Hypersonic Slender Body Aerodynamics E-Book

Ethirajan Rathakrishnan

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Aerospace Series
• Sprache: Englisch

Seitenzahl: 191

Veröffentlichungsjahr: 2025

Beschreibung

One-of-a-kind resource on theoretical and application aspects of hypersonic slender body aerodynamics with many didactic features included throughout

Developed using class-tested course material, Hypersonic Slender Body Aerodynamics presents the theoretical and application aspects of the subject in a precise, concise, and student-friendly manner. The text includes a large number of worked examples, figures, diagrams, tables, and exercise problems.

This book covers the subject material beginning from the definition of the slender body geometry through to the study of flow field around the body and the calculation of the aerodynamic and thermal loads acting on the body at speeds ranging from low to high (i.e., from incompressible to hypersonic speeds). The Mach number independence principle and approximate theories for caret wings are also covered, among many other key topics.

This book is unique in its comprehensive coverage of the topic, enabling readers to find information in one place instead of scattered throughout proprietary wind tunnel test data, flight test data, government technical reports, scientific literature sources, and numerical methods.

Some of the concepts explored in Hypersonic Slender Body Aerodynamics include:

• Wings of supersonic aircraft, covering sharp leading edges and ground and viscous effects, and pressure distribution on surfaces, covering transverse and longitudinal flow
• Hypersonic aerodynamics, covering atmospheric properties, hypersonic-flow characteristics, governing equations, and flow past a semi-wedge
• Application of slender-body theory, covering leading-edge heat transfer, sublimation, aerodynamic effects, nose bluntness, blast-wave theory, and thin shock layers
• Axisymmetric slender bodies, covering potential flow solutions and pressure distribution, and drag of slender bodies, covering shape factor and blunt after-body corrections

Skillfully written with a clear and engaging writing style, Hypersonic Slender Body Aerodynamics is an essential learning resource on the subject for undergraduate and graduate students of aerospace engineering and practicing engineers working in aerospace research labs and industries. It is a perfect textbook for courses on slender body aerodynamics.

Leseprobe

Table of Contents

Cover

Table of Contents

Title Page

Copyright

Dedication

Preface

About the Author

Nomenclature

Greek symbols

Subscripts

About the Companion Website

1 Basics

1.1 Introduction

1.2 Supersonic Transport Aircraft

1.3 Wings of Supersonic Aircraft

1.4 Basic Equations

1.5 Pressure Distribution on the Surface

1.6 Theoretical Methods – Inviscid Flow

1.7 Stability Derivatives for Delta Wings

1.8 Method of Vortex (Source and Sink) Distribution

1.9 Cone in Supersonic Flow

1.10 Optimization (Supersonic Flow)

1.11 Lift-Case

1.12 Nonlinear Theories

1.13 Summary

Exercise Problems

Notes

2 Hypersonic Aerodynamics (Slender Bodies)

2.1 Introduction

2.2 Mach Number Independence Principle

2.3 Atmospheric Properties

2.4 Hypersonic Flow Characteristics

2.5 Governing Equations

2.6 Comparison of Supersonic and Hypersonic Flow

2.7 Re-entry Problem

2.8 Flow Past a Semi-wedge

2.9 Hypersonic Limiting Case

2.10 Newtonian Formula

2.11 Surface Pressure Distribution

2.12 Modified Newtonian Formula

2.13 Tangent Wedge or Tangent Cone Method

2.14 Busemann Correction for Centrifugal Force

2.15 Shock-Expansion Method

2.16 Theory of Slender Hypersonic Bodies

2.17 Principle of Equivalence for Slender Hypersonic Bodies

2.18 Design of Three-Dimensional Hypersonic Slender Bodies

2.19 Caret-Wing or Nonweiler Wing or Wave-Rider

2.20 Off-design Conditions for Caret-Wings

2.21 Approximate Theories for Caret-Wings

2.22 Supersonic Test Facilities

2.23 Comparison of Theoretical and Experimental Results

2.24 Stability Derivatives

2.25 Summary

Exercise Problems

Notes

3 Application of Slender-body Theory

3.1 Introduction

3.2 Leading-Edge Heat Transfer

3.3 Stagnation-Point Heat Transfer

3.4 Heat Transfer Limitations for Slender-body Vehicles

3.5 Sublimation

3.6 Aerodynamic Effects

3.7 Nose Bluntness

3.8 Blast-wave Theory

3.9 Thin Shock Layers

3.10 Summary

Exercise Problems

Notes

4 Experimental Approach

4.1 Introduction

4.2 Drag of Slender Bodies

4.3 Axisymmetric Slender Bodies

4.4 Summary

Exercise Problems

A Appendix

References

Further Readings

Index

End User License Agreement

List of Tables

Chapter 2

Table 2.1 Supersonic and hypersonic flows.

