Optimization of Nonlinear, Coupled Fluid-Thermal Systems

Сентябрь 3, 2022

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Optimization of Nonlinear, Coupled Fluid-Thermal Systems

Содержание

2. Presentation Outline Overview Project Goals Microgravity Research MGFLO Optimization Theory Previous Work Code Details Overview Validation
3. Project Goals To Design and Implement an optimization algorithm for a fluid-thermal simulator MGFLO Boundary Condition
4. Microgravity Fluid Research Surface Tension Smallest Surface Area Possible Dominated on Earth by Gravity, which Makes
5. Strong Field Weak Field
6. Microgravity Test Facilities Drop Towers Evacuated tubes used to expose experiments to several seconds of microgravity
7. Test Facilities NASA’s KC-135 “Vomit Comet” Parabolic flight pattern can produce up to 30 seconds of
8. Test Facilities Sounding Rockets Also flown in a parabolic flight path to produce microgravity Can provide
9. Microgravity Simulation Computational Fluid Dynamics (CFD) allows cost-effective microgravity simulation Advances in parallel supercomputing allow large
10. Incompressible Navier-Stokes Equations: Energy Equation: Governing Equations
11. MGFLO Developed Under NASA-Grand Challenge Support Parallel, Finite Element Formulation of Navier-Stokes and Energy Equations Allows
12. Optimization Theory Attempt to find “best value” of a merit function within defined constraints Gradient versus
13. Nelder and Mead’s Method Efficient search method for minimizing a merit function of up to six
14. Simplex Steps Reflection Expansion Contraction
15. Previous Work Investigated Operation of the MGFLO Code Designed Simple Optimization Routine in Matlab Established Algorithms
16. Code Overview Developed Matlab Routines to Analyze MGFLO Output. Matlab Can Compute Quantities of Interest: Vorticity,
17. Code Functions Initializes the solution Calls MGFLO for each simplex step Checks that user-specified constraints are
19. Debugging & Validation Attempt to find answer to a known problem Position heat source on top
22. Optimization Path
23. Limitations Merit function dependence for pathological problems Not successful at maximizing vorticity in previous case Non-smooth
24. Applications Solve more complicated problem whose answer is not known a-priori System exposed to external environment
26. Case 1: Tdesired=310K
27. Particle Tracing Algorithm Heun predictor-corrector method Second-order accurate in time Allows visualization/quantification of mixing
30. Convergence History
31. Case 2: Tdesired=340K
34. Convergence History
35. Conclusions We became familiar with the CFDLab and the MGFLO code Successfully developed a method to
36. Recommendations Use particle tracing algorithm to optimize system mixing (currently takes a long time!) Implement feedback
38. Скачать презентацию

Слайд 2

Presentation Outline
Overview
Project Goals
Microgravity Research
MGFLO
Optimization Theory
Previous Work
Code Details
Overview
Validation
Applications

Conclusions
Recommendations

Слайд 3

Project Goals
To Design and Implement an optimization algorithm for a fluid-thermal

simulator
MGFLO
Boundary Condition Manipulation

Слайд 4

Microgravity Fluid Research
Surface Tension
Smallest Surface Area Possible
Dominated on Earth by Gravity,

which Makes Surfaces Flat

Liquid Bridges
ALEX: A Liquid Electrohydrodynamics eXperiment
Surface Tension Dominates with Decreased Electric Field

In a microgravity environment, surface tension and
thermocapillary effects can be dominant.

