Calculation of the interaction of planar jets of ideal gas with different Bernoulli constants

A numerical method is proposed for calculating stationary planar jet flows with unequal total heads in different jets in the case when the medium is ideal and compressible and the flow is subsonic, adiabatic, and irrotational in each individual jet. Features of the method are considered in the example of the calculation of the interaction of two free jets flowing along the sides of a wedge. The line separating the jets is the line of a shear discontinuity. The results of the calculations are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–143, May–June, 1981.I thank V. P. Karlikov for helpful discussions of the results.     

Advance of the interface of liquids with pressure filtration

The article is a continuation of the investigations of a number of authors [1–3] on the advance of the interface between different liquids: it gives a solution of the problem in the case of one-dimensional filtration of liquids with different viscosities in distorted layers of variable permeability; it indicates a method for determining the interface between multicolored liquids, and the method is generalized for the case of a series of two-dimensional flows, connected by a conformai transformation. The article discusses problems that reduce to formation of the functions determining the flow, and to calculation of the integrals.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 185–191, September–October, 1971.     

Investigation of hydrodynamic flow inside a disk valve by photochromic visualization

Photochromic visualization has been used to investigate the hydrodynamic flow which arises inside a sliding valve during its operation. The experimental setup and results of observations of the flows are described. Unsteady flows with different amplitudes and frequencies of the oscillations of the flow rate through the valve were investigated. The method makes is possible to determine the flow structure, construct profiles of the velocities and tangential stresses in the complete region within the valve, and also obtain data for calculating the hydrodynamic characteristics of valves.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–117, May–June, 1993.     

Investigation of supersonic flows in conical nozzles

The article gives the results of an investigation of flows in supersonic axisymmetric conical nozzles with the presence of shock waves in the flow. The method of straight-through calculation [1] and the method of small perturbations [2] are used. An investigation is made of the effect of various geometric parameters and of the adiabatic index on the flow of a gas in conical nozzles. A comparison is made with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 101–107, May–June, 1974.In conclusion, the authors thank N. V. Drozdov for his participation in carrying out the calculations.     

Steady seepage flow under aprons in anisotropic ground

Seepage under a flat apron in a two-layer ground consisting of homogeneous isotropic layers of equal thickness was investigated by means of the analytic theory of linear differential equations by Polubarinova-Kochina [1]. An approximate solution of the same problem for layers of different thickness by the methods of the variational calculus was given in [2]. The solution to such a problem for homogeneous anisotropic layers of different thickness by means of a special complex variable representation and linear conjugation was given in [3] by Prusov and the author of the present paper. The method of [3] is now used to investigate two-dimensional steady seepage flow under two aprons in a multilayer ground consisting of n homogeneous anisotropic layers of different thickness, the principal directions of anistropy of each layer having an arbitrary position relative to the horizontal.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 155–158, October–December, 1981.     

One class of self-similar flows of a radiating gas

This article discusses self-similar statements of the problem of the motion of a completely radiating and absorbing gas. The field of radiation is assumed to be quasi-steady-state, and the contribution of the radiation to the internal energy, as well as the pressure and the viscosity of the medium, are not taken into account. The presence of local thermodynamic equilibrium is assumed. The absorption coefficient is approximated by a power function of the pressure and the density. Scattering of the radiation is not taken into account. Under these assumptions, there exist self-similar statements of the problem for one-dimensional unsteady-state flows (a strong detonation, the problem of plug-flow, motion under the effect of a radiation source, and others) and two-dimensional steady-state flows (flow in a diffuser, supersonic flow around a wedge or a cone). It is shown that there exists a non steady-state spherically symmetrical flow depending on four parameters; this flow is adiabatic in spite of the presence of radiation. This article is made up of seven sections. It is shown in the first section that the presence of radiation leads to the appearance of new dimensional constants, entering into the equations of the problem. The second section is devoted to self-similar nonsteady-state one-dimensional flows. The third section contains a detailed study of one class of such flows. In a partial case, adiabatic flows of a radiating gas are obtained. In the fourth and fifth sections, a detailed analysis is made of the initial and boundary conditions from the point of view of dimensionality. The sixth section describes self-similar two-dimensional steady-state flows of a radiating-absorbing gas. The seventh section consists of remarks with respect to approximations of the transfer equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–22, July–August, 1970.     

Method of calculation of interaction of wall flows

A flow of viscous compressible fluid in the neighborhood of the line of interaction of wall flows is considered. A method of calculating the line of interaction and the direction of the self-induced secondary flow is developed. Papers [1–3] are devoted to the simulation of a separation flow with singularities in the neighborhood of singular lines and points, where boundary-layer equations are invalid. However, the theories of local separation used at present have mainly been developed only for two-dimensional problems, while the models of viscous-inviscid interaction have restrictions in application for turbulent flows with developed separation. The interaction of three-dimensional wall turbulent flows is considered below. It is assumed that the thickness of the boundary layers and the scales of the interaction zones are small in comparison with the characteristic dimension of the system, while the line of discontinuity of the solutions of the three-dimensional boundary layer equations is the same as the line of interaction of the wall flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1987.The author is grateful to G. Yu. Stepanov and V. N. Ershov for their interest in my work and their valuable remarks.     

Spatial interaction of jets propagating in an accompanying supersonic flow

A numerical method of calculating a three-dimensional laminar supersonic underexpanded jet escaping into an accompanying supersonic flow is developed. The simplified Navier-Stokes equations for a steady-state three-dimensional flow are employed. Numerical calculations are carried out for several cases relating the outflow of jets from a four-nozzle assembly into an accompanying supersonic flow, and a number of the characteristics of three-dimensional flows of this kind are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 88–93, November–December, 1972.     

