Multi-objective adjoint optimization of flow in ducts and ... · PDF fileMulti-objective...

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Multi-objective adjoint optimization of flow in ducts

and pipe networks

Eugene de Villiers

Flow Problems Analysis in Oil & Gas Conference,

Dynaflow, Rotterdam, Netherlands,

13 January 2011

© 2010 Engys Ltd.

Flow Problems Analysis in Oil & Gas, 2011

Content

• Introduction to Engys

• Optimisation

• Adjoint Method

• Examples

Right angled duct

Duct network

Air-inlet filter

• Conclusions

• Looking ahead

© 2010 Engys Ltd.


Engys

• UK, Germany and Italy

• Open Source software for industrial application

CFD, FEM, Optimisation

OPENFOAM , Code_Aster, Dakota

• Software services

Outsourcing/Consultancy

Training

Support

Development

© 2010 Engys Ltd.

OPENFOAM® is a registered trademark of OpenCFD Ltd.


Optimisation

• What is Design Optimisation?

Design for increased efficiency

Better performance, lower operating cost, robustness, increased reliability, etc.

• Why optimise?

Reduced process and product cost

Better product

Regulatory pressure

• Virtually anything can be optimised given a favourable cost-benefit ratio

© 2010 Engys Ltd.

Competitive advantage


Optimisation | Practical Examples

• Catalytic converter Increase flow uniformity

Conversion efficiency

Improve component longevity

• Ship hull Reduce hull drag

Improve displacement

• LNG BOG compressor Lower losses in system components

Reduced operating power

© 2010 Engys Ltd.

Images from Hinterberger & Olesen, OSCIC 2009



© 2010 Engys Ltd.







Reduced operating power



© 2010 Engys Ltd.







Reduced operating cost

Images from Kubo, OFWS 2010


Optimisation | Oil & Gas Applications

• Fluid applications (CFD)

System pressure drop minimisation

Maximise flow uniformity into heat exchangers, filters, catalysts and duct networks

Maximise mixing and separation efficiency

Erosion minimisation

Superstructure aerodynamics and hydrodynamics (forces, frequency responses, etc.)

Ventilation strategies

Multi-objective and optimisation under constraints

© 2010 Engys Ltd.


Design Optimisation | Approaches

• How to optimise geometry

Experience (cognitive model)

Analytical (limited class of problems)

Reduced order models (response surface, POD)

Evolutionary (genetic, neural)

Finite difference (gradient methods)

Adjoint

Hybrid© 2010 Engys Ltd.

0

0),(

,0),(

L

p

LpR

VV


Adjoint Methods | Background

• Conceptually, what is the adjoint method?

“Method for the evaluation of the derivative of a function I(s) with respect to parameters s in situations where I depends on s indirectly, via an intermediate variable w(s), which is computationally expensive to evaluate.” - René Schneider, 2006

In figurative terms, its like turning the governing equations inside-out to see how local changes will affect global objectives.

In the context of CFD, it can tell you how changes to any cells porosity or a surface vertex’s position (s) will affect an objective function like pressure drop (I), without having to calculate the effect of such changes (in s) on the velocity and pressure (w).

There is a lot of mathematics.

© 2010 Engys Ltd.


• Derived using augmented cost function and the method of Lagrange multipliers:


© 2010 Engys Ltd.

0,0),(

,0),(

L

p

LpR

VV

dRqJL ,U

),,( pR VNavier-Stokes:

Augmented cost function:

),,( pJ VObjective:

Adjoint variables (unknown)

For L to be an optimum, the following must be true:

Adjoint equations Sensitivity gradients



• Continuous adjoint equations:

• Adjoint sensitivity:

finds the source of a specific anomaly

does NOT model physical quantities

models the sensitivity of a property to these quantities

© 2010 Engys Ltd.

0

00

),(T

e

T qp

L

UUIVUU

U

V

d

LVU

Upstream convection

of adjoint rate of strain


Adjoint Methods | Implementation

• Basic equations fixed

Only boundary conditions and source terms change for different objectives

• Can be easily implemented in OPENFOAM

see Othmer, De Villiers & Weller; AIAA-2007-3947

• Solution time independent of number of parameters to be optimised

Main benefit over conventional optimisation techniques

© 2010 Engys Ltd.



• “One shot” solution approach

Single matrix solution

Partial convergence

Incomplete gradients

“Frozen” turbulence

Under-relaxed geometry update

© 2010 Engys Ltd.

Adjoint Setup

Primal – N-S

Adjoint

Topology

Objectives Main

loop

Ob

j. loop

Final design



• New components

Multi-objective framework

Objectives:

• Minimise power loss

• Match target velocity at outlet

• Maximum uniformity at outlet

• Minimise force on surface

• Maximise swirl in volume

Compressible/Incompressible primal

Marching front geometry engine

Stabilised numerics

© 2010 Engys Ltd.


Right-angled Duct

• Basic 2D case to show the fundamental properties of the adjoint

Steady incompressible laminar flow

Porous jump outlet

• Performance

p = 14.4 mPa

= 0.92

© 2010 Engys Ltd.

ii

ii

mean

i

A

AVV15.01


Right-angled Duct

• Pressure drop optimisation only

p = 12.9 mPa, = 0.949

© 2010 Engys Ltd.

MOVIE


Right-angled Duct

• Snapshot after 500 iterations

© 2010 Engys Ltd.

Solid

Zero sensitivity line

Grow solid boundary

outward where VU < 0Shrink solid boundary

where VU > 0


Right-angled Duct

• Weighting Pressure:Uniformity – 1:100

p = 13.5 mPa, = 0.986

© 2010 Engys Ltd.

MOVIE


Right-angled Duct

• Snapshot after 200 iterations

© 2010 Engys Ltd.

Low outlet velocity

encourages adjoint outflow

Above average outlet velocity

generates uniformity adjoint

inflow


Right-angled Duct

• Single adjoint calculation for pressure drop optimisation improves design:

-10.4% pressure loss, +3% uniformity

• Multi-objective more difficult due to conflicting sensitivities for pressure and uniformity

-6.3% pressure loss, +7% uniformity

• Undemanding case with porous jump outlet dominating flow morphology

Demonstrates principles

© 2010 Engys Ltd.


Duct Network

• Typical fluid dynamic issues in duct systems

Pressure loss

Flow distribution

Mixing/Separation

NVH

© 2010 Engys Ltd.


Duct Network

• 2D duct network representative of a fluid distribution system

• Objectives:

Minimise pressure drop

Try to get target mean velocity at all outlets(1 m/s)

• Steady incompressible RANS

© 2010 Engys Ltd.

inlet1fixedValue

V = (5 0 0) m/sTurbulence: I = 0.1,

L = 1cm

outletsPorous jumpdP ~ 1.5 Pa


Duct Network

• 2D duct network – pressure loss only

1500 iteration

© 2010 Engys Ltd.

P = 9.08 Pa = 0.75

U = 0.78

U = 0.96

U = 0.81

U = 0.68

U = 1.10

U = 1.84

U = 0.58

U = 0.72

U = 1.42P = 15.1 Pa = 0.63

U = 0.04

U = 2.04

U = 1.46

U = 0.04

U = 0.16

U = 1.27

U = 1.16

U = 1.10

U = 1.47


Duct Network

• 2D duct network – pressure loss:uniformity –1:100

• Solution – 5000 iterations

© 2010 Engys Ltd.

MOVIE


• 2D duct network – pressure loss:uniformity –1:100

Duct Network

© 2010 Engys Ltd.

P = 10.5 Pa = 0.95

U = 0.99

U = 0.91

U = 0.92

U = 0.99

U = 0.97

U = 1.05

U = 1.03

U = 1.01

U = 1.07

P = 15.1 Pa = 0.63

U = 0.04

U = 2.04

U = 1.46

U = 0.04

U = 0.16

U = 1.27

U = 1.16

U = 1.10

U = 1.47


Duct Network

• Pressure loss only optimisation:

-39.9% pressure loss, +19.0% uniformity

• Multi-objective 1:100 relative uniformity weighting

-30.5% pressure loss, +50.1% uniformity

• Large improvements when design space permits

• Issues

Multi-objective much more costly than single (x5)

Not a real case, will adjoint produce similar improvements in more constrained design space?

© 2010 Engys Ltd.


Air-intake

• Automotive air intake system with particulate filter and water separation components

• Objectives

Reduce losses

Improve outlet uniformity to increase filter utilisation

Produce pressure-loss, uniformity trade-off curve

© 2010 Engys Ltd.

Geometry courtesy of Volkswagen AG

MOVIE


• Steady incompressible RANS

Air-intake | Setup

© 2010 Engys Ltd.

outletresistivePressure

p0 = 0 PaC1 = 36.56C2 = 36.38resistiveVelocity:Vt = 0 m/s Vn = (0 0 0)

wallsNo slip

inlet1fixedValue

V = (2.78 0 0) m/sk = 0.02898 m2/s2

omega = 2.7969 1/s

inlet2fixedValue

V = (-14.87 0 0) m/sk = 0.5461 m2/s2

omega = 12.1415 1/s

nn VVCCpp **5.0*210


Air-intake | Objectives

© 2010 Engys Ltd.

CASE Pressure Drop [Pa] p % Outlet Uniformity %

p0u0 2886.6 - 0.8655 -

p1u0 2169.3 -24.9 0.8993 +3.9

p1u9 2161.0 -25.1 0.8994 +3.9

p1u999 2211.6 -23.4 0.9229 +6.6

p5u9995 2290.2 -20.7 0.9493 +9.7

ii

ii

mean

i

A

AVV

15.01

2140

2160

2180

2200

2220

2240

2260

2280

2300

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0 500 1000 1500 2000

Pre

ssu

re d

rop

Un

ifo

rmit

y In

dex

Relative Uniformity Weighting


Air-intake | Topology & Streamlines

© 2010 Engys Ltd.

• Baseline – p0u0

• Unsteady mixing of inlet streams

• Many recirculation zones and secondary vortices

• High non-uniformity at outlet

MOVIE


Air-intake | Topology & Streamlines

© 2010 Engys Ltd.

• Uniformity ratio – 1:2000

• Stabilised inlet stream mixing

• No recirculation

• Blockage of high outlet velocity regions improves overall (but not local) uniformity MOVIE


Air-intake

• Significant improvements in system performance despite constrained highly complex design space

• Issue

Some parts difficult to manufacture –requires interpretation

Due to explicit global minimum curvature specification which is not sensitive to local requirements

• Too large minimum curvature produces poor objectives

• Too small, noisy geometry

© 2010 Engys Ltd.


Summary

• Next generation geometric design aid based on adjoint technology 1-2 orders of magnitude faster than conventional methods

(depending on number of parameters).

Cost does not increase with number of parameters.

• Limitations Gradient based sensitivities – cannot always find global optima.

Current surface representation method does not reliably produce easy to manufacture geometries.

Adding new objectives requires deriving new boundary conditions and source terms for adjoint equations – complex process.

© 2010 Engys Ltd.


Looking ahead

• Improved immersed boundary handling

• Surface based morphing More accurate surface representation

Coupling to traditional morphing tools

• Free-surface treatment for ship wave drag optimisation

• Inclusion of additional scalar transport for mixing and heat transfer optimisation

• Transient

© 2010 Engys Ltd.

MOVIE

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