Computation of the two-dimensional viscous incompressible fluid flow with separation at the nlet edge around a cascade

A complex flow consisting of an outer inviscid stream, a dead-water separation domain, and a boundary layer, which interact strongly, is formed in viscous fluid flows with separation at the streamlined profile with high Re numbers. Different jet and vortex models of separation flow are known for an inviscid fluid; numerical, asymptotic, and integral methods [1–3] are used for a viscous fluid. The plane, stationary, turbulent flow through a turbine cascade by a constant-density fluid without and with separation from the inlet edge of the profile and subsequent attachment of the stream to the profile (a short, slender separation domain) is considered in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–44, May–June, 1978.     

Solution of the inverse boundary-value problem of aerohydrodynamics with allowance for a boundary layer

The problem of constructing the contour of a wing profile in a viscous (incompressible or compressible) flow from the velocity distribution, given in terms of the arc abscissa, is solved in the approximation of boundary layer theory. The solvability conditions are obtained. Numerical calculations are carried out. Wing profile contours are constructed from velocity distributions that ensure the nonseparation of the flow. The effect of viscosity and compressibility on the solution of the problem is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–32, July–August, 1989.The authors are grateful to G. Yu. Stepanov for useful discussions.     

Contribution to the theory of thin-profile trailing edge separation

The conditions of nonsymmetric trailing edge flow with separation are investigated. Solutions of the equations for the interaction zone in the neighborhood of the trailing edge of a thin profile at an angle of attack of the order O(Re^–1/16) in the separated flow regime are constructed numerically. It is shown that for this zone a solution exists up to a certain angle of attack. In all the regimes the value of the friction on the upper surface at the very end of the trailing edge remains a positive quantity. The solution of the equations in the separated flow regimes is found to be nonunique. The flow over the leading edge is assumed to be unseparated, and the separation at the trailing edge, if present, is assumed to be localized in the interior of the boundary layer. The flow over a Kutta profile at zero angle of attack is taken as an example. In this case the satisfaction of the Chaplygin-Joukowsky condition at the trailing edge ensures smooth flow over both the trailing and leading edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 55–59, July–August, 1989.     

Nonlinear far field in the case of transonic flow past a nonlifting profile

A new analytic solution is constructed for the nonlinear transonic equations describing the irrotational far flow field (with two symmetry axes) in the case of transonic flow past a nonlifting profile. With increasing distance from the profile, the nonlinear field goes over continuously into the field of the linear theory. The solution is expressed in terms of an elliptic Weierstrass function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 171–173, Novembe–December,1982.     

Design of an airfoil with a given velocity distribution near an interface

Solutions for problems of profile design near a rigid wall or free surface are found as particular cases of the more general inverse problem of flow over an airfoil near an interface. The solution is based on a modification of the iteration method developed in [3, 4] for the direct problem of flow over a profile near an interface. In each step the apparatus of quasisolutions is employed. The calculations carried out demonstrate the efficiency of the method and reveal the effect of an interface, a rigid wall and a free surface on the geometric and aerodynamic characteristics of the profile.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 15–21, November–December, 1992.     

Transition flow of a fibrous suspension in a pipe as the flow of an anisotropic fluid

The transition flow is considered of a fibrous suspension in a pipe. The flow region consists of two subregions: at the center of the flow a plug formed by interwoven fibers and fluid moves as a rigid body; between the solid wall and the plug is a boundary layer in which the suspension is a mixture of the liquid phase and fibers separated from the plug [1–3]. In the boundary region the suspension is simulated as an anisotropic Ericksen—Leslie fluid [4, 5] which satisfies certain additional conditions. Equations are obtained for the velocity profile and drag coefficient of the pipe, which are both qualitatively and quantitatively in good agreement with the experimental results [6–8]. Within the framework of the model, a mechanism is found for reducing the drag in the flow of a fibrous suspension as compared to the drag of its liquid phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–98, September–October, 1985.     

