The effect of longitudinal viscosity on the flow at a nozzle throat

Abstract

An inviscid transonic theory appears to be inadequate to describe the flow near the throat of a converging–diverging nozzle during the transition from the symmetrical Taylor (1930) type of flow to the subsonic–supersonic Meyer (1908) flow. A viscous transonic equation taking account of heat conduction and longitudinal viscosity has been developed previously (Cole 1949; Sichel 1963; Szaniawski 1963). An exact, nozzle-type of similarity solution of the viscous transonic equation, similar to the inviscid solution of Tomotika & Tamada (1950), has been found. This solution does provide a description of the gradual transition from the Taylor to the Meyer flow and shows the initial stages in the development of a shock wave downstream of the nozzle throat. The solution provides a viscous, shock-like transition from an inviscid, supersonic, accelerating flow to an inviscid, subsonic, decelerating flow.

An axisymmetric similarity solution for viscous-transonic nozzle flow

“…therefore, the properties of equation 5are similar to those of the two dimensional equation, which has been discussed in detail by Sichel (1966).…”

“…If the longitudinal or compressive viscosity and the thermal conductivity are taken into account the inviscid transonic equation should be replaced by a "viscous-transonic" equation (Cole 1949, Sichel 1963, Szaniawski 1963. Sichel (1966) found nozzle type similarity solutions of the two dimensional viscous-transonic equation, that do permit the smooth transition from the Taylor to the Meyer type of flow and display the initial stages in shock wave formation downstream of the nozzle throat. An axisymmetric viscous transonic nozzle solution has also been found and is the main subject of the present paper.…”

Asymptotic research of transonic gas flows

“…The structure of gas flows in some cases is significantly influenced by viscosity and thermal conductivity. The viscosity was taken into account in the works of M. Sichel [21,22], O. S. Ryzhov, G. M. Shefter [23], P. A. Velmisov, S. V. Falkovich [24].…”

Unsteady transonic flows with shock waves in an asymmetric channel

“…Two approaches have generally been used in constructing analytical solutions for transonic channel flows with shock -waves. In one, similarity solutions of the transonic smalldisturbance equation are sought through various transforrjnations, resulting in solutions for steady 1 or unsteady 2 Hows. The solutions thus obtained, however, satisfy only very special boundary conditions, which may or may not.…”