Table 2.2 Drag for two-dimensional bodies of shape, and .

Table 2.3 Drag for axisymmetric bodies of shape, , , and .

Chapter 3

Table 3.1 Graphite erosion rates for an unswept two-dimensional leading edge...

Appendix

Table A.1 SI units and their conversion to US units.

Table A.2 Properties of standard atmosphere.

List of Illustrations

Chapter 1

Figure 1.1 A slender wing.

Figure 1.2 (a) Ogee shape and (b) Gothic shape.

Figure 1.3 Rocket configuration: (a) Older type and (b) New type.

Figure 1.4 Flat plate in (a) subsonic flow and (b) supersonic flow.

Figure 1.5 Flow past a slender wing.

Figure 1.6 A slender wing at an angle of attack: (a) vortex sheets over the ...

Figure 1.7 Slender body in a uniform flow.

Figure 1.8 Flow past a slender body.

Figure 1.9 Flow past a slender body.

Figure 1.10 (a)–(f) Potential distribution and and for conical slender b...

Figure 1.11 Transverse flow past a slender wing.

Figure 1.12 Flow separation from a slender body.

Figure 1.13 Pressure variation over the slender body.

Figure 1.14 A slender wing body with zero camber and zero thickness.

Figure 1.15 Pitching moment, , of a slender wing.

Figure 1.16 Flight path of a slender body.

Figure 1.17 A slender body at an incidence.

Figure 1.18 A control volume.

Figure 1.19 A slender wing in a vertical freestream.

Figure 1.20 A slender cross section with corners.

Figure 1.21 Two adjacent points on a slender wing.

Figure 1.22 Velocity components at a point on the surface of a slender body....

Figure 1.23 Cross section of a slender body.

Figure 1.24 Surface area of a slender body.

Figure 1.25 A slender body in an uniform flow.

Figure 1.26 Flow at an angle, past a slender body.

Figure 1.27 Flow separation due to large angle of attack.

Figure 1.28 An axisymmetric cone in a supersonic flow.

Figure 1.29 Flow separation due to large angle of attack.

Figure 1.30 Slender body in a flow.

Figure 1.31 Slender wing of different cross-sectional shapes.

Figure 1.32 Flow separation and vortex rolling over a slender wing.

Figure 1.33 Vortex rolling over a slender wing.

Figure 1.34 Vortex build up over a slender wing.

Figure 1.35 Vortex sheet over a slender rectangular wing.

Figure 1.36 Two large opposite vortices at the trailing edge of a slender wi...

Figure 1.37 variation with . (a) for vortex breakdown and (b) for curving...

Chapter 2

Figure 2.1 Flow past a slender body in hypersonic flow.

Figure 2.2 A slender body in a uniform flow.

Figure 2.3 Uniform hypersonic flow past a semi-wedge.

Figure 2.4 Newtonian limiting hypersonic flow past a slender body.

Figure 2.5 A slender body in hypersonic flow.

Figure 2.6 Pressure distribution over the surface of a slender body in hyper...

Figure 2.7 Tangent cone.

Figure 2.8 (a) Convex and (b) concave cones in hypersonic flow.

Figure 2.9 Concave cone in hypersonic flow.

Figure 2.10 Hypersonic flow past a slender body.

Figure 2.11 Expanding flow.

Figure 2.12 Similar flows.

Figure 2.13 A slender two-dimensional body in a hypersonic flow.

Figure 2.14 A body expanding with time.

Figure 2.15 A slender body in hypersonic flow.

Figure 2.16 Shock position for slender two-dimensional body in a hypersonic ...

Figure 2.17 Pressure distribution for slender two-dimensional body in a hype...

Figure 2.18 A wave-rider in hypersonic flow.

Figure 2.19 Cone flow wave-rider.

Figure 2.20 Nonweiler’s wing.

Figure 2.21 Nonweiler’s wing.

Figure 2.22 Shock shapes for caret-wings.

Figure 2.23 Slender wedge in a hypersonic flow.

