Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Viscosity of a suspension of ellipsoidal ferromagnetic particles in a magnetic field

The motion of a suspension of solid magnetized ellipsoids of rotation in a uniform magnetic field is considered. The ellipsoids are assumed to be magnetized along the axes of symmetry. Relaxation processes in the solid phase are not considered. The stress tensor of the suspension is calculated taking into account the rotational Brownian motion of the particles. It is shown that the viscosity tensor contains six independent kinetic coefficients, which are even with respect to the magnetic field. The relation between these coefficients and the field and the ratio of the semiaxes of the ellipsoid is obtained. As an example, the effect of the magnetic field on the symmetrical flow of the suspension in a contractile cylinder is considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 75–82, September–October, 1973.     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

The pressure and temperature behind bodies with flat bases in a supersonic flow when inert and active gases are introduced into the base region

The effect of introducing active and inert gases into the base region behind two-dimensional and axisymmetric bodies on the pressure and temperature in that region is studied in the absence of heat transfer between the body and the base region. The flow in the mixing zone is assumed to be turbulent. To investigate the effect of introducing active gases on the parameters in the base region, a model of diffusion combustion is used. The base pressure is calculated by Korst's method [1]. For the velocity profile in the mixing zone an expression is used which results from integrating the equation of motion in von Mises variables. The temperature and concentrations of the components in the base region are determined from integral equations for the conservation of enthalpy and concentration, which make it possible to calculate the parameters in the base region for arbitrary flow rates of the active gas, including arbitrarily small rates. The results are given of calculating the base pressure when hydrogen and argon are blown into the base region. In the latter case computational and experimental results are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 48–57, March–April, 1971.     

Boundary layer on a flat plate with strong longitudinal magnetic field

The influence of a magnetic field on the boundary layer on a flat plate in a sufficiently strongly ionized gas stream is studied. The magnetic field is parallel to the plate and to the velocity of the free stream, and it is so strong that the transport coefficients become anisotropic (the cyclotron rotation frequency of the charged particles is greater than or equal to the order of the frequency of the particle collisions). Using the results of [1–3] it is shown that the effect of the strong longitudinal magnetic field with a sufficiently high degree of gas ionization leads to a reduction in the thermal flux to the plate. For low degrees of ionization this effect is very small, since the viscosity and heat conduction in this case are determined by the neutral component of the gas.Results are presented of numerical calculations of the considered problem with account for the dependence of the transport coefficients on the thermodynamic parameters. It is assumed throughout that the magnetic Reynolds number is small (R_m1).     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Relaxation-Induced Suppression of Vortex Disturbances in a Molecular Gas

The influence of thermal excitation on a finite-amplitude vortex disturbance in a shear flow of a molecular gas is studied in a model problem. The evolution of such vortex structures is typical of both the nonlinear stage of the laminar–turbulent transition and for developed turbulence. Since the excitation level was assumed to be comparatively low, full Navier–Stokes equations for a compressible heat-conducting gas were used in calculations; nonequilibrium was taken into account by the coefficient of bulk viscosity. As the bulk viscosity increases in the range of realistic values, the disturbance-energy damping rate in a weakly compressible flow increases approximately by 10%. The increase in the Mach number enhances the effect of disturbance suppression.     

Variational model of a turbulent rotating flow

A model of effectively viscous turbulent flows satisfying the Navier-Stokes equations and certain slip conditions at the walls is analyzed. The turbulent viscosity is determined on the basis of the principle of minimum energy dissipation rate, whose significance and conditions of applicability are discussed in detail. A new separated turbulent flow model is outlined. The problem of turbulent flow in a porous rotating tube is solved. The existence of two metastable flow regimes is predicted: one with an axial circulation zone, the other straight-through. In the case of a strongly swirled flow the first of these has a greater probability of realization; however, as the rotation weakens, in a certain critical situation the circulation zone collapses, after which the flow can only be straight-through. Despite the absence of empirical content, every aspect of the proposed theory is in good agreement with the experimental research on vortex chamber flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–32, May–June, 1985.     

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

A two-dimensional problem of the flow of a gas containing an impurity through a porous medium is considered. At the initial time, the gas containing a uniformly distributed impurity is at a high pressure in a spherical cavity in a porous medium at a certain distance from a flat surface. It is assumed that for t > the motion of the carrier gas is described by the system of equations for flow in a porous medium and the dispersion of the impurity is described by the equations of convective diffusion and nonequilibrium adsorption. A numerical method for solving the problem is discussed. Some results of calculations are given. The influence of the flat surface on the flow of the gas and the dispersion of the impurity is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1982.We thank V. N. Nikolaevskii for comments which permitted a significant improvement in the paper.     

