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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.
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
Optimisation | Practical Examples
© 2010 Engys Ltd.
• 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
Flow Problems Analysis in Oil & Gas, 2011
Optimisation | Practical Examples
© 2010 Engys Ltd.
• 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 cost
Images from Kubo, OFWS 2010
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
• Derived using augmented cost function and the method of Lagrange multipliers:
Adjoint Methods | Background
© 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
Flow Problems Analysis in Oil & Gas, 2011
Adjoint Methods | Background
• 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
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
Adjoint Methods | Implementation
• “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
Flow Problems Analysis in Oil & Gas, 2011
Adjoint Methods | Implementation
• 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.
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
Right-angled Duct
• Pressure drop optimisation only
p = 12.9 mPa, = 0.949
© 2010 Engys Ltd.
MOVIE
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
Right-angled Duct
• Weighting Pressure:Uniformity – 1:100
p = 13.5 mPa, = 0.986
© 2010 Engys Ltd.
MOVIE
Flow Problems Analysis in Oil & Gas, 2011
Right-angled Duct
• Snapshot after 200 iterations
© 2010 Engys Ltd.
Low outlet velocity
encourages adjoint outflow
Above average outlet velocity
generates uniformity adjoint
inflow
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
Duct Network
• Typical fluid dynamic issues in duct systems
Pressure loss
Flow distribution
Mixing/Separation
NVH
© 2010 Engys Ltd.
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
Duct Network
• 2D duct network – pressure loss:uniformity –1:100
• Solution – 5000 iterations
© 2010 Engys Ltd.
MOVIE
Flow Problems Analysis in Oil & Gas, 2011
• 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
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
• 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
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
Air-intake | Z-velocity @ Outlet
© 2010 Engys Ltd.
p0u0 p1u0 p1u9 p1u999 p5u9995
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
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
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
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.
Flow Problems Analysis in Oil & Gas, 2011
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