Evolution of weak discontinuities in a non-ideal radiating gas

A method of wavefront analysis is used to study the formation of shock waves in a two-dimensional steady supersonic flow of a non-ideal radiating gas past plane and axisymmetric bodies. The gas is taken to be sufficiently hot for the effect of thermal radiation to be significant, which is, of course, treated by the optically thin approximation to the radiative transfer equation. Transport equations, which lead to the determination of the shock formation distance and also to conditions which insure that no shock will ever evolve on the wavefront, is derived. The influence of the parameter of the non-idealness, upstream flow Mach number in the presence of thermal radiation on the behavior of the wavefront are examined.     

The growth and decay of sonic waves in a radiating gas at high temperature

The propagation of a sonic discontinuity in an optically thick gray gas at temperature 10⁵°K or higher has been studied. The effects of radiation pressure and radiation energy density have been taken into account, while the profiles structured by radiant heat transfer are imbedded in the discontinuities under high temperature conditions of an optically thick medium. When the sonic discontinuity is propagating into a gas at rest, its velocity of propagation is found to be a constant which is the effective speed of sound in a radiating gas. The fundamental differential equations governing the growth of the sonic discontinuity are obtained and solved. It is concluded that if the sonic discontinuity is a compressive wave of order 1, then it terminates into a shock wave after a critical timet _c which has been determined. But on the other hand, when the sonic discontinuity is an expansion wave of order 1, then it will decay and will vanish ultimately. Particular cases of interest have been studied in details.     

Nonlinear breaking of waves in an electrically conducting and radiating gas

The effects of radiative transfer are treated by the use of a differential approximation which is valid over the entire optical depth range from the transparent limit to the optically thick limit. The singular surface theory is used to determine the modes of wave propagation and to evaluate the behaviour at the wave head. It is shown that there are two modes of wave propagation namely (i) the radiation induced waves which are always damped, and (ii) the modified magnetogasdynamic waves which break at the wave front if the initial discontinuity is sufficiently strong. The effects of thermal radiation, the magnetic field intensity, the finite electrical conductivity and the initial wave front curvature on the non-linear breaking of modified magnetogasdynamic waves are discussed.

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Zusammenfassung Der Einfluß der Strahlung wird mit Hilfe von Differential-Näherungen behandelt, die im ganzen Bereich von optischen Tiefen Gültigkeit haben, von der Transparenz bis zur optisch dicken Grenze. Die Theorie singulärer Flächen wird benützt um die Wellenausbreitung und das Verhalten an der Wellenfront zu behandeln. Es wird gezeigt, daß es zwei Formen von Wellenausbreitung gibt, nämlich (i) Wellen erzeugt durch Strahlung, die immer gedämpft sind, und (ii) die modifizierte magnetogasdynamische Welle, die an der Front immer bricht, wenn die ursprüngliche Diskontinuität stark genug ist. Es werden die Einflüsse der Wärmestrahlung, der magnetischen Feldstärke, der endlichen elektrischen Leitfähigkeit und der ursprünglichen Wellenkrümmung auf die nicht-lineare Frontbildung untersucht.

     

Propagation of weak discontinuities in binary mixtures of ideal gases

The propagation of the weak discontinuities in binary non-reacting mixtures of classical ideal monoatomic gases is analyzed. The normal speeds of propagation are determined and compared with those of a single fluid. The differential equation governing the growth and the decay of the acceleration waves is obtained and the solutions for plane, cylindrical and spherical waves are shown. The influence of the different atomic masses of the constituents is also investigated.     

An optically thin radiating gas jet

A radiating gas jet near the optically thin limit is examined. The gas is assumed to be inviscid, optically grey, and in the state of chemical equilibrium or to obey the ideal gas law. The jet is assumed to be plane-symmetric or axi-symmetric and is fully expanded. Under these conditions and by the method of quasi-one-dimensional flow, the problem is analyzed. In addition to this, numerical examples are also included to illustrate the radiative effects.

