Turbulent flow of gas in a curvilinear channel in the presence of suction from a separation region

Integral parameters that characterize reversible and irreversible changes in the flux of the total pressure in channels with perforated walls are introduced. An experimental investigation was made of subsonic gas flow in curvilinear channels of rectangular cross section in the presence of suction of gas from a separation region of the flow formed on an internal (convex) strongly curved wall of the channel. The optimal position of the suction slit was determined and it was shown to be possible to reduce appreciably the loss in the channel and improve its gas-dynamic characteristics. Two-dimensional turbulent flow of an incompressible fluid in curvilinear channels in the presence of suction was simulated numerically. The mathematical model is based on the complete system of Navier-Stokes equations, additional differential equations for the energy of the turbulence and the rate of its dissipation, special correction equations to take into account the curvature of the streamlines, and model boundary conditions for the sections of the walls through which the suction of the fluid takes place.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 4, pp. 72–80, July–August, 1984.     

Propagation of three-dimensional acoustic perturbations in channels of variable cross sectional area at frequencies near the cutoff frequency

A study is made of the propagation of three-dimensional acoustic perturbations in a two-dimensional gas flow in axisymmetric channels of variable cross sectional area at frequencies near the cutoff frequency. The cross sectional area of the channel is assumed to vary slowly along its length. The obtained results are of interest, for example, from the point of view of estimating the level of noise carried through the gas ducts of a jet engine. The singularities of a solution found earlier in [1] (essentially the analog of the WKB approximation) are investigated. These singularities are due to the existence of turning points in the theory of the WKB approximation. The formalism of this theory [2] is used to develop a method for calculating the reflection coefficient of acoustic perturbations; in this approximation, reflection is found to be appreciable only at the channel sections where the frequency is near the cutoff frequency. Calculated examples are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–159, November–December, 1980.I am grateful to A. N. Kraiko, who pointed out the connection between the singularities investigated in the present paper and turning points in the theory of the WKB approximation and suggested that the formalism of this theory should be used to calculate the reflection coefficient. Discussions that I had with Kraiko during the work were very helpful.     

Influence of surface tension on damping of the oscillations of a viscous incompressible fluid in a cylindrical channel

A numerical calculation is made of small oscillations of a viscous incompressible fluid that fills half of a horizontal cylindrical channel. The calculation is made with and without allowance for surface tension. The results of the calculation show that allowance for surface tension increases the damping of the oscillations. The general properties of problems of the normal oscillations of a heavy and capillary viscous incompressible fluid were studied in [1–3], in which the possibility of applying the Bubnov-Galerkin method to these problems was pointed out. A method for calculating the oscillations of a viscous incompressible fluid that partly fills an arbitrary vessel at large Reynolds numbers was developed in [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1980.     

Hydrodynamics in weak gravitational fields two-dimensional oscillations of an ideal fluid in a rectangular channel

The two-dimensional problem of determining the frequencies and modes of small natural osciliations of an ideal fluid in a rectangular channel under near-weightless conditions is considered. It is assumed that a weak gravitational field acts parallel to the vertical walls of the channel. The Ritz method is employed for the variational problem, which is equivalent to the problem of oscillations of a fluid under weightless conditions [1, 2].Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–13, September–October, 1972.     

Electric field in the transverse cross section of the channel of an MHD generator

During the motion of a partially ionized gas in magnetohydrodynamic channels the distribution of the electrical conductivity is usually inhomogeneous due to the cooling of the plasma near the electrode walls. In Hall-type MHD generators with electrodes short-circuited in the transverse cross section of the channel the development of inhomogeneities results in a decrease of the efficiency of the MHD converter [1]. A two-dimensional electric field develops in the transverse section. Numerical computations of this effect for channels of rectangular cross section have been done in [2, 3], At the same time it is advisable to construct analytic solutions of model problems on the potential distribution in Hall channels, which would permit a qualitative analysis of the effect of the inhomogeneous conductivity on local and integral characteristics of the generators. In the present work an exact solution of the transverse two-dimensional problem is given for the case of a channel with elliptical cross section stretched along the magnetic field. The parametric model of the distribution of the electrical conductivity of boundary layer type has been used for obtaining the solution. The dependences of the electric field and the current and also of the integral electrical characteristics of the generator on the inhomogeneity parameters are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–10, January–February, 1973.     

