Two-dimensional Turbulent Boundary Layer Research Articles

Mean flow measurements in turbulent boundary layers along mildly curved surfaces

An experimental investigation of the mean flow characteristics of two-dimensional turbulent boundary layers over surfaces of mild longitudinal curvature is reported. The study covered both convex and concave walls of \d/Rw I « 0.013 (d being the boundary-layer thickness and Rw being the wall radius). It was found that, whereas the region close to the wall was not affected significantly by wall curvature, the outer region was very sensitive to even mild wall curvature. A detailed study of the wake region using present and other available data suggests a systematic effect of b/Rw on the wake structure. The paper also discusses in detail the effect of mild wall curvature on the boundary-layer development with particular emphasis on the difference in behavior of the boundary layer at short and long distances from the leading edge of the curved wall, an aspect which has not received sufficient attention in previous experimental investigations. An attempt has been made to explain this behavior from a consideration of the structure of turbulence in boundary layers over curved surfaces taken into account.

The spanwise non-uniformity of nominally two-dimensional turbulent boundary layer : 4th Report, Uniformalization of flow field and Comparison of various flows

In this report, results of an experimental investigation which was performed to eliminate the streamwise vortices arising in the nominally two-dimensional turbulent boundary layer, using the procedures which made the main stream uniform completely by replacing bad screens with appropriate ones and cutting those off, are presented. The results are compared with the previous authors' values and the effects of the open area ratio of the screen are confirmed. The differences between the flow fields in which the streamwise vortices exist and the completely two-dimensional flow fields are discussed and the feature of velocity defect region is clarified.

The spanwise non-uniformity of nominally two-dimensional turbulent boundary layer : 3rd Report, Influence of the streamwise vortices arising from the protrusion

In this report, results of an experimental investigation which was performed to eliminate the streamwise vortices arising in a nominally two-dimensional turbulent boundary layer of which behaviour was examined in detail in the authors previous paper, are presented. Though there may be two procedures of obliteration of streamwise vortices, the present work is concerned with the method to place the vortex generators like roughness element at the leading edge of a flat plate inducing the counter rotating vortices against pre-existing vortices in the boundary layer. Using this set, the authors measured the downstream development and uniformalization of the spatial variations of the boundary layer characteristics. From these results, it was revealed that the streamwise vortices were extremely stable, and large vortex generators must be used to eliminate these vortices. In addition, these streamwise vortices, which disappeared once in the course of the boundary layer development, exhibited a tendency to appear again in the downstream region. And a weak variation of velocity with large wave length at the outside of the layer produced by the protuberances was observed.

Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 4th Report, Uniformalization of Flow Field and Comparison of Various Flows

Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 4th Report, Uniformalization of Flow Field and Comparison of Various Flows

A study of turbulent boundary-layer separation and reattachment

An experimental and theoretical study is made of a suddenly separating and reattaching two-dimensional turbulent boundary layer on a flat surface. A separation bubble is formed on the floor of a wide parallel-sided wind-tunnel duct with the pressure field causing the bubble formation produced by fixing the shape of the flexible roof of the duct. Boundary layers on the roof are controlled and remain attached. It is found that a very satisfactory model for the flow is an inviscid one.The boundary layer on the floor of the duct is represented by a region of constant vorticity with slip at the boundary, and it is assumed that the separation process is dominated by the interaction between this ‘vortical’ region and the irrotational field between the vortical region and the roof (of prescribed shape). The interface between the rotational and irrotational regions is a free boundary and may be located when all necessary boundary conditions are given. These conditions include two characteristic parameters for the adverse-pressure-gradient turbulent boundary layer which is developing upstream of the region of interest.The problem is solved by an electrical analog method. The theoretical size and shape of the bubble and positions of separation and reattachment are in agreement with observations. The advantage of the model over most previous attempts to predict separation is that the governing equations are elliptic rather than parabolic or hyperbolic and therefore the interaction between the boundary-layer flow and the irrotational free stream is included in the calculations.

The spanwise non-uniformity of nominally two-dimensional turbulent boundary layer : 1st Report Characteristics of spanwise velocity distribution

In order to investigate the factors which affect the spanwise non-uniformity of the boundary layer and its property, measurements were carried out on the mean velocity, the turbulence intensity and wall shear stress in the transverse direction in the turbulent boundary layers which developed on two types of smooth flat plates of which the shapes of leading edge are different. The tunnel used had a moderately low turbulence, that is about 0.05 % of free stream velocity. Measuring stations were 9 cross sections. Various measurements were carried out in the transverse direction at very small intervals in these sections. From the results of experiments, it was found that a steady spatial quasi-periodic variation increased slightly and its pattern remained fixed toward downstream, and an appreciable negative correlation was calculated between the mean transverse velocity distribution and the turbulence intensity distribution in the same cross section. With regard to the open area ration of a screen which may affect the spanwise variations definitely, flow patterns through a screen with open area ratios 0.41, 0.52, 0.57 and 0.68 were observed by flow visualization by means of hydrogen bubble method. From these experimental results, it was obtained an appropriate value of the open area ratio of the screen used in the wind tunnel.

