Estimation of the acoustic emission spectrum of a boundary layer on a rough surface

Under engineering conditions the surfaces over which fluids flow are not usually hydraulically smooth. In this connection it is important to investigate the generation of sound by a turbulent boundary layer on a rough surface. Turbulent flow over a deformed surface creates dipole sources of sound, which may considerably increase the acoustic emission as compared with the quadrupole emission from a boundary layer on a smooth plate [1, 2]. In the case of sandy roughness estimates of the acoustic field are usually based on the energy summation of the fields generated by flow over the individual roughness elements [3, 4]. In this case not easily verifiable assumptions are made concerning the nature of the turbulent flow near the roughness, and the intensity of the emission is found correct to a constant factor subject to experimental determination. In the present study, in order to calculate the acoustic emission of a boundary layer on a surface with sandy roughness, it is proposed to employ the available experimental data on the cross of the surface pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–26, September–October, 1985.     

Laminar boundary layer stability on membrane type deformable surfaces

In connection with the successful experiments of Kramer [l, 2] on models sheathed by flexible coverings, attempts have been made to explain theoretically the effect of boundary deformation on the position of the point of stability loss in the boundary layer. Korotkin [3] examined the stability of a plane laminar boundary layer on an elastic surface under the assumption of a linear connection between the pressure perturbation and the normal deformation of the surface. Benjamin [4] and Landahl [5] investigated the stability of the laminar boundary layer on a membrane type surface under the assumption that the physical characteristics of the surface depend on the perturbing flow wavelength. In the following we examine stability of Blasius flow on a membrane type surface whose physical characteristics are constant along the length.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, vol. 10, no. 6, pp. 52–56, November–December, 1969.     

A Numerical Study of the Recirculation Zones During Spin-Up and Spin-Down for Confined Rotating Flows<Superscript>*</Superscript>

This paper reports computational simulations of the Navier–Stokes equations for confined axisymmetric rotating flows induced by rotating the endwalls instantaneously at a different rate to the sidewall. The transient behavior of the recirculation zones in the meridional plane is investigated during the temporal evolution. The changes in the topological structure of the meridional-plane streamline pattern are significant and the temporal evolution from one pattern to another reveals similarities between spin-up and spin-down at the early stages but subsequently differs. As the onset bubble for the first recirculating period always sets out from a certain axial station, a recirculation factor, R_f, is suggested to predict the onset time and location for the first period of recirculation. Accordingly, a stagnation point is observed numerically from a central axial station for low Reynolds numbers around 70–80. The effect of changing the rotation of the sidewall is also discussed, but no substantial influence is observed on the characteristics of the recirculation zones if there is no appearance of the Taylor–Görtler vortices in the sidewall boundary layer.     

Investigation of the influence of blowing on the flow in a hypersonic viscous shock layer near the stagnation streamline on a blunt body

In the framework of the approximation of local similarity to the Navier-Stokes equations, an investigation is made of the axisymmetric flow of homogeneous gas in a hypersonic shock layer, this including the region of transition through the shock wave. Boundary conditions, which take into account blowing of gas, are specified on the surface of the body and in the undisturbed flow. A numerical solution to the problem is obtained in a wide range of variation of the Reynolds number and the blowing parameter. Expressions are found for the dependences on the blowing parameter usually employed in boundary layer theory of the coefficients of friction and heat transfer on the surface of the body, which are divided by their values obtained for blowing parameter equal to zero. It is shown that these dependences are universal and the same as the dependences obtained from the solution of the equations of a hypersonic viscous shock layer with modified Rankin-Hugoniot relations across the shock wave and from the solution of the boundary layer equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 199–202, January–February, 1980.     

Investigation of the mechanism of surface turbulent friction reduction by means of large-eddy breakup devices

The results of an experimental investigation of the mechanism of reducing surface friction by mounting thin plates — large-eddy break-up devices (LEBUs) — in a turbulent boundary layer parallel to the surface are given. The conditions under which the surface friction reduction is minimal are determined. It is shown that the presence of LEBUs in the turbulent boundary layer leads to a decrease in the frequency of decelerated-fluid ejection from the wall region into the outer region of the boundary layer.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 80–89, September–October, 1996.     

Influence of the viscous boundary layer on the deposition of particles from a gas suspension flowing past a sphere

The flow of incompressible gas containing particles past bodies of simple shapes at moderate and high velocities is investigated in [1–5], in which the flow of the carrier medium is assumed to be irrotational. The estimates made in [3] for the neighborhood of the stagnation point show that it is necessary to take into account the viscous boundary layer in the case of fine particles. In the present paper, the viscous flow of a gas suspension over the front surface of a sphere at Reynolds numbers R = 10³–10⁷ is considered. It is assumed that the carrier gas is incompressible and the particle concentra ion negligibly small. The influence of the boundary layer on the particle trajectories and the deposition of the disperse phase on the surface of the sphere is investigated. It is shown that there is a wide range of flow parameters for the gas suspension in which the influence of the boundary layer is important. The limits of this range are established.Translated from Izvestiya Akademli Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–66, January–February, 1982.I thank Yu. P. Savel'ev for a helpful discussion of the work.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

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.     

