Shock Response to Downstream Disturbances

Abstract

Shock Response to Upstream Disturbances, Roy Gundersen. 226 Variational Analysis of Ablation, M. A. Biot and H. Daughaday 227 Shock-Wave Profiles of Sharp Wedges in Helium Flow at M = 28.9, Robert H. Johnson 229 Roll Damping of a Fleet Ballistic-Missile Submarine, Frank J. Regan 230 Dusty-Gas Flow Through an Oblique Shock Wave, Kinge Okauchi 230 Constant-Electric-Field and Constant-Magnetic-Field Magnetogasdynamic Channel Flow, Gordon C. Oates 231 Effect of Porosity on the Two-Dimensional Supersonic Sail, E. A. Boyd 232 Response of a Schuler-Tuned Inertial Guidance System to Random Errors, James T. Ephgrave 233 A Method of Obtaining an Approximate Solution of the Falkner and Skan Boundary-Layer Problem, Eleanor M. James 234 The Use of the Howarth Transformation in Turbulent, Compressible Flow, William T. Snyder 235 Special Solutions to the Equations of Motion for Maneuvering Entry, W. Scott Jackson 236 An Experimental Test of Compressibility Transformations for Turbulent Boundary Layers, William Squire 237 Blunt-Cone Pressure Distributions at Hypersonic Mach Numbers, Andrew F. Burke and James T. Curtis 237 The Evaluation of Response of Aeroelastic Systems to Transient and Random Turbulence by Kernel-Function Techniques, Arthur K. Cross 239 Pressure Variation of Strong-Detonation Limits, K. M. Foreman 240 A Uniqueness Theorem for a Nonlinear Maxwell Body, Jerome L. Sackman 240 On the Hodograph Method in Magnetogasdynamics, Milomir M. Stanisic 242 Historical Note on the 1.5 Factor of Safety for Aircraft Structures, F. R. Shanley 243 A Magnetofluid-Dynamic Kutta-Joukowsky Condition, E. Cumberbatch, L. Sarason, and H. Weitzner 244 A Technique for Determining the Nozzle-Flow Properties of Air in an Equilibrium, Nonequilibrium, or Frozen State, Lovick 0. Hayman, Jr. and Roger B. Stewart 245 A Note on the Design of a Two-Dimensional Contracting Channel, Y. S. Nanjunda Swamy 246 An Approximate Solution for Laminar Channel Flow of a Conducting Fluid under Transverse Magnetic Field, Fujihiko Sakao 246 Direct Beam Stiffness-Matrix Calculations Including Shear Effects, Claus J. Meissner 247 A LINEARIZED ANALYSIS, based on small area variations, > 2 is utilized to determine the perturbation of an initially plane and uniform shock wave propagating through a tube of varying cross-sectional area into an initially uniform and isentropic state, which is subjected to a nonisentropic perturbation at some section, x = a, say. (The case of conditions prescribed at t = 0 would be treated similarly.) The shock is perturbed by the area variations and further by the perturbed flow upstream so that the flow behind the shock is nonisentropic. By applying the conditions on x = a to the general solution for the nonisentropic perturbation of an initially uniform state, the perturbed flow in front of the shock is completely determined. By writing the shock relations in perturbation form, a formula for the shock-velocity perturbation is derived by superposition of the perturbations due to the area variations and upstream perturbation. I t is found that the shock-velocity perturbation is singular for sonic flow just behind the shock with the singularity contained in the terms arising from the upstream perturbation. The results obtained may be applied to the case of an initially stationary shock obtained by setting the original shock-velocity equal to zero. When the equations which govern the one-dimensional, unsteady flow of an inviscid, ideal compressible gas in a tube of variable cross-sectional area are linearized in the neighborhood of a known (isentropic) solution, the general solution for an initially uniform state is: