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Two-dimensional oscillating flow over a step

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University of Florida
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TWO-DIMENSIONAL OSCILLATING FLOW OVER A STEP By DOUGLAS CARL HOFER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 1987 TWO-DIMENSIONAL OSCILLATING FLOW OVER A STEP By DOUGLAS CARL HOFER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 1987 ACKNOWLEDGMENTS I first express gratitude to Dr. Tom I-P. Shih for his invaluable guidance and essential encouragement during the course of my research. I also thank Dr. Shih for his exceptional help in preparing this manu- script. I am grateful to Dr. R. A. Gater and Dr. U. H. Kurzweg for serving on my master's committee. In particular, I am indebted to Dr. Gater for his editorial completeness. Finally, I thank my wife whose patience, encouragement, moral support and hard work made this study possible. 11 TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES iv NOMENCLATURE v ABSTRACT viii CHAPTERS I INTRODUCTION 1 II DESCRIPTION OF PROBLEM 3 III FORMULATION OF PROBLEM 6 3.1 Governing Equations in Cartesian Coordinates 6 3.2 Boundary and Initial Conditions in Cartesian Coordinates 8 3.3 Governing Equations in Transformed Coordinates 11 3.4 Boundary Conditions in Transformed Coordinates 12 IV NUMERICAL METHOD OF SOLUTION 16 4.1 Grid Generation 16 4.2 Finite Difference Equations at Interior Grid Points . . 21 4.3 Finite Difference Equations at Boundary Grid Points . . 22 4.4 Solution Procedure 31 4.5 Vectorization of Computer Program 32 V RESULTS 34 5.1 Steady Flows Past a Step 34 5.2 Oscillating Flows Past a Step: Pistons Oscillating in Phase 37 5.3 Oscillating Flows Past a Step: Pistons Oscillating Out of Phase . 39 VI SUMMARY 88 REFERENCES 90 BIOGRAPHICAL SKETCH 94 iii LIST OF TABLES Page 3-1. Conservation equ

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