Optimization of a Turbo Charger Compressor using AxCent ...

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Robert D. Lotz, PHD

BorgWarner Turbo Systems

November, 2015

Optimization of a Turbo Charger Compressor using AxCent and modeFRONTIER

Copyright © 2015 BorgWarner Inc.

Outline

Acknowledgements

Introduction

Turbo Charger Overview

General Setup

Problem Statement

AxCent Geometry Parameterization

CFD Setup and Benchmarking

Optimization Setup

modeFrontier

Optimization Methodology

A little test case

Evaluation of Optimization Schedulers

Influence of Number of Variables

Objectives vs Constraints, Initialization

2


Outline

Aerodynamic Optimization

Single Objective

Multi Objective – Single Operating Condition

Multi Objective – Multi Operating Condition

Even more complexity – a real case

Structural Optimization

Interaction with CFD Optimization.

Loosely Coupled Multi Objective

Summary

3


Acknowledgements

I am very grateful to ESTECO for allowing me to participate in this User

Meeting.

I will try to present optimization and analysis of turbo machines from the

view point of an engineer/designer. My experience is based on

turbocharger compressors (i.e. small, low cost, wide map width radial

impellers).

This talk was adapted from a Seminar presentation. I will describe my

approach to using numerical and optimization methods to improve turbo

designs, but also the path I took in arriving at this methodology.

4


Approach

Design of turbocharger impellers is time and resource intensive. Current

designs are relatively close to optimal, the effort required to improve

performance is high.

Multiple iterations between design and gas stand testing are typically

required. We would like to replace some of the testing with numerical

simulations.

For a formal optimization (not just a DOE), typically hundreds to

thousands of designs need to be evaluated. This cannot possibly be

accomplished using testing alone.

My approach tries to combine a fast simplified 3D CFD analysis method

with a geometrically (somewhat) complex model. This has shown some

promising results in practice, but does have some known drawbacks as

well.

There are different philosophies how to balance accuracy and

complexity.

5


Introduction

6


Turbocharger

7


Compressor Performance Map

8

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

0.0 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000 1.125 1.250 1.375 1.500 1.625

Map Width

Efficiency Contours

hISC/hISC Ref Peak

Surge Line

Choke

Speed Line


General Setup

9


Turbo Compressor Layout

Design targets:

Maximize efficiency.

Provide adequate margins

on all sides of the map.

Constraints

Structural requirements.

Manufacturability.

Packaging.

Value/Cost.

Turbine consideration.

Rotor dynamics.

Minimize inertia impact.

NVH.

Etc., etc.

10


Geometric Setup - General

AxCent is a Turbo Machinery

design code developed by

Concepts NREC.

Geometry is based on Bezier

splines for contours, blade angles

and normal thickness.

Non-interactive geometry

manipulation is accomplished using

TurboOpt.

Geometric Variables:

Individual Bezier points for hub and

shroud contours, blade angles and

diffuser parameter.

Geometric Constraints:

Manufacturability, mechanical and

modal requirements.

11


Analytical Setup – Methodology

12

AxCent/pbCFD

~100,000 elements

8 min. runtime

Outputs: Pressure Ratio.

Efficiency.

Run success/failure.

Required Features for Optimization: Automatic geometry and mesh generation.

Parallel run execution.

Robustness and reliability.

Result evaluation and output.

Turn around time!!

Push-button CFD is a part of

AxCent and can be driven through

TurboOpt.

Setup Details: 3D, Axi-symmetric single passage.

No volute or casing treatment.

All Hex H-Grid, automatic generation.

Tip clearance is part of the mesh.

Dawes based solver, Central Differencing.

Spalart-Allmaras turbulence model.

Fixed mass flow boundaries.


CFD Benchmarking

13

Why: CFD only approximates reality.

Discretization, modeling assumptions.

Ultimately, the GS test still decides.

Methodology: Comparison of a complete map.

Understand what is being measured on the

stand.

Total-total quantities only (simplified CFD)

Adjustment factors (?)

