The effect of gas motion on the reaction kinetics of vibrationally excited molecules

The effect is considered of gas motion on the kinetics of reactions whose energy threshold is overcome as the result of vibrational excitation of the reactant molecules. The conditions are determined for which such an effect may be realized. An expression is obtained for the rate of thermal dissociation of diatomic molecules considered as harmonic oscillators representing a small impurity in a monoatomic inert gas; the expression depends explicitly and nonlinearly on the divergence of the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–105, November–December, 1984.     

Vortex flows of a viscous heat-conducting gas in a slightly divergent tube with volume energy supply

The results of a numerical investigation of viscous vortex flow in a slightly divergent tube with thermal energy supplied to the flow are presented. The initial stage of vortex flow development is considered for two different longitudinal velocity distributions simulating the velocity profiles in jet-like and wake-like vortex flows in the vicinity of the vortex axis. The first type of flow can be considered as a model for the near-axis region of the vortex formed in the flow around a delta wing at incidence. The second type can serve as a model for the near-axis region of the trailing vortex downstream of a high-aspect-ratio wing. The development of the two flows is studied for a constant area tube, a slightly divergent tube, and in the case of thermal energy supply from a volume energy source at a constant wall temperature.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 90–97, September–October, 1996.     

Numerical investigation of viscous gas secondary flows in a rotating cylinder with sources and sinks

A source-sink model of secondary flow excitation in a rotating cylinder, which describes the interaction between a circulator and a rotating gas, is proposed for a nonlinear system of Navier-Stokes equations, and the results of a numerical calculation of the resulting circulating flows are presented. The modified Newton's method employed in the numerical solution makes use of regularizing perturbations to ensure its stability and convergence at low Ekman numbers and high rates of rotation of the cylinder. The combined effect of mechanical and thermal means of flow excitation and the influence of viscous energy dissipation are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–44, July–August, 1989.     

Nonequilibrium dissociation of diatomic molecules in flows with convective and diffusive particle transport

The nonequilibrium effects in the kinetics of the thermal dissociation which occurs in a streaming gas of diatomic molecules are investigated. Expressions are obtained for the macroscopic reaction rate and the vibrational energy distribution of the molecules, taking into account the influence of the gas motion. Cases of flows with convective and diffusive particle transport are considered. The dissociating molecules are simulated by cutoff harmonic oscillators. The vibrational kinetics is described in the framework of the so-called diffusion approximation.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1985.     

Piston problem with allowance for finite rate of exothermic reactions and nonlinear heat conduction

One-dimensional nonstationary flows of a combustible mixture of gases are considered with allowance for nonlinear heat conduction. The possible existence of similarity solutions is studied, and conditions are found under which such solutions do exist. The results are given of a numerical calculation of the similarity problems of a piston and self-sustaining thermal wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1. pp. 146–151, January–February, 1979.I thank V. A. Levin for continuous assistance in the work.     

Interface crack with a contact zone in an isotropic bimaterial under thermomechanical loading

A plane problem for a thermally insulated interface crack with a contact zone in an isotropic bimaterial under tension–shear mechanical loading and a temperature flux is considered. The expressions for the stresses and the electrical flux as well as for the derivatives of the displacement and the temperature jumps at the material interfaces via sectionally holomorphic mechanical and thermal potential functions are given. After the solution of the thermal problem the inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved exactly. The stresses at the interface and the stress intensity factors at the singular points are presented in a clear analytical form. Special attention is devoted to the case of a small contact zone when the stress intensity factors can be presented in form similar to the associated presentation for an “open” crack model. A transcendental equation and an asymptotic analytic formula for the determination of the real contact zone length are derived. It is shown that for a certain bimaterial this length as well as the correspondent stress intensity factor are defined by a single parameter which depends on the normal-shear loading and the heat flux.     

Effective thermal conductivity of a medium with ellipsoidal particles

The principal components of the effective thermal conductivity tensor, characterizing stationary heat macrotransfer in a dense medium with dispersed ellipsoidal particles of a different material are calculated by a method suggested in [1]. The case of equally oriented ellipsoids and of isotropically distributed ones are considered as examples.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 107–111, January–February, 1974.The author is grateful to Yu. A. Buevich for his interest.     

The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Convective heat transfer in laser-irradiated graphite

The gas dynamic and thermal processes developing near the surface of graphite after exposure to a 20-nsec laser pulse with an energy E- 0.1–1 J and a wavelength of 0.6943 m are investigated experimentally and by mathematical modeling. The times required for the shock wave to degenerate into an acoustic wave are also considered. Typical density profiles over the axial section of the inhomogeneity are presented for various moments of time. It is noted that the rate of ascent of the thermal inhomogeneity is much higher than the free convection velocity. The convective heat-transfer processes are studied in detail through numerical solution of the system of two-dimensional Navier-Stokes equations. The results of the calculations are in satisfactory agreement with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–182, May–June, 1989.     

Thermal convection in a cylindrical enclosure with intense internal heat generation in the presence of a longitudinal magnetic field

Steady convection in a gaseous medium with intense heat generation is considered without making use of the Boussinesq approximation. The effect on convection of the thermal boundary conditions at the walls of the enclosure is investigated, together with the influence of a longitudinal magnetic field which is effective when the medium is strongly heated and becomes electrically conducting.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 11–18, May–June, 1992.The authors are grateful to the participants in the G. A. Lyubimov seminar for discussing their work.     

