• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Gas Dynamics
 

Gas Dynamics

on

  • 1,825 views

This revised and updated fourth edition continues to provide the most accessible and readable approach to the study of all the vital topics and issues associated...

This revised and updated fourth edition continues to provide the most accessible and readable approach to the study of all the vital topics and issues associated
with gas dynamic processes. At every stage, the physics governing the process, its applications and limitations are discussed in depth.
With a strong emphasis on the basic concepts and problem-solving skills, this text is suitable for a course on Gas Dynamics/Compressible Flows/High-speed
Aero-dynamics at both undergraduate and postgraduate levels in aerospace engineering, mechanical engineering, chemical engineering and applied physics.
The elegant and concise style of the book, along with illustrations and worked examples, makes it eminently suitable for self-study by scientists and engineers
working in the field of gas dynamics in industries and research laboratories.

Statistics

Views

Total Views
1,825
Views on SlideShare
1,825
Embed Views
0

Actions

Likes
0
Downloads
103
Comments
0

0 Embeds 0

No embeds

Accessibility

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Gas Dynamics Gas Dynamics Document Transcript

    • Fourth EditionGASDYNAMICS Ethirajan Rathakrishnan
    • ` 425.00GAS DYNAMICS, Fourth EditionEthirajan Rathakrishnan© 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of thisbook may be reproduced in any form, by mimeograph or any other means, withoutpermission in writing from the publisher.ISBN-978-81-203-4605-5The export rights of this book are vested solely with the publisher.Eleventh Printing (Fourth Edition) … … … June, 2012Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,New Delhi-110001 and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV,HSIDC, Kundli-131028, Sonepat, Haryana.
    • ContentsPreface ................................................................................................ xiPreface to the Third Edition ................................................................ xiiiPreface to the Second Edition ............................................................... xvPreface to the First Edition ................................................................ xvii1. Some Preliminary Thoughts ................................................... 1–17 1.1 Gas Dynamics—A Brief History .............................................. 1 1.2 Compressibility ........................................................................... 2 1.3 Supersonic Flow—What Is It? ................................................. 5 1.4 Speed of Sound .......................................................................... 6 1.5 Temperature Rise ..................................................................... 10 1.6 Mach Angle .............................................................................. 12 1.7 Summary ................................................................................... 152. Basic Equations of Compressible Flow ................................. 18–42 2.1 Thermodynamics of Fluid Flow ............................................. 18 2.2 First Law of Thermodynamics (Energy Equation) .............. 19 2.3 The Second Law of Thermodynamics (Entropy Equation).... 23 2.4 Thermal and Calorical Properties .......................................... 24 2.5 The Perfect Gas ...................................................................... 26 2.6 Summary ................................................................................... 35 Problems ...................................................................................... 393. Wave Propagation ................................................................ 43–46 3.1 Introduction .............................................................................. 43 3.2 Wave Propagation .................................................................... 43 3.3 Velocity of Sound .................................................................... 44 3.4 Subsonic and Supersonic Flows .............................................. 44 3.5 Summary ................................................................................... 454. Steady One-Dimensional Flow .............................................47–105 4.1 Introduction .............................................................................. 47 4.2 The Fundamental Equations ................................................... 47 4.3 Discharge from a Reservoir .................................................... 51 4.4 Streamtube Area–Velocity Relation ....................................... 61 vii
    • viii Contents 4.5 De Laval Nozzle ...................................................................... 64 4.6 Supersonic Flow Generation ................................................... 72 4.7 Diffusers .................................................................................... 82 4.8 Dynamic Head Measurement in Compressible Flow ............ 86 4.9 Pressure Coefficient ................................................................. 91 4.10 Summary ................................................................................... 93 Problems ...................................................................................... 965. Normal Shock Waves ......................................................... 106–145 5.1 Introduction ............................................................................. 106 5.2 Equations of Motion for a Normal Shock Wave ................. 107 5.3 The Normal Shock Relations for a Perfect Gas ................. 