Elements of gas turbine propulsion part 1

Elements of Gas Turbine Propulsion • Jack D Mattingly ELEMENTS OF GAS TURBINE PROPULSION ' McGraw-Hill Series in Aeronautical and Aerospace Engineering Consulting Editor John D Anderson, Jr., University of Maryland Anderson: Computational Fluid Dynamics: The Basics with Applications Anderson: Fundamentals of Aerodynamics Anderson: Hypersonic and High Temperature Gas Dynamics Anderson: Introduction to Flight Anderson: Modern Compressible Flow: With Historical Perspective Burton: Introduction to Dynamic Systems Analysis D' Azzo and Houpis: Linear Control System Analysis and Design Donaldson: Analysis of Aircraft Structures: An Introduction Gibson: Principles of Composite Material Mechanics Kane, Likins, and Levinson: Spacecraft Dynamics Katz and Plotkin: Low-Speed Aerodynamics: From Wing Theory to Panel Methods Mattingly: Elements of Gas Turbine Propulsion Nelson: Flight Stability and Automatic Control Peery and Azar: Aircraft Structures , , , Rivello: Theory and Analysis of Fligh? Sfructures Schlichting: Boundary Layer Theory White: Viscous Fluid Flow Wiesel: Spaceflight Dynamics • McGraw-Hill Series in Mechanical Engineering Consulting Editors Jack P Holman, Southern Methodist University John R Lloyd, Michigan State University Anderson: Computational Fluid Dynamics: The Basics with Applications Anderson: Modern Compressible Flow: With Historical Perspective Arora: Introduction to Optimum Design Bray and Stanley: Nondestructive Evaluation: A Tool for Design, Manufacturing, and Service Burton: Introduction to Dynamic Systems Analysis Culp: Principles of Energy Conversion Dally: Packaging of Electronic Systems: A Mechanical Engineering Approach Dieter: Engineering Design: A Materials and Processing Approach Doebelin: Engineering Experimentation: Planning, Execution, Reporting Oriels: Linear Control Systems Engineering Eckert and Drake: Analysis of Heat and Mass Transfer Edwards and McKee: Fundamentals of Mechanical Component Design Gebhart: Heat Conduction and Mass Diffusion Gibson: Principles of Composite Material Mechanics Hamrock: Fundamentals of Fluid Film Lubrication Heywood: Internal Combustion Engine Fundamentals Hinze: Turbulence Holman: Experimental Methods for Engineers Howell and Buckius: Fundamentals of Engineering Thermodynamics Hutton: Applied Mechanical Vibrations Juvinall: Engineering Considerations of Stress, Strain, and Strength Kane and Levinson: Dynamics: Theory and Applications Kays and Crawford: Convective Heat and Mass Transfer Kelly: Fundamentals of Mechanical Vibrations Kimbrell: Kinematics Analysis and Synthesis Kreider and Rabi: Heating and Cooling of Buildings Martin: Kinematics and Dynamics of Machines Mattingly: Elements of Gas Turbine Propulsion Modest: Radiative Heat Transfer Norton: Design of Machinery Phelan: Fundamentals of Mechanical Design Raven: Automatic Control Engineering Reddy: An Introduction to the Finite Element Method Rosenberg and Kamop,P: Introduction to Physical Systems Dynamics Schlichting: Boundary-Layer Theory Shames: Mechanics of Fluids Sherman: Viscous Flow Shigley: Kinematic Analysis of Mechanisms Shigley and Mischke: Mechanical Engineering Design Shigley and Vicker: Theory of Machines and Mechanisms Stiffler: Design with Microprocessors for Mechanical Engineers Stoecker and Jones: Refrigeration and Air Conditioning Turns: An Introduction to Combustion: Concepts and Applications Ullman: The Mechanical Design Process Vanderplaats: Numerical Optimization: Techniques for Engineering Design, with Applications Wark: Advanced Thermodynamics for Engineers White: Viscous Fluid Flow Zeid: CAD I CAM Theory and Practice ELEMENTS OF GAS TURBINE PROPULSION Jack D Mattingly Department of Mechanical and Manufacturing Engineering Seattle University With a Foreword By Hans van O hain Tata McGraw Hill Education Private Limited NEW DELHI McGraw-Hill Offices New Delhi New York St Louis San Francisco Auckland Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Thi s book wa., sci in Times Roman The editors were John J CorTigan a nd James W radl ey; the product io n supe rvisor was Leroy A Young The cover wa, designed by MerTill Haber Drawings were done by ECL An R R Donne lley & Sons Company was print er and hinder lffll Tata McGraw-Hill ELEMENTS OF GAS TURBINE PROPULS ION Copyri ght © 1996 by The McGraw-Hill Compa nie,, Inc A ll rights resen ed No pan ot' th is publi cat ion may be reproduced or di stributed in any form or by any mean, or stored 111 a data base or retrieval , ystem without the pri or written permi ss ion o t' the publisher Tata McGraw-llill Edition 2005 Sixth reprint 2013 RLQZRRDODLCXL Reprinted in India by arTangcment with The McGraw-Hill Companie, Inc New York Saks territories: India Pakistan Nepal , l:langladesh , Sri Lanka and Bhutan Library of Congress Cataloging-in-Publication Data Matt ingly, Jack D Elements or gas turbine propulsion/Jack D Mallingly: with a foreword by Hans von O hain p c m.