Motion of a fluid between rotating cones

A study is made of the steady axisymmetric flow of a viscous fluid between two cones rotating in opposite ways round a common axis. It is shown that as in the case of the flow of fluid swirled by plane disks rotating at different speeds [1], there can be two regimes of motion in the system: a Batchelor regime with quasirigid rotation of the fluid outside the boundary layers [2] and a Stewartson regime in which the azimuthal flow is concentrated only in the boundary layers [3]. In the Stewartson regime, a boundary layer analogous to that in the single disk problem (see, for example, [4–6]) forms in the region of each cone far from the apex. For the flows outside the boundary layers, simple expressions are found which make it possible to obtain a conception of the circulation of the fluid as a whole. With minor alterations, the results can be applied to the case of the rotation of other curved surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–64, March–April, 1985.The author thanks A. M. Obukhov for suggesting the subject and for his interest in the work, and A. V. Danilov and S. V. Nesterov for useful discussions.     

超声速边界层/混合层组合流动的稳定性分析

利用可压缩线性稳定性理论研究了超声速混合层考虑壁面影响流动时的失稳特性. 基本流场选取了具有不同速度特征的2 股均匀来流,进入存在上下壁面的流道中. 混合层与边界层的距离为1~3 个边界层厚度,其中壁面取为绝热壁. 分析了该流动在超声速情况下的稳定性特征,同时还讨论了不同波角下的三维扰动波的演化特点,并与二维扰动波进行了比较和分析. 研究结果表明,在此流动情况下,边界层流动和混合层流动的稳定性特征同时存在,并互有影响,其流动稳定性特征既有别于单纯的平板边界层,也有别于单纯的平面混合层,呈现出了新的稳定性特征.      

Instability of two-layer film flow along an inclined surface

In [1–3] the method of expansion in a small wave number is used to investigate stability of two-layer flows; the results are valid for the neutral curves and in their neighborhood. Here, the eigenvalue problem is solved numerically, the wave disturbances are considered over the entire region of instability and the effect of the governing parameters on the characteristics of the most unstable disturbances is established.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 10–18, March–April, 1992.     

Calculation of the flow in ejector nozzles

A method is proposed for calculating the two-dimensional nonviscous flows in ejector nozzles of arbitrary shape, for two operating cycles: the subsonic flow cycle of a secondary stream and a cycle when the secondary stream attains critical velocity, i.e., it is cut off. In the second case, the possibility is allowed for the appearance of a direct compression shock in the supersonic part of the secondary stream.Translated from Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–118, January–February, 1974.The authors thank A. N. Kraiko and M. Ya. Ivanov for useful discussions and assistance, V. V. Polyakov for interest in the project and L. P. Frolova for assistance in drawing up the task.     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Fingering associated with immiscible displacement in a two-layer porous medium

The effect of capillary cross flows on the structure of the displacement front in a two-layer porous medium with different layer permeabilities is examined. It is shown that capillary cross flows along the curved displacement front may lead to stabilization of the displacement. Approximate expressions are obtained for the limiting finger length and the oil displacement coefficient at the moment of breakthrough of the water as functions of the displacement parameters and the form of the functional parameters of the two-phase flow in the porous medium; the results obtained are compared with the results of numerical calculations and the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–104, January–February, 1991.     

Calculation of the trajectory of a plane free jet

A method is proposed for calculating the trajectory of a plane jet of an incompressible liquid, subjected to the action of two flows, directed at different angles to the original direction of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 178–182, May–June.     

超声速边界层/混合层组合流动的稳定性分析简

利用可压缩线性稳定性理论研究了超声速混合层考虑壁面影响流动时的失稳特性. 基本流场选取了具有不同速度特征的2 股均匀来流,进入存在上下壁面的流道中. 混合层与边界层的距离为1~3 个边界层厚度,其中壁面取为绝热壁. 分析了该流动在超声速情况下的稳定性特征,同时还讨论了不同波角下的三维扰动波的演化特点,并与二维扰动波进行了比较和分析. 研究结果表明,在此流动情况下,边界层流动和混合层流动的稳定性特征同时存在,并互有影响,其流动稳定性特征既有别于单纯的平板边界层,也有别于单纯的平面混合层,呈现出了新的稳定性特征.     

Connective instability of a two-layer system with thermally insulated boundaries

The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–28, March–April, 1986.The authors wish to thank O. V. Kustova for assisting with the computations.     

Heat transfer at the surface of a triangular body in a hypersonic viscous gas flow

The boundary layer on a semi-infinite triangular body of power-law shape is calculated for viscous interaction with an external hypersonic flow. The results of calculating the characteristics of the three-dimensional boundary layer are presented. The formation of secondary return flows and zones of intensified heat transfer on the surface of the body in the neighborhood of lines of flow divergence is noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 77–82, January–February, 1988.     

Calculation of two-phase flow in an axisymmetric laval nozzle with allowance for particle reflection from the walls

A method and the results of calculating the parameters of two-phase monodisperse and polydisperse flows in a Laval nozzle are presented. A general particle-wall interaction model based on the results of experimental research is used. It is shown that taking the real characteristics of the interaction between the condensate and the walls into account makes it possible to determine a number of important flow parameters with much greater accuracy.deceasedTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 79–85, March–April, 1990.     

Boundary layer on a circular sector

The finite difference method is used to investigate laminar and turbulent boundary layers on a flat surface in the case of circular streamlines of the exterior flow. It is shown that when the flow is turned through large angles the behavior of the boundary layer over a finite circular sector differs qualitatively from an infinite sector. A study is made of the influence of the Mach number, the angle through which the flow is turned, and the wall temperature on the secondary flows in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1982.