Class Of Self-similar Solutions Research Articles

Localization of gas-dynamic processes and structure when the material is compressed adiabatically, in the peaking mode

Adiabatic compression of gas by a piston, the pressure on which increases in the peaking mode, is studied. The entropy is distributed over the mass. A class of selfsimilar solutions (the LS mode) is constructed and its properties are studied. It is shown that the effective dimensions of the compression wave decrease with time and all gas-dynamic perturbations are localized within a finite mass of the gas. The solutions obtained are characterized by the presence of a structure (inhomogeneities) in the density and temperature. The compression occurs without the formation of shock waves.

A class of similarity solutions for the nonlinear thermal conduction problem

A class of self-similar solutions are rederived for the nonlinear thermal conduction problem. Variational methods applied to the heat flux provide an expression valid over a broad range of physical parameters. The results are particularly useful for the understanding of heat flux in the plasmas of internal confinement fusion. They describe both rapid laser and radiant heating of matter. The developments are shown to correspond well to several classical examples.

Transonic rarefaction flow in the neighborhood of a convex corner

A new solution of the problem of perfect gas flow over a corner is considered in the case when a sonic line issues from the corner point, and a mixed flow is formed, it satisfies the Fal'kovich-Kármán equation, belongs to its class of self-similar solutions /1/, and obtains when the self-similarity parameter n=2.

Self-similar solutions of the external condensation problem

A new class of self-similar solutions of the external condensation problem is constructed, which takes account of the change in the process parameters a long the length of the condensation section.

Self-generated magnetic fields in plasmas

The generation of magnetic fields by currents driven by the electron pressure gradient in non-uniform plasmas is considered. The equations for field generation and energy balance are derived under the MHD approximation. It is shown that there exists a class of waves, thermal magnetic waves, which propagate along surfaces of constant density. The properties of such waves are examined. In addition, a class of self-similar solutions are presented. These represent an unstable growth of magnetic field in localized plasma regions, i.e. magnetic hot spots.

Laminar flow between porous disks for intense homogeneous asymmetric inflow and outflow

In [1–3], a class of self-similar solutions was considered for the flow of incompressible fluid in a plane channel with porous walls, through which there is homogeneous symmetric inflow or outflow. An analogous class of self-similar solutions for flow between porous disks with natural homogeneous conditions at the periphery was considered in [4], where the asymptotic behavior of these solutions at a small Reynolds number of the outflow R was investigated, and the limiting form of the solution for symmetric outflow with R=∞ was noted. In the present paper, the boundary-function method is applied to the singular problem corresponding to the flow between porous disks for asymmetric inflow and outflow characterized by large R.

Unsteady flow of gas in laval nozzles with local supersonic zones: PMM vol. 39, n≗2, 1975, pp.271–279

Exact particular solutions of nonlinear equations defining unsteady transonic flows of gas are derived. These solutions are used for analyzing unstable flows in Laval nozzles with local supersonic zones, Local supersonic zones in stationary flows were investigated with the use of the simplified equations for transonic flows of gas in [1] in plane nozzles and in [2] in nozzles of circular cross section. These solutions were then extended in [3] to three-dimensional flows in Laval nozzles. Since the investigation of variation of local supersonic zones with time is complicated by the nonlinearity of the equation for unstable transonic flows, hence even particular examples are of interest. A solution of this equation for an unsteady flow of the Taylor kind in a nozzle with two planes of symmetry was indicated in [3]. Similar solutions were later considered in [4] for unstable flows in plane nozzles. It was established that all of the above solutions can be extended. One of such generalized solutions of the transonic equation defining an unsteady flow of the Taylor kind in plane and axisymmetric Laval nozzles is presented in [5]. Here this solution is used for analyzing the variation of local supersonic zones with time (their onset, development, and joining at the nozzle axis, or the inverse process) for two classes of self-similar solutions.

A class of self-similar solutions of problems involving hypersonic flow of a gas over porous axially symmetric bodies

A class of self-similar solutions of problems involving hypersonic flow of a gas over porous axially symmetric bodies

On self-similar blast waves headed by the Chapman–Jouguet detonation

Consideration of the whole class of self-similar solutions for blast waves bounded by Chapman-Jouguet detonations that propagate into a uniform, quiescent, zero counterpressure atmosphere of a perfect gas with constant specific heats. Since such conditions can be approached quite closely by some actual chemical systems at NTP, this raises the interesting possibility of the existence of Chapman-Jouguet detonations of variable velocity. The principal virtue of the results presented is, however, more of theoretical significance. They represent the limiting case for all the self-similar blast waves headed by gasdynamic discontinuities associated with a deposition of finite amounts of energy, and they exhibit some unique features owing to the singular nature of the Chapman-Jouguet condition.