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 QUALITY CERTIFICATE 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. Signature of HD Name: Mr. E.R.Sivakumar SEAL CONTENTS S.NO TOPIC PAGE NO UNIT-1 BASIC CONCEPTS AND ISENTROPIC 1.1 Concept of Gas Dynamics 1 1.1.1 Significance with Applications 1 1.2 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 S.NO TOPIC PAGE NO 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 TOPIC PAGE NO 3.3 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 4.3 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 4.4 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 S.NO TOPIC PAGE NO 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 PAGE NO 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 SCE 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.