Asymptotic analysis of turbulent boundary layer flow on a flat plate at high Reynolds numbers

The equations of the turbulent boundary layer contain a small parameter — the reciprocal of the Reynolds number, which makes it possible to carry out an asymptotic analysis of the solutions with respect to that small parameter. Such analyses have been the subject of a number of studies [1–5]. In [2, 5] for closing the momentum equation algebraic Prandtl and turbulent viscosity models were used. In [1, 3, 4] the structure of the boundary layer was analyzed in general form without formulating specific closing hypothesis but under additional assumptions concerning the nature of the asymptotic behavior of the limiting solutions in the various regions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 106–117, May-June, 1993.     

Effect of free-stream turbulence on surface friction in a turbulent boundary layer

The combined effect of the turbulence intensity , the turbulence scaleL, and the Reynolds number Re^** on the surface friction coefficientc _f in a turbulent boundary layer is studied. The dependence of the relative friction increment on the equivalent turbulence level _cq, which takes into account the simultaneous variation in ,L and Re^**, is determined. The threshold value _cq ^* below which the value ofc _f does not depend on _cq is found.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–75, March–April, 1995.     

Effect of system rotating on turbulent boundary layer flow

This paper experimentally investigated the effect of rotating on the turbulent boundary layer flow using hot-wire. The experiments were completed in a rotating rig with a vertical axis and four measured positions along the streamwise direction in channel, which focuses on the flow flied in the rotating channel. The rotating effects on velocity profile, wall shear stress and semi-logarithmic mean velocity profile are discussed in this paper. The results indicated that: due to the Coriolis force induced by rotating, the phenomenon of velocity deficit happens near the leading side. The velocity deficit near the leading side, do not increase monotonically with the increase of Ro. The trend of the velocity deficit near the leading side is also affected by the normal component of pressure gradient, which is another important force in the cross-section of the rotating channel. The wall shear stress near the trailing side is larger than that on the leading side, and the semi-logarithmic mean velocity profile is also different under rotating effects. The phenomenon reveals that the effect of rotation penetrates into the logarithm region, and the flow near the leading side tends to turn into laminar under the effect of rotation. The rotation correction of logarithmic law is performed in current work, which can be used in the wall function of CFD to increase the simulating accuracy at rotating conditions.     

Interaction of a laminar boundary layer with external turbulence

Transition in the boundary layer on a flat plate in a turbulent flow is investigated experimentally and theoretically. It is established that over a broad range of flow conditions (variation of the intensity and scale of the external turbulence, the angle of attack, the shape of the leading edge, etc.) transition takes place without the formation of Tollmien-Schlichting waves, and its initial stages, including the amplification of disturbances, are described by the linearized unsteady three-dimensional boundary layer equations without a pressure gradient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 55–65, September–October, 1989.The authors are grateful to N. F. Polyakov, V. S. Kosorygin, and O. S. Ryzhov for useful discussions and to N. N. Bychkov and O. N. Konstantinovskii for assisting with the experiments.     

Experimental study of the structure of a turbulent boundary layer at a plate on injecting helium

The results of an experimental investigation into the structure of a turbulent boundary layer at a porous plate during the injection of helium are presented. The effect of the injection parameter on the averaged and pulsating velocity and concentration distributions in the layer is analyzed. The sequence of the repulsion (displacement) process is described, and the repulsion parameter is given.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–67, May–June, 1972.     

Ignition of hydrogen in a turbulent boundary layer on a plate

The ignition of hydrogen blown into a turbulent supersonic boundary layer on a flat plate is investigated numerically. It is assumed that the mixture consists of six chemically active components H, O, OH, H₂O, O₂, H₂ and inert nitrogen N₂. The boundary layer is divided into outer and inner regions, for which different expressions for the coefficients of turbulent transport are used. The influence of pulsations on the rates of the chemical reactions, and also the back reaction of the chemical processes on the mechanism of turbulent transfer are not taken into account. The surface of the plate is assumed to be absolutely catalytic with respect to the recombination reactions of the H and O atoms. The influence of the blowing intensity, the Mach number in the outer flow, and the pressure on the ignition delay is analyzed. The possibility of effective porous cooling of the surface when there is combustion in the boundary layer is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 33–40, November–December, 1979.I thank V. G. Gromov and V. A. Levin for their interest in the work.     