Simulation of ordered structures in open turbulent flows

Extensive experimental material [1–4] indicates that ordered (coherent) structures play an important part in determining the nature of the flow, the generation of Reynolds stresses and turbulence energy, and the transport of heat, momentum, and passive admixtures in a turbulent flow. In the present paper, a model is constructed for describing coherent structures in which, given the profile of the mean velocity, one can determine the characteristic sizes, the propagation velocities, and also the frequency and amplitude characteristics of these ordered motions. The model is based on the analogy between the ordered formations and secondary flows in a subsidiary laminar flow whose velocity profile is the same as the turbulent profile of the mean velocity. The influence of small-scale pulsations is described by the introduction of the coefficient of turbulent viscosity. In the framework of the model, numerical calculations are made for two-dimensional turbulent flows in a mixing layer, a jet, and a wake behind a cylinder. The results of the calculations are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–52, July–August, 1981.     

Flow past a thin profile in a channel with permeable working part

An exact solution is obtained to the problem of flow of an ideal incompressible fluid past a thin profile in a straight channel. The channel walls are continuous except for the working part, where they are permeable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–185, July–August, 1982.I thank Yu. B. Lifshitz for constant interest in the work.     

Natural oscillations arising from loss of stability in parallel flows of a viscous liquid under long-wavelength periodic disturbances

It was shown in [1] that a parallel flow with an arbitrary nonconstant velocity profile is unstable for long-wavelength spatially periodic disturbances along the flow. The present paper shows that this instability leads to a supercritical natural oscillation mode of the simple wave type. This mode is calculated using the Lyapunov-Schmidt method in the form given in [2], along with the asymptotic curve of the wavelengths [1]. If the long wavelength disturbances are the most dangerous (this occurs, for example, when there is a sinusoidal velocity profile), then the natural oscillation mode is stable for spatially periodic disturbances having the same wavelength.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 32–35, January–February, 1973.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Turbulent friction in the flow of liquid in tubes and channels

A calculating relationship is presented for turbulent flow; it takes a unique form over the whole cross section of the flow. A relationship is also derived between turbulent friction and the mean velocity profile on the basis of the equation for the maximum turbulent friction, which follows directly from the equation of motion. The proportionality factor in this relationship is obtained with due allowance for twelve boundary conditions relating to the turbulent flow, the mean velocity, and their derivatives. The resultant turbulent-friction profiles agree with the experimental data of Laufer. The profile parameters may be related to the Reynolds number.Leningrad. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 140–145, March–April, 1972.     

Experimental investigation of the boundary layer on ablating specimens in the joint presence of convective and radiant heat fluxes

The emission spectrum of the boundary-layer vapor on the interval 3800–6600 Å is presented for a specimen of asbestos-filled plastic in the air-plasma flow created by an electrodeless high-frequency discharge. The temperature profile in the boundary layer has been measured in the neighborhood of the stagnation point. A model of the boundary layer on an ablating specimen is proposed and the convective component of the heat flow to it is estimated.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 25–29, March–April, 1972.     

Possibility of separationless flow in a nozzle with strongly curved walls

An example is given of calculation of the flow in a two-dimensional Laval nozzle whose profile in the subsonic part is concave with respect to the direction of the oncoming flow. Under the hypothesis of a separationless flow of ideal gas on the walls of the nozzle, regions of deceleration of the flow are absent. Then the well-known criteria suggest the existence of a separationless boundary layer, which must ensure that the flow as a whole is separationless.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 188–189, September–October, 1980.     

