Upstream propagating curved shock in a steady transonic flow∗
نویسنده
چکیده
We derive a new set of equations to give successive positions of slowly moving and slowly turning curved shock front in a transonic flow. The equations are in conservation form two of these are kinematical conservation laws. keywords Curved shock propagation, shock dynamics, ray theory, transonic flow.
منابع مشابه
A Proof of Existence of Perturbed Steady Transonic Shocks via a Free Boundary Problem
We prove the existence of a solution of a free boundary problem for the transonic small-disturbance equation. The free boundary is the position of a transonic shock dividing two regions of smooth flow. Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hyperbolic upstream where the flow is supersonic, and elliptic in the downstream subs...
متن کاملOn Transonic Shocks in Two-Dimensional Variable-Area Ducts for Steady Euler System
This paper concerns transonic shocks in compressible inviscid flow passing a twodimensional variable-area duct for the complete steady Euler system. The flow is supersonic at the entrance of the duct, whose boundaries are slightly curved. The condition of impenetrability is posed on the boundaries. After crossing a nearly flat shock front, which passes through a fixed point on the boundary of t...
متن کاملExistence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-sections
We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip bo...
متن کاملExistence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-sections
We establish the existence and stability of multidimensional transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Lavel nozzle. The transonic flow is governed by the inviscid steady potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the infinite exit, and the slip bound...
متن کاملUniqueness of Transonic Shock Solutions in a Duct for Steady Potential Flow
We study the uniqueness of solutions with a transonic shock in a duct in a class of transonic shock solutions, which are not necessarily small perturbations of the background solution, for steady potential flow. We prove that, for given uniform supersonic upstream flow in a straight duct, there exists a unique uniform pressure at the exit of the duct such that a transonic shock solution exists ...
متن کامل