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.

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.

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.

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.

Calculation of unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity

1977 ◽  
Vol 355 