Figure 2.24 Slender wedge at different angles of incidence.

Figure 2.25 Slender wedge at positive angle of incidence.

Figure 2.26 Wedge at angle of incidence between .

Figure 2.27 Wedge at an angle of incidence .

Figure 2.28 Shock shapes and the pressure distribution.

Figure 2.29 variation with .

Figure 2.30 Schematic sketch of a blowdown tunnel (without heating).

Figure 2.31 Schematic sketch of a blowdown tunnel (with heating).

Figure 2.32 Schematic sketch of helium tunnel.

Figure 2.33 Schematic sketch of hot-shot tunnel.

Figure 2.34 Schematic sketch of gun tunnel.

Figure 2.35 Schematic sketch of shock tunnel.

Figure 2.36 Schematic sketch of arc-heated tunnel.

Figure 2.37 Schematic sketch of a low-density tunnel.

Figure 2.38 Schematic sketch of ballistic range.

Figure 2.39 A wedge at an angle to the freestream.

Figure 2.40 variation with .

Figure 2.41 Shock angle variation with .

Figure 2.42 Displacement thickness variation with pitching moment .

Figure 2.43 A slender delta-wing in an uniform flow.

Figure 2.44 Maximum lift coefficient for slender wings.

Figure 2.45 Maximum -values for slender wings.

Chapter 3

Figure 3.1 Flow regimes for a cooled sphere.

Figure 3.2 Heat transfer to a circular cylinder at low Reynolds number.

Figure 3.3 Surface pressure, , variation along the surface.

Figure 3.4 Drag coefficient of spherical-nosed cone modified with Newtonian ...

Figure 3.5 Drag coefficient of cylindrically blunted wedge using modified Ne...

Chapter 4

Figure 4.1 A typical slender body.

Figure 4.2 Variation of with Reynolds number.

Figure 4.3 A slender body in a freestream.

Figure 4.4 Variation of with .

Guide

Cover

Table of Contents

Title Page

Copyright

Dedication

Preface

About the Author

Nomenclature

About the Companion Website

Begin Reading

A Appendix

References

Further Readings

Index

End User License Agreement

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Hypersonic Slender Body Aerodynamics

Ethirajan Rathakrishnan

This edition first published 2025© 2025 by John Wiley & Sons Ltd

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Library of Congress Cataloging-in-Publication Data Applied for:Hardback: 9781394285631

Cover image: © SONGPHOL THESAKIT/Getty ImageCover design: Wiley

This book is dedicated to my parents,Mr. Thammanur Shunmugam EthirajanandMrs. Aandaal Ethirajan

Preface

This book is developed to serve as text for a course on Slender Body Aerodynamics at the introductory level course for undergraduate and graduate level.

The basic aim of this book is to make a complete text covering the basic and applied aspects of slender body aerodynamics for students, engineers, and applied physicists. The philosophy followed in this book is that the subject of aerodynamic theory is covered combining the theoretical analysis, physical features, and the application aspects.

Considerable number of solved examples are given in all the chapters to fix the concepts introduced, and large number of exercise problems along with answers are listed at the end of these chapters to test the understanding of the material studied.

The book is organized in a logical manner and the topics are discussed in a systematic way, beginning with the basic aspects and then proceeding to the involved aspects of theory and application.

The selected references given at the end are hoped to be a useful guide for further study of the voluminous subject.

This book is the outgrowth of lectures presented by the author over a number of years, both at undergraduate and graduate level. The student, or reader, is assumed to have a background in the basic courses of fluid mechanics, gas dynamics, thermodynamics, and heat transfer. Advanced undergraduate students should be able to handle the subject material comfortably. Sufficient details have been included, so that the text can be used for self study. Thus, the book can be useful for scientists and engineers working in the field of aerodynamics in industries and research laboratories.

My sincere thanks to my undergraduate and graduate students in India and abroad, who are directly and indirectly responsible for the development of this book.

I thank Dr. S. M. Aravindh Kumar, Assistant Professor, Department of Aerospace Engineering, SRM Institute of Science and Technology, for checking the manuscript and suggesting some useful changes that made the manuscript impressive.

For instructors only, a companion Solutions Manual that contains typed solutions to all the end-of-chapter problems and lecture slides for the complete book are available from the publisher.