Steady two-phase flow in a vertical tube subject to combined free and forced convection

Using the two-velocity, two-temperature model of a continuous medium, the viscousgravitational flow of a mixture of incompressible liquid and solid particles in a vertical round tube is considered. The free-convection equations are written down on the basis of the general equation of motion and the energy equation of a two-phase medium [1, 2]. Using a finite Hankel integral transformation, a solution is constructed for the case of a linear wall-temperature distribution along the tube. The results of some practical calculations of the velocity and temperature fields over the cross section of the tube are presented, together with the dimensionless heat-transfer coefficient expressed as a function of the Rayleigh number and phase concentration. Here it is assumed that the dynamic and thermal-interaction coefficients between the phases correspond to the Stokes mode of flow for each particle, as a result of which the velocity and thermal phase lag is very small [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1975.     

Rarefied gas flow past a sphere with injection

Hypersonic rarefied gas flow over the windward face of a sphere is considered in the presence of distributed injection from the surface of the body. A similar problem was previously solved in [1–3] within the framework of continuum mechanics and in [4] on the basis of model kinetic equations. In the present study the calculations were carried out using the Monte Carlo method of direct statistical modeling [5, 6]. The injected gas was the same as the free-stream gas. A simple monatomic gas model with a rigid sphere interaction potential was employed. The reflection of the molecules from the surface of the body was assumed to be diffuse with total energy accommodation. The calculation procedure using weighting factors is described in [7]. The influence of injection on the mechanical and thermal effect of the gas flow on the body is investigated for various degrees of rarefaction of the medium and injection rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1990.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.     

Reflection of a strong shock wave from an ellipsoid

The reflection from an ellipsoid of a strong shock wave (with uniform parameters behind the wave) moving along one axis of the ellipse is considered. Viscosity and thermal conductivity of the gas are not considered. A solution is sought in the vicinity of the critical point using the small parameter method [1]. The nonlinear differential equations for the dimensionless components of the gas velocity in this region are solved by the method of separation of variables with the additional condition of [2]. Analytical expressions are found for the flow parameters, which for the cases of an elliptical cylinder and ellipsoid of revolution coincide with the corresponding expressions obtained previously in [2].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 19–23, November–December, 1980.     

Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Gradient elasticity and nonstandard boundary conditions

Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain energy is shown to include a bulk and surface strain energy. A minimum total potential energy principle is provided for the related structural boundary-value problem. The Toupin–Mindlin polar-type strain gradient material model is also addressed and compared with the above one, their substantial differences are pointed out, particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations. A gradient one-dimensional bar sample in tension is considered for a few applications of the proposed theory.     

Influence of anisotropy of the permeability on the convection and heat transfer in a porous annular layer

Investigations into the convective transport of heat in porous materials are of interest for many applications in connection with the problem of increasing the efficiency of thermal insulation. In [1–5], convection in Isotropic porous media was considered. However, in many cases porous materials have an essential anisotropy of their permeability. Convective heat transfer has been inadequately studied for this case. In [6], the linearized equations were used to study the convection between infinite horizontal planes with a filling of an anisotropic material; the value of the critical Rayleigh number was found, and this agreed satisfactorily with experimental data. In the present paper, we investigate numerically convection between two infinite coaxial cylinders with an anisotropic porous filling, using the equations of convection in the Darcy—Boussinesq approximation [1–3]. The permeability tensor in the annular region is constructed from its principal values, which can be found experimentally. A method of calculation is developed and a parametric study made of the structure of the flow and of the local and averaged characteristics of the heat transfer, which are of interest for the design of thermal insulation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–64, January–February, 1980.     

Calculation of one transient mode of combustion of a condensed system

A one-dimensional process representing the combustion of a powder sample on a metal substrate at constant pressure is considered on the basis of a two-phase model of the thermal decomposition of a condensed system. The results of numerical computer calculations are presented. Qualitative comparison is made with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 23–30, January–February, 1972.     

Non-Darcian Effects on the Onset of Convection in a Porous Layer with Throughflow

The Brinkman extended Darcy model including Lapwood and Forchheimer inertia terms with fluid viscosity being different from effective viscosity is employed to investigate the effect of vertical throughflow on thermal convective instabilities in a porous layer. Three different types of boundary conditions (free–free, rigid–rigid and rigid–free) are considered which are either conducting or insulating to temperature perturbations. The Galerkin method is used to calculate the critical Rayleigh numbers for conducting boundaries, while closed form solutions are achieved for insulating boundaries. The relative importance of inertial resistance on convective instabilities is investigated in detail. In the case of rigid–free boundaries, it is found that throughflow is destabilizing depending on the choice of physical parameters and the model used. Further, it is noted that an increase in viscosity ratio delays the onset of convection. Standard results are also obtained as particular cases from the general model presented here.     

Structure of a shock wave in which multiple ionization of the atoms is taking place

Ionization relaxation in a shock wave of very large amplitude is considered, the atoms behind the front of the shock wave being multiply ionized. In calculating the structure of the shock wave and the kinetics of ionization, allowance is made for the electron component of the thermal conductivity which plays an important role in this. A simplified method of calculating the kinetics of multiple ionization is proposed, and an application of this method is presented. The results of the structure calculation show that, as a result of heating by thermal conduction, the gas is considerably ionized even in front of the jump in compression, while the electron component of the thermal conductivity passes through a maximum.Translated from Zhurnal Prikladnoi Mekhnika i Tekhnicheskoi Fiziki, No. 5, pp. 11–21, September–October, 1970.