ME2351 GDJP - Lecture notes all PDF

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A Course Material on

GAS DYNAMICS AND JET PROPULSION

By Mr. C.RAVINDIRAN. ASSISTANT PROFESSOR DEPARTMENT OF MECHANICAL ENGINEERING SASURIE COLLEGE OF ENGINEERING VIJAYAMANGALAM – 638 056

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This is to certify that the e-course material Subject Code

: ME2351

Subject

: GAS DYNAMICS AND JET PROPULSION

Class

: III Year MECHANICAL ENGINEERING

being prepared by me and it meets the knowledge requirement of the university curriculum.

Signature of the Author Name

: C. Ravindiran

Designation: Assistant Professor

This is to certify that the course material being prepared by Mr. C. Ravindiran is of adequate quality. He has referred more than five books amount them minimum one is from abroad author.

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CONTENTS S.NO

TOPIC

PAGE NO

UNIT-1 BASIC CONCEPTS AND ISENTROPIC Concept of Gas Dynamics

1

1.1.1 Significance with Applications

1

Compressible Flows

1

1.2.1 Compressible vs. Incompressible Flow

2

1.2.2 Compressibility

2

1.2.3. Compressibility and Incompressibility

3

1.3

Steady Flow Energy Equation

5

1.4

Momentum Principle for a Control Volume

5

1.5

Stagnation Enthalpy

5

1.6

Stagnation Temperature

7

1.7

Stagnation Pressure

8

1.8

Stagnation velocity of sound

9

1.9

Various regions of flow

9

1.10

Flow Regime Classification

11

1.11

Reference Velocities

12

1.11.1 Maximum velocity of fluid

12

1.11.2 Critical velocity of sound

13

1.12

Mach number

16

1.13

Mach Cone

16

1.14

Reference Mach number

16

1.15

Crocco number

19

1.16

Isothermal Flow

19

1.17

Law of conservation of momentum

19

1.17.1 Assumptions

20

1.1

1.2

S.NO

TOPIC

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1.18

Problems

22

1.19

Flow through Nozzles

28

1.20

Diffuser

29

1.21

Tutorial Problems

38

UNIT – 2 FLOW THROUGH DUCTS 2.1

Introduction

39

2.2

Fanno Flow

39

2.2.1Applications

39

2.3

Fanno line or Fanno curve

40

2.4

Important features of Fanno curve

42

2.5

Chocking in Fanno flow

42

2.6

Adiabatic Flow of a Compressible Fluid Through a Conduit

42

2.7

Variation of flow properties

44

2.8

Variation of Mach number with duct length

53

2.9

Problems Based on Fanno Flow

54

2.10

Rayleigh Flow

58

2.11

Rayleigh line

59

2.12

Governing Equations

59

2.13

Fundamental Equations

62

2.14

Problems based on Rayleigh flow

68

2.15

Intersection of Fanno and a Rayleigh Line

72

2.16

Tutorial Problems

75

UNIT – 3 NORMAL AND OBLIQUE SHOCKS 3.1

Normal Shocks

77

3.2

Shock Waves and Expansion Waves Normal Shocks

77

3.2.1 Assumptions

78

S.NO 3.3

TOPIC

PAGE NO

Governing Equations

78

3.3.1Property relations across the shock.