Influence of blowing on the characteristics of the nonstationary boundary layer on an oscillating wedge in a supersonic stream

A study is made of the influence of blowing on the characteristics of a nonstationary boundary layer. For this, we solve the equations of the laminar boundary layer on an infinite wedge moving with supersonic velocity and executing small oscillations about the tip. It is shown that increased blowing improves the damping of the oscillations of the wedge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–175, January–February, 1981.     

Free oscillations of a liquid rotating in a cylindrical vessel under conditions of weightlessness

The plane problem of determination of the natural frequencies of small oscillations of a viscous liquid rotating in a partially filled cylindrical vessel under conditions of weight-lessness is examined. If the angular velocity of vessel rotation is sufficiently low, surface forces acting on the liquid-gas boundary prove to be of the same order as the centrifugal forces and significantly affect the oscillatory frequencies. Asymptotic formulas expressing the dependence of the oscillatory frequencies on the parameters of the problem are obtained by the boundary layer method, with the assumption that the ratio of viscous to centrifugal forces is low.Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostii Gaza, No. 4, pp. 3–9, July–August, 1972.     

Calculation of the longitudinal velocity in the linear problem of a vibrator in a subsonic boundary layer

The linear problem is considered of a localized vibrator mounted on a flat plate in a subsonic boundary layer. The plate and the vibrator are assumed to be heat-insulated, and the dimensions of the vibrator and the frequency of the oscillations are such that the flow may be described by means of the equations of a boundary layer with self-induced pressure. The amplitude of the oscillations of the vibrator and the perturbations of the flow parameters corresponding to it are assumed to be small, and this makes it possible to linearize these equations. Integral transformations are used to construct a solution for values of the time greatly exceeding the period of the oscillations of the vibrator. The profiles of the perturbations of the longitudinal velocity are calculated in dependence on the transverse coordinate for various values of the longitudinal coordinate. A comparison is made with the profiles of the perturbations of the longitudinal velocity which have been obtained experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 61–67, May–June, 1987.     

Hydrodynamic flows and heat transfer in slightly noncylindrical channels

Viscous incompressible laminar flow and heat transfer in channels with a small arbitrary deviation from a cylindrical surface are examined. A linear system of equations and boundary conditions for the disturbed dynamic and thermal fields, obtained by linearizing the complete system of Navier-Stokes equations with respect to the solution for developed flows in cylindrical tubes of arbitrary cross section, is presented. In the important practical case in which the perturbations of the channel surface are concentrated on an interval of finite length it is shown that the integral dynamic and thermal characteristics of the channel can be found without solving the three-dimensional equations by going over to effective two-dimensional boundary-value problems which are fundamentally no more difficult to solve than those for developed flows. Extensions of the theory to flows with low-efficiency power sources are given. Applications to plane channels and circular tubes with deformed surfaces are considered. Among the numerous applications requiring information about the integral characteristics of flows in channels whose initially cylindrical surface is slighty deformed, we note the problem of heat transfer intensification by slightly deforming the tube surface with careful estimation of the accompanying increase in resistance [1] and the calculation of the resistance of capillaries and biological transport systems in the form of tubes and channels when the walls are deformed [2]. Below we consider laminar flow in channels with deformed walls. Whereas for the first problem this class of flows is only one of those possible (in general it is necessary to analyze the transition, turbulence and flow separation effects), in the second case, which is characterized by low Reynolds numbers, the laminar flow model is perfectly adequate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 21–30, March–April, 1990.The authors are grateful to A. Yu. Klimenko for useful discussions.     