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Zusammenfassung Es wird ein strahlender Gasstrahl untersucht, nahe zum optisch dünnen Grenzfall. Das Gas wird reibungsfrei, optisch grau und im chemischen Gleichgewicht (oder als ideales Gas) vorausgesetzt. Der Strahl wird eben oder axisymmetrisch angenommen und ist voll expandiert. Unter diesen Voraussetzungen und mit der Methode der fast-eindimensionalen Strömung wird das Problem analysiert. Zudem sind numerische Beispiele angegeben, um den Strahlungseffekt zu veranschaulichen.

     

The thermodynamic functions of an ideal gas mixture in an equilibrium state

We find expressions for the entropy and thermodynamic potentials (chemical, internal energy, and the like) for a one-component ideal gas, and also for a mixture of ideal gases in equilibrium.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 134–140.     

On the symmetric algebra of an ideal

The symmetric algebra of an ideal I may be compared to the Rees algebra via the canonical epimorphism :Sym(I)R(I). A necessary and sufficient criterion is given for a to be an isomorphism, and sequential conditions on the symmetric algebra are studied. Some applications are given to Proj :ProjR(I)Pro'j Sym(I) and to the theory of approximation complexes.The material presented in this paper constitutes part of the author's thesis submitted to Universität Essen     

Unlimited cumulation under one-dimensional unsteady compression of an ideal gas

Various methods of unlimited cumulation (UC) of an ideal (inviscid and non-heat-conducting) gas subject to one-dimensional unsteady compression by a plane, cylindrical, or spherical piston are considered. The most perfect method, namely, UC with isentropic compression from rest to rest, which is referred to as “ideal” (IUC), is compared with three other methods of UC, which correspond to well-known self-similar solutions of one-dimensional gas compression. The most effective of these is UC with a reflected shock wave, behind which the compressed gas is homogeneous and at rest, as in IUC. The efficiency of various methods of UC is estimated by the ratio of the work done during compression to the work in the case of IUC, the ratio of the internal energy to the total energy of the compressed gas, and the degree of gas homogeneity with respect to the Lagrangian variable. Computations of these characteristics are carried out for a perfect gas with various adiabatic exponents.     

The plane isothermal motions of an ideal gas without expansions

A general solution of the equations of plane isothermal motions of an ideal gas without expansions is obtained. A method of reducing the overdetermined system of differential equations to an involution is proposed, which consists of obtaining integrable relations. All representations of the solution in time are obtained: polynomial, harmonic and biharmonic, and representations of linearly and exponentially increasing harmonics. All the representations give solutions of the overdetermined system, among which there are all the solutions with linear velocity fields, obtained by Ovsyannikov.     

Growth of weak discontinuities in arbitrarily moving gas

The theory of singular surfaces is combined with the ray theory to the study of anisotropic, non-linear wave-propagation in an arbitrarily moving gas. The governing equation for the strength of the wave along the rays is expressed in an integral form. Use of the analysis is made by working out two examples in detail.     

Decay of a model system of radiating gas

This paper concerns the Cauchy problem of a model system to the radiating gas in . Large time behaviors of classical solutions to the Cauchy problem are studied without needing the smallness assumption of initial perturbation in L¹‐norm. We obtain the optimal H^N‐norm time‐decay rates of the solutions in with 1 ≤ n ≤ 4 by applying the Fourier splitting method introduced by Schonbek (1980) with a slight modification and an energy method. Furthermore, when initial perturbation is bounded in L^p‐norm (p ∈ (1,2]), optimal L^p‐ L² decay estimates of the derivatives of solutions are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

A refinement of the Zipf-Mandelbrot law and the lacunarity in an ideal gas

The Zipf-Mandelbrot formula for occurrence frequencies is refined and is applied to an ideal gas. This refinement essentially affects the value of the prefactor c₂ and consequently the value of the lacunarity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 511–512, June, 2006.     

On an inverse spectral problem for first-order integro-differential operators with discontinuities

A convolution integro-differential operator of the first order with a finite number of discontinuities is considered. Properties of its spectrum are studied and a uniqueness theorem is proven for the inverse problem of recovering the convolution kernel along with the boundary condition from the spectrum.     

Clustering in an ideal gas in nanostructures as a Bose-condensation-type phenomenon in an asymptotically probabilistically quantized space

We describe a space quantization model that allows treating the phenomenon of particle clustering in an ideal gas in nanostructures with a fractal dimension. Dedicated to Vasilii Sergeevich Vladimirov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 468–469, December, 2008.