Phase 1

Phase 2

Current


CFD Benchmarking

pbCFD Predictions vs. Gas Stand Test.

After adjustment of mesh and physics settings, there is good

agreement with the test at the design point.

Efficiencies are also reasonable in the middle of the map, but there

are significant deviations at low and high speed.

Choke predictions are compromised by the lack of fillets in the

model.

Surge cannot be predicted reliably with a steady state method.

pbCFD gives reasonably reliable predictions. Turn around time are

adequate if design evaluations can be performed in parallel.

CFD predictions need to be continuously checked and methodology

adjusted.

14


Optimization Setup

15


Optimization Setup

modeFRONTIER® is an

integration platform for multi-

objective and multi-disciplinary

optimization.

Coupling with third party

engineering tools.

Automation of design

simulation process.

Results post processing and data analysis tools.

At BorgWarner’s request, a modeFrontier plug-in was created that allows the use

of AxCent/TurboOpt within the modeFrontier environment and optimization on

the mFgrid system for parallel optimization runs on our HPC Cluster.

16


Optimization Setup

Typical questions encountered in setting up turbo

compressor optimizations Multiple conflicting requirements.

Large number of variables to consider.

Strongly non-linear response surface.

Restrictive constraints.

Uncertainty of predictions (fault tolerance).

Time and resource constraints.

How to choose an “optimal” design?

Specifically: Which optimization algorithm?

How many variables?

Constraints/Objectives.

Initialization (size of DOE, population size for GA).

Number of required designs.

A typical multi-objective Aero optimization takes many

days/weeks to run. How to choose the best algorithm?

17


Similarities: Multiple “unrelated” variables.

Narrow optimal space.

Conflicting objectives.

Differences: Response surface is continuous.

No failed designs.

“Concave” Pareto front.

All variables are equally important.

Optimization Setup – Test Case

A little optimization test case:

16 sided polyhedron with 16 independent values

for radius (ri)

Objectives: Maximize area and minimize perimeter

length. (expected Pareto front ri=constant - circle)

Constraint: 100.0 < Area < 200.0 (mm2)

Variable Range: 1 < ri < 10 (mm)

Results evaluated after 500 designs

18

A

P ri

Valid Design

Space

Constraint Violated

Constraint

Violated Impossible


Optimization Setup – Test Case

19


Optimization Setup – Evaluation of Algorithms - DOE

500 points for 16 variables Design of Experiment using ULH.

Result of just using “Random” variable values.

20

Pareto Designs only


Optimization Setup – Evaluation of Algorithms - GA

GA initialized with a 16 point ULH DOE, same values for each case.

500 design evaluations total, 30 generations with population size of 16.

NSGA has most designs with close to ideal values.

ARMOGA comes closest to the ideal Pareto front.

21

Pareto Designs only

DOE MOGA

ARMOGA NSGA


Optimization Setup – Evaluation of Algorithms – Other MO

Initialized with a 16 point ULH DOE, same values for each case.

500 design evaluations total.

Game Theory (SIMPLEX) has slight advantage at larger values, but small values are severely under represented.

No real improvement over GA.

22

Pareto Designs only

DOE Sim. Annealing

Particle Swarm Game Theory


Optimization Setup – Evaluation of Algorithms – Multi-Strategy

Initialized with a 16 point ULH DOE, same values for each case.

500 design evaluations total, 30 generations with population size of 16.

SAnGeA is not successful (given problem setup, perhaps not a surprise).

HRYBRID, FAST and pilOPT are all significant improvements, capture the Pareto front quite well.

FAST does better when using NSGA than with ARMOGA.

23

Pareto Designs only

SanGeA HYBRID

pilOPT FAST


Optimization Setup – Evaluation of Algorithms – Multi-Strategy

HYBRID vs. FAST more detailed view.

FAST has much more narrow focus, captures the upper end of the Pareto front very soon, then propagates down.

Hybrid is much more spread out, much wider exploration of the design space.

24

FAST HYBRID


Optimization Setup – Population Size

Initialized with a 8, 16 and 32 point ULH DOE. (This also sets the size of each generation)

500 design evaluations total, 61, 30 and 14 generations each for the 8, 16 and 32 design/generation runs.

