Investigation of isothermal flow of a mixture of gas and particles in a channel of variable section

Isothermal flow of a gas with particles is investigated analytically, which makes it possible to analyze all possible flow regimes in channels of different shapes. It is shown that in a channel of constant section there are two possibilities: either an equilibrium regime is established with constant flow parameters, or the gas reaches the velocity of sound, and then further flow in the channel is impossible (blocking of the channel). In a contracting nozzle, blocking also occurs if the channel is sufficiently long. In an expanding nozzle when there are particles in the gas with a velocity lower than the gas velocity, it is possible to have flow regimes with transition through the velocity of sound: a subsonic flow goes over into a supersonic flow and, conversely, it is also possible to have a flow in which there is blocking of the channel, which is quite different from the flow of a pure gas in an expanding nozzle and is due to the influence of interphase friction on the flow. The variation of the pressure along the flow can be nonmonotonic with points of local maximum or minimum which do not coincide with the singular point at which the gas velocity reaches the velocity of sound. In the case of nonequilibrium gas flows with particles in a Laval nozzle, the velocity of the gas may become equal to the isothermal velocity of sound not only in the exit section of the nozzle or in its expanding part, as noted in [4–6], but also at the minimal section, since it is possible to have flows for which the velocities of the phases are equalized at this section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 61–68, October–December, 1981.     

Fission of solitons in a symmetric triangular channel with variable cross section

In this paper, we study the disintegration of a soliton in a symmetric triangular channel when it propagates from one uniform cross section of the channel into another through a transition region. A criterion under which a soliton is split into n solitons is given. Numerical results for n = 3 are presented to confirm the analytical predictions.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.     

Acoustic,entropy, and vorticity perturbations in a channel of variable cross section

A study is made of the problem of the propagation of infinitesimally small perturbations in a gas stream moving in a channel of variable cross section when the flow cannot be regarded as isentropic and irrotational. The solution is found in the framework of the linear theory of the flow of an ideal gas and the quasi-one-dimensional hydraulic approximation for the steady regime. For irrotational and isentropic perturbations in a nozzle, this problem was considered in [1–4]. In [1], the problem is generalized to take into account entropy perturbations in the nozzle for the case of longitudinal oscillations. The present paper treats arbitrary modes in a nozzle and takes into account not only entropy but also vorticity perturbations in the moving stream. For each of the three perturbation types — acoustic, entropy, and vorticity — the solutions are expanded in series in cylindrical functions. It is shown that in the considered approximation each oscillation mode can be analyzed independently of the others. In the special case of flow in a Laval nozzle, the concept of impedance (admittance), which is widely used in acoustics, is generalized to take into account entropy and vorticity perturbations. The contribution to the flow dynamics of the acoustic, entropy, and vorticity perturbations is estimated numerically for longitudinal and transverse modes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–98, January–February, 1982.     

Simple waves on a shear gas flow in a channel of constant cross section

The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found for a polytropic equation of state in a class of isentropic flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999.     

Light-induced kinetic effects in a single-component gas with a small change in molecular cross section due to excitation

Linearized transport equations for describing the light-induced effects in a single-component gas are proposed. The equations were obtained by expanding the initial transport equations in the small parameter/ — the relative change in molecular cross section on excitation. The linear equations are solved numerically by the moment method.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 149–154, May–June, 1992.The author wishes to thank M. N. Kogan and N. K. Makashev for their interest in his work and for discussing the results.     

Motion of shock waves in a channel of variable cross section in the presence of a steady flow regime

The motion of shock waves against a steady flow in a channel of variable cross section is considered. Situations for which Chisnell's hypothesis [1] or a quasistationary flow model are valid are considered. The problem is of interest, in particular, in connection with the investigation of the starting of shock wind tunnels.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 103–110, July–August, 1981.I am very grateful to A. N. Kraiko and V. T. Grin' for valuable advice and support during the work.     