79

3.4

Prandtl-Meyer relationship

89

3.5

Governing relations for a normal shock

90

3.6

The Rankine – Hugoniot Equatios

92

3.7

Strength of a Shock Wave

96

3.8

Problems

99

3.9

Tutorial Problems

106 UNIT – 4 JET PROPULSION

4.1

Jet Propulsion System

107

4.2

Types of Jet Propulsion System

107

4.2.1 Air Breathing Engines

107

4.2.2 Rocket Engines

108

The Ramjet Engine

108

4.3.1 Principle of Operation

109

4.3.2 Advantages

110

4.3.3 Disadvantages

110

4.3.4 Application

111

Pulse Jet Engine

111

4.4.1 Operations

111

4.4.2 Characteristics

112

4.4.3 Advantages

113

4.4.4 Disadvantages

113

4.4.5 Applications

113

4.5

The Turbojet Engine

114

4.6

Turboprop Engine

116

4.3

4.4

S.NO

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4.6.1 Advantages

119

4.6.2 Disadvantages

119

4.7

The Turbofan Engine

120

4.8

Nozzle and diffuser efficiencies

121

4.8.1 Nozzle performance

121

4.9

Problems

123

4.10

Tutorial Problems

127 UNIT -5 SPACE PROPULSION

5.1

Rocket Propulsion

129

5.2

General Principles of a Rocket Motor

129

5.3

Propellants

129

5.4

Energy Conversion

129

5.5

Kinetic energy of a body

130

5.6

Thrust

131

5.7

Flow expansion

131

5.8

Types of Rocket Engines

132

5.9

Grains

133

5.10

Composition

134

5.11

Composite

134

5.12

Liquid propellant

134

5.13

Rocket Ignition

135

5.14

Rocket Combution

135

5.15

Rocket nozzles

136

5.16

Propellant efficiency

136

5.17

Back pressure and optimal expansion

137

5.18

Thrust vectoring

138

S.NO

TOPIC

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5.19

Overall rocket engine performance

138

5.20

Space Flights

138

5.20.1 Types of spaceflight

139

5.21

Effective Speed Ratio

140

5.22

Problems

144

5.23

Tutorial problems

145

TEXT BOOKS: 1. S.M. Yahya, fundamentals of Compressible Flow, New Age International (P) Limited 2. H. Cohen, G.E.C. Rogers and Saravanamutto, Gas Turbine Theory, Longman Group Ltd 3. A.H. Shapiro, Dynamics and Thermodynamics of Compressible fluid Flow, , John wiley 4. N.J. Zucrow, Aircraft and Missile Propulsion, vol.1 & II, John Wiley 5. S.Senthil, Gas Dynamics and Jet Propulsion, A.R.S. Publicatons.

ME2351

GAS DYNAMICS AND JET PROPULSION

L T P C 3 1 0 4

AIM: To impart knowledge to the students on compressible flow through ducts, jet propulsion and space propulsion. OBJECTIVE:  To understand the basic difference between incompressible and compressible flow.  To understand the phenomenon of shock waves and its effect on flow. To gain some basic knowledge about jet propulsion and Rocket Propulsion. UNIT I BASIC CONCEPTS AND ISENTROPIC FLOWS 6 Energy and momentum equations of compressible fluid flows – Stagnation states, Mach waves and Mach cone – Effect of Mach number on compressibility – Isentropic flow through variable ducts – Nozzle and Diffusers – Use of Gas tables. UNIT II FLOW THROUGH DUCTS 9 Flows through constant area ducts with heat transfer (Rayleigh flow) and Friction (Fanno flow) – variation of flow properties – Use of tables and charts – Generalised gas dynamics. UNIT III NORMAL AND OBLIQUE SHOCKS 10 Governing equations – Variation of flow parameters across the normal and oblique shocks – Prandtl – Meyer relations – Use of table and charts – Applications. UNIT IV JET PROPULSION 10 Theory of jet propulsion – Thrust equation – Thrust power and propulsive efficiency – Operation principle, cycle analysis and use of stagnation state performance of ram jet, turbojet, turbofan and turbo prop engines. UNIT V SPACE PROPULSION 10 Types of rocket engines – Propellants-feeding systems – Ignition and combustion – Theory of rocket propulsion – Performance study – Staging – Terminal and characteristic velocity – Applications – space flights. TUTORIALS: 15, TOTAL: 60 PERIODS TEXT BOOKS: 1. Anderson, J.D., Modern Compressible flow, McGraw Hill, 3rd Edition, 2003. 2. H. Cohen, G.E.C. Rogers and Saravanamutto, Gas Turbine Theory, Longman Group Ltd., 1980. 3. S.M. Yahya, fundamentals of Compressible Flow, New Age International (P) Limited, New Delhi, 1996. REFERENCES: 1. P. Hill and C. Peterson, Mechanics and Thermodynamics of Propulsion, Addison – Wesley Publishing company, 1992. 2. N.J. Zucrow, Aircraft and Missile Propulsion, vol.1 & II, John Wiley, 1975. 3. N.J. Zucrow, Principles of Jet Propulsion and Gas Turbines, John Wiley, New York, 1970. 4. G.P. Sutton, Rocket Propulsion Elements, John wiley, 1986, New York. 5. A.H. Shapiro, Dynamics and Thermodynamics of Compressible fluid Flow, , John wiley, 1953, New York. 6. V. Ganesan, Gas Turbines, Tata McGraw Hill Publishing Co., New Delhi, 1999. 7. PR.S.L. Somasundaram, Gas Dynamics and Jet Propulsions, New Age International Publishers, 1996. 8. V. Babu, Fundamentals of Gas Dynamics, ANE Books India, 2008.