108 5.4 Change of Stagnation or Total Pressure across the Shock ... 112 5.5 Hugoniot Equation .................................................................. 115 5.6 The Propagating Shock Wave ............................................... 118 5.7 Reflected Shock Wave ............................................................ 124 5.8 Centred Expansion Wave ....................................................... 129 5.9 Shock Tube .............................................................................. 132 5.10 Summary .................................................................................. 137 Problems .................................................................................... 1416. Oblique Shock and Expansion Waves ................................ 146–212 6.1 Introduction ............................................................................. 146 6.2 Oblique Shock Relations ........................................................ 147 6.3 Relation between b and q ........................................................... 150 6.4 Shock Polar ............................................................................. 153 6.5 Supersonic Flow over a Wedge ............................................. 155 6.6 Weak Oblique Shocks ............................................................. 158 6.7 Supersonic Compression ......................................................... 160 6.8 Supersonic Expansion by Turning ......................................... 161 6.9 The Prandtl–Meyer Expansion .............................................. 162 6.10 Simple and Nonsimple Regions ............................................. 170 6.11 Reflection and Intersection of Shocks and Expansion Waves .................................................................... 170 6.12 Detached Shocks ..................................................................... 186 6.13 Mach Reflection ...................................................................... 187 6.14 Shock-Expansion Theory ........................................................ 191 6.15 Thin Aerofoil Theory ............................................................. 196 6.16 Summary .................................................................................. 203 Problems .................................................................................... 2057. Potential Equation for Compressible Flow ........................ 213–231 7.1 Introduction ............................................................................. 213 7.2 Crocco’s Theorem ................................................................... 213 7.3 The General Potential Equation for Three-Dimensional Flow ......................................................... 217 7.4 Linearization of the Potential Equation ............................... 219
    • Contents ix 7.5 Potential Equation for Bodies of Revolution ...................... 222 7.6 Boundary Conditions .............................................................. 224 7.7 Pressure Coefficient ................................................................ 227 7.8 Summary .................................................................................. 228 Problems .................................................................................... 2318. Similarity Rule .................................................................. 232–269 8.1 Introduction ............................................................................. 232 8.2 Two-Dimensional Flow: The Prandtl–Glauert Rule for Subsonic Flow ................................................................... 232 8.3 Prandtl–Glauert Rule for Supersonic Flow: Versions I and II .................................................................... 240 8.4 The von Karman Rule for Transonic Flow ......................... 243 8.5 Hypersonic Similarity ............................................................. 246 8.6 Three-Dimensional Flow: The Gothert Rule ........................ 249 8.7 Critical Mach Number ........................................................... 259 8.8 Summary .................................................................................. 264 Problems .................................................................................... 2689. Two-Dimensional Compressible Flows .............................. 270–282 9.1 Introduction ............................................................................. 270 9.2 General Linear Solution for Supersonic Flow ...................... 271 9.3 Flow along a Wave-Shaped Wall .......................................... 276 9.4 Summary .................................................................................. 280 Problems .................................................................................... 28110. Prandtl–Meyer Flow ......................................................... 283–289 10.1 Introduction ............................................................................. 283 10.2 Thermodynamic Considerations ............................................. 284 10.3 Prandtl–Meyer Expansion Fan .............................................. 284 10.4 Reflections ............................................................................... 287 10.5 Summary .................................................................................. 288 Problems .................................................................................... 28811. Flow with Friction and Heat Transfer ............................... 290–317 11.1 Introduction ............................................................................. 290 11.2 Flow in Constant-Area Duct with Friction ......................... 