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

1970 ◽  
Vol 21 (3) ◽  
pp. 243-262 ◽  
Author(s):  
V. C. Patel ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Computing Time ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Simplified Approach ◽  
Appreciable Increase ◽  
Momentum Integral

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.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

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.

On the Shear-Stress Integral of Turbulent Boundary Layers

1986 ◽  
Author(s):  
H. Pfeil ◽  
M. Göing
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Integral Method ◽  
Turbulent Boundary Layers ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Basic Assumptions ◽  
Turbulent Shear Stress ◽  
The Moment ◽  
Momentum Integral

The paper presents an integral method to predict turbulent boundary layer behaviour in two-dimensional, incompressible flow. The method is based on the momentum and moment-of-momentum integral equations and a friction law. By means of the compiled data of the 1968-Stanford-Conference, the results show that the integral of the turbulent shear-stress across the boundary layer, which appears in the moment-of-momentum integral equation, can be described by only two basic assumptions for all cases of flow.

Calculation of the Development of Turbulent Boundary Layers With a Turbulent Freestream

1974 ◽  
Vol 96 (4) ◽  
pp. 348-352 ◽  
Author(s):  
R. L. Evans ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Model Equation ◽  
Plate Boundary ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Integral Boundary ◽  
Momentum Integral ◽  
Flat Plate Boundary Layer ◽  
Good Agreement

An existing integral boundary layer calculation procedure is modified to predict turbulent boundary layers developing in a turbulent freestream. Extra terms in both the turbulence model equation and the momentum integral equation are introduced to account for the effects of freestream turbulence. Good agreement with flat plate boundary layer measurements in a turbulent freestream has been obtained, while comparison with measurements in a severe adverse pressure gradient shows qualitative agreement with experiments.

A Simple Integral Method for the Calculation of Thick Axisymmetric Turbulent Boundary Layers

1974 ◽  
Vol 25 (1) ◽  
pp. 47-58 ◽  
Author(s):  
V C Patel
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Integral Method ◽  
Turbulent Boundary Layers ◽  
Acceptable Accuracy ◽  
Approximate Form ◽  
Momentum Integral

SummaryA simple integral method is described for the calculation of a thick axisymmetric turbulent boundary layer. It is shown that the development of the boundary layer can be predicted with acceptable accuracy by using an approximate form of the momentum-integral equation, an appropriate skin-friction law, and an entrainment equation obtained for axisymmetric boundary layers. The method also involves the explicit use of a velocity profile family in order to interrelate some of the integral parameters. Available experimental results have been used to demonstrate the general accuracy of the method.

Stabilizing and Destabilizing Effects of Coriolis Force on Two-Dimensional Laminar and Turbulent Boundary Layers

1979 ◽  
Vol 101 (1) ◽  
pp. 23-29 ◽  
Author(s):  
H. Koyama ◽  
S. Masuda ◽  
I. Ariga ◽  
I. Watanabe
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Coriolis Force ◽  
Stable Boundary Layer ◽  
Numerical Evaluation ◽  
Critical Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Boundary Layer Development ◽  
Layer Development

To investigate the effects of Coriolis force on two-dimensional laminar and turbulent boundary layers, quantitative experiments were performed. A numerical evaluation was also carried out utilizing the Monin-Oboukhov coefficient including the effect of rotation. From the experimental results, the boundary layer development was found to be promoted on the unstable side and suppressed on the stable side, in comparison with the case of zero-rotation. In the stable boundary layer, the critical Reynolds number for relaminarization was observed to increase as rotation number was decreased. Calculated results were seen to predict the stabilizing effect of Coriolis force fairly well.

Effects of sandpaper roughness and stream turbulence on the turbulent boundary layer

1999 ◽  
Vol 213 (5) ◽  
pp. 507-515 ◽  
Author(s):  
J. C. Gibbings ◽  
S. M. Al-Shukri
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Pipe Flow ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Experimental Measurements ◽  
Two Dimensional

This paper reports experimental measurements of two-dimensional turbulent boundary layers over sandpaper surfaces under turbulent streams to complement the Nikuradse experiments on pipe flow. The study included the recovery region downstream of the end of transition. Correlations are given for the thickness, the shape factor, the skin friction and the parameters of the velocity profile of the layer. Six further basic differences from the pipe flow are described to add to the five previously reported.

Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances

2019 ◽  
Vol 866 ◽  
pp. 526-566 ◽  
Author(s):  
Jiho You ◽  
Tamer A. Zaki
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Boundary Layers ◽  
Large Scale ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Direct Numerical Simulations ◽  
Free Stream Turbulence ◽  
Conditional Statistics

Direct numerical simulations are performed to study zero-pressure-gradient turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from direct numerical simulations of homogeneous isotropic turbulence. A level-set approach is employed in order to objectively distinguish the boundary-layer and free-stream fluids, and to accurately evaluate their respective contributions to flow statistics. When free-stream turbulence is present, the skin friction coefficient is elevated relative to its value in the canonical boundary-layer configuration. An explanation is provided in terms of an increase in the power input into production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream perturbations being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the logarithmic layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn enhances turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second, indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall.

Sign in / Sign up

Export Citation Format

Share Document