The spanwise non-uniformity of nominally two-dimensional turbulent boundary layer : 2nd Report Wall shear stress and flow field

In some cases the velocity distribution in a turbulent boundary layer shows remarkable spanwise non-uniformity even though the outer condition is is sufficiently two-dimensional from a practical point of view. In the previous paper, the authors described the characteristics of the spanwise non-uniformity in detail, from the experimental results of the spatial distributions of the streamwise velocity, turbulent intensity in the turbulent boundary layer and wall shear stress on two types of flat plates. In this report, the scale and mechanism of the streamwise vortices are investigated by the measurements of the flow direction in the turbulent boundary layer. A floating element type device is made and the local wall shear stress is measured by this apparatus. The values of wall shear stress obtained by this method are compared with the values obtained by other methods such as Clauser chart and the Preston tube method. From the result, it is inferred that the mean value of wall shear stress can be expressed by a two-dimensional equation even though the spatial variations of the mean velocity are remarkably large as in this case. The mechanism of the spatial variation of this turbulent boundary layer is clarified by using these experimental results.

Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 3rd Report, Influence of the Streamwise Vortices Arisen from the Protrusion

Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 3rd Report, Influence of the Streamwise Vortices Arisen from the Protrusion

The Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 2nd Report, Wall Shear Stress and Flow Field

The Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 2nd Report, Wall Shear Stress and Flow Field

The Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 1st Report, Characteristics of the Spanwise Velocity Distribution

The Spanwise Non-Uniformity of Nominally Two-Dimensional Turbulent Boundary Layer : 1st Report, Characteristics of the Spanwise Velocity Distribution

Selected Statistical Properties in the Inner Region of a Transpired Turbulent Boundary Layer

ISTORICALLY, the study of turbulence phenomena has developed along two quite independent paths. The study of boundary-layer phenomena proceeded from a need to understand surface shear stress and hence the basic analysis was cast in the form that had been successful in laminar flow, resulting in the introduction of an empirical eddy viscosity. Simultaneously, the study of uniform, iso tropic turbulence proceeded from a statistical basis yielding significant results concerning the spectral transfer of energy across the wave numbers. It has recently become apparent that solutions are imperative for problems in which the fluctuating characteristics of turbulence in addition to the mean profiles of the variables of interest are of paramount importance in an evaluation of the problem. It has, thus, become necessary for progress in the engineering solution of many problems in turbulent flow to involve more of the statistical description of the turbulence in the analysis of the problem. New methods for computing turbulent mixing and shear flows are being developed which attempt to overcome the limitations of the phenomenological approaches and which also attempt to incorporate more of the physics of turbulence into the solution. These new techniques have been largely based upon incorporating in one fashion or another the turbulent kinetic energy equation into the set of equations requiring solution. Usually this is accomplished by modeling the various terms in the turbulent kinetic energy equation in terms of the basic properties of turbulence and local flow conditions. This Note presents the results of a study directed toward the experimental evaluation of the turbulent modeling parameters utilized in the turbulent kinetic energy equation and their application in correlating the mean velocity distribution across the inner region of a turbulent boundary layer with surface mass addition. The case considered is that of a uniform two-dimensional incompressible turbulent boundary layer developed initially over an impermeable surface with mass injected uniformly over the surface into the boundary layer from a downstream station. The axial pressure gradient is considered zero. For this case, the turbulent kinetic energy equation may be written as

Mean velocity profiles in three-dimensional incompressible turbulentboundary layers.

Some aspects of mean velocity profiles in three-dimensi onal incompressible turbulent boundary layers are discussed using experimental data from different sources. An estimate of the change in the flow angle across the viscous sublayer of a skewed profile is obtained. Results are presented which exhibit the complex shape of crossflow profiles behind streamline inflection points and close to three-dimensional separation. The two-dimensional wall law is valid for moderate pressure gradients and the effect of higher pressure gradients on the inner velocity distribution is seen to be similar to that in two dimensions. The outer region, resolved into components parallel and normal to the wall flow, is correlated in terms of a geometric parameter in each direction for a fairly large body of data. Based on these results, it is postulated that the two-layer hypothesis of two-dimension al turbulent boundary layers is applicable to three-dimensional flows also.