Simulation of the motion of thin rotating jets of a viscous incompressible fluid

A regular procedure is proposed for deriving approximate equations of motion of straight thin rotating jets of a viscous incompressible fluid, and similarity parameters of such flows are established. The problem of the stability of free steady motion of a finite jet is considered in the framework of a model that takes into account in the zeroth approximation the effects of viscosity, the rotation of the jet, and capillarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 51–59, March–April, 1984.     

Stability of a liquid layer with bubbling

The article discusses a new type of instability of a horizontal layer of a motionless liquid, due to the motion of bubbles of gas or of particles of a suspension through the layer. It is shown that, when a certain critical mass flow rate of the gas or the suspension is attained, due to the essential inhomogeneity of the velocity of the gas bubbles, the layer becomes unstable and convective flow develops in a Bénard cell. With the motion of bubbles in the field of gravity, the criterion of instability is found to be independent of the size of the bubbles and the kinematic viscosity of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, July–August, 1974.     

Large-scale vortex generation driven by nonequilibrium turbulence

The development of large-scale perturbations in a heated layer of rotating fluid is studied within the framework of the nonequilibrium turbulence model with asymmetric Reynolds stress tensor. It is shown that, as in spiral turbulence, when there is no equilibrium on one of the boundaries of the layer large-scale structures develop. Conditions under which both perfect intrinsic matching of turbulence and convection and internal resonance development exist are determined. It is shown that the manifestation in a turbulent medium of properties of the convective vector field such as spirality may be caused by constraints imposed by the angular momentum conservation law.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 47–55, January–February, 1996.     

Numerical investigation of the influence of gravitational convection on processes of heterogenous ignition

A numerical method is used to investigate the influence of free convective motion of a gas on the process of heterogenous ignition. The dependence of the critical condition for ignition on the intensity of convection is obtained. The flow structure for different parameters and the features of the ignition process are investigated. It is noted that the ignition begins at a point and there is subsequent transition of the complete surface of the catalyst to the high-temperature region by a combustion wave that travels along the catalyst.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 144–149, January–February, 1980.     

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.     

An improved algorithm for simulating three-dimensional, viscoelastic turbulence

We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov and Tadmor [A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations, J. Comput. Phys. 160 (2000) 241–282] that guarantees a scalar field remains everywhere positive. We have extended the algorithm to guarantee a tensor field remains everywhere positive definite following an update. Extensive testing of the algorithm shows that the volume average of the conformation tensor is conserved. Furthermore, volume averages of the conformation tensor in homogeneous turbulent shear flow made over the Eulerian grid are in quantitative agreement with Lagrangian averages made over fluid particles moving throughout the domain, highlighting the accuracy of the treatment of the convective terms.     

Motion of particles in a nonstationary layered flow of an incompressible fluid

The motion of spherical particles in a nonstationary layered flow are considered. It is assumed that the fluid is incompressible and that the particles do not interact with one another or influence the parameters of the fluid. Allowance is made for the influence of the pressure gradient, the apparent mass, the Magnus force, and the viscosity of the fluid on the motion of the particles. The formulation of the problem corresponds to the conditions of motion of the two-phase mixture in the channels of the rotatory-pulsatory apparatus [1] used in technology to realize various processes such as solution, emulsification, dispersing, etc. The processes in such an apparatus are strongly nonsteady and have hitherto been hardly investigated at all.Translated from 'Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 53–58, July–August, 1981.We thank A. R. Gurvich for making the calculations.     

Heat transfer at and near the stagnation point in turbulent flow over bodies

Results are presented of experimental investigations of heat transfer in the neighborhood of the stagnation point in flow of a turbulent gas over bodies. It is assumed that the outer flow is capable of rendering the boundary layer turbulent over the whole body surface, i.e., the hypothesis is invoked that there is a turbulent stagnation point. Using the method of integral relations [1] and the flat plate heat-transfer law, transformed in such a way as to satisfy the heat-transfer conditions at the stagnation point, simple formulas have been obtained for calculating the heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–181, July–August, 1975.     

Equations of laminar boundary layer in a two-phase medium

The motion of a two-phase medium in which the carrier component has low viscosity is considered. The equations obtained in [1], to which the viscous stress tensor in the fluid is added, are used. The boundary layer method [2] makes it possible to obtain asymptotic equations for the wall region. These equations have different forms depending on the characteristic values of the dimensionless determining parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 51–60, January–February, 1979.I thank A. N. Kraiko for discussing the work.