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.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Effect of moving wall on the three-dimensional separation of an incompressible fluid in front of an obstacle

The problem of the laminar boundary layer formed on the surface of a semiinfinite plate with a perpendicular semi-infinite circular cylinder in a uniform steady incompressible flow normal to the leading edge is considered. Near its sharp edge the plate has a stationary part and, located at a finite distance further downstream, a part of the surface moving downstream at a constant velocity. The first-order boundary layer equations are solved numerically by an implicit finite-difference method. The effect of the moving wall on the variation of the dimensions of the separation zone ahead of the obstacle over a broad range of the governing parameters and flow characteristics is investigated. The flow in the laminar boundary layer on the surface of a plate ahead of such an obstacle was calculated in [1, 2] without motion of the wall. Data on the structure of the separated flow are given in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–53, November–December, 1990.     

Least-drag bodies moving in media subject to the locality hypothesis

A solution is constructed for the variational problem of a body of minimum drag moving at constant velocity in media in which under certain assumptions the force exerted by the medium on an area element of the body surface depends only on its orientation relative to the direction of motion (locality hypothesis). The representations of the normal (pressure) and tangential (friction) components of the force embrace a broad range of the conditions realized in the motion of a body through gases and dense media.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 95–106, January–February, 1992.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Laminar boundary layer on a partly moving surface in the presence of blowing or suction

Planar and axisymmetric flows of a multicomponent compressible gas in a laminar boundary layer with nonzero tangential component of the velocity on a permeable surface are considered. The asymptotic solutions of the boundary-layer equations obtained earlier [1–4] for large values of the blowing and suction parameters are generalized to the case when the velocity vector of the blown or extracted gas makes an acute angle with the surface of the body, this angle depending on the longitudinal coordinate. The region of applicability of the asymptotic formulas is estimated on the basis of the results of numerical solution of the boundary-layer equations. The results are given of some calculations of the boundary layer on a partly moving surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 28–36, September–October, 1979.We thank G. A. Tirskii and G. G. Chernyi for a helpful discussion of the results.     

Formation of recirculation zones in the boundary layer on a moving surface

A study is made of the region of free interaction of a supersonic boundary layer on a moving surface formed by a weak shock wave impinging on it from without. In the equations of motion, allowance is made for the contribution of the pressure induced by the growth in the displacement thickness of jets passing near the surface. The results are given of the numerical solution of the corresponding nonlinear problem, and the basic structure of the recirculation zones is discussed. It is noted that there are regimes in which the main recirculation zone is accompanied by an additional eddy formation with circulation in the opposite direction. In contrast to a boundary layer on a fixed body, the points at which the streamlines separate are not on the wall but within the flow.Translated from Izvestiya Akademii Nauk SSSR, Meklianika Zhidkosti i Gaza, No. 5, pp. 3–10, September–October, 1980.     

Effect of a moving wall on a fully developed, equilibrium turbulent boundary layer

Experiments were conducted in a wind tunnel to assess the effect of a moving wall on a fully developed, equilibrium turbulent boundary layer. Pitot-static and total head probes were used in conjunction with both single- and two-component hot-wire anemometer probes to quantify the effect of wall motion on the boundary layer velocity statistics. A variable speed, seamless belt formed the wind tunnel test section wall. When stationary, the belt was found to possess a fully developed, equilibrium turbulent boundary layer in excellent agreement with archival data. With the tunnel wall moving at the free-stream speed, and at a sufficient distance above the wall, the velocity statistics in the moving-wall boundary layer were found to collapse well when scaled as a self-preserving turbulent wake. The near-wall mean velocity profile of the moving wall was found to exhibit an extended region of linearity compared to canonical turbulent boundary layer and internal flows. This can be attributed to the reduced shear resulting from wall motion and the subsequent reduction in Reynolds stress. Received: 2 June 1999/Accepted: 8 August 2000     

Interaction of an elastic boundary with a viscous sublayer of a turbulent boundary layer

The boundary region of a turbulent boundary layer contributes greatly to the drag. Intense turbulence is generated in this region. Below we investigate the interaction of an elastic boundary with a viscous sublayer for a decrease in the Reynolds stresses, and for a corresponding decrease in the drag. It does not seem possible to investigate the general case. Therefore, the problem is solved within the framework of the limitations made by Sternberg [1] for the theory of a viscous sublayer in a turbulent flow near a solid smooth wall.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 58–62, May–June, 1971.The authors thanks G. S. Migirenko for advice and remarks given during a discussion of the work.     

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.     