Asymptotic representation of the solution in the hodograph plane in transonic flow problems around profiles

The flow around a slender profile by an ideal gas flow at a constant, almost sonic, velocity at infinity is considered. The behavior of the perturbed stream in the domain upstream of the compression shocks sufficiently remote from the streamlined body is studied. The question is investigated of what conditions the solution in the hodograph plane satisfies when it corresponds to a flow without singularities on the limit characteristic in the physical flow plane. It is known that cases are possible when a regular solution in the hodograph plane loses its regularity property upon being mapped into the physical plane [1]. A regular flow on the limit characteristic can be continued analytically downstream into the supersonic domain between the limit characteristic and the shock. The requirement of analyticity of the streamlined profile is essential for realizability of the flow under consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–88, January–February, 1976.In conclusion, the author is grateful to O. S. Ryzhov for discussing the research.     

Flow of a two-phase medium in a laval nozzle

The back reaction of particles on a gas flow in Laval nozzles was investigated experimentally. Experimental data were obtained that characterize the change produced by the particles of a solid phase in the shape of the sonic line, the pressure distribution on the nozzle profile, and the configuration of the shock waves in the jet. Flow rate coefficients are given for different nozzle profiles and mass fraction and sizes of the particles in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–111, January–February, 1981.     

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.     

Use of direct variational methods to optimize axisymmetric Laval nozzles in the case of equilibrium and nonequilibrium two-phase flows

In the construction of the optimal profile of a Laval nozzle when there are subsonic regions in the flow, the use of effective methods such as the general method of Lagrangian multipliers [1] becomes very difficult. In the present paper, direct variational methods are therefore used. For nozzles, these methods were used for the first time to profile the supersonic parts of nozzles in the case of nonequilibrium two-phase flows by Dritov and Tishin [2]. For equilibrium flows, they have been used to optimize supersonic nozzles [3, 4] and in the construction of a profile of the subsonic part of a nozzle ensuring parallel sonic flow in the minimal section of the nozzle [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–183, January–February, 1982.I thank A. N. Kraiko for a number of helpful comments in a discussion of the formulation of the problem.     

Determination of hydrodynamic reactions acting on an oscillating profile

Sedov's equations [1], which make it possible to calculate the total hydrodynamic reactions exerted by an ideal fluid on an oscillating profile, are well known. These equations are expressed by contour integrals containing the complex potential of the unsteady flow past the profile. Certain modifications of these equations are proposed in paper [2]. In this paper, other equations are proposed for the calculation of the same quantities, based on the specification of the tangential velocity component of the fluid along the contour of the oscillating profile. In a number of cases, the application of these equations can be more useful than that of Sedov's equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 189–192, July–August, 1985.     

Similarity autooscillations in a plane jet

Experimental investigations into the stability of a plane jet [1, 2] show that after the stationary flow has lost its stability a stable autooscillatory regime arises. In the present paper, an autooscillatory flow in a jet is studied theoretically on the basis of a plane-parallel flow in a fairly wide channel in the presence of a field of external forces. The external forces are such that at zero amplitude of the autooscillations they produce a Bickley—Schlichting velocity profile. The excitation of the secondary regimes is studied by the methods of bifurcation theory [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–32, May–June, 1979.We thank M. A. Gol'dshtik and V. N. Shtern for discussing the formulation of the problem and the results.     

Drag associated with transitional flow regime of a fiber suspension in a tube

A semlempirical model is constructed of the flow of a fiber suspension of low and medium concentration in regimes that are usually called mixed and undeveloped turbulent regimes [1–4]. It is shown that although the flow of fiber suspensions in these regimes has features similar to those of the turbulent flow of a Newtonian fluid, for example, a logarithmic velocity profile, the characteristic features of the flow in both regimes can be better explained, not by turbulence of the flow, but by orientation of the fibers in it and by plastic flow of the fiber continuum. For this reason, to distinguish the mixed and undeveloped turbulent regimes from a truly turbulent regime it is proposed here to describe them by a general name — transitional flow. The obtained expressions agree qualitatively and quantitatively with the experimental results of Lee and Duffy [2], Sanders and Meyer [3], and Mih and Parker [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1984.I thank V. N. Nikolaevskii and A. N. Golubyatnikov for interest in the work and helpful comments.