Wall Shear Stress Inference From Two and Three-Dimensional Turbulent Boundary Layer Velocity Profiles

A method is developed to infer a local wall shear stress from a two-dimensional turbulent boundary layer velocity profile using all near-wall data with the Spalding single formula law of the wall. The method is used to broaden the Clauser chart scheme by providing for the inclusion of data in the laminar sublayer and transition region, as well as the data in the fully turbulent near-wall flow region. For a skewed velocity profile typical of pressure driven three-dimensional turbulent boundary layer flows, the method is extended to infer a wall shear stress for a three-dimensional turbulent boundary layer. Either wall shear stress or shear velocity values are calculated for two different sets of three-dimensional experimental data, with good agreement found between calculated and experimental results.

Experimental investigation of the heat exchange in separation zones of a turbulent boundary layer ahead of a step

Results of an experimental investigation of the heat exchange in separation zones of a two-dimensional turbulent boundary layer ahead of a rectangular step are elucidated for a subsonic air stream velocity.

Impact Probe Displacement in a Supersonic Turbulent Boundary Layer

Eight circular pitot probes ranging in size from 2 to 70 percent of the boundary-layer thickness were tested to provide experimental probe displacement results in a two-dimensional turbulent boundary layer at a nominal free-stream Mach number of 2 and unit Reynolds number of 8 million per meter. The displacement obtained in the study was larger than that reported by previous investigators in either an incompressible turbulent boundary layer or a supersonic laminar boundary layer. The large probes indicated distorted Mach number profiles, probably due to separation. When the probes were small enough to cause no appreciable distortion, the displacement was constant over most of the boundary layer. The displacement in the near-wall region decreased to negative displacement in some cases. This near-wall region was found to extend to about one probe diameter from the test surface.

An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients

A wind-tunnel model was developed to study the two-dimensional turbulent boundary layer in adverse and favourable pressure gradients with out the effects of streamwise surface curvature. Experiments were performed at Mach 4 with an adiabatic wall, and mean flow measurements within the boundary layer were obtained. The data, when viewed in the velocity transformation suggested by Van Driest, show good general agreement with the composite boundary-layer profile developed for the low-speed turbulent boundary layer. Moreover, the pressure gradient parameter suggested by Alber & Coats was found to correlate the data with low-speed results.

Separation of Turbulent Boundary Layer : Wall Pressure Distribution Near Separation

This paper treats the separation of a two-dimensional incompressible turbulent boundary layer caused by a strong adverse pressure gradient. From the equations of motion, we derive an equation which enables the stream function ψm is examined on strongly retarded flows. It is indicated that ψm and the total a section within the log-law region to the separation point. With these results concerning the behavior of the inner layer, two expressions are deduced for describing the pressure distribution in the constant -ψm region. A method is also proposed for predicting the pressure coefficient at separation. These theoretical results are compared with various experimental results and satisfactory agreements are obtained.

The effect of a discontinuity in wall blowing on the turbulent incompressible boundary layer

Experiments are reported for two-dimensional incompressible turbulent boundary layers for which there was an abrupt change in wall blowing. Skin-friction and mean velocity profile results indicate that asymptotically downstream the flow behaves according to the local momentum thickness Reynolds number and blowing conditions. It is found that during the relaxation length, the flow is separated by a ‘penetration point’ trajectory into an outer region described by upstream conditions and an inner region dependent upon local blowing conditions. The path of these trajectories appear very independent of the downstream wall condition. The penetration point trajectories are found to closely coincide with the last upstream outgoing characteristic of the hyperbolic set of governing partial differential equations presented by Bradshaw, Ferriss and Atwell [4]. These results suggest that the outgoing characteristic is more than a mathematical result and can be observed experimentally with flows with abrupt changes in wall blowing.

Measurements of the wave-number/phase velocity spectrum of wall pressure beneath a turbulent boundary layer

Measurements are presented of the wave-number/frequency and wave-number/phase velocity spectrum of wall pressure for a two-dimensional turbulent boundary layer in zero pressure gradient, obtained from a Fourier transform of experimental filtered spatial correlations. This method allows the results to be corrected for acoustic disturbances in the wind tunnel, and for finite transducer size. An empirical form for the pressure field is proposed, based on the measurements, and is used to predict a frequency spectrum correction for transducer size which agrees well with measured values.

A Simplified Version of Bradshaw’s Method for Calculating Two-dimensional Turbulent Boundary Layers

SummaryBradshaw’s method of calculating the development of two-dimensional turbulent boundary layers involves the simultaneous solution of partial differential equations of mean motion and turbulent kinetic energy. The present approach avoids the computational complexities of this procedure.The use of Thompson’s two-parameter family of velocity profiles and associated skin-friction law enables the momentum integral equation to be satisfied, along with Bradshaw’s version of the turbulent kinetic-energy equation at a specified fraction of the boundary layer thickness. This fraction (y/δ = 0·5) is chosen as representing the position in the boundary layer where Bradshaw’s equation, which contains several empirical functions, is shown by comparisons with experiment to hold with greatest accuracy. Thus the present simplified approach leads not only to a reduction in computing time but also to an appreciable increase in the general accuracy of prediction.