290 11.3 Adiabatic, Constant-Area Flow of a Perfect Gas ............... 292 11.4 Flow with Heating or Cooling in Ducts .............................. 302 11.5 Summary .................................................................................. 309 Problems .................................................................................... 31312. Method of Characteristics ................................................. 318–342 12.1 Introduction ............................................................................. 318 12.2 The Concepts of Characteristics ........................................... 318 12.3 The Compatibility Relation ................................................... 319 12.4 The Numerical Computational Method ................................ 322 12.5 Theorems for Two-Dimensional Flow ................................... 330
    • x Contents 12.6 Numerical Computation with Weak Finite Waves .............. 332 12.7 Design of Supersonic Nozzle .................................................. 336 12.8 Summary .................................................................................. 34113. Measurements in Compressible Flow ................................ 343–415 13.1 Introduction ............................................................................. 343 13.2 Pressure Measurements .......................................................... 343 13.3 Temperature Measurements ................................................... 350 13.4 Velocity and Direction ........................................................... 354 13.5 Density Problems .................................................................... 356 13.6 Compressible Flow Visualization ........................................... 356 13.7 High-Speed Wind Tunnels ..................................................... 374 13.8 Instrumentation and Calibration of Wind Tunnels ............. 400 13.9 Summary .................................................................................. 407 Problems .................................................................................... 41514. Rarefied Gas Dynamics ..................................................... 416–423 14.1 Introduction ............................................................................. 416 14.2 Knudsen Number .................................................................... 417 14.3 Slip Flow ................................................................................. 420 14.4 Transition and Free Molecule Flow ...................................... 420 14.5 Summary .................................................................................. 42215. High Temperature Gas Dynamics ..................................... 424–426 15.1 Introduction ............................................................................. 424 15.2 The Importance of High-Temperature Flows ....................... 424 15.3 The Nature of High-Temperature Flows .............................. 425 15.4 Summary .................................................................................. 426Appendix A ........................................................... 427–495 Table A1 Isentropic Flow of Perfect Gas (g = 1.4) ................... 427 Table A2 Normal Shock in Perfect Gas (g = 1.4) ..................... 440 Table A3 Oblique Shock in Perfect Gas (g = 1.4) .................... 450 Table A4 One-Dimensional Flow with Friction ( g = 1.4) .......... 484 Table A5 One-Dimensional Frictionless Flow with Change in Stagnation Temperature (g = 1.4) ............ 490Appendix B ............................................................ 496–503 Listing of the Method of Characteristics Program ...................... 496Appendix C ............................................................ 504–507 Output for Mach 2.0 Nozzle Contour ............................................ 504Appendix D ........................................................... 508–509 Oblique Shock Chart 1 .................................................................... 508 Oblique Shock Chart 2 .................................................................... 509Selected References ................................................. 511–512Index .................................................................... 513–517
    • 1 Some Preliminary Thoughts1.1 GAS DYNAMICS—A BRIEF HISTORYUntil the nineteenth century very little knowledge of gas dynamics had beenassimilated by man. The motion of air, its effects and power were felt by humanbeings only through storms or from the disturbances created for lighting firesand other similar natural phenomena. Only those who were gifted withimagination beyond their times observed the flying of birds and dreamt of flyingmachines. Many efforts were made in those directions, costing priceless humanlives. The early manned flights like those of Icarus and Bladud were not basedon any aerodynamic concept. The theory of air resistance was first proposed by Sir Isaac Newton in 1726.According to him, aerodynamic forces depend on the density and velocity of thefluid, and the shape and size of the displacing object. Newton’s theory was soonfollowed by other theoretical solutions to fluid motion problems. Fluid motionwas assumed to occur under idealized conditions, i.e. air was assumed topossess constant density and to move in response to pressure and inertia.Interest in gaining a deep understanding of dynamics of air motion arosebecause of its application to hot air balloon, windmill, ballistic devices (gunsand cannons), and so on. Knowledge was mostly derived by trial and error, andcodes of practice did not exist. The experimental techniques introduced formeasurement during the eighteenth century provided a breakthrough in thestudy of aerodynamics. Benjamin Robins in the UK constructed a whirling armto determine the air resistance of bodies, and a “ballistic pendulum” to find thevelocity of a bullet or shell. In the former experiment, a horizontal arm wasrotated about a vertical axis by the tension of a string holding a falling weight.After a few rotations the speed of the end of the whirling arm was constant, atapproximately 7.6 m/s. Test objects were mounted at the end of the arm andtheir air resistance altered the speed of rotation. This device was used tocompare the resistance of different shapes, and to show how the resistance of 1
