Modeling of unsteady two-phase reactive flow in porous beds of propellant PDF20160206-23789-FF78UC

Title	Modeling of unsteady two-phase reactive flow in porous beds of propellant
Author	Herman Krier
Pages	39
File Size	3.2 MB
File Type	PDF20160206-23789-FF78UC
Total Downloads	542
Total Views	835

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Prog. Energy Combust. Sci.. 1982, VoL 8, pp. 1-39 0360-1285/82/010001-39519.50/0 Printed in Great Britain. All rights reserved. Copyright © 1982 Pergamon Press Ltd MODELING OF UNSTEADY TWO-PHASE REACTIVE FLOW IN POROUS BEDS OF PROPELLANT SADANAND S. GOKHALE* a n d HERMAN KRIER** Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, U.S.A. Abstract--A model describing reactive two-phase flow through a gas-solid mixture is presented based upon either the concept of continuum mixture or the concept of separated-flow continuum. The resulting governing equations are solved by the method of finite differences. Details of two distinct numerical methods to solve these nonlinear, coupled hyperbolic partial differential equations simultaneously are also presented. In addition, artificial smearing techniques which are generally needed for the shock capturing methods are investigated. The analysis of the transient convective mode combustion process in a highly loaded granular bed of energetic solid propellant indicates a rapidly burning pressure front and an accelerating deflagration front. During the final stages of the burn, the velocity of this deflagration front can range from 1 to 3 mm/lxs. A detailed discussion is included which attempts to explain the limits of the theoretical model presented in this study. Assessments are also made regarding the validity of many of the constitutive laws utilized and the assumptions necessary for this analysis. The study concludes with assessment of the modeling effort and how such unsteady flow processes could lead to DDT (deflagration- to-detonation transition) in such porous beds. 2. 3. 4. CONTENTS An Introduction To Deflagration and Detonation Fundamentals 1.1. Introduction 1.2. Gaseous detonations 1.3. Condensed phase detonations and DDT 1.4. DDT in porous medium 1.5. Modeling of DDT processes Page Theoretical Models 6 2.1. Introduction 6 2.2. Continuum Theory 7 2.2.1. Theory of mixture 7 2.2.2. Separated flow concept 9 2.3. Multisize Particle Formulation 10 2.4. Auxiliary Relations 12 2.4.1. Solid propellant gasification 12 2.4.2. Ignition criteria 12 2.4.3. Interphase drag 12 2.4.4. Heat transfer 13 2.4.5. Nonideal equation of state for gases 13 2.4.6. Particle-particle force l 4 2.4.7. Equation of state for compressible solid 15 Numerical Methods 15 3.1. Introduction 15 3.2. MacCormack scheme 16 3.3. Lax Wendroffmethod 17 3.4. Boundary conditions 17 3.5. Initial conditions 18 3.6. Stability criteria 18 3.7. Other instabilities 19 Computed Results 20 4.1. Introduction 20 4.2. Preliminary considerations 20 4.2.1. Mesh size 20 * Research Associate, Ph.D.; currently Assistant Professor, Indian Institute of Technology, Madras, India. ** Professor; currently Dept. of Mechanical and Industrial Engineering, University of Illinois. Work supported by US Air Force Office of Scientific Research under Grant AFOSR 77-3337, D. B. T. Wolfson and Dr. Leaonard H. Caveny were contract monitors. 1 J P E C S 8 : 1 ~ A...