Combined effect of longitudinal riblets and LEBU-devices on turbulent friction on a plate

The possibility of reducing turbulent friction with the help of large-eddy-breakup devices (LEBUs) and riblets is studied experimentally. The tests were conducted in a low-turbulence wind tunnel on a flat plate for 2·10⁶ Re 7·10⁶. The local friction coefficient was measured using internal strain-gauge balances, and the total drag was estimated by the momentum-transfer method. It is shown that a combination of LEBUs and riblets makes it possible to reduce the total turbulent friction drag of a flat plate 1800 mm long by 16%. The effects of the length of a ribbed surface on the efficiency of friction reduction and of LEBUs and riblets on the structure of a turbulent boundary layer are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–46, May–June, 1995.     

Investigation of laminar sublayer on permeable surfaces with injection

The thin-wall region — the laminar (or viscous) sublayer, in which the molecular mechanism of transfer predominates — plays an important role in friction and heat-transfer processes in a turbulent boundary layer. In particular, the relation between the sublayer thickness and the height of the surface roughness determines the nature of the flow — hydrodynamically smooth or rough — over the surface. This is of great practical importance and, hence, the roughness criterion has become the subject of numerous and systematic investigations. There are exhaustive data for the majority of the commonest cases encountered in practice [1]. The velocity on the boundary of the laminar sublayer appears as an important parameter in two-layer calculation schemes (e.g., [2–4], etc.). Although the theoretical analysis of a turbulent boundary layer with injection started several decades ago, there are at present hardly any reliable experimental data which can be used to determine the variation of the parameters within and at the boundary of the sublayer in relation to the injection rate. In this work we used interferometric diagnostics for precision experimental investigations of the parameters of the laminar sublayer on permeable surfaces with injection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–72, September–October, 1977.     

Experimental study of the effect of riblets and LEBU-devices on the drag of a body of revolution

The effect of ribbed coatings and large-eddy-breakup devices (LEBUs) on the turbulent friction and total drag of a body-of-revolution model has been studied in a low-speed wind tunnel.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–157, May–June, 1996.     

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.     

Law of friction in the region of a gas screen behind a permeable section

The results are given of measurements of friction behind a permeable section in a subsonic turbulent boundary layer at blowing intensity j = 0.003–0.04. Methods are proposed for calculating the local coefficients of friction in the region of a gas screen and the Reynolds number determined from the momentum loss thickness; these are in satisfactory agreement with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 159–162, March–April, 1979.     

Mechanism of turbulent boundary layer separation from a smooth wall

The mechanism of turbulent boundary layer separation under the influence of a positive pressure gradient is analyzed. The process of turbulent separation from a smooth wall in a plane diffuser channel has been experimentally investigated. It is shown that separation is determined by the nature of the flow in a certain inner part of the boundary layer, where the friction effect is unimportant. This region of the boundary layer is most exposed to the action of the positive pressure gradient and it is there that the stagnant zone primarily appears.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–77, November–December, 1990.     

Influence of viscosity on the flow over the sharp edge of bodies consisting of a spherical segment joined to an inverted cone

The results are given of an experimental investigation of the supersonic axisymmetric flow over a body consisting of a spherical segment joined to an inverted cone in the neighborhood of the point of inflection of the profile (Fig. 1a). For the limiting case of a cylinder with a flat end and M = 3, a study was made of the influence of the Reynolds number and the state of the boundary layer on the parameters of the local separation region formed near the inflection (Fig. 1b). It was found that there is an appreciable decrease in the length of the separation region and the pressure in it when the Reynolds number increases in the range Re = 10⁵– 10⁷ in the case of a laminar boundary layer on the flat end near the inflection point. A low level of the pressure on the surface of the body was achieved — of the order of thousandths of the pressure behind a normal shock. There was found to be a sharp increase in the pressure in the separation region when the boundary layer on the end becomes turbulent with transition to a flow regime that is self-similar with respect to the Reynolds number. Under conditions of a turbulent boundary layer, systematic experimental data on the pressure on the inverted cone near the point of inflection of such bodies were obtained and generalized.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 154–157, January–February, 1981.     