Analysis of turbulent boundary layer interaction with an external supersonic flow behind a step

An integral method of analyzing turbulent flow behind plane and axisymmetric steps is proposed, which will permit calculation of the pressure distribution, the displacement thickness, the momentum-loss thickness, and the friction in the zone of boundary layer interaction with an external ideal flow. The characteristics of an incompressible turbulent equilibrium boundary layer are used to analyze the flow behind the step, and the parameters of the compressible boundary layer flow are connected with the parameters of the incompressible boundary layer flow by using the Cowles-Crocco transformation.A large number of theoretical and experimental papers devoted to this topic can be mentioned. Let us consider just two [1, 2], which are similar to the method proposed herein, wherein the parameter distribution of the flow of a plane nearby turbulent wake is analyzed. The flow behind the body in these papers is separated into a zone of isobaric flow and a zone of boundary layer interaction with an external ideal flow. The jet boundary layer in the interaction zone is analyzed by the method of integral relations.The flow behind plane and axisymmetric steps is analyzed on the basis of a scheme of boundary layer interaction with an external ideal supersonic stream. The results of the analysis by the method proposed are compared with known experimental data.Notation x, y longitudinal and transverse coordinates - X, Y transformed longitudinal and transverse coordinates - , ^*, ^** boundary layer thickness, displacement thickness, momentum-loss thickness of a boundary layer - , ^*, ^** layer thickness, displacement thickness, momentum-loss thickness of an incompressible boundary layer - u, velocity and density of a compressible boundary layer - U, velocity and density of the incompressible boundary layer - , stream function of the compressible and incompressible boundary layers - , dynamic coefficient of viscosity of the compressible and incompressible boundary layers - r₁ radius of the base part of an axisymmetric body - r radius - R transformed radius - M Mach number - friction stress - p pressure - a speed of sound - s enthalpy - v Prandtl-Mayer angle - P Prandtl number - P_t turbulent Prandtl number - r₂ radius of the base sting - b step depth - =0 for plane flow - =1 for axisymmetric flow Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 33–40, May–June, 1971.In conclusion, the authors are grateful to M. Ya. Yudelovich and E. N. Bondarev for useful comments and discussions.     

A quasi-similarity analysis of the turbulent boundary layer on a flat plate

The partial differential equation of the boundary layer on a flat plate are simplified by using the universal variables for turbulent flow. For laminar flow this gives boundary layer having a finite thickness and a friction coefficient differing by a few percent from the Blasius value. For a turbulent flow a differential equation for the velocity distribution is obtained with a parameter which varies slowly with the streamwise coordinate. The numerical value of this parameter is determined as an eigenvalue of the differential equations giving a velocity profile which evolves as the boundary layer thickens. Numerical calculations using a simple eddy viscosity model gave results in very good agreement with experiment.     

Effect of external turbulence on the development of a turbulent jet

The effect of external turbulent agitation on jet development has been investigated in [1–3]. The difference of the method employed in the present work lies in the assumption that the turbulence scale of the external flow is substantially larger than the turbulence scales in either the jet or the mixing layer. Utilizing this assumption, it becomes possible to solve separately the energy equations for the turbulence of the external flow and of the jet. Solutions obtained on the basis of this assumption are found to be in qualitative agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–29, January–February, 1977.     

Effect of local forcing on a turbulent boundary layer

An experimental study is performed to analyze flow structures behind local suction and blowing in a flat-plate turbulent boundary layer. The local forcing is given to the boundary layer flow by means of a sinusoidally oscillating jet issuing from a thin spanwise slot at the wall. The Reynolds number based on the momentum thickness is about Re _θ =1700. The effects of local forcing are scrutinized by altering the forcing frequency (0.011 ≤ f ⁺≤ 0.044). The forcing amplitude is fixed at A ₀=0.4. It is found that a small local forcing reduces the skin friction and the skin friction reduction increases with the forcing frequency. A phase-averaging technique is employed to capture the large-scale vortex evolution. An organized spanwise vortical structure is generated by the local forcing. The cross-sectional area of vortex and the time fraction of vortex are examined by changing the forcing frequency. An investigation of the random fluctuation components reveals that turbulent energy is concentrated near the center of vortical structures. Received: 17 March 2000/Accepted: 3 April 2001     

Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer

 Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced by approximately 50%. Received: 28 October 1997/Accepted: 4 February 1998     

Interaction of a turbulent boundary layer with a shock wave at transonic flow velocities

An asymptotic theory of the interaction of a turbulent boundary layer on a plate with a normal shock wave of low intensity has been constructed in various studies [1–4] under the assumption that the averaged velocity of the particles in the boundary layer in front of the interaction region satisfies a logarithmic law. In the present paper a different approach to this problem is proposed based on a power law of the velocity in the undisturbed boundary layer. The obtained results give different estimates for not only the sizes of the characteristic flow regions in the interaction region but also for the shock intensity leading to boundary layer separation.     

Displacement in the turbulent boundary layer on a permeable plate with supercritical injection

The displacement thickness in a turbulent boundary layer is determined for supercritical injection parameters. Experimental relations between the displacement thickness and the injection parameter are obtained for air, helium, and freon-12 injected into air.     

