FUNDAMENTALS OF GAS DYNAMICS

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1 FUNDAMENTALS OF GAS DYNAMICS Second Edition ROBERT D. ZUCKER OSCAR BIBLARZ Department of Aeronautics and Astronautics Naval Postgraduate School Monterey, California JOHN WILEY & SONS, INC.

2 Contents PREFACE TO THE STUDENT 1 REVIEW OF ELEMENTARY PRINCIPLES Units and Notation Some Mathematical Concepts Thermodynamic Concepts for Control Mass Analysis Review Questions Review 2 CONTROL VOLUME ANALYSIS PART Flow Dimensionality and Average Velocity Transformation of a Material Derivative to a Control Volume Approach Conservation of Mass Conservation of Energy 3 CONTROL VOLUME AN ALYSIS PART II 3.1 xi xiii V

3 Comments on Entropy Pressure-Energy Equation The Stagnation Concept Stagnation Pressure-Energy Equation Consequences of Constant Density Momentum Equation INTRODUCTION TO COMPRESSIBLE FLOW Sonic Velocity and Mach Number Wave Propagation Equations for Perfect Gases in Terms of Mach Number h-s and T-s Diagrams VARYING-AREA ADIABATIC FLOW General Fluid No Losses Perfect Gases with Losses The * Reference Concept Isentropic Table Nozzle Operation Nozzle Performance Diffuser Performance When у Is Not Equal to (Optional) Beyond the Tables

4 VÜ 6 STANDING NORMAL SHOCKS Shock Analysis General Fluid Working Equations for Perfect Gases Normal-Shock Table Shocks in Nozzles Supersonic Wind Tunnel Operation When у Is Not Equal to (Optional) Beyond the Tables MOVING AND OBLIQUE SHOCKS Normal Velocity Superposition: Moving Normal Shocks Tangential Velocity Superposition: Oblique Shocks Oblique-Shock Analysis: Perfect Gas Oblique-Shock Table and Charts Boundary Condition of Flow Direction Boundary Condition of Pressure Equilibrium Conical Shocks (Optional) Beyond the Tables PRANDTL-MEYER FLOW Argument for Isentropic Turning Flow Analysis of Prandtl-Meyer Flow Prandtl-Meyer Function Overexpanded and Underexpanded Nozzles Supersonic Airfoils 226

5 When у Is Not Equal to l.4 (Optional) Beyond the Tables FANNO FLOW Analysis for a General Fluid Working Equations for Perfect Gases Reference State and Fanno Table Applications Correlation with Shocks Friction Choking When у Is Not Equal to 1.4 (Optional) Beyond the Tables RAYLEIGH FLOW Analysis for a General Fluid Working Equations for Perfect Gases Reference State and the Rayleigh Table Applications Correlation with Shocks Thermal Choking due to Heating When у Is Not Equal to 1.4 (Optional) Beyond the Tables REAL GAS EFFECTS

6 IX What's Really Going On Semiperfect Gas Behavior, Development of the Gas Table Real Gas Behavior, Equations of State and Compressibility Factors Variable у Variable-Area Flows Variable у Constant-Area Flows PROF»ULSION SYSTEMS Brayton Cycle Propulsion Engines General Performance Parameters, Thrust, Power, and Efficiency Air-Breathing Propulsion Systems Performance Parameters Air-Breathing Propulsion Systems Incorporating Real Gas Effects Rocket Propulsion Systems Performance Parameters Supersonic Diffusers APPENDIXES A. of the English Engineering (ЕЕ) System of Units 396 B. of the International System (SI) of Units 400 С Friction-Factor Chart 404 D. Oblique-Shock Charts (y = 1.4) (Two-Dimensional) 406 E. Conical-Shock Charts (y = 1.4) (Three-Dimensional) 410 F. Generalized Compressibility Factor Chart 414 G. Isentropic Flow Parameters (y = 1.4) (including Prandtl-Meyer Function) 416 H. Normal-Shock Parameters (y = 1.4) 428 I. Fanno Flow Parameters (y = 1.4)

7 X CONTENTS J. Rayleigh Flow Parameters (y = 1.4) 450 K. Properties of Air at Low Pressures 462 L. Specific Heats of Air at Low Pressures 470 SELECTED REFERENCES 473 ANSWERS TO PROBLEMS 477 INDEX 487

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