Localized Coherent Structures in the Boundary Layer

A Blasius laminar boundary layer and a steady turbulent boundary layer on a flat plate in an incompressible fluid are considered. The spectral characteristics of the Tollmien—Schlichting (TS) and Squire waves are numerically determined in a wide range of Reynolds numbers. Based on the spectral characteristics, relations determining the three–wave resonance of TS waves are studied. It is shown that the three–wave resonance is responsible for the appearance of a continuous low–frequency spectrum in the laminar region of the boundary layer. The spectral characteristics allow one to obtain quantities that enter the equations of dynamics of localized perturbations. By analogy with the laminar boundary layer, the three–wave resonance of TS waves in a turbulent boundary layer is considered.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Detached flow over a step with the formation of a turbulent wake

A method of calculating the plane turbulent layer behind a step interacting with a free potential flow of incompressible fluid is developed. The method includes consideration of the initial boundary layer and injection (or suction) in the isobaric bottom region. Friction on the wall behind the step is neglected, which corresponds to symmetric quasisteady flow behind the straight edge of a plate. The inviscid flow is represented by the Keldysh-Sedov integral equations; the flow in the wake with a one-parameter velocity profile is represented by three first-order differential equations—the equations of momentum for the wake and motion along its axis and the equation of interaction (through the displacement thickness) of the viscous flow with the external potential flow. The turbulent friction in the wake is given, accurate to the single empirical constant, by the Prandtl equation. The different flow regions — on the plate behind the step, the isobaric bottom region, and the wake region — are joined with the aid of the quasi-one-dimensional momentum equation for viscous flow. The momentum equation for the flow as a whole serves as the closure condition. The obtained integrodifferential system of equations is approximated by a system of nonlinear finite-difference equations, whose solution is obtained on a computer by minimization of the sum of the squares of the discrepancies. The results of the calculations agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1977.We are grateful to V. I. Kuptsov for consultation and help in programming and to Z. A. Donskova who assisted in the calculations and preparation of the paper.     

Turbulent boundary layers on porous surfaces in the case of blowing at different angles to the wall

The results are given of an experimental investigation of turbulent boundary layers on porous plates in the case of homogeneous blowing at various angles to the wall. It is shown that the intensity and angle of the blowing influence the profiles of the averaged and pulsating components of the velocities, the characteristic thicknesses, the surface friction, and the turbulent tangential stresses in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 59–64, May–June, 1982.We thank V. I. Kondrat'ev and V. S. Senterov for participating in the work.     

Large-Eddy BreakUp Devices – a 40 Years Perspective from a Stockholm Horizon

In the beginning of the 1980’s Large Eddy BreakUp (LEBU) devices, thin plates or airfoils mounted in the outer part of turbulent boundary layers, were shown to be able to change the turbulent structure and intermittency as well as reduce turbulent skin friction. In some wind-tunnel studies it was also claimed that a net drag reduction was obtained, i.e. the reduction in skin-friction drag was larger than the drag on the devices. However, towing-tank experiments with a flat plate at high Reynolds numbers as well as with an axisymmetric body showed no net reduction, but instead an increase in total drag. Recent large-eddy simulations have explored the effect of LEBUs on the turbulent boundary layer and evaluations of the total drag show similar results as in the towing tank experiments. Despite these negative results in terms of net drag reduction, LEBUs manipulate the boundary layer in an interesting way which explains why they still attract some interest. The reason for the positive results in the wind-tunnel studies as compared to drag measurements are discussed here, although no definite answer for the differences can be given.     

Recovery factors for a permeable surface and a gas surface film in a supersonic turbulent boundary layer

The recovery factor on a permeable surface has been experimentally determined at various rates of injection of air into a supersonic turbulent boundary layer. On the basis of an analysis of the solutions of the integral momentum and energy equations for a turbulent boundary layer an expression is obtained for the recovery factor. The recovery factor in the region of a protective gas surface film in a supersonic external flow has been experimentally determined.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 131–136, March–April, 1972.     

Three-dimensional turbulent boundary layer on a body of complex shape

Flow and heat transfer problems associated with three-dimensional compressible gas flow past a body of complex shape at a small angle of attack are investigated on the basis of a finite-difference calculation. The results of a numerical solution of the equations of the three-dimensional turbulent boundary layer are presented. The effect of the leading parameters on three-dimensional flow development and heat transfer is analyzed. The characteristic flow regions in the boundary layer are found: lines of divergence and convergence on the surface, separation zones and flow interfaces. The location of the maximum values of the heat flux and friction on the surface is determined, the behavior of the limiting streamlines on the body is described, and the intensity of the secondary flows in the boundary layer is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 25–35, September–October, 1986.     