Shock compressibility of polystyrene of variable initial density

The dynamic compressibility of polystyrene [C₆H₅-CH-CH₂]_n with initial densities of 1.0, 0.7, 0.5, and 0.3 g/cm³ has been investigated at pressures of 200–400 kbars. The D–₀ (wave velocity-initial density) relations are presented for specimens of normal and reduced density tested under identical conditions. Wave velocity-particle velocity relations are given for polystyrene of normal and reduced density together with the shock Hugoniots. The simplest equation of state satisfactorily describing the entire set of experimental data is selected.     

Problem of gas motion in tubes of variable cross section and its application to solar wind perturbations

A qualitative study of self-similar flows with consideration of possible initial gas motion is performed for the problem of motion of a variable density gas in shock tubes with varying cross section. Asymptotic formulas are obtained near the contact discontinuity, and a numerical solution is obtained for the case of finite density on the contact surface. The equations are applied to the problem of gas motion in solar flares, and the parameters of the disturbed magnetic field are calculated. The results of the computation are compared with data from shock-wave observation in outer space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–89, May–June, 1976.The author thanks V. P. Korobeinikov for his valuable advice and interest in the study.     

Effect of compressibility on vortex breakdown in a gas flow in a circular tube

Vortex breakdown in a steady axisymmetric viscous gas flow within a circular tube is numerically simulated. The conditions under which reverse flow regions are formed are determined over a wide range of Mach and Reynolds numbers. Data on the effect of the Mach number and inlet flow swirl on the extent and location of the recirculation zone are obtained.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–43, September–October, 1996.     

Fluid flow in a rotating channel of square section

Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.     

Heat propagation in a nonuniform rod of variable cross section

An integral formula is used to average a coupled problem of thermoelasticity for a nonuniform rod of variable cross section. Effective characteristics are found. It is shown that, in addition to the expected effective coefficients, there appear five independent coefficients characterizing the temperature change rate effect on the stresses in the rod, on the longitudinal heat flux, and on the entropy distribution along the length of the rod. A feature of these new coefficients is that they become equal to zero in the case of a uniform rod. The homogenization of the thermoelasticity equations for nonuniform rods allows one to propose a new theory of heat conduction in rods. This new theory differs from the classical one by the fact that some new terms are added to the Duhamel–Neumann law, to the Fourier heat conduction law, and to the entropy expression. These new terms are proportional to the temperature change rate with time. It is also shown that, in the new theory of heat conduction, the propagation velocity of harmonic heat perturbations is dependent on the oscillation frequency and is finite when the frequency tends to infinity.     

Motion of a conductive piston in a channel with variable inductance

The motion of a conductive piston in the channel of a magnetohydrodynamic (MHD) generator of the conduction type with compound electrodes is considered. Formulas are obtained for calculation of the energy characteristics of the pulse MHD generator for various operational regimes. It is shown that in an MHD generator at magnetic Reynolds number values Re_m = ₀u₀ 1 (where ₀ is the permeability of a vacuum, is the electrical conductivity of the piston, u₀ is the initial velocity, and is the characteristic dimension), the energy transferred to an ohmic load may significantly exceed the values obtained in [1, 2]. Conditions for high-efficiency transformation of piston kinetic energy to electrical energy are considered for limiting values of the ratio of the latter to initial magnetic field energy in the generator channel.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 41–46, November–December, 1973.The authors thank V. I. Yakovlev for his helpful evaluation.     

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.     

Flow in a symmetric channel with an expanded section

We consider the flow in a symmetric two-dimensional channel with an expanded section. By examining the effect of varying the ratio of the inlet and outlet channel widths, we are able to place the earlier results of Mizushima et al. (Phys. Fluids 8 (1996) 2933) within an entire spectrum of nonlinear phenomena. Laboratory experiments support predicted behaviour in two regions of parameter space and highlight the importance of imperfections in the experimental apparatus.