Wave dynamics of mixed,periodically nonstationary flows of a spontaneously condensing vapor

A study is made of the dynamics of mixed flows of a condensing vapor with nonequilibrium phase transitions and gas-dynamic discontinuities in channels of variable area in the presence of periodically nonstationary boundary conditions at the entrance. The results are given of a numerical investigation of the flows of superheated and spontaneously condensing water vapor in a supersonic nozzle. It is shown that the periodic nonstationarity of the flow at the entrance can lead to a qualitative rearrangement of the flow structure in the presence of spontaneous condensation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–121, November–December, 1980.     

Laminar boundary layer on an oscillating wedge

A study is made of the nonstationary laminar boundary layer on a sharp wedge over which a compressible perfect gas flows; the wedge executes slow harmonic oscillations about its front point. It is assumed that the perturbations due to the oscillations are small, and the problem is solved in the linear approximation. It is also assumed that the thickness of the boundary layer is small compared with the thickness of the complete perturbed region. Then in a first approximation the influence of the boundary layer on the exterior inviscid flow can be ignored, and the parameters on the outer boundary of the boundary layer can be taken equal to their values on the body for the case of inviscid flow over the wedge. They are determined from the solution to the inviscid problem that is exact in the framework of the linear formulation. The wall is assumed to be isothermal. The dependence of the viscosity on the temperature is linear. Under these assumptions, the problem of calculating the nonstationary perturbations in the boundary layer on the wedge is a self-similar problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–151, July–August, 1980.     

Flow of viscous gas out of a cylindrical channel into vacuum

A study is made of the exhausting of a jet of viscous gas from a cylindrical channel into vacuum in the presence of a flat bounding surface outside the channel in the plane of its exit section. The problem is solved numerically using the complete system of Navier—Stokes equations. The developed flow model makes it possible to take into account the influence of an external medium into which the jet exhausts on the structure of the flow in the exit section of the channel, and also the influence of the subsonic part of the boundary layer in the channel on the flow field of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1981.     

Seiche oscillations in a rectangular channel with an abrupt expansion of the cross section

The natural frequencies and modes of seiche oscillations in a closed water reservoir consisting of a long narrow channel connected to a wide basin were investigated theoretically and experimentally. Calculations were made using linear shallow-water theory in two-dimensional and one-dimensional formulations. The spectral properties of free-surface oscillations at points lying on the nodal lines of the first four modes of seiche oscillations were studied experimentally. The one-dimensional model adequately predicts lower-mode frequencies, but the data on the positions of the nodal points of seiche oscillations obtained using this model are somewhat different from those obtained experimentally and using the two-dimensional model.     

Development of the boundary layer on a plate in a rotating system

A numerical investigation in the approximation of boundary layer theory has been made of the development of the flow near the surface of a rotating plate in a two-dimensional flow with rectilinear streamlines perpendicular to the leading edge in a rotating coordinate system attached rigidly to the plate. In an earlier investigation [1] using the approximate method of integral relations, Kurosaka obtained and described quantitatively a transition from a Blasius boundary layer to an Eckmann boundary layer in the form of three-dimensional oscillations. The solution described in the present paper confirms the oscillatory nature of the development of the boundary layer, but the quantitative results differ strongly from Kurosaka's.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–157, May–June, 1982.     

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.     

Oscillations of a viscous fluid in a thin layer between two coaxial disks rotating together

A study is made of the problem of the motion of an incompressible viscous fluid in the space between two coaxial disks rotating together with constant angular velocity under the assumption that the pressure changes in time in accordance with a harmonic law. The problem is solved using the equations of unsteady motion of an incompressible viscous fluid in a thin layer. It is shown that the velocity field in this case is a superposition on a steady field of damped oscillations with cyclic frequency equal to twice the angular velocity of the disks and forced oscillations with cyclic frequency equal to the cyclic frequency of the oscillations of the pressure field. It is shown that the amplitude of the forced oscillations of the velocity field depends strongly on the ratio of the cyclic frequency of the oscillations of the pressure field to the angular velocity of the disks. It is shown that there is a certain value of the ratio at which the amplitude of the forced oscillations has a maximal value (resonance). It is shown that even for very small amplitudes of the pressure oscillations the amplitude of the oscillations of the relative velocity at resonance may reach values comparable with the mean velocity of the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–169, January–February, 1984.     