Laminar boundary layer on swept-back wings of infinite span at an angle of attack

A study is made of the flow of a compressible gas in a laminar boundary layer on swept-back wings of infinite span in a supersonic gas flow at different angles of attack. The surface is assumed to be either impermeable or that gas is blown or sucked through it. For this flow and an axisymmetric flow an analytic solution to the problem is obtained in the first approximation of an integral method of successive approximation. For large values of the blowing or suction parameters, asymptotic solutions are found for the boundary layer equations. Some results of numerical solution of the problem obtained by the finite-difference method are given for wings of various shapes in a wide range of angles characterizing the amount by which the wings are swept back and also the blowing or suction parameters. A numerical solution is obtained for the equations of the three-dimensional mixing layer formed in the case of strong blowing of gas from the surface of the body. The analytic and numerical solutions are compared and the regions of applicability of the analytic expressions are estimated. On the basis of the solutions obtained in the present paper and studies of other authors a formula is proposed for the calculation of the heat fluxes to a perfectly catalytic surface of swept-back wings in a supersonic flow of dissociated and ionized air at different angles of attack. Flow over swept-back wings at zero angle of attack has been considered earlier (see, for example, [1–4]) in the theory of a laminar boundary layer. In [5], a study was made of flow over swept-back wings at nonzero angle of attack at small and moderate Reynolds numbers in the framework of the theory of a hypersonic viscous shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–39, May–June, 1980.We thank G. A. Tirskii for a helpful discussion of the results.     

Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

The coefficient of regeneration of the enthalpy in a three-dimensional laminar boundary layer

Self-similar solutions of the equations of a three-dimensional laminar boundary layer are of interest from two points of view. In the first place, they can be used to construct approximate calculating methods, making it possible to analyze several variants and to consider complex flows, in which it is impossible to neglect the interaction between the boundary layer and the external flow (for example, in the region of hypersonic interaction [1–3]). In the second place, the analysis of self-similar solutions permits clarifying the effect of individual parameters on one or another characteristic of the boundary layer and representing this effect in predictable form. One of the principal characteristics of a three-dimensional boundary layer, as also of a two-dimensional, is the coefficient of regeneration of the enthalpy. The value of this coefficient is needed for determining the temperature of a thermally insulated surface, as well as for finiing the real temperature (or enthalpy) head, which determines the value of the heat flux from a heated gas to the surface of the body around which the flow takes place. The article presents the results of calculations of the coefficient of regeneration of the enthalpy for locally self-similar solutions of the equations of a three-dimensional boundary layer, forming with flow around a cylindrical thermally insulated surface at an angle. It is clarified that the dependence of the coefficient of regeneration of the enthalpy on the determining parameters is not always continuous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–63, January–February, 1973.     

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.     

Structure of the disturbed boundary layer near a cold surface

A study is made of a laminar boundary layer near a cold plate in the regime of weak viscous -inviscid interaction in the limit in which the free-stream Mach number tends to infinity and the temperature factor to zero. Local disturbed flow regions formed due to the presence of small elements of roughness on the surface of the plate are investigated. It is found that thick regions of roughness elements induce disturbances of the frictional stresses and the heat flux of the same order as these quantities in the undisturbed boundary layer, while all thin regions of roughness elements induce only small, linear perturbations and, therefore, cannot cause separation of the boundary layer; the different regimes of flow past the roughness elements are described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 19–27, January–February, 1991.     

Stability of preseparation boundary layer on the leading edge of a thin airfoil

Numerous experiments on subsonic flow of gas past thin wing profiles (see the reviews [1, 2]) have shown that the flow near the leading edge of an airfoil is separationless only at angles of attack less than a certain critical value, which depends on the shape of the airfoil. If the angle of attack reaches the critical value, a closed region of recirculation flow of small extension is formed on the upper surface of the airfoil. Under ordinary flow conditions, the boundary layer on the leading edge of the airfoil remains laminar in the entire preseparation range of angles of attack. However, the appearance of the closed separation region is, as a rule, accompanied by transition from a laminar to a turbulent flow regime. Moreover, generation of turbulence is observed precisely in the flow separation region. The present paper is devoted to a study of the stability of the boundary layer on the leading edge of a thin airfoil in a flow of incompressible fluid. The case when the angle of attack of the airfoil relative to the oncoming flow differs little from the critical value is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 55–63, November–December, 1982.     