Turbulent boundary layer with positive pressure gradient on a permeable surface under nonisothermal conditions

It is known that the longitudinal pressure gradient can exert a strong influence on the friction law and the characteristics of a dynamic turbulent boundary layer. The thermal and diffusion boundary layers are more conservative to the effect of the pressure gradient, and, hence, methods of analyzing them are based, in the majority of cases, on the hypothesis of conservativity of the heat- and mass-transfer laws to the longitudinal pressure gradient [1]. This hypothesis is verified by experimental results [2, 3] on heat transfer on an impermeable surface in a turbulent stream with positive pressure gradient under almost isothermal conditions. However, such investigations under nonisothermal conditions are practically nonexistent. An approximate theoretical analysis of the heat transfer in a turbulent boundary layer of a nonisothermal stream with a positive pressure gradient is given in this paper. Experimental results are presented. The experimental investigation was conducted in a burned-out graphite diffuser both with and without injection of an inert gas through the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–49, July–August, 1976.     

Construction of a method for calculating a plane boundary layer in weak solutions of polymers with laminar,transitional, and turbulent flow zones

The investigation of the effect of small polymer additives on the characteristics of the flow of a viscous liquid is, at the present time, one of the most promising approaches to the lowering of the friction resistance. One interesting question in this connection is the study of the effect of small polymer additives on the characteristics of the transitional region of flow in a boundary layer, as well as on the value of the friction resistance with the presence of laminar, transitional, and turbulent sections in the boundary layer. The article sets forth a possible method for calculation of a plane boundary layer and the friction resistance for the case of the motion of a body in weak polymer solutions with a constant concentration, taking account of the change in the flow conditions in the layer and based on the use of integral relationships. Questions connected with the development of a boundary at a body, with the feeding of a polymer in it, as well as with the effect of degradation or destruction of the polymer in the solution, are not discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1977.     

Heat and mass transport in nonisothermal turbulent flow when there is a screen formed by a gas of a different nature

We obtain a limiting relative law for heat and mass transport when there is a gas screen in a turbulent boundary layer, which makes it possible to take into account the effect of nonisothermal flow on the turbulent heat and mass transport beyond the region where the foreign gas is injected. The theoretical results are compared with experimental data on the intensity of burn-up of a graphite surface in an air flow when helium is injected through a tangential slit. The experimental data were obtained from the diffusion region of the burn-up.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 152–156, September–October, 1971.     

The damping factor in the theory of the Prandtl mixing length

An introduction to the classical Prandtl equation of the additional factor which takes account of the effect of molecular velocity -the damping factor — enables us to describe the process of flow in the transition sector of the boundary region of a turbulent boundary layer by relying on the model of interaction of molecular and molar momentum exchange between the layers of averaged turbulent motion. The application of not only the universal forms of physical variables but also special conservative variables, the connection between which does not depend on the conditions on the outer edge of the boundary layer, widens the opportunities for applying the method to the boundary region of the gradient boundary layer. The comparatively laborious nature of the calculation from the conservative equations brought about the introduction of much simpler but at the same time fairly accurate approximation equations.The content of the article was delivered at a session of the Sixth All-Union Congress on Theoretical and Applied Mechanics, Tashkent, 24–30 September, 1986.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 46–53, September–October, 1987.     

Use of a three-parameter family of locally similar velocity profiles in the calculation of turbulent separation regions in a compressible gas

A method is proposed for calculating two-dimensional leading turbulent separation regions based on the use of integral relations of boundary layer theory and integral characteristics of a three-parameter family of locally similar velocity profiles. The method makes it possible to calculate the characteristics of a turbulent boundary layer, including friction and heat transfer, without separation of discontinuities and special regions and to do this in both attached and separated flow regions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 3, pp. 24–33, May–June, 1982.I thank V. N. Shmanenkov for interest in the work and L. V. Gogish for reading and discussing the draft.     

Law of heat transfer in the region of a gas curtain

The article gives the result of an experimental investigation of heat transfer in the region of a gas curtain behind the permeable part of the surface in a subsonic turbulent boundary layer in the range of blowing intensities j=0.001–0.04.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–163, March–April, 1976.The authors thank G. A. Lyubimov for his continuing interest and aid in the work.