Uniqueness and stability of steady states of continuous chemical reactors

We examine the uniqueness and stability of the solutions to the problem of steady-state operation of a continuous chemical reactor in which longitudinal diffusion and heat conduction are taken into account. We investigate an adiabatic reactor in which the concentration and temperature distributions are similar (the thermal diffusivity and diffusion coeffecient are equal) and an isothermic reactor. These two cases are considered together because the mathematical formulations of the problem are equivalent.The question of the existence and number of steady states was analyzed in [1, 2], where references were made to earlier investigations. The results obtained in [1, 2] are now extended. The stability of the steady states is investigated by the small-perturbation method.     

Interaction of a turbulent wake with the outer flow

The integral methods of boundary-layer theory are used to examine the interaction of a turbulent wake with the outer flow for the example of planar flow.In contrast with the known Crocco-Lees theory [1], the turbulent layer in the gas is described with the aid of an appropriate family of velocity profiles rather than by means of a Dorodnitsyn-type transformation of the incompressible turbulent layer. The selection of the simplest among the possible systems of first order interaction equations is justified; this system reduces to a single differential equation and an estimate is given of the influence of the arbitrariness in the equation selection on the final results.The hydrodynamic meaning of the singular and nonsingular integral curves and the singular point of the interaction equation is clarified on the basis of an examination of the interaction of compression and rarefaction waves in the outer supersonic stream with the wake. The effect of blowing (suction) and the initial boundary layer on the base pressure and the supersonic interaction flow as a whole is examined on the basis of the integral conditions for the splicing of the interaction flow with the isobaric mixing flow behind the corner. It is shown that, with proper selection of the single constant in the turbulent viscosity formula, the computational results are in satisfactory agreement with experiment.In conclusion, the authors wish to thank G. G. Chernyi for helpful discussions of the study, and L. V. Kapranova and Z. A. Donskova for assistance in the calculations.     

Viscosity of the liquid phase in a dispersion

The motion of a dispersion (continuous medium and particles) may be described [1] via the equations ot conservation of matter and momentum for the two phases separately. Here it is necessary to know how the viscosity, pressure in the solid, and other quantities vary with the parameters of the motion. This difficulty occurs even for the very simple model where the internal stresses in the dispersed phase are taken as zero, as there is then an uncertainty as to the viscosity of the medium, which is not a material constant and is dependent on the concentration. There is also uncertainty as to the forces of interaction between the phases. There are numerous empirical relationships for these forces, and also a theoretical one [2]. Here an analogous method is applied to derive an expression for the viscosity of the liquid. This viscosity applies to a liquid filtering through a porous medium in the particular case where the concentration is such as to produce close packing of the solid particles. The result corresponds to standard formulas in the case of low concentrations.     

The acceleration of electrons in a boundary layer

The effect of the redistribution of energy between ion and electron components for the motion of a plasma in a nonuniform magnetic field is considered on the example of a flat model of an equilibrium boundary layer between a rarefied plasma and a magnetic field in the relativistic invariant form. The relativistic and polarization corrections to the classical theory are found. Results are given for a numerical solution of the problem.     

A particular solution for the chaplygin equation

In the theoretical studies of several gasdynamic problems a major role is played by the hodograph plane, where the equations in terms of velocity component variables are linear. In these studies a primary role is played by the Chaplygin equation for the stream function . Chaplygin [1] obtained a general solution for the equation of motion in the hodograph plane. Particular exact solutions of the hodograph are also known [2]: radial flow, spiral flow, etc. Below we consider a particular solution of the Chaplygin equation.     

Shape of a shock wave diffracted by a rounded corner

The diffraction of shock waves by rounded corners has been studied experimentally. Some features introduced by the rounding of the corner in the profile of the diffracted shock wave are found. The velocity of the wall part of the diffracted shock wave in the flat section after the rounding is determined. The unsteady motion of a shock wave along a cylindrical surface is considered.     

Concerning the description of long nonlinear waves in channels

A method of deriving the equations that describe long nonlinear waves in channels of arbitrary cross section, taking the transverse acceleration of fluid particles into account (the Boussinesq approximation), is proposed. For channels of certain cross sections the equations are written in explicit form. In the case of narrow channels the Boussinesq equations and those of the next approximation are written in explicit form for arbitrary cross sections.     

NUMERICAL SIMULATION OF COMPLICATED PIPE FLOW WITH k-εMODEL

In this paper, turbulence in a complicated pipe is simulated by using the k-ε model. The ladder-like mesh approximation is used to solve the problem of complicated boundary with the result of numerical simulation favorable. Two computational examples are given to validate the strong adaptability and stability of k-ε model.     

Estimates of nonequilibrium radiative heating of blunt bodies in a hypersonic flow of carbon dioxide gas

The solution to the problem of hypersonic nonequilibrium flow over cones with rounded noses [1, 2] is used to estimate the radiative heating of the surfaces of the bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1979.