Nonisothermal flow of non-Newtonian fluids in a channel

A study is made of the nonisothermal motion of a rheologically complex fluid in a plane-parallel channel in the case of boundary conditions of the third kind on the outer surfaces of the channel walls and with allowance for the dissipation of mechanical energy and temperature dependence of the coefficients. A qualitative investigation of the problem is made for arbitrary temperature dependence of the yield. Special cases are considered: flow of linear viscoplastic medium and a power-law medium with abrupt change with the temperature of the yield point and consistency. It is shown that under certain conditions several different flow regimes can be realized simultaneously in the channel and the change in the flow rate of the medium in a channel with varying temperature of the surrounding medium can exhibit hysteresis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–10, May–June, 1980.     

Shock stability in magnetogasdynamic channel flows

The question of shock stability in a perfect-gas channel flow was examined in [1] in the onedimensional approximation under various assumptions: the disturbances are not reflected from the channel exit section, weak shock, etc. The results were found to coincide for two specific forms of the boundary conditions at the channel exit, from which it was concluded that the shock was not sensitive to the exit boundary condition. In [2] the question of shock stability was studied numerically in relation to a conducting-gas flow in a flat channel of constant cross section in the presence of a magnetic field (zero electric field intensity). It was established that the shock stability is significantly affected by the form of the conductivity law. A condition for the limiting regime between the stable and unstable regions was also given for flow with a shock wave. It was assumed that the pressure in the channel exit section is given. In this paper the effect of the exit boundary condition on shock stability in gasdynamic and magnetogasdynamic flows is demonstrated for small magnetic Reynolds numbers. Stability criteria are obtained for shocks near the channel exit for a specific exit condition. The influence of electromagnetic effects (conductivity law, electric load factor) on shock stability is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 16–23, January–February, 1970.The author is grateful to A. G. Kulikovskii for discussing his work.     

Hydrodynamics in weak gravitational fields small oscillations of an ideal liquid in a cylindrical vessel

The problem of determining the frequencies and forms of small natural oscillations of an ideal liquid in a cylindrical vessel under conditions close to weightlessness is examined. It is assumed that a weak homogeneous gravitational field acts parallel to the vertical generatrix forming the cylinder. In contrast to [1], where only the first antisymmetric oscillation frequency is found for a semiinfinite cylindrical vessel, the frequencies of several axiosymmetric, antisymmetric, etc. oscillations are obtained as functions of the gravitational-field intensity and other parameters of the problem. The Ritz method is employed for two different variations of the problem, equivalent to that of oscillations of an ideal liquid under conditions of weightlessness [1–5].Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–13, March–April, 1973.     

Flow to wells in river valleys with silted channels

A study is made of the three-dimensional steady flow of ground water in a stratum of infinite depth in the case of pumping from a well situated near a river. The problem is solved in an approximate formulation, the boundary conditions on the free surface and the bottom of the channel being transferred to a horizontal plane. It is assumed that the silting and inhomogeneity of the river deposits are manifested in the same way as regards the flow properties and can be taken into account in a generalized manner by a coefficient a in a boundary condition of impedance type for the piezometric head H [1]. For simplicity, the well is simulated by a point sink, and the ground is assumed to be homogeneous and isotropic. The problem is treated in the framework of linear potential theory based on Darcy's law, and the results of numerical calculations are presented in the form of graphs.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 168–173, March–April, 1982.I thank V. B. Baranov and V. M. Shestakov for constant interest in the work and for discussing the results.