Asymptotic model of the development of separations inside a boundary layer under the action of a traveling pressure wave

A model of the nonlinear interaction between a pressure perturbation traveling at a constant velocity and an incompressible boundary layer is constructed when its near-wall part is described by the “inviscid boundary layer” equations. A steady-state solution is managed to obtain in the finite form under the assumption that it exists in a moving coordinate system. It is shown that the boundary layer can easily overcome pressure perturbations whose amplitude is not higher than the dynamic pressure calculated from the velocity of the pressure perturbation. At the higher pressure perturbation amplitudes a vortex sheet sheds from the body surface to the boundary layer. The vortex sheet represents an unstable surface of the tangential discontinuity which separates the regions of the direct and reverse separation flows. In the case of an arbitrary shape of the pressure perturbation the surface of the tangential discontinuity sheds from the body surface at a finite angle with the formation of a stagnation point. An example of the pressure perturbation in which the vortex sheet sheds from the body surface along the tangent is constructed.     

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.     

Asymptotic solution of the equations for a three-dimensional multicomponent laminar boundary layer with large injection

The asymptotic method of outer and inner expansions is used to analyze the flow of a multicomponent gas in a three-dimensional boundary layer on a smooth blunt body with large injection. Asymptotic expressions are derived for the friction coefficients, the heat and diffusion fluxes of the components on the surface of the body, and the velocity, temperature, and concentration profiles of the components across the layer of injected gases. It is shown that with large injection the limiting (bottom) streamlines on the surface of the body coincide in the first approximation with the vectorial lines of the pressure gradient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 47–56, March–April, 1975.The author is indebted to G. A. Tirskii for a discussion of the work.     

Investigation of three-dimensional boundary layers on blunt bodies with permeable surface

Numerical and approximate analytic methods are used to investigate three-dimensional laminar boundary layers on blunt bodies with permeable surface in a supersonic gas stream. In the first approximation of the integral method of successive approximation an analytic solution is obtained to the problem for an impermeable surface, small values of the blowing parameter, and arbitrary suction. For large parameters of the blowing (or suction), whose velocity vector in the general case is directed at a certain angle to the vector of the outer normal to the body, asymptotic expressions are derived for the components of the frictional stress and the heat flux. A numerical solution is obtained to the equations of the three-dimensional boundary layer in a wide range of variation of the blowing (or suction) parameter. The accuracy and region of applicability of the analytic solutions is estimated by comparison with the numerical solutions. On the basis of the solutions obtained in the present paper and the work of other authors an expression is proposed for calculating the heat fluxes to a perfectly catalytic surface of a body in a three-dimensional supersonic flow of dissociated or ionized air. The present paper continues earlier work of the authors [1, 2] on boundary layers in the neighborhood of a symmetry plane and on sweptback wings of infinite span.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 49–58, May–June, 1982.     

Construction of liquid flow past a solid body with an air layer

It is known that the friction drag for a body moving in a liquid may be reduced by varying the physical properties of the liquid at the body surface and, in particular, by creating an artificial air cavity on the body surface.The question of the magnitude of the drag gain in the case of the presence of a wall fluid layer with different physical constants was considered in [1–3].In [4, 5] results are presented of theoretical and experimental studies on the question of determining the parameters of artificial air cavities created on the lower surface of a horizontal wall in order to reduce the drag.In the following an attempt is made to construct the three-dimensional flow of an ideal liquid past a body which is enveloped entirely in an air cavity.     

Reynolds number effects on a turbulent boundary layer with separation,reattachment, and recovery

The present paper addresses experimental studies of Reynolds number effects on a turbulent boundary layer with separation, reattachment, and recovery. A momentum thickness Reynolds number varies from 1,100 to 20,100 with a wind tunnel enclosed in a pressure vessel by varying the air density and wind tunnel speed. A custom-built, high-resolution laser Doppler anemometer provides fully resolved turbulence measurements over the full Reynolds number range. The experiments show that the mean flow is at most a very weak function of Reynolds number while turbulence quantities strongly depend on Reynolds number. Roller vortices are generated in the separated shear layer caused by the Kelvin–Helmholtz instability. Empirical Reynolds number scalings for the mean velocity and Reynolds stresses are proposed for the upstream boundary layer, the separated region, and the recovery region. The inflectional instability plays a critical role in the scaling in the separated region. The near-wall flow recovers quickly downstream of reattachment even if the outer layer is far from an equilibrium state. As a result, a stress equilibrium layer where a flat-plate boundary layer scaling is valid develops in the recovery region and grows outward moving downstream.     