Слайд 5

Strong
Field
Weak
Field

Слайд 6

Microgravity Test Facilities
Drop Towers
Evacuated tubes used to expose experiments to several

seconds of microgravity
Only short durations of microgravity are achieved

Слайд 7

Test Facilities
NASA’s KC-135 “Vomit Comet”
Parabolic flight pattern can produce up to

30 seconds of microgravity
Several periods of microgravity in one flight

Слайд 8

Test Facilities
Sounding Rockets
Also flown in a parabolic flight path to produce

microgravity
Can provide 6-7 minutes of microgravity

Слайд 9

Microgravity Simulation
Computational Fluid Dynamics (CFD) allows cost-effective microgravity simulation
Advances in parallel

supercomputing allow large problems to be solved

Слайд 10

Incompressible Navier-Stokes Equations:
Energy Equation:
Governing Equations

Слайд 11

MGFLO
Developed Under NASA-Grand Challenge Support
Parallel, Finite Element Formulation of Navier-Stokes and

Energy Equations
Allows for Coupled and Uncoupled Solution
Systems Optimized Through Matlab Using Existing Algorithms

Слайд 12

Optimization Theory
Attempt to find “best value” of a merit function within

defined constraints
Gradient versus non-gradient methods
Gradient methods can be complex and require several merit function evaluations
Non-gradient methods optimize based on a sample set of merit function values
Nelder-Mead Simplex Search Algorithm

Слайд 13

Nelder and Mead’s Method
Efficient search method for minimizing a merit function

of up to six variables
Optimization points are nodes of a polygon
Optimal solution is determined by:
Reflection
Expansion
Contraction

Слайд 14

Simplex Steps
Reflection
Expansion
Contraction

Слайд 15

Previous Work
Investigated Operation of the MGFLO Code
Designed Simple Optimization Routine in

Matlab
Established Algorithms to Optimize Complex Fluid-Thermal Systems

Слайд 16

Code Overview
Developed Matlab Routines to Analyze MGFLO Output.
Matlab Can Compute Quantities

of Interest:
Vorticity, Divergence
Gradient, Laplacian
0th, 1st, 2nd Order Derivatives Normal to Walls
Average Quantities in Large Datasets

Слайд 17

Code Functions
Initializes the solution
Calls MGFLO for each simplex step
Checks that user-specified

constraints are satisfied
Calculates the user-specified merit function
Allows user to monitor solution progression

Слайд 18

Слайд 19

Debugging & Validation
Attempt to find answer to a known problem
Position heat

source on top surface to maximize heat flux out of the bottom
Run on the 16-node Beowulf cluster in the CFDLab

Слайд 20

Слайд 21

Слайд 22

Optimization Path

Слайд 23

Limitations
Merit function dependence for pathological problems
Not successful at maximizing vorticity in

previous case
Non-smooth merit functions (too many local maxima)

Слайд 24

Applications
Solve more complicated problem whose answer is not known a-priori
System exposed

to external environment via Newton’s law of cooling (mixed boundary condition)
Use particle tracing as a visualization technique

Слайд 25

Слайд 26

Case 1: Tdesired=310K

Слайд 27

Particle Tracing Algorithm
Heun predictor-corrector method
Second-order accurate in time
Allows visualization/quantification of

mixing

Слайд 28

Слайд 29

Слайд 30

Convergence History

Слайд 31

Case 2: Tdesired=340K

Слайд 32

Слайд 33

Слайд 34

Convergence History

Слайд 35

Conclusions
We became familiar with the CFDLab and the MGFLO code
Successfully developed

a method to optimize nonlinear fluid-thermal systems
Implemented a particle tracing algorithm in Matlab to visualize fluid mixing

Слайд 36

Recommendations
Use particle tracing algorithm to optimize system mixing (currently takes a

long time!)
Implement feedback control for time-varying systems
Calculate merit function interior to MGFLO
Faster
More accurate
Support unstructured grids

Optimization of Nonlinear, Coupled Fluid-Thermal Systems

Содержание

Presentation OutlineOverviewProject GoalsMicrogravity ResearchMGFLOOptimization TheoryPrevious Work Code Details Overview Validation Applications

Project Goals To Design and Implement an optimization algorithm for a fluid-thermal

Microgravity Fluid ResearchSurface TensionSmallest Surface Area PossibleDominated on Earth by Gravity,