ME2351

GAS DYNAMICS AND JET PROPULSION

UNIT-1 BASIC CONCEPTS AND ISENTROPIC FLOWS 1.1. Concept of Gas Dynamics Gas dynamics mainly concerned with the motion of gases and its effects .It differ from fluid dynamics .Gas dynamics considers thermal or chemical effects while fluid dynamics usually does not. Gas dynamics deals with the study of compressible flow when it is in motion. It analyses the high speed flows of gases and vapors’ with considering its compressibility. The term gas dynamics is very general and alternative names have been suggested e.g.: Supersonic flow, compressible flow and aero thermodynamics etc., 1.1.1 Significance with Applications: Gas dynamics is of interest to both mechanical and the aeronautical engineers but particular field of interest of the two different .It may be said that thermodynamicist is concerned with how an object in motion influenced as it flies through still air. In contrast to it the thermodynamicist in more interested in the cases in which the object in stationary and the fluid is in motion .The applications of gas dynamics are given below.    

It is used in Steam and Gas turbines High speed aero dynamics Jet and Rocket propulsion High speed turbo compressor

The fluid dynamics of compressible flow problems which involves the relation between forse, density, velocity and mass etc.Therfore the following laws are frequently used for solving the dynamic problems. 1. Steady flow energy equation 2. Entropy relations 3. Continity equation 4. Momentum equation 1.2 Compressible Flows –

Compressible flow - Density changes

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Department of Mechanical Engineering 1

ME2351

GAS DYNAMICS AND JET PROPULSION

We know that fluids, such as gas, are classified as Incompressible and Compressible fluids. Incompressible fluids do not undergo significant changes in density as they flow. In general, liquids are incompressible; water being an excellent example. In contrast compressible fluids do undergo density changes. Gases are generally compressible; air being the most common compressible fluid we can find. Compressibility of gases leads to many interesting features such as shocks, which are absent for incompressible fluids. Gas dynamics is the discipline that studies the flow of compressible fluids and forms an important branch of Fluid Mechanics. 1.2.1 Compressible vs. Incompressible Flow    

A flow is classified as incompressible if the density remains nearly constant. Liquid flows are typically incompressible. Gas flows are often compressible, especially for high speeds. Mach number, Ma = V/c is a good indicator of whether or not compressibility effects are important.  Ma < 0.3 : Incompressible  Ma < 1 : Subsonic  Ma = 1 : Sonic  Ma > 1 : Supersonic  Ma >> 1 : Hypersonic

1.2.2 Compressibility: Measure of the relative volume change with pressure

A measure of the relative volume change with pressure for a given process. Consider a small element of fluid of volume v, the pressure exerted on the sides of the element is p. Assume the pressure is now increased by an infinitesimal amount dp. The volume of the element will change by a corresponding amount dv , here the volume decrease so dv is a negative quantity. By definition, the compressibility of fluid is

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Department of Mechanical Engineering 2

ME2351

GAS DYNAMICS AND JET PROPULSION

The terms compressibility and incompressibility describe the ability of molecules in a fluid to be compacted or compressed (made more dense) and their ability to bounce back to their original density, in other words, their "springiness." An incompressible fluid cannot be compressed and has relatively constant density throughout. Liquid is an incompressible fluid. A gaseous fluid such as air, on the other hand, can be either compressible or incompressible. Generally, for theoretical and experimental purposes, gases are assumed to be incompressible when they are moving at low speeds--under approximately 220 miles per hour. The motion of the object traveling through the air at such speed does not affect the density of the air. This assumption has been useful in aerodynamics when studying the behavior of air in relation to airfoils and other objects moving through the air at slower speeds. In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.