Experimental Control of Turbulent Boundary Layers with In-plane Travelling Waves

The experimental control of turbulent boundary layers using streamwise travelling waves of spanwise wall velocity, produced using a novel active surface, is outlined in this paper. The innovative surface comprises a pneumatically actuated compliant structure based on the kagome lattice geometry, supporting a pre-tensioned membrane skin. Careful design of the structure enables waves of variable length and speed to be produced in the flat surface in a robust and repeatable way, at frequencies and amplitudes known to have a favourable influence on the boundary layer. Two surfaces were developed, a preliminary module extending 152 mm in the streamwise direction, and a longer one with a fetch of 2.9 m so that the boundary layer can adjust to the new surface condition imposed by the forcing. With a shorter, 1.5 m portion of the surface actuated, generating an upstream-travelling wave, a drag reduction of 21.5% was recorded in the boundary layer with Re _τ =?1125. At the same flow conditions, a downstream-travelling produced a much smaller drag reduction of 2.6%, agreeing with the observed trends in current simulations. The drag reduction was determined with constant temperature hot-wire measurements of the mean velocity gradient in the viscous sublayer, while simultaneous laser Doppler vibrometer measurements of the surface recorded the wall motion. Despite the mechanics of the dynamic surface resulting in some out-of-plane motion (which is small in comparison to the in-plane streamwise movement), the positive drag reduction results are encouraging for future investigations at higher Reynolds numbers.     

On the generation of yawing moment using active flow control

The generation of control moments without moving control surfaces is of great practical importance. Following a successful flight demonstration of creating roll motion without ailerons using differential, lift oriented, flow control the current study is a first step towards generating yawing motion via differential flow controlled drag.A wind tunnel study was conducted on a 21% thick Glauert type airfoil. The upper surface flow is partially separated from the two-thirds chord location and downstream on this airfoil at all incidence angles. An array of mass-less Piezo-fluidic actuators, located at x/c = 0.65, are capable of fully reattaching the flow in a gradual, controlled manner. The actuators are individually operated such that the boundary layer could be controlled in a 3D fashion.Several concepts for creating yaw motion without moving control surface are examined. The ultimate goal is to generate the same lift on both wings, while decreasing the drag on one wing and increasing the drag on the other, therefore creating a yawing moment. Decreased drag is created by effective part-span separation delay while increased drag can be created by enhanced generation of vortex shedding or by highly localized 3D actuation.Detailed measurements of 3D surface pressure distributions and wake data with three velocity and streamwise vorticity components are presented and discussed along with surface flow visualization images. The data provide evidence that yawing moments can be generated with AFC.     

The effect of a systematic change in surface roughness skewness on turbulence and drag

Previous work by the authors (Flack and Schultz, 2010) has identified the root-mean-square roughness height, k_rms, and the skewness, Sk, of the surface elevation distribution as important parameters in scaling the skin-friction drag on rough surfaces. In this study, three surfaces are tested in turbulent boundary layer flow at a friction Reynolds number, Re_τ = 1600–2200. All the surfaces have similar root-mean-square roughness height, while the skewness is varied. Measurements are presented using both two-component LDV and PIV. The results show the anticipated trend of increasing skin-friction drag with increasing skewness. The largest increase in drag occurs going from negative skewness to zero skewness with a more modest increase going from zero to positive skewness. Some differences in the mean velocity and Reynolds stress profiles are observed for the three surfaces. However, these differences are confined to a region close to the rough surface, and the mean velocity and Reynolds stress profiles collapse away from the wall when scaled in outer variables. The turbulence structure as documented through two-point spatial correlations of velocity is also observed to be very similar over the three surfaces. These results support Townsend’s (1976) concept of outer-layer similarity that the wall boundary condition exerts no direct influence on the turbulence structure away from the wall except in setting the velocity and length scales for the outer layer.     

Boundary-layer separation on a cooled body and interaction with a hypersonic flow

In previous papers, e.g., [1, 2], boundary-layer separation was investigated by analyzing solutions of the boundary-layer equations with a given external pressure distribution. In general, this kind of solution cannot be continued after the separation point. Study of the asymptotic behavior of solutions of the Navier-Stokes equations [3–5] shows that, in boundarylayer separation in supersonic flow over a smooth surface, the main effect on the flow in the immediate vicinity of the separation point is a large local pressure gradient induced by interaction with the external flow. The solution can be continued beyond the separation point and linked to the solutions in the other regions, located downstream [5]. Similar results for incompressible flow were recently obtained in [6]. We can assume that in general there is always a small region near the separation point in which separation is self-induced, and where the limiting solution of the Navier-Stokes equations does not contain unattainable singular points. However, this limiting slope picture can be more complex and can contain more regions where the behavior of the functions differed from that found in [3–6]. The present paper investigates separation on a body moving at hypersonic speed, where the ratio of the stagnation temperature to the body temperature is large. It is shown that both. for hypersonic and supersonic speeds the flow near the separation point is appreciably affected by the distribution of parameters over the entire unperturbed boundary layer, and not only in a narrow layer near the body, as was true in the flows studied earlier [3–6]. Regions may appear with appreciable transverse pressure drops within the zone occupied by layers of the unperturbed boundary layer. Similarity parameters are given, the boundary problems are formulated, and the results of computer calculation are presented. The concept of subcritical and supercritical boundary layers is refined, and the dependence of pressure coefficients responsible for separation on the temperature factor is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–109, November–December 1973.