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№1 слайд
Содержание слайда: Optimization of Nonlinear, Coupled Fluid-Thermal Systems
Carrie Keyworth and Benjamin Kirk
Advisors: Dr. Graham Carey and Bill Barth
ASE 463Q
May 3, 2000
№2 слайд
Содержание слайда: Presentation Outline
Overview
Project Goals
Microgravity Research
MGFLO
Optimization Theory
Previous Work
№3 слайд
Содержание слайда: Project Goals
To Design and Implement an optimization algorithm for a fluid-thermal simulator
MGFLO
Boundary Condition Manipulation
№4 слайд
Содержание слайда: Microgravity Fluid Research
Surface Tension
Smallest Surface Area Possible
Dominated on Earth by Gravity, which Makes Surfaces Flat
№5 слайд
№6 слайд
Содержание слайда: Microgravity Test Facilities
Drop Towers
Evacuated tubes used to expose experiments to several seconds of microgravity
Only short durations of microgravity are achieved
№7 слайд
Содержание слайда: 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
№8 слайд
Содержание слайда: Test Facilities
Sounding Rockets
Also flown in a parabolic flight path to produce microgravity
Can provide 6-7 minutes of microgravity
№9 слайд
Содержание слайда: Microgravity Simulation
Computational Fluid Dynamics (CFD) allows cost-effective microgravity simulation
Advances in parallel supercomputing allow large problems to be solved
№10 слайд
Содержание слайда: Governing Equations
Incompressible Navier-Stokes Equations:
Energy Equation:
№11 слайд
Содержание слайда: 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
№12 слайд
Содержание слайда: 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
№13 слайд
Содержание слайда: 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
№14 слайд
Содержание слайда: Simplex Steps
№15 слайд
Содержание слайда: Previous Work
Investigated Operation of the MGFLO Code
Designed Simple Optimization Routine in Matlab
Established Algorithms to Optimize Complex Fluid-Thermal Systems
№16 слайд
Содержание слайда: 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
№17 слайд
Содержание слайда: 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
№18 слайд
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Содержание слайда: 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
№20 слайд
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Содержание слайда: Optimization Path
№23 слайд
Содержание слайда: Limitations
Merit function dependence for pathological problems
Not successful at maximizing vorticity in previous case
Non-smooth merit functions (too many local maxima)
№24 слайд
Содержание слайда: 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
№25 слайд
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Содержание слайда: Case 1: Tdesired=310K
№27 слайд
Содержание слайда: Particle Tracing Algorithm
Heun predictor-corrector method
Second-order accurate in time
Allows visualization/quantification of mixing
№28 слайд
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№30 слайд
Содержание слайда: Convergence History
№31 слайд
Содержание слайда: Case 2: Tdesired=340K
№32 слайд
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Содержание слайда: Convergence History
№35 слайд
Содержание слайда: 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
№36 слайд
Содержание слайда: 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
№37 слайд
Содержание слайда: Questions?