IHS-Präsentation, 2008 Ruprecht University of Stuttgart Institute of Fluid Mechanics and Hydraulic Machinery, IHS Experience in mathematical optimization Automatic shape optimisation parameterized geometry Wells- Tool
Dec 17, 2015
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Experience in mathematical optimization
Automatic shape optimisation
parameterized geometry
Wells-Tool
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Optimisation Methods
• Directe optimisation• “Response Surface” method
– Estimation of an continous approximate function by• Neuronal net• Polynomial approach• Spline
– Search for the optimum of the approximate function
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parameter
Qu
alit
äts
fun
ktio
nberechnete Werte
Optimierung an der Response Surface
Response Surface Methode
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
1
2
3
assumed optimum
search direction
cost
fu
nct
ion
relaxation
• Gradient type algorithmus, with search direction• Opjective funktion is locally approximated and the minimum is
calculated along the search direction
EXTREME
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Self Adaptive Evolution (SAE)
• Start with a randomly chosen population
• New population is obtained by
– Mutation
– Crossover
– Survival of the fittest– Live time of each individual is exactly 1 generation
(Comma Strategie)
Evolution methode
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parallel Optimisation
simultaneous simulation on different resources
each simulation is run in parallel
Research: Asynchronous, parallel optimisation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parallel OptimisationGrid Compting
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Applied Algorithm
randomly choseninitial parameter sets
CFD
CFD
CFD
CFD
CFD
survival of the fittest
new sets by discrete operation, e. g. mirror
new sets randomlywith weighting
CFD
CFD
CFD
CFD
gri
d p
ort
al
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Example Guide vane shape
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Guide vane geometry
Inlet angle, Outlet angle,
chamber line angle, Weighting factor inlet,
Weighting factor outlet,Overlapping,
Profile a, Profile b,
Trailing edge thickness
Geometry Parameterisation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Automatic block structured mesh
Automatic Grid Generation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Simulation
Results:
Flow patterns (e. g pressure distribution)
Overall quantities (e. g. efficiency, losses)
Restrictions (e. g. cavitation)
Typical computational time for one geometry: 1-4 hon a Cluster of HPC
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
9 free parameters:
- 45 different designs (individuals) per generation
- 8 generations- in total 360 calculations
Guide vane shape
optimized with evolution strategy
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Convergence
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Optimised Geometrie
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Test example: Draft tube cone
Assumption:Cone length
Optimisation: Outlet diameter
L
Din
Dout
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
randomly chosen starting points
Cone length: 6 D_in
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the first generation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the second generation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the third generation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
computed pointssurvivors of the seventh generation
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
The draft tube contour can only be changed slightly.
Optimization of the area distribution
Draft tube area distribution
Application: Refurbishment of an existing power plant
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Area
Draft tube length length
area distribution
• Area distribution represented by B-Spline curves • Inlet and outlet kept constant• other cross sections scaled up
Draft tube area distribution
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Draft tube area distribution
Investigated area distribution during the optimisation
Design point
IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Draft tube area distribution
Design point
Obtained area distribution
original draft tube
maximum efficiency
minimum efficiency
draft tube efficiency increase: 8%overall efficiency increase: 0.4%