Boundary Layers over Infinite Yawed Wings

1960 ◽  
Vol 11 (4) ◽  
pp. 333-347 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Free Flow ◽  
Momentum Thickness ◽  
Displacement Thickness

SummaryA method of calculating turbulent boundary layers on infinite yawed wings is given, making use of a method of calculating turbulent boundary layers due to Spence and of an analogy between three-dimensional and axi-symmetric boundary layers. It is also shown that the displacement thickness is equal to that computed using chordwise components and that the streamwise momentum thickness is approximately equal to the chordwise momentum thickness. Shock-free flow and small boundary layer cross-flow are assumed.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Prediction of Turbulent Boundary Layer Development in Conical Diffusers

1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Energy Deficit ◽  
Momentum Thickness ◽  
Boundary Layer Development ◽  
Layer Development

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.

A Family of Hodograph Models for the Cross Flow Velocity Component of Three-Dimensional Turbulent Boundary Layers

1972 ◽  
Vol 94 (2) ◽  
pp. 321-329 ◽  
Author(s):  
J. R. Shanebrook ◽  
D. E. Hatch
Keyword(s):  
Flow Velocity ◽  
Boundary Layers ◽  
Velocity Component ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Flow Profiles ◽  
Rectangular Channels ◽  
Cross Flow Velocity ◽  
The Cross

A family of hodograph models for the cross flow velocity component of three-dimensional, turbulent boundary layers is presented. The principal advantage of this family is its flexibility which allows a wide variety of possible shapes for the hodograph. An integral method based on this family is developed and applied to data obtained in curved, rectangular channels. For the cases treated, the method gives acceptable results for cross flow profiles with and without flow reversal. Suggestions for refining the method are given.

Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers

1951 ◽  
Vol 3 (1) ◽  
pp. 51-60 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Three Dimensions ◽  
Momentum Thickness ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Good For ◽  
Layer Flow ◽  
Accelerated Flow

SummaryWild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β>0 (accelerated flow) but not so good for β<0 (retarded flow).)

A Simplified Form of the Auxiliary Equation for Use in the Calculation of Turbulent Boundary Layers

1958 ◽  
Vol 62 (567) ◽  
pp. 215-219
Author(s):  
T. J. Black
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Auxiliary Equation ◽  
Pressure Gradients ◽  
Momentum Thickness ◽  
Form Parameter ◽  
New Type ◽  
Simple Quadrature

A New type of auxiliary equation is given for calculating the development of the form-parameter H in turbulent boundary layers with adverse pressure gradients. The chief advantage of this new method lies in the rapidity and ease of calculation which has been achieved, without apparent sacrifice of accuracy.Whereas the growth of momentum thickness in the turbulent boundary layer can now be rapidly calculated by methods involving only simple quadrature, the prediction of the form parameter development remains a laborious task, while the results obtained do not always appear to justify the complexity of the calculations.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers

2017 ◽  
Vol 820 ◽  
pp. 667-692 ◽  
Author(s):  
A. Bobke ◽  
R. Vinuesa ◽  
R. Örlü ◽  
P. Schlatter
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
History Effects ◽  
Displacement Thickness ◽  
Gradient Parameter

Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter $\unicode[STIX]{x1D6FD}$. In order to fulfil the near-equilibrium conditions, the free stream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of $\unicode[STIX]{x1D6FD}$ (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant $\unicode[STIX]{x1D6FD}$ distributions at matched values of $\unicode[STIX]{x1D6FD}$ and friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. An additional case at matched Reynolds number based on displacement thickness $Re_{\unicode[STIX]{x1D6FF}^{\ast }}$ was also considered. It was noticed that non-constant $\unicode[STIX]{x1D6FD}$ cases appear to approach the conditions of equivalent constant $\unicode[STIX]{x1D6FD}$ cases after long streamwise distances (approximately 7 boundary-layer thicknesses). The relevance of the constant $\unicode[STIX]{x1D6FD}$ cases lies in the fact that they define a ‘canonical’ state of the boundary layer, uniquely characterized by $\unicode[STIX]{x1D6FD}$ and $Re$. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of $\unicode[STIX]{x1D6FD}$ and $Re$. Comparisons with the flat-plate cases at matched values of $\unicode[STIX]{x1D6FD}$ and $Re$ revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the $\unicode[STIX]{x1D6FD}$ history. Furthermore, a scaling law suggested by Kitsios et al. (Intl J. Heat Fluid Flow, vol. 61, 2016, pp. 129–136), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterize the state of the boundary layer.

Three-dimensional turbulent boundary layers in external flows: a report on Euromech 60

1975 ◽  
Vol 71 (4) ◽  
pp. 815-826 ◽  
Author(s):  
T. K. Fanneløp ◽  
P. Å. Krogstad
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Flows ◽  
Special Report ◽  
Flow Problems ◽  
The Subject ◽  
External Flows ◽  
Layer Flow

Euromech 60 is the third in a series of European Mechanics Colloquia dealing primarily with three-dimensional turbulent boundary layers. The Colloquium was held in Trondheim at the Technical University (NTH) from 14–16 April 1975 with forty-two participants from ten different countries, and was organized by L. N. Persen and T. K. Fanneløp. A total of 23 papers were presented, dealing with both experiments on and predictions of turbulent boundary-layer flows and related topics. Those concerned with the development of prediction methods were challenged by a set of boundary-layer flow problems defined well in advance in order to be calculated prior to the Colloquium. The results show close agreement for some calculated variables and surprisingly large discrepancies in others. A brief account of this exercise is included and it will also be the subject of a special report.

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