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...

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...

In this paper, two-dimensional and axisymmetric, time dependent transonic and supersonic flows over a projectile overtaking a moving shock wave are considered. The flow is simulated numerically by solving full time averaged Navier-Stokes equations. The equations are linearized by Newton approach. The roe’s flux splitting method, second order central difference scheme for the diffusion terms, an...

A small transonic wind tunnel was designed, constructed and calibrated in order to provide a tool for the study and demonstration of transonic flow phenomena. The wind tunnel makes use of flow properties following the propagation of a shock wave along a tube in order to create the transonic flow. This is in contrast to conventional transonic facilities which are supplied from a reservoir or com...

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...

S U M M A R Y The transonic flow near the throat of a converging-diverging nozzle of a gas with infinite electrical conductivity is considered. The magnetic field B is everywhere aligned with the velocity q so that the equations describing the flow are reducible to those of ordinary gasdynamics. Thus, it is possible to utilize the transonic similarity solution of Tomotika and Tamada [3] to stud...

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 ...

The paper presents a detailed theory of the finite element approximations of two-dimensional transonic potential flow. We consider the boundary value problem for the full potential equation in a general bounded domain fi with mixed Dirichlet-Neumann boundary conditions. In the discretization of the problem we proceed as usual in practice: the domain Q is approximated by a polygonal domain, conf...

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.

Critical points arising in transonic flow profiles of the steady compressible Euler equations with heat conduction are investigated. Two examples of transonic flow profiles are studied, namely, radial outflow in a gravitational field, and flow in a quasi-one-dimensional nozzle. The stationary flow equations are reformulated in terms of a dynamical system that parametrizes the flow profiles. Add...