Calculation of the stability characteristics of a boundary layer with blowing in the presence of a negative pressure gradient

A study is made of the viscous and inviscid stability of self-similar Falkner-Skan flow on a permeable surface in a wide range of blowing intensities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 60–64, March–April, 1984.     

Stability of two-dimensional flow near a stagnation point in the presence of massive blowing

In the framework of linear theory, a study is made of the stability of laminar flow in the boundary layer on a flat porous plate near a stagnation point in the presence of massive blowing. The problem is solved in the inviscid approximation. The neutral curves are calculated, and the values of the critical parameters and the position of the point at which stability is lost are determined. It is found that the extension of the region of laminar flow is directly proportional to the blowing velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 157–158, March–April, 1982.     

Compressibility effects under conditions of convective stability of miscible fluids in a porous medium

The effect of compressibility on the convective stability of equilibrium of a binary mixture in a homogeneous porous medium is analyzed. It is shown that the contribution of compressibility significantly increases the equilibrium stability with respect to oscillatory perturbations.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–23, January–February, 1995.     

Laminar flow between porous disks for intense homogeneous asymmetric inflow and outflow

In [1–3], a class of self-similar solutions was considered for the flow of incompressible fluid in a plane channel with porous walls, through which there is homogeneous symmetric inflow or outflow. An analogous class of self-similar solutions for flow between porous disks with natural homogeneous conditions at the periphery was considered in [4], where the asymptotic behavior of these solutions at a small Reynolds number of the outflow R was investigated, and the limiting form of the solution for symmetric outflow with R= was noted. In the present paper, the boundary-function method is applied to the singular problem corresponding to the flow between porous disks for asymmetric inflow and outflow characterized by large R.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1976.     

Some physical aspects of radiative and convective heat transfer in the case of nonself-similar blowing on a plate

Heat shielding by blowing has been fairly fully studied in the neighborhood of the stagnation point of a body in a stream [1–3], but for other flow regions the investigation has barely begun [4]. It has been found that the influence of blowing on the radiative and convective fluxes and the influence of radiation on the convection on the side wall can be very different from what is obtained for the flow conditions at the stagnation point. The present paper is a study of the radiative and convective heat transfer on a plate in a H₂ + He stream for constant and self-similar blowing of carbon vapor in the form of C, C₂, and C₃.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–35, January–February, 1981.     

Rayleigh stability of shear flow in relaxing media

The stability of steady-state flow is considered in a medium with a nonlocal coupling between pressure and density. The equations for perturbations in such a medium are derived in the linear approximation. The results of numerical integration are given for shear motion. The stability of parallel layered flow in an inviscid homogeneous fluid has been studied for a hundred years. The mathematics for investigating an inviscid instability has been developed, and it has been given a physical interpretation. The first important results in flow stability of an incompressible fluid were obtained in the papers of Helmholtz, Rayleigh, and Kelvin [1] in the last century. Heisenberg [2] worked on this problem in the 1920's, and a series of interesting papers by Tollmien [3] appeared subsequently. Apparently one of the first problems in the stability of a compressible fluid was solved by Landau [4]. The first investigations on the boundary-layer stability of an ideal gas were carried out by Lees and Lin [5], and Dunn and Lin [6]. Mention should be made of a series of papers which have appeared quite recently [7–9]. In all the papers mentioned flow stability is investigated in the framework of classical single-phase hydrodynamics. Meanwhile, in recent years, the processes by which perturbations propagate in media with relaxation have been intensively studied [10–12].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 87–93, May–June, 1976.     

Choice of a self-similar solution in boundary-layer theory

If the speed of the outer flow at the edge of the boundary layer does not depend on the time and is specified in the form of a power-law function of the longitudinal coordinate, then a self-similar solution of the boundary-layer equations can be found by integrating a third-order ordinary differential equation (see [1–3]). When the exponent of the power in the outerflow velocity distribution is negative, a self-similar solution satisfying the equations and the usually posed boundary conditions is not uniquely determinable [4], A similar result was obtained in [5] for flows of a conducting fluid in a magnetic field. In the present paper we study the behavior of non-self-similar perturbations of a self-similar solution, enabling us to provide a basis for the choice of a self-similar solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–46, July–August, 1974.     