StrongFieldWeak Field

Microgravity Test FacilitiesDrop TowersEvacuated tubes used to expose experiments to several

Test FacilitiesNASA’s KC-135 “Vomit Comet”Parabolic flight pattern can produce up to

Test FacilitiesSounding RocketsAlso flown in a parabolic flight path to produce

Microgravity SimulationComputational Fluid Dynamics (CFD) allows cost-effective microgravity simulationAdvances in parallel

Incompressible Navier-Stokes Equations:Energy Equation:Governing Equations

MGFLODeveloped Under NASA-Grand Challenge SupportParallel, Finite Element Formulation of Navier-Stokes and

Optimization TheoryAttempt to find “best value” of a merit function within

Nelder and Mead’s MethodEfficient search method for minimizing a merit function

Simplex StepsReflectionExpansionContraction

Previous WorkInvestigated Operation of the MGFLO CodeDesigned Simple Optimization Routine in

Code OverviewDeveloped Matlab Routines to Analyze MGFLO Output.Matlab Can Compute Quantities

Code FunctionsInitializes the solutionCalls MGFLO for each simplex stepChecks that user-specified

Debugging & ValidationAttempt to find answer to a known problemPosition heat

Optimization Path

LimitationsMerit function dependence for pathological problemsNot successful at maximizing vorticity in

ApplicationsSolve more complicated problem whose answer is not known a-prioriSystem exposed

Case 1: Tdesired=310K

Particle Tracing AlgorithmHeun predictor-corrector methodSecond-order accurate in time Allows visualization/quantification of

Convergence History

Case 2: Tdesired=340K

Convergence History

ConclusionsWe became familiar with the CFDLab and the MGFLO codeSuccessfully developed

RecommendationsUse particle tracing algorithm to optimize system mixing (currently takes a

Похожие презентации

Presentation Outline
Overview
Project Goals
Microgravity Research
MGFLO
Optimization Theory
Previous Work
Code Details
Overview
Validation
Applications

Project Goals
To Design and Implement an optimization algorithm for a fluid-thermal

Microgravity Fluid Research
Surface Tension
Smallest Surface Area Possible
Dominated on Earth by Gravity,

Strong
Field
Weak
Field

Microgravity Test Facilities
Drop Towers
Evacuated tubes used to expose experiments to several

Test Facilities
NASA’s KC-135 “Vomit Comet”
Parabolic flight pattern can produce up to

Test Facilities
Sounding Rockets
Also flown in a parabolic flight path to produce

Microgravity Simulation
Computational Fluid Dynamics (CFD) allows cost-effective microgravity simulation
Advances in parallel

Incompressible Navier-Stokes Equations:
Energy Equation:
Governing Equations

MGFLO
Developed Under NASA-Grand Challenge Support
Parallel, Finite Element Formulation of Navier-Stokes and

Optimization Theory
Attempt to find “best value” of a merit function within

Nelder and Mead’s Method
Efficient search method for minimizing a merit function

Simplex Steps
Reflection
Expansion
Contraction

Previous Work
Investigated Operation of the MGFLO Code
Designed Simple Optimization Routine in

Code Overview
Developed Matlab Routines to Analyze MGFLO Output.
Matlab Can Compute Quantities

Code Functions
Initializes the solution
Calls MGFLO for each simplex step
Checks that user-specified

Debugging & Validation
Attempt to find answer to a known problem
Position heat

Limitations
Merit function dependence for pathological problems
Not successful at maximizing vorticity in

Applications
Solve more complicated problem whose answer is not known a-priori
System exposed

Particle Tracing Algorithm
Heun predictor-corrector method
Second-order accurate in time
Allows visualization/quantification of

Conclusions
We became familiar with the CFDLab and the MGFLO code
Successfully developed

Recommendations
Use particle tracing algorithm to optimize system mixing (currently takes a