Showing papers on "Similarity solution published in 1970"

An exact similarity solution in radiation-gas-dynamics

Abstract: We have found an exact similarity solution of the point explosion problem in the case when the total energy of the shock wave that is produced is not constant but decreases with time and when the loss due to radiation escape is significant. We have compared the results of our exact solution with those of exact numerical solutions of Elliot and Wang and have explained the cause why our solution differs from theirs in certain aspects.

Interaction of a laminar hypersonic boundary layer and a corner expansion wave

Abstract: There are three distinct effects involved in the interaction of a laminar boundary layer and a supersonic corner expansion wave. These are: the upstream influence effect causing some pressure decay ahead of the corner, transverse pressure gradients in the immediate neighborhood of the corner, and the interaction of the boundary layer downstream with the external flow. Arguments are presented to suggest that, when the flow is locally hypersonic and the wall is highly cooled, the dominant effect is the downstream interaction process. Hence the major features can be calculated by using a simple interaction analysis down stream of the corner based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave. Numerical results are obtained by using the "cold wall" similarity solution to the boundary-layer equations. These show that pressure decay extends over a region which can be many times larger than the original plate length used to generate the boundary layer.

Swirling Axisymmetrical Laminar Jet

Abstract: A similarity solution for the complete Navier‐Stokes equations describing the flow of an incompressible laminar swirling jet was obtained. The solution clearly shows the effect of swirl on the other velocity components, and it is valid for all degrees of swirl. It thus differs from the previous solutions which were of the perturbation type.

A pressure-interaction theory for axisymmetric, hypersonic, laminar, unseparated flows.

Abstract: : Theories for axisymmetric viscous interaction are extended to include arbitrary values of the ratios of both surface to free-stream pressure and boundary-layer to body thickness, by identification of a new measure of transverse curvature in the boundary layer. Methods for four limit flows are isolated. Two of the methods are existing solutions for cones with either a strong shock wave or very thin boundary layer. One is a new local solution for general, very thin bodies; it becomes exact when the pressure ratio approaches one or is unbounded. The fourth is a local similarity solution for power-law bodies with linearizable small-disturbance flow; it becomes exact when the ratio of boundary-layer to body thickness vanishes or is unbounded. These methods have provided interpolated estimates of pressure on a very slender cone-cylinder in hypersonic flow that compare well with original experimental data. Similar predictions of heat transfer rate compare poorly. (Author)

Similarity Analysis For Laminar Natural Convection Flow

Abstract: This paper deals with a theoretical study of laminar natural convection over a semi-infinite vertical plate. It is assumed that the plate is maintained at a given concentration in some chemical species and convection is induced by diffusion into and chemical reaction with the ambient fluid. The fluid is assumed to be viscous and the induced fluid flow, steady. A similarly transform to one variable is possible in the absence of chemical reaction. However, when the chemical reaction takes place between the plate and the ambient fluid, a similarity solution is not available. Thus to obtain an analytical solution of the problem, perturbation expansions about an additional similarity variable which is dependent on the reaction rate must be employed. It has been found that the Schmidt number Sc and the reaction order n are the two fundamental parameters of the problem.