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Linearized analysis of the flow field induced by a steady discontinuity traveling in an infinite tube

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PROJECT TUBEFL/GHT
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TR PT 6809 LINEARIZED ANALYSIS OF THE FLOW FIELD INDUCED BY A STEADY DISCONTINUITY TRAVELING IN AN INFINITE TUBE by Joseph…
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I. II. TABLE OF CONTENTS ACKNOWLEDGMENT ABSTRACT LIST OF SYMBOLS LIST OF FIGURES INTRODUCTION A. Review of Past Work B…
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ACKNOWLEDGMENT The author wishes to extend his personal appreciation to Dr. T. R. Goodman of Oceanics Inc., and to Professors…
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ABSTRACT The present work investigates the steady flow of a compressible, viscous, heat conducting fluid induced by a frontal…
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SYMBOLS A a o B C F H h M m Pr P R r Re T t u v w x constant of integration (see equation 29) speed of…
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dynamic viscosity gas density Prandt1 number (also defined as Pr; ~ ) k Superscripts * o Subscripts d o u…
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FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 LIST OF FIGURES Reference System Linearized Solutions Downstream of a Subsonic…
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I. INTRODUCTION A. Review of Past Work This analysis was motivated by recent studies 1 ,2,3 which analyzed the flow field…
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In this work, the disturbance is treated as a discontinuity, across which the velocity and the thermodynamic variables, such…
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II. LINEARIZED PERTURBATION ANALYSIS A. Background 1 2 Previous work' related to the development of the flow field…
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4 Energy Eguation Eguation of State to It::. ~.o *4.. ~ 1-'- { . (5) The boundary conditions for this probem are…
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'" A '" The terms u, h, and p are dimensionless perturbations on the wall velocity (uo )' enthalpy…
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By combining equations 18 through 23, integrating over the cross sectional area, the equations become: (for ~ = 1) <1£.+…
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Equation 28 shows: 2 (a) For Mo > 1 the downstream boundary condition (x+69) l' can be met and the integration…
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both upstream and downstream of the disturbance. This was not con- sidered in previous work. These equations then become:…
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9 Since Mo < 1, the boundary conditions on both u and h upstream and downstream of the disturbance cannot be arbitrarily…
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10 The relationship expressed by equation 47 for the downstream flow field is the same as that previously found by Hagerup,2…
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11 and equations 29-30 need only be applied for x ~ o. For the above conditions and with the jump values of equa- tions 41-…
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that is exerted on a stationary structure. 1. Internal Propulsion For internal propulsion there is no change in the stream…
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is expressed as ~here ~fI, the increase in the nondimensiona1 stagnation enthalpy across the disturbance, equals zero for…
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14 4 steady asymptoic values obtained by Skinner from a nonsteady one- dimensional analysis using the method of…
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subsonic speeds, it is necessary to consider the flow field both upstream and downstream of the disturbance. But, for a…
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REFERENCES 1. Foa, J.V., "Propulsion of a Vehicle in a Tube," Rensselaer Polytechnic Institute, Troy, New York, TR…
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17 APPENDIX I Equations 43-44 for the linearized upstream solution show that (1-1) Now the stagnation enthalpy, in a…
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