Stability of self-similar pipe flow with suction

The stability of self-similar flows with various boundary conditions at the wall is investigated. In the region of nonexistence of self-similar solutions an oscillatory regime is detected. The problem of stability with respect to disturbances of general form is studied. The dependence of the critical values of the axial Reynolds number and the Strouhal number on Re is calculated for various suction rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 18–25, September–October, 1991.     

Tangential gas blowing and boundary layer stability of a compressible gas

The effect of distributed blowing of a gas mass through a porous surface on the stability characteristics of a supersonic boundary layer is studied at a moderate supersonicMach numberM= 2. Tangential blowing when only the U-component of the mean velocity is not equal to zero on the wall is considered. The effect of the porous surface parameters on vortex perturbations is investigated and a comparison with the variant of the so-called “cutoff” regime is carried out. Different-density gas blowing is simulated by means of variation of the temperature factor (wall heating or cooling), namely, blowing of a heavy gas is simulated via blowing of a cold gas and vice versa.     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

The results of solution of the self-similar problem of planar flow of gas through a porous medium in the case of a quadratic law of resistance [1] are generalized to the case of axisymmetric motion. The equation in similarity variables for the velocity of isothermal gas flow is reduced to an equation having cylindrical functions as solution. Analytic dependences of the pressure and the gas velocity on the coordinate and time are obtained for a given flow rate of the gas at the coordinate origin and for zero Initial gas pressure in the porous medium.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 168–171, July–August, 1982.     

Self-similar solutions for energy liberation in a gas stream

By using dimensional analysis some possible kinds of nonstationary and stationary gas flows with energy liberation which result in self-similar problems are investigated. The cases of energy liberation in a gas at rest and in uniform supersonic and hypersonic streams are examined. The gas is assumed inviscid and perfect. Results of a computation of some hypersonic self-similar gas motions are presented. Three classes of self-similar gas motions have been well studied at this time: the strong explosion, the power-law flow caused by the expansion of a plane, cylindrical, or spherical piston [1], and conical flow (including combustion and detonation waves [2–4]). Some new self-similar motions caused by energy liberation on certain lines, surfaces, or in volumes will be examined below.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–113, November–December, 1974.     

The nonlinear evolution of two-dimensional and three-dimensional waves in mixing layers

The authors consider problems connected with stability [1–3] and the nonlinear development of perturbations in a plane mixing layer [4–7]. Attention is principally given to the problem of the nonlinear interaction of two-dimensional and three-dimensional perturbations [6, 7], and also to developing the corresponding method of numerical analysis based on the application to problems in the theory of hydrodynamic stability of the Bubnov—Galerkin method [8–14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 1, pp. 10–18, January–February, 1985.     

Stability of plane magnetohydrodynamic couette flow with asymmetrical velocity profile

The hydrodynamic stability of plane magnetohydrodynamic Couette flow with asymmetrical velocity profile formed by a transverse magnetic field is investigated within the framework of the linear theory. The complete spectrum of the small perturbations is studied for the characteristic Hartmann numbers. The perturbations are classified in accordance with their phase velocity at large wave numbers. It is established that the stability of the flow is controlled by only one type of perturbations. The critical parameters of the problem are determined. The instability in question recalls the instability of Hartmann flow against asymmetrical perturbations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 12–18, May–June, 1971.The author thanks M. A. Gol'dshtik for interest in the work and V. A. Sapozhnikov and V. N. Shtern for useful discussions.     

Thermocapillary instability of a liquid layer in the presence of a soluble surfactant

The effect of capillarity on the stability of a plane layer of viscous heat-conducting liquid in the presence of a soluble surfactant is investigated. It is found that an increase in surfactant solubility has a stabilizing effect on equilibrium. Monotonic instability is the most dangerous mode in the case of long-wave perturbations, whereas in the short-wave region loss of stability is induced by oscillatory perturbations.Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1996.     

