Self-similar scattering of evaporation products of a solid wall subjected to variable energy liberation

A system of self-similar equations of motion of the evaporation products (ideal gas) under the effect of variable energy liberation is considered. Conditions are formulated for the existence and uniqueness of a solution of the problem of evaporation and scattering of a material in a vacuum.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 49–54, May–June, 1973.The author is grateful to V. F. Kuropatenko and V. E. Neuvazhaev for aid and interest in the research.     

Self-similar solutions for plasma dynamics in a high-density pinch

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 30, No. 6, pp. 3–7, November–December, 1989.     

Self-similar gas motions in a gravity field

The decelerating effect of a homogeneous gravity field on the plane shock wave acceleration near the outside surface of a gas layer, initially in equilibrium, is analyzed within the framework of the self-similar formulation. A qualitative investigation is performed, the cases in which the first integrals exist are noted, and certain exact solutions of the problem are obtained at different power laws of the initial density variation.     

Plane nonstationary self-similar gas flow with energy liberation in shock waves

Two plane nonstationary, self-similar problems occurring with energy supply in shock waves are examined in a linear formulation; the pressure distributions in the perturbed flow domains are obtained. Results and methods used extensively in the theory of diffraction of shock waves [1–3] are employed in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 164–167, July–August, 1978.In conclusion, the author is grateful to M. N. Kogan for supervising the research, and also to A. I. Golubinskii and V. P. Kolgan for useful comments and valuable discussion.     

Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas

Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture \(K_p\) , and the ratio of the density of solid particles to the initial density of the gas \(G_a\) are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.     

Self-similar turbulent compressible gas flows in a channel

In this study we establish for turbulent compressible gas flow (to within a constant factor) the laws governing the variation of the height (radius) and the static pressure along the length of a planar or axisymmetric channel for which the longitudinal velocity component and gas temperature are functions only of the transverse dimensionless coordinate. In such channels the gas density decrease due to friction is compensated by the increase of the cross-sectional area so that the velocity and temperature profiles remain unchanged at all sections of the channel.The results obtained are a generalization to the gas case of the known laws governing the turbulent flow of an incompressible fluid in a cylindrical channel.The author wished to thank A. P. Byrkin for helpful discussions.     

Self-similar movement of a viscous gas in a channel

The results presented in [1] refer primarily to dropping liquids for which the influence exerted by the thermal conditions on the flow is related to the temperature dependence of the viscosity. The self-similar flow of a viscous gas in a channel with a linearly increasing wall temperature is examined in this paper. The influence exerted by the Reynolds and Prandtl numbers on heat exchange and the hydrodynamics of the flow is analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 47–54, May–June, 1976.The author wishes to thank A. F. Seleznev for carrying out the calculations and V. N. Shtern for discussing the paper.     

Self-similar solutions to Lin-Reissner-Tsien equation

The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.     

Self-similar solutions for infiltration of dopant into semiconductors

Communicated by J. Serrin     

Self-similar growth of a gas hydrate layer separating gas and liquid

The plane one-dimensional Stefan-type problem of the growth of a layer of solid phase separating a gas and a liquid is studied. A self-similar solution and the necessary conditions of its existence are obtained. A number of estimates of the characteristic rates of growth of the layer and the concentration and temperature gradients in the phases are presented, and the results of calculating the growth of the hydrate layer in a water-methane system at a pressure of 10 MPa and a temperature of 283°K are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 78–85, September–October, 1992.     

Self-similar solutions of some nonlinear equations

The method of group invariance under an infinitesimal transformation is applied to a class of nonlinear partial differential equations. Besides yielding a large number of known forms of self-similar solutions, the method also gives new types of solutions.     

Self-similar solutions of thermal two-phase filtration

This work is concerned with deriving generalized self-similar solutions for a thermal model of two-phase filtration in porous media. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 9–17, May–June, 1999.     

Self-similar channel flow of a viscous gas with heat transfer

We examine self-similar flows of a viscous gas in long, smooth channels with a special heat transfer law at the wall, corresponding to the same Mach number profile at all cross sections.     

Self-similar solutions for displacement of non-Newtonian fluids through porous media

This paper presents a class of self-similar solutions describing piston-like displacement (single-phase flow is included as a special case) of one slightly compressible non-Newtonian, power-law, dilatant fluid by another through a homogeneous, isotropic porous medium. These solutions can be used to evaluate the validity and accuracy of existing approximate solutions, such as the assumption of constant flow rate at each radial distance that Ikoku and Ramey use to linearize the partial differential equation for the flow of non-Newtonian, power-law fluid through a porous medium.Nomenclature a parameter, defined by (A8) - A cross-section area of linear reservoir - B constant - c fluid compressibility - c _f formation compressibility - c _t system compressibility - c t dimensionless system compressibility, defined by (24) - C constant of integration - D _I dimensionless coefficient, directly proportional to injection rate, for linear displacement case, defined by (22). - D ₂ dimensionless coefficient, directly proportional to injection rate, for radial displacement case, defined by (55) - erf(x) error function - ercf(x) complementary error function - Ei(x) exponential integral - f dimensionless pressure, defined by (10) - h formation thickness - k permeability - l linear location of moving boundary between the displacing and displaced fluids - n flow behavior parameter - p pressure - p _i injection pressure - p ₀ initial pressure; reference pressure - p ₀ dimensionless initial pressure, defined by (19) - q injection rate - r radial distance - R radial location of moving boundary between the displacing and displaced fluids - t time - u superficial velocity - U substitution of variable - x linear distance - _e effective viscosity - _e dimensionless effective viscosity, defined by (24) - dimensionless variable, defined by (9) or (45) - _i0 value of corresponding to the location of the moving boundary between the displacing and displaced fluids - density - ₀ value of density at reference pressure - porosity - ₀ value of porosity at reference pressure - 1 displacing fluid - 2 displaced fluid