    • 18 Gas Dynamics 2 Basic Equations of Compressible Flow2.1 THERMODYNAMICS OF FLUID FLOWEntropy and temperature are the two fundamental concepts of thermodynamics.The energy changes associated with compressible flow, unlike low-speed orincompressible flow, are substantial enough to strongly interact with otherproperties of the flow. Hence, the energy concepts play an important role in thestudy of compressible flow. In other words, the study of thermodynamicswhich deals with energy (and entropy) is an essential component in the studyof compressible flow. The following are the broad divisions of the fluid flow studies classified,based on thermodynamic considerations: Fluid mechanics of perfect fluids, i.e.fluids without viscosity and heat (transfer) conductivity, is an extension ofequilibrium thermodynamics to moving fluids. The kinetic energy of the fluidhas to be considered in addition to the internal energy which the fluid possesseswhen at rest. Fluid mechanics of real fluids goes beyond the scope of classical thermo-dynamics. The transport processes of momentum and heat are of primaryinterest here. But, even though thermodynamics is not fully and directlyapplicable to all phases of real fluid flow, it is often extremely helpful in relatingthe initial and final conditions. For low speed flow problems, thermodynamic considerations are notneeded because the heat content of the fluid flow is so large compared to thekinetic energy of the flow that the temperature remains nearly constant even ifthe whole kinetic energy is transformed into heat. In modern high-speed problems, the kinetic energy content of the fluid canbe so large compared to its heat content that the variations in temperature canbecome substantial. Hence, the emphasis on thermodynamic concepts assumesimportance. 18
    • Home > PHI Learning > Gas Dynamics GAS DYNAMICS RATHAKRISHNAN, E. EDITION: FOURTH EDITION ISBN: 978-81-203- 4605-5 Pages: 536 Price: R 425.00 About The BookDescription:This revised and updated fourth edition continues to provide the most accessible and readable approach to the study of all the vital topics and issues associatedwith gas dynamic processes. At every stage, the physics governing the process, its applications and limitations are discussed in depth.With a strong emphasis on the basic concepts and problem-solving skills, this text is suitable for a course on Gas Dynamics/Compressible Flows/High-speedAero-dynamics at both undergraduate and postgraduate levels in aerospace engineering, mechanical engineering, chemical engineering and applied physics.The elegant and concise style of the book, along with illustrations and worked examples, makes it eminently suitable for self-study by scientists and engineersworking in the field of gas dynamics in industries and research laboratories.Some of the Distinguishing Features of the Book :Concise coverage of the thermodynamic concepts to serve as a revision of the background material.Logical and systematic treatment of fundamental aspects of gas dynamics, waves in the supersonic regime and gas dynamic processes.In-depth presentation of potential equations for compressible flows, similarity rule and two-dimensional compressible flows.Introduction to measurements in compressible flows and optical flow visualization techniques.Introduction to rarefied gas dynamics and high-temperature gas dynamics.Solution Manual for instructors containing the complete worked-out solutions to chapter-end problems.New to the Fourth Edition :Some vital aspects associated with the compression and expansion waves are explained, with suitable worked numerical examples.A brief section on critical Mach number is added in Chapter 8, highlighting its influence on the aerodynamic efficiency of flying mechanics.Nozzle flow process has been illustrated with worked examples focusing on the design and application aspects.A considerable number of worked examples are added, focusing attention on the design aspects.Some new problems along with answers are added at the end of many chapters.Contents:Preface • Preface to the Third Edition • Preface to the Second Edition Preface to the First Edition1. Some Preliminary Thoughts. 2. Basic Equations of Compressible Flow. 3. Wave Propagation. 4. Steady One-Dimensional Flow.5. Normal Shock Waves. 6. Oblique Shock and Expansion Waves. 7. Potential Equation for Compressible Flow. 8. Similarity Rule.9. Two-Dimensional Compressible Flows. 10. Prandtl-Myer Flow. 11. Flow with Friction and Heat Transfer. 12. Method of Characteristics. 13. Measurements inCompressible Flow. 14. Rarefied Gas Dynamics. 15. High Temperature Gas Dynamics.AppendicesA: Table-A1: Isentrophic Flow of Perfect Gas (γ = 1.4). A2: Normal Shock in Perfect Gas (γ = 1.4). A3: Oblique Shock in Perfect Gas(γ = 1.4). A4: One-Dimensional Flow with Friction (γ = 1.4). A5: One-Dimensional Frictionless Flow with Change in Stagnation Temperature (γ = 1.4). B: Listingof the Method of Characteristics Program. C: Output for Mach 2.0 Nozzle Contour. D: Oblique Shock Chart I, Oblique Shock Chart IISelected References • Index