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Optimization of Nonlinear, Coupled Fluid-Thermal Systems Carrie Keyworth and Benjamin Kirk Advisors: Dr. Graham Carey and Bill Barth ASE 463Q May 3, 2000

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Presentation Outline Overview Project Goals Microgravity Research MGFLO Optimization Theory Previous Work

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Project Goals To Design and Implement an optimization algorithm for a fluid-thermal simulator MGFLO Boundary Condition Manipulation

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Microgravity Fluid Research Surface Tension Smallest Surface Area Possible Dominated on Earth by Gravity, which Makes Surfaces Flat

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Microgravity Test Facilities Drop Towers Evacuated tubes used to expose experiments to several seconds of microgravity Only short durations of microgravity are achieved

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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

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Test Facilities Sounding Rockets Also flown in a parabolic flight path to produce microgravity Can provide 6-7 minutes of microgravity

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Microgravity Simulation Computational Fluid Dynamics (CFD) allows cost-effective microgravity simulation Advances in parallel supercomputing allow large problems to be solved

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Governing Equations Incompressible Navier-Stokes Equations: Energy Equation:

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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

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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

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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

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Simplex Steps

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Previous Work Investigated Operation of the MGFLO Code Designed Simple Optimization Routine in Matlab Established Algorithms to Optimize Complex Fluid-Thermal Systems

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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

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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

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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

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Optimization Path

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Limitations Merit function dependence for pathological problems Not successful at maximizing vorticity in previous case Non-smooth merit functions (too many local maxima)

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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

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Case 1: Tdesired=310K

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

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Convergence History

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Case 2: Tdesired=340K

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Convergence History

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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

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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