Best coverage of Pareto front with population = # of variables.

Small population provides closest approach to Pareto front, but only partial coverage.

Using number of variables as the a guide to set the size of the population of each generation appears to be a good

compromise.

25

Pareto Designs only

16

32 8


Optimization Setup – Number of Variables

Change to a 32 sided polygon. Initialization with 32 ULH DOE points.

1900 design evaluations total (~60 generations).

DOE coverage of the design space is much worse than with the smaller number of variables.

FAST struggles with the upper constraint (get’s “stuck”).

GA provides slightly more complete coverage of the Pareto front.

Initialization is important.

26

Pareto Designs only

NSGA

HYBRID FAST


Optimization Setup – Initialization

Initialization of multi-dimensional

problems DOE initialization for large number of variables decreases in

usefulness with increasing number of variables.

Highly constrained design space my preclude any valid designs

from a randomly seeded DOE data set.

Initialization options 1. Large DOE and then pick a selection of successful designs for

the first generation.

2. Use the Pareto front from a similar run.

3. Existing (legacy) designs as seeds.

Convergence to a true optimum (?)

27

Starting Design

Optimized Design


Optimization Setup – Objectives/Constraints

Objectives: I like to limit a optimization to 2-3 objectives, if

possible.

Complementary vs. Incompatible -> Pareto front.

Use of target functions vs. multiple objectives?

Example: Multi-operating point setup to increase operating

range.

Three operating points on one speed line.

Assume that increasing efficiency near surge and

choke is a good stand-in for map-width.

Also need to meet a specific pressure and mass

flow range.

28

Constraints: Restricts the available design space.

Constraints can be applied to objectives that are

already met.

Start with loose constraints, tighten as the run

progresses.

↑h ↑P

↑h



Example (cont.)

Objective:

1. Increase efficiency at surge.

2. Increase efficiency at choke.

3. Maximize pressure ratio at mid point

(Incompatible with 1. and 2., this builds the

Pareto front)

Constraint

1. Pressure ratio (we just need part of the

Pareto front)

2. If running CFD with fixed mass flow rate,

constrain minimum pressure ratio at the

choke OP.

3. Geometry, etc.

29

Eff

icie

ncy


Example (cont.)


30

Eff

icie

ncy

Design 1

Design 2

Objective function for efficiency:

Can we get a compromise design from two

different objectives (?)

Weighted average or least square of

efficiencies at surge and choke, replacing

Objectives 1 and 2.

Design 3


Summary

My current approach to problem setup:

1. Number of variables is determined by the complexity of the

geometry.

2. Hybrid Scheduler.

3. 2-3 objectives.

4. Remaining objectives implemented via constraints.

5. Minimum number of constraints.

6. Initialization/GA population size ~ number of variables.

7. Initialization uses a mix of known and random designs.

8. Number of required designs is primarily determined by 1) and 3).

31


Aerodynamic Optimization

32


Setup – Single Objective

modeFRONTIER setup

Scheduler

NSGA/SIMPLEX.

Sequential evaluation.

Objectives:

Maximize Efficiency.

Input Constraints:

None.

Result Constraints:

Pressure Ratio Minimum.

33

Runs Statistics: 1 AxCent/pbCFD analysis per design.

640 design evaluations.

Run on 8 core workstation.

~5 days elapsed time.

↑h


PR/PRRef

0.9 0.93 0.97 1.0 1.03 1.07 1.1 1.13 1.17

ht-

s/h

t-s R

ef

1.067

1.053

1.04

1.027

1.013

1.0

Results – Single Objective

34

ht-

s/h

t-s R

ef

1.067

1.053

1.04

1.027

1.013

1.0

Design ID

0 66 132 198 264 330 396 462 528 594 660

Co

nstr

ain

t

NSGA SIMPLEX



35

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

Efficiency Contours

hISC/hISC Ref Peak

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625



36

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

Efficiency Contours

hISC/hISC Ref Peak

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625

Design Assessment:

Positive:

Efficiency improvement.

modeFRONTIER finds an improvement over the starting geometry.