Direct drag measurements in a turbulent flat-plate boundary layer with turbulence manipulators

The effect of turbulence manipulators on the turbulent boundary layer above a flat plate has been investigated. These turbulence manipulators are often referred to as Large Eddy Break Up (LEBU) devices. The basic idea is that thin blades or airfoils are inserted into the turbulent flow in order to reduce the fluctuating vertical velocity component v above the flat plate. In this way, the turbulent momentum transfer and with it the wall shear stress downstream of the manipulator should be decreased. In our experiments, for comparison, a merely drag-producing wire also was inserted into the boundary layer.In particular, the trade-off between the drag of the turbulence manipulator and the drag reduction due to the shear-stress reduction on the flat plate downstream of the manipulator has been considered. The measurements were carried out with very accurate force balances for both the manipulator drag and the shear stress on the flat plate. As it turns out, no net drag reduction is found for a fairly large set of configurations. A single thin blade as a manipulator performed best, i.e., it was closest to break-even. However, a further improvement is unlikely, because the device drag of the thin blade elements used here has already been reduced to only that due to laminar skin friction, and is thus the minimum possible drag. Airfoils performed slightly worse, because their device drag was higher. A purely drag-producing wire device performed disastrously. The wire device, which consisted of a wire with another thin wire wound around it to suppress coherent vortex shedding and vibration, was designed to have (and did have) the same drag as the airfoil manipulator with which it was compared. The comparison showed that airfoil and blade manipulators recovered 75–90% of their device drag through a shear-stress reduction downstream, whereas the wire device recovered only about 25–30% of its device drag.Conventional LEBU manipulators with airfoils or thin blades produce between 0.25% and 1% net drag increase, whereas the wire device (with equal device drag) produces as much as 4% net drag increase. These data are valid for the specific plate length of our experiments, which was long enough in downstream extent to realize the full effect of the LEBU manipulators. Turbulence manipulators do indeed decrease the turbulent momentum exchange in the boundary layer by rectifying the turbulent fluctuations. This generates a significant shear-stress reduction downstream, which is much more than just the effect of the wake of the manipulator. However, the device drag of the manipulator cannot be reduced without simultaneously reducing the skin friction reduction. Thus, the manipulator's device drag exceeds, or at best cancels, the drag reduction achieved by the shear-stress reduction downstream. A critical survey of previous investigations shows that the suggestion that turbulence manipulators may produce net drag reduction is also not supported by the available previous drag force measurements. The issue had been stirred up by less conclusive measurements based on local velocity data, i.e., data collected using the so-called momentum balance technique.List of symbols b lateral breadth of test plate - c chord length of turbulence manipulator - d diameter of wire manipulator - e distance of the elastic center from the leading edge of the manipulator airfoil - h height of manipulator above test plate - q dynamic pressure of the potential flow above the test plate - s spacing of turbulence manipulator elements - t thickness of turbulence manipulator elements - u,v,w fluctuating velocities in downstream, platenormal, and lateral directions - x distance from the leading edge of the test plate in the downstream direction - x ₀ location of the trailing edge of the first manipulator - z distance from test plate center in the lateral direction - C _D drag coefficient - C _L lift coefficient - D _m drag of manipulated plate including device drag and shear stress, calculated from manipulator location to downstream location - D ₀ drag of unmanipulated plate boundary layer, consisting of the shear stress calculated from manipulator location to downstream location - F drag force - F ₀ total skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream of manipulator, measured without turbulence manipulator - F _LEBU device drag force of the LEBU, i.e., the turbulence manipulator - F _m total drag force of manipulated plate, consisting of - F _LEBU and skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream - F _cf skin friction force as measured by the floating element balance, manipulated case - F _cfo skin friction force, as measured by the floating element balance, unmanipulated case - F _cf skin friction saving, defined as F _cf = F _cf – F _cfo - F _cf cumulative skin friction savings, i.e., the sum of the skin friction savings F _cf , added up from the location of the manipulator to the downstream location , as shown in Fig. 11. In Fig. 13 the cumulative skin friction savings are summarized up to their asymptotic value, reached at 200 - Re _c Reynolds number of the manipulator elements, calculated with the chord length c and the local velocity in the boundary layer - Re ₀ Reynolds number at the location x ₀ of the manipulator, calculated with the momentum thickness of the boundary layer and the mean flow velocity U - U mean flow velocity in the potential regime of the wind tunnel test section - angle of attack of the manipulator airfoils - ₀ boundary layer thickness at the location x ₀ of the manipulator - dimensionless distance from the manipulator in the downstream direction, defined as - density of the air - ₀ local skin friction shear stress, unmanipulated case - _{0 Average} skin friction shear stress, average value over the lateral span (b = 2 m) of the test plate, unmanipulated case - _m local skin friction shear stress, manipulated case - momentum thickness of the undisturbed turbulent boundary layer at the location x ₀ The authors would like to thank Prof. H. H. Fernholz for his scientific and administrative support. The hardware for the experiments was designed and built by C. Daase, W. Hage and R. Makris. Funding for the project was provided by the Deutsche Forschungsgemeinschaft and is gratefully acknowledged.     

The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China