- (McGraw-Hill series in mechanical engineering) (Mc Hraw- Hill ,eries in aeronautical and aerospace engi neering) Includes bibliographical references and index ISBN 0-07-9 I 196-9 (sell I Airp la nes- Jet propulsion I Title II Series Ill Series: McGraw-Hill series in aero nauti cal and aerospace engineerin g L 709.MJ8 1996 95 -897 29 I 34 J5 J -dc20 ISBN-13: 978-0-07 -060628-9 ISBN-JO: 0-07-060628-5 Published by Tata McGraw Hill Education Pri vate Limited West Patel Nagar New Delhi I JO 008 " nd printed at Sai Printo Pack Pvt Ltd Delhi I 10 020 The McGraw·Hi/1 Companies , r~ ABOUT THE AUTHOR Jack D Mattingly received his B.S and M.S in Mechanical Engineering from the Uni·:ersity of Notre Dame, and his Ph.D in Aeronautics and Astronautics at the University of Washington While studying for his doctorate under Gordon C Oates, he pioneered research in the mixing of coannular swirling flows and developed a major new test facility During his 28 years of experience in analysis and design of propulsion and thermodynamic systems, he has developed aerothermodynamic cycle analysis models and created engineering software for air-breathing propulsion systems Dr Mattingly has more than 23 years of experience in Engineering Education, previously as a senior member of the Department of Aeronautics at the United States Air Force Academy, where he established a top undergraduate propulsion program He retired from active duty with the U.S Air Force in 1989 and joined the faculty of Seattle University In addition, he has taught and done research in propulsion and thermal energy systems at the Aeropropulsion and Power Laboratory, Air Force Institute of Technology, University of Washington, University of Notre Dame, University of Wisconsin, and IBM Corp He was also founder of the AIAA/ Air Breathing Propulsion Team Aircraft Engine Design Competition for undergraduate students Among his many distinguished teaching awards is Outstanding Educator for 1992 from Seattle University Having published more than 20 technical papers, articles, and textbooks in his field , Dr Mattingly was the principal author of Aircraft Engine Design (1987), an unprecedented conceptual design textbook for air breathing engines He is currently Chair, Department of Mechanical and Manufacturing Engineering at Seattle University I have been blessed to share my life with Sheila, my best friend and wife She has been my inspiration and helper, and the one who sacrificed the most to make this work possible I dedicate this book and accompanying software to Sheila I would like to share with all the following passage I received from a very close friend over 18 years ago This passage provides guidance and focus to my life I hope it can be as much help to you FABRIC OF LIFE I want to say something to all of you Who have become a part Of the fabric of my life The color and texture Which you have brought into My being Have become a song And I want to sing it forever There is an energy in us Which makes things happen When the paths of other persons Touch ours And we have to be there And let it happen When the time of our particular sunset comes Our thing, our accomplishment Won't really matter A great deal But the clarity and care With which we have loved others Will speak with vitality Of the great gift of life We have been for each other Anonymous 446 GAS TURBINE Cycle Analysis-Turbojet with Afterburning Figure 7-8 shows a cross-sectional drawing of the turbojet engine with afterburning and its station numbering The uninstalled specfic thrust is given in Eqs (7-1) and (7-2) and is written in terms of the engine stations, or (7-115) where fo is the overall fuel/air ratio, defined by Eq (5-82) as fa= mj· +mfAB · mo (5-82) The exit velocity V9 is determined from the total and static enthalpies at station by using (6-44) The total enthalpy at station is obtained from application of the first law of thermodynamics to the engine and from tracking the changes in energy from the engine's inlet to its exit The static state at station (h , Tg, etc.) is obtained by using the following relationship between the reduced pressure at the static state P, , the reduced pressure at the total state P, ,9, and the nozzle pressure ratio P, 9/ P9 : (6-45) The nozzle pressure ratio is obtained by using Eq (7-27), which tracks the ratios of total pressure from engine inlet to exit P,9 ~ r9 Po 1C,1Cd1CJCb1T:r1'CAB1Cn P9 =- (7-27) The enthalpy leaving the compressor h, is obtained by first determining the reduced pressure leaving the compressor P,,3 From a rewrite of Eq (6-31), we have (7-116) Application of the first law of thermodynamics to the compressor and turbine gives the required turbine exit enthalpy Equating the required compressor power to the net output power from the turbine, we have l-fc = Tim wt PARAMETRIC CYCLE ANALYSIS OF REAL ENGINES 447 Rewriting in terms of mass flow rates and total enthalpies gives rho(hr3 - hr2) = 1/m(rho + rht )(hr4 - hrs)= 1Jmrho(l + t)(hr4 - hrs) Solving for hrs gives (7-117) where both hr4 and hrs are functions of the fuel/air ratio The turbine pressure ratio n, is obtained from Eq (6-40) The fuel/air ratio for the main burner is given by Eq (6-36), where h,4 is a function off: f = ht4 -ht3 (6-36) 1/bhPR - ht4 Application of the first law to the afterburner gives the following equation for its fuel/air ratio !AB, where hr6 is a function of the entering fuel/air ratio and h is a function of the leaving fuel/air ratio Uo = f + [AB): (7-118) Summary of Equations-Afterburning Turbojet with Variable Specific Heats INPUTS: Mo, To (K, R), hPR (kJ/kg, Btu/lbm), lrdmax, nb, nAB, nn, ec, et, 1/b, 1JAB, 1/m, Pol P9, T,4 (K, R), T,7 (K, R), nc OUTPUTS: F ( N lbf ) f, -r -r s(mg/sec lbm/hr) rho kg/sec' lbm/sec ' ' JAB, Jo, N 'lbf ' 1/T> 1/P, 1/o, 1/c, 1/1, etc EQUATIONS: F AIR(l, T0 , h , P, ,