Not so positive:

x High speed performance loss.

x Fails to meet pressure ratio target.

Objective for next try: o Better exploration of design space.

o Influence pressure ratio.


Setup – Multi Objective

modeFRONTIER setup

Scheduler

Hybrid (GA + SQP).

Parallel evaluations.

Objectives:

Maximize Efficiency.

Maximize Pressure Ratio.

Input Constraints:

Geometric constraints on inducer and

exducer.

Result Constraints:

Pressure Ratio Minimum and Maximum.

37

Runs Statistics: 1 AxCent/pbCFD analysis per design.

14,000 design evaluations.

Run on 8 nodes of a parallel cluster

server using mFGrid.


↑h,P


1.027

1.013

1.0

0.987

PR/PRRef

0.97 1.0 1.03 1.06 1.09

ht-

s/h

t-s R

ef

Results – Multi Objective

38

ht-

s/h

t-s R

ef

Design ID

0 2000 4000 6000 8000 10000 12000 14000

Co

nstr

ain

t

Co

nstr

ain

t 1.027

1.013

1.0

0.987



39

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

Efficiency Contours

hISC/hISC Ref Peak

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625



40

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

Efficiency Contours

hISC/hISC Ref Peak

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625

Design Assessment

Positive:

Substantial efficiency improvement.

Meets pressure ratio target at design point.

modeFRONTIER can make substantial modifications to an existing design.

Not so positive:

x Significant loss of map width.

x High speed performance is inadequate.

x “Point” design, not of practical use.

Objective for next try: o Expand map width.


Setup – Multi Objective Multi Operating Condition

modeFRONTIER setup

Scheduler

Hybrid (GA + SQP).


Objectives:

Minimize Efficiency Target Function.


Input Constraints:

Geometric constraints on inducer and

exducer.

Fixed diffuser diameter.

Result Constraints:


41

Runs Statistics: 3 AxCent/pbCFD analyses per design.

6,500 design evaluations.

Run on 8 nodes of a parallel cluster

server using mFGrid.


↑h

↑h,P

↑h


0.987

0.973

0.96

0.947

0.933

PR/PRRef

0.97 0.985 1.0 1.015 1.03

ht-

s/h

t-s R

ef

Results – Multi Objective Multi Operating Condition

42

Design ID

0 1000 2000 3000 4000 5000 6000 7000

Co

nstr

ain

t

Co

nstr

ain

t

0.987

0.973

0.96

0.947

0.933

ht-

s/h

t-s R

ef



43

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625

Efficiency Contours

hISC/hISC Ref Peak

Note: Opt. design map scaled

for better comparison



44

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

0.0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25 1.375 1.5 1.625

Efficiency Contours

hISC/hISC Ref Peak

Note: Opt. design map scaled

for better comparison

Design Assessment

Positive:

Substantial map width improvement.

modeFRONTIER can make substantial modifications to an existing design.

This is getting close to being a useful design!

Not so positive:

x Some loss in peak efficiency.

x Map has shifted to higher mass flow rates.

Objective for next try: o More control over details of the map.

o Create a practical compressor.


Setup – Real Case

modeFRONTIER setup

Scheduler

Hybrid (GA + SQP).


Objectives:

Minimize Efficiency Target Function.

Minimize Surge Target Function.


Maximize Choke mass flow rate.

Input Constraints:

Geometric constraints on inducer and exducer.

Fixed diffuser diameter.

Result Constraints:


Efficiency.

45

Runs Statistics: Several AxCent/pbCFD analyses per design.

“A lot” of design evaluations.

Run on 14 nodes of a parallel cluster server

using mFGrid.

~1 month elapsed time.