On the convective instability of a liquid in an inclined layer of a porous medium

In this paper we study the stability of the equilibrium of a liquid heated from below, wherein the liquid saturates a planar layer of a porous medium arbitrarily inclined to the direction of gravity. We consider the cases for which the boundaries of the layer are heat-conducting and also thermally insulated. In a horizontal layer with heat-conducting boundaries equilibrium is destroyed by perturbations of cellular structure [1], In a vertical layer the minimum critical temperature gradient corresponds to perturbations of plane-parallel structure. The transition to cellular perturbations in the case of heat-conducting boundaries takes place at an arbitrarily small angle of inclination of the layer to the vertical. For the thermally insulated layer the crisis of equilibrium is connected with plane-parallel perturbations at all angles of inclination.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 127–131, May–June, 1973.The author thanks G. Z. Gershuni for stating the problem and his interest in the work.     

Stability of stationary convective flow of a mixture in a vertical porous layer

In contrast to the corresponding viscous flow, the convective flow of a homogeneous liquid in a planar vertical layer whose boundaries are maintained at different temperatures is stable [1]. When a porous layer is saturated with a binary mixture, in the presence of potentially stable stratification one must expect an instability of thermal-concentration nature to be manifested. This instability mechanism is associated with the difference between the temperature and concentration relaxation times, which leads to a buoyancy force when an element of the fluid is displaced horizontally. In viscous binary mixtures, the thermal-concentration instability is the origin of the formation of layered flows, which have been studied in detail in recent years [2–4]. The convective instability of the equilibrium of a binary mixture in a porous medium was considered earlier by the present authors in [5]. In the present paper, the stability of stationary convective flow of a binary mixture in a planar vertical porous layer is studied. It is shown that in the presence of sufficient longitudinal stratification the flow becomes unstable against thermal-concentration perturbations; the stability boundary is determined as a function of the parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–157, January–February, 1980.     

Blowing coefficient with arbitrary variation of the mass flow rate of the blown gas past a body around which flows a stream with an exponential change in the velocity

Formulas are derived permitting calculation of the linear corrections to the friction and heat-transfer coefficients with the blowing into the boundary layer of different gases, in small amounts but with a mass flow rate varying arbitrarily along the body. The case of a Mach number equal to zero and a temperature factor equal to unity was studied. Here it is postulated that bringing the relative heat-transfer coefficient down to a dependence on the dimensionless blowing renders possible, as with blowing which permits a self-similar solution, the use of the results obtained for arbitrary values of these parameters [1]. The proposed method of solution is based on the application, in the linear approximation, of a Duhamel integral for an arbitrary law of change in the mass flow rate along the body, if a solution is known with a discontinuous change in the mass flow rate. For a discontinuous change in the mass flow rate, the solution is sought using a Laplace transform; in this sense, the proposed method is similar to the method of [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 55–63, July–August, 1970.     

Investigation of hypersonic flow of rarefied gas past wings of infinite span

In the framework of the locally self-similar approximation of the Navier-Stokes equations an investigation is made of the flow of homogeneous gas in a hypersonic viscous shock layer, including the transition region through the shock wave, on wings of infinite span with rounded leading edge. The neighborhood of the stagnation line is considered. The boundary conditions, which take into account blowing or suction of gas, are specified on the surface of the body and in the undisturbed flow. A method of numerical solution of the problem proposed by Gershbein and Kolesnikov [1] and generalized to the case of flow past wings at different angles of slip is used. A solution to the problem is found in a wide range of variation of the Reynolds numbers, the blowing (suction) parameter, and the angle of slip. Flow past wings with rounded leading edge at different angles of slip has been investigated earlier only in the framework of the boundary layer equations (see, for example, [2], which gives a brief review of early studies) or a hypersonic viscous shock layer [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–154, May–June, 1984.     

Convective instability of a horizontal layer of fluid between permeable membranes

The equilibrium stability is investigated of a system consisting of two semi-infinite isothermal masses of fluid divided by a horizontal layer of finite thickness of the same fluid with a vertical temperature gradient directed downwards. The transition layer is separated by thin permeable membranes. Neutral stability curves are constructed for different membrane resistances. In the case of high permeability, the equilibrium is absolutely unstable with respect to monotonic-type longwave perturbations. For low permeability membranes, instability with respect to monotonic finite-wavelength perturbations is characteristic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 171–173, July–August, 1985.