Where V is volume and p is pressure. The above statement is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal. Accordingly we define the isothermal compressibility as:

Where the subscript T indicates that the partial differential is to be taken at constant temperature. The adiabatic compressibility as:

Where S is entropy. For a solid, the distinction between the two is usually negligible. The inverse of the compressibility is called the bulk modulus, often denoted K(sometimes B). 1.2.3. Compressibility and Incompressibility The terms compressibility and incompressibility describe the ability of molecules in a fluid to be compacted or compressed (made more dense) and their ability to bounce back to their original density, in other words, their "springiness." An incompressible fluid cannot be compressed and has relatively constant density throughout. Liquid is an incompressible fluid. A gaseous fluid such as air, on the other hand, can be either SCE

Department of Mechanical Engineering 3

ME2351

GAS DYNAMICS AND JET PROPULSION

compressible or incompressible. Generally, for theoretical and experimental purposes, gases are assumed to be incompressible when they are moving at low speeds--under approximately 220 miles per hour. The motion of the object traveling through the air at such speed does not affect the density of the air. This assumption has been useful in aerodynamics when studying the behavior of air in relation to airfoils and other objects moving through the air at slower speeds. However, when aircraft began traveling faster than 220 miles per hour, assumptions regarding the air through which they flew that were true at slower speeds were no longer valid. At high speeds some of the energy of the quickly moving aircraft goes into compressing the fluid (the air) and changing its density. The air at higher altitudes where these aircraft fly also has lower density than air nearer to the Earth's surface. The airflow is now compressible, and aerodynamic theories have had to reflect this. Aerodynamic theories relating to compressible airflow characteristics and behavior are considerably more complex than theories relating to incompressible airflow. The noted aerodynamicist of the early 20th century, Ludwig Prandtl, contributed the Prandtl-Glaubert rule for subsonic airflow to describe the compressibility effects of air at high speeds. At lower altitudes, air has a higher density and is considered incompressible for theoretical and experimental purposes.

Compressibility  Compressibility of any substance is the measure of its change in volume under the action of external forces.  The normal compressive stress on any fluid element at rest is known as hydrostatic pressure p and arises as a result of innumerable molecular collisions in the entire fluid.  The degree of compressibility of a substance is characterized by the bulk modulus of elasticity E defined as

Where Δ and Δp are the changes in the volume and pressure respectively, and is the initial volume. The negative sign (-sign) is included to make E positive, since increase in pressure would decrease the volume i.e for Δp>0 , Δ M0 > 1.2) Supersonic Flow (M0 > 1.2) Hypersonic Flow (M0 > 5)

 Incompressible region In incompressible flow region fluid velocity (c) is much smaller than the sound velocity (a). Therefore the Mach number ( M = c/a) is very low. Eg: flow through nozzles

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ME2351

GAS DYNAMICS AND JET PROPULSION

 Subsonic flow region The subsonic flow region is on the right of the incompressible flow region. In subsonic flow, fluid velocity (c) is less than the sound velocity (a) and the Mach number in this region is always less than unity. i.e. M = ca  1. Eg: passenger air craft  Sonic flow region If the fluid velocity (c) is equal to the sound velocity (a), that type of flow is known as sonic flow. In sonic flow Mach number value is unity. M = ca = 1  c  a. Eg: Nozzle throat  Transonic flow region If the fluid velocity close to the speed of sound, that type of flow is known as transonic flow .In transonic flow, Mach number value is in between 0.8 and 1.2. i.e.0.8 < M < 1.2.  Supersonic flow region The supersonic region is in the right of the transonic flow region. In supersonic flow, f...