↑h, Surge ↑h,P

↑h, ↑𝒎

↑h

↑h


PR/PRRef

Results – Real Case

46

Design ID

0 1000 2000 3000 4000 5000 6000 7000 8000

Eff-T

arg

et F

un

ctio

n

Eff-T

arg

et F

un

ctio

n

0.07

0.065

0.06

0.055

0.05

0.045

0.04

0.97 0.985 1.0 1.015 1.03

Co

nstr

ain

t

Co

nstr

ain

t

0.07

0.065

0.06

0.055

0.05

0.045

0.04



47

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Efficiency Contours

hISC/hISC Ref Peak

Note: Top SL missing on

Reference Design



48

1.53

1.40

1.27

1.13

1.00

0.87

0.73

0.60

0.47

0.33

PR

t-s/P

Rt-

s R

ef

𝒎 /𝒎 Ref

Starting Geometry

Optimized Design

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Efficiency Contours

hISC/hISC Ref Peak

Note: Top SL missing on

Reference Design

Design Assessment

Positive:

Improvement on all sides of the map over the legacy design.

Higher peak efficiency.

Higher specific pressure ratio.

Higher choke mass flow.

Better surge behavior.

Not so positive:

x Efficiency islands moved to higher mass flow.

x Structurally less capable than the legacy design.


Summary

A methodology was developed to improve turbo compressor designs.

3D CFD on a simplified geometry is used to evaluate design

performance.

modeFRONTIER optimization with Hybrid scheduler.

Results show the potential for creating higher performing stages.

Work on a optimization strategy for balancing on-design and off-design

performance is still a work in progress. (probably always will be)

49



50


Optimization Approach

“Loosely” Coupled (iterative)

51

“Strongly” Coupled

Design Targets

Final Design

New hub,

shroud and

blade shapes

New blade

thickness and

back wall

Aero

Stress & Modal

Design Targets

Final Design

Aero Stress & Modal

Simultaneous

Evaluation Iterate


Optimization Approach

Loosely Coupled:

Advantages:

Speed, fewer variables.

Aero design is “unconstrained”.

Disadvantages

Potential of yielding a design that cannot be mechanically qualified.

Closely Coupled:

Advantages:

Interaction between structural and aerodynamic design trade-offs is captured.

Disadvantages

Number of variables to consider is overwhelming (especially if including modal).

Initialization and convergence is very difficult.

Simplification required may result in sub-optimal results as well.

52



The example shown here was a study for stress

reduction on an aero optimized design. Modal

optimization was performed in the traditional way.

Our structural analysis utilizes ANSYS and

ProEngineer. (and Concepts Max5 to transfer

geometry from AxCent to ProE).

Concepts also offers a FEA solver for AxCent

(pbFEA). We do not currently have a license, but are

very interested in integrating it into our process once

some enhancements have been implemented.

53

modeFRONTIER setup

Scheduler HYBRID (GA + SQP).

Serial evaluations.

Objectives:

Minimize Stress (several locations).

Input variables: Backwall shape, Fillet radii.

Input Constraints: Maximum fillet radius, packaging.

Result constraints: Maximum allowable stress (several locations).

Runs Statistics: 1 analysis per design.

600 design evaluations.

Run on a desktop workstation (4 cpu’s for each

FEA analysis), ~5 days elapsed time.



The optimal design is a trade off primarily between fillet and bore stress.

Very narrow range of acceptable solutions.

modeFRONTIER required just under 600 designs to find a significant improvement over the baseline design.

RSM methods are more successful when applied to structural design problems.

54

Co

nstr

ain

t

Co

nstr

ain

t



Outcomes:

Bore stress and back wall stress reduced.

x Fillet stresses are higher than in the

baseline. (this was a conscious choice)

Design now meets the minimum

mechanical requirements.

.

55

Baseline

Optimized

% of Max Allowable

% of Max Allowable

100%

0%

95%

0%


Summary

Similar methodology as was developed for aerodynamic design can also

be applied to structural optimization.

FEA methods are generally faster than CFD, but automatic geometry

generation is more challenging.

modeFRONTIER optimization with Hybrid or FAST scheduler.

RSM based schedulers are more successful with FEA than CFD.

Results show the potential for stress reduction.

56


Thank You

57

Optimization of a Turbo Charger Compressor using AxCent ...

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