Pre-Stress)
• Static Solution:
• Displacement
• Strain & Stress
• Numerical Error
• Pre-Stress for
further Analysis
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Modal Analysis
• Pre-Stressed Modal Analysis:
• Eigen Frequencies and Vectors
• Data for further MOR-Analysis
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Forced Response Analysis
• Harmonic Analysis:
• Modal Superposition
• Fluid Load F(Ω)
• v. Mises Stress σv.M(Ω)
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47 (59) Input
Parameter
24 Output
Parameter
Objective:
Efficiency = max
Total Pressure = max
Stress < Limit
No Resonance
Process Summary and Objectives
11 Input
Constraints
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optiSLang Integration/Interface
• Direct Integration
• Correlation Matrix
• Coefficient of Prognosis
• 2D and 3D Plot
• Anthill Plot
• Pictures of Design xxxx
• …
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Sensitivity Analysis
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Sensitivity Analysis, Maximal Stress
Blade Angle: Hub,
Mid Leading Edge
β
• CoP=86%
Statistic is reliable
Detect important Variables
Parameter Reduction
• MoP is plausible
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Sensitivity Analysis, Eigen Mode 2
• CoP=91%
Statistic is reliable
Detect important Variables
Parameter Reduction
• MoP is plausible
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Sensitivity Analysis, Aero Dynamic
• CoP=64% and 65%
small value
Numerical error?
Model error?
• Important Variables
Parameter Reduction
• MoP is plausible
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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“!
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Design Optimization
Gradient-Based
Algorithms
Evolutionary
Algorithm
Pareto Optimization
Adaptive
Response Surface
Generic
Algorithm
Optimization
Algorithms:
Which one is the best?
Strategy is required!
and derived from SA
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Design Optimization, Strategy
Sensitivity Analysis:
• Shows potential
• Indicates global optimum
• Parameter reduction
• Modify parameter space
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
Initial Design
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Design Optimization, Summary
Initial Design
Best Design SA
Best DesignSolved (MoP)
Best Design ARSM
Efficiency [%] 87.0 88.0 88.9 (91.0) 88.9
ptot Ratio [-] 1.41 1.41 1.41 (1.44) 1.41
Max. Stress [MPa] 219 235 232 (230) 239
#Designs 1 150 1 (0) 100
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X1X5X4
Robustness Evaluation
CHECK COP/MOP
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Robustness, Maximum Stress
Limit = 300 MPa
μ=219 MPa
σ= 18 MPa
Failure ~ 0 %
~4.5 σ
Limit = 300 MPa
μ=239 MPa
σ= 25 MPa
Failure ~ 2 %
~2.5 σ
Original
Optimized
Robustness
decreased
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Robustness, Efficiency
Limit = 85.0 [%]
μ=87.0 [%]
σ= 1.5 [%]
Failure ~ 8 %
~2 σ
Limit = 85.0 [%]
μ=88.8 [%]
σ= 1.5 [%]
Failure ~ 5 %
~3 σ
Original
Optimized
Robustness
increased
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Robustness, Total Pressure Ratio
Limit = 1.38
μ=1.41
σ= 1.2 [%]
Failure ~ 2 %
~2.5 σ
Limit = 1.38
μ=1.41
σ= 0.017
Failure ~ 6 %
~2.0 σ
Original
Optimized
Robustness
approx. equal
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BREADTHDEPTH
MULTIPHYSICSCOUPLING
AUTOMATIZATIONOPTIMIZATION
In-houseSolution
Summary
Structural
Fluids
Thermal
Emag
CADImport
Param-terization
Meshing
Workflow
Post-processing
PlantD(s)y(t)u(t)+
-