ChennaiJanuary 2025    

Ethirajan Rathakrishnan

About the Author

Ethirajan Rathakrishnan is a professor of aerospace engineering at the Indian Institute of Technology Kanpur, India. He is well known internationally for his research in the area of high-speed jets. The limit for the passive control of jets, called the Rathakrishnan Limit, is his contribution to the field of jet research, and the concept of breathing blunt nose (BBN), which simultaneously reduces the positive pressure at the nose and increases the low pressure at the base, is his contribution to drag reduction at hypersonic speeds. Positioning the twin-vortex Reynolds number at around 5000, by changing the geometry from cylinder, for which the maximum limit for the Reynolds number for positioning the twin-vortex was found to be around 160, by von Karman, to flat plate, is his addition to vortex flow theory. He has published a large number of research articles in many reputed international journals. He is a fellow of many professional societies including the Royal Aeronautical Society. Rathakrishnan serves as the editor-in-chief of the International Review of Aerospace Engineering (IREASE) and International Review of Mechanical Engineering (IREME) journals. He has authored the following books: Gas Dynamics, 7th ed. (PHI Learning, New Delhi, 2020); Fundamentals of Engineering Thermodynamics, 2nd ed. (PHI Learning, New Delhi, 2005); Fluid Mechanics: An Introduction, 4th ed. (PHI Learning, New Delhi, 2021); Gas Tables, 3rd ed. (Universities Press, Hyderabad, India, 2012); Theory of Compressible Flows (Maruzen Co., Ltd. Tokyo, Japan, 2008); Gas Dynamics Work Book, 2nd ed. (Praise Worthy Prize, Napoli, Italy, 2013); Elements of Heat Transfer (CRC Press, Taylor & Francis Group, Boca Raton, Florida, USA, 2012); Theoretical Aerodynamics (John Wiley, New Jersey, USA, 2013); High Enthalpy Gas Dynamics (John Wiley & Sons Inc., 2015); Dynamique Des Gaz (Praise Worthy Prize, Napoli, Italy, 2015); and Instrumentation, Measurements and Experiments in Fluids, 2nd ed. (CRC Press, Taylor & Francis Group, Boca Raton, Florida, USA, 2017), Helicopter Aerodynamics, (PHI Learning, New Delhi, 2019); Applied Gas Dynamics 2nd ed. (John Wiley & Sons Inc., 2019), Introduction to Aerospace Engineering – Basic Principles of Flight (John Wiley, New Jersey, USA, 2021), Encyclopedia of Fluid Mechanics (CRC Press, Taylor & Francis Group, Boca Raton, Florida, USA, 2022), Fluid and Thermal Dynamics Answer Bank for Engineers: The Concise Guide with Formulas and Principles for Students and Professionals (Brown Walker Press, FL, USA, 2023) and Mind Power The Sixth Sense (Routledge, Taylor & Francis Group, Boca Raton, Florida, USA, 2023).

Nomenclature

A

aspect ratio

speed of sound

ac

aerodynamic center

span

Btu

British thermal unit

chord

inner chord

outer chord

center of gravity

c.p

center of pressure

drag coefficient

coefficient of drag due to lift

skin friction drag coefficient

skin friction coefficient

lift coefficient

pitching moment coefficient

normal force coefficient

coefficient of pressure

thrust coefficient

specific heat at constant pressure

specific heat at constant volume

diameter

drag

drag due to friction

drag due to lift

dB

decibel

gravitational acceleration

altitude

height

specific enthalpy

total enthalpy

ISA

International Standard Atmosphere

hypersonic similarity parameter

Kn

Knudsen number

lift

aerodynamic efficiency

Mach number

shock detachment Mach number

moment

mean molecular weight

molecular mass of air

number of degree of freedom

pressure

stagnation pressure

dynamic pressure ()

source strength/length

average rate at which heat is transferred to the nose per unit frontal area of the body

surface radiative heat flux

gas constant

radius of curvature

universal gas constant

R

Reynolds number

span

wing area

base area (reference area)

wetted area

St

Stanton number

temperature

stagnation temperature

time

velocity

volume

nondimensionalized volume

perturbation velocity along the flow direction

normal component of velocity at any point on the body contour

perturbation velocity in the transverse direction

velocity component normal to the contour

perturbation velocity in the normal direction

flow direction

transverse direction

normal direction

compressibility factor

Greek symbols

angle of attack

local angle of attack

energy-accommodation coefficient

shock angle

“the change in”

density ratio

surface emissivity

leading-edge angle

mean free path

slenderness ratio

circulation

isentropic index

specific heats ratio