Allowance for longitudinal diffusion in the neighborhood of a discontinuity of catalytic surface properties

In the investigation of flow near surfaces with discontinuous changes in the catalytic properties the question arises of the applicability of parabolic boundary and viscous shock layer equations in the neighborhood of the discontinuity. In the present paper, three types of problem are solved in which longitudinal diffusion is taken into account. In the first an insertion with different catalytic properties is placed in the neighborhood of the stagnation point, in the second the discontinuity lines of the catalytic properties are perpendicular to the oncoming flow, while in the third they are parallel. On the main surface and on the insertion surface the heterogeneous catalytic reactions are assumed firstorder reactions with various rate constants whose values vary in a wide range. The data of the solution are compared with the solution obtained using the boundary layer approximation and the regions of influence of the longitudinal diffusion are estimated. In [1–4] a problem similar to the second one was solved by the numerical method of [1] and the Wiener-Hopf method for the case of transition from a noncatalytic to a perfectly catalytic surface and the region of applicability of the boundary layer was estimated [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 99–105, July–August, 1986.     

The turbulent boundary layer on the moving surface of a cylindrical body

A study is made of the problem of a two-dimensional turbulent boundary layer on the moving surface of a cylindrical body (a Rankine oval with a relative elongation of four) moving at constant velocity in an incompressible fluid. For the numerical simulation of the turbulent flow of the fluid, the boundary layer is divided into exterior and interior regions in accordance with a two-layer model, using different expressions for the coefficients of turbulent transfer for each region. A study was nade of the development of the boundary layer on the body at different speeds of the body surface and different Reynolds numbers. The following integral characteristics were found by numerical calculation: the work of friction as the body is displaced; the work expended on the movement of its surface; and, for a flow regime with separation, the work of the pressure force. In this case the following model of separation flow is assumed: beyond the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow, the pressure and friction stress on the wall are constant and are determined by their values at the singular point.Translated from Izvestiya Akademii Nauk SSSH, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1984.Finally, the author would like to thank G. G. Chernyi and Yu. D. Shevelev for useful discussions and for their interest in this work.     

Energy spectra of velocity pulsations in a turbulent boundary layer on a penetrable plate

Results of measurements of the pulsation characteristics of a turbulent boundary layer on a flat penetrable plate, in a range of variation of the parameters of in-blow from 0 to 20, are presented. It is shown that for supercritical in-blows close to the surface there exists a zone in which the energy spectra of velocity pulsations do not vary as the distance from the surface increases, and they differ from the spectra in the core of the boundary layer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 115–119, May–June, 1973.     

Stability of laminar boundary layer on an elastic surface in an incompressible fluid

Interest in the present problem arose after the publication of the results of the experiments of Kramer [1–3]. In addition to the studies indicated in [4], the articles [5–8] are devoted to the question of the interaction of a flexible elastic surface with the boundary layer. In the present paper the problem of the interaction of an elastic surface with disturbances arising in the boundary layer is posed as in [4]. The approximate nature of the methods of solving the problem of the hydrodynamic stability of the laminar boundary layer leads to a difference in the final computational formulas even in the case when authors use the same Heisenberg-Tollmien-Schlichting-Lin scheme. Therefore, in what follows we present a comparison of the data on the stability of the boundary layer on a solid wall obtained by several authors with the calculations using the formulas, which are then generalized to the case of the elastic surface.The author wishes to thank G. I. Petrov and V. A. Medvedev for discussions of the present study.     

Investigation of transport processes in the high-temperature boundary layer on an ablating graphite surface

A study is made of the transport processes in the boundary layer on a graphite surface in a stream of dissociated air. The diffusion and sublimation ablation regimes of the grahite are considered. In contrast to earlier investigations [1, 3], allowance is made for a larger number of components in the boundary layer, the multicomponent nature of the diffusion, and the disequilibrium of the chemical reactions in the gas phase. On the basis of a critical analysis of the experimental and theoretical investigations of the intermolecular interaction potentials, a model is chosen that makes it possible to calculate the transport properties of gas mixtures containing ablation products with satisfactory accuracy. The results of the numerical investigation of the problem were used to obtain the dependences of the characteristics of heat and mass transfer on the stagnation parameters of the oncoming flow and the temperature of the surface. The influence of the extent to which the chemical reactions are in disequilibrium on these characteristics is estimated. The results of the calculations are presented in the form of approximation formulas. The method of numerical solution is described elsewhere [4, 5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 97–103, May–June, 1983.     

Free surface asymptotics for thermocapillary flow at high marangoni numbers

Formal asymptotic expansions of the solution of the steady-state problem of incompressible flow in an unbounded region under the influence of a given temperature gradient along the free boundary are constructed for high Marangoni numbers. In the boundary layer near the free surface the flow satisfies a system of nonlinear equations for which in the neighborhood of the critical point self-similar solutions are found. Outside the boundary layer the slow flow approximately satisfies the equations of an inviscid fluid. A free surface equation, which when the temperature gradient vanishes determines the equilibrium free surface of the capillary fluid, is obtained. The surface of a gas bubble contiguous with a rigid wall and the shape of the capillary meniscus in the presence of nonuniform heating of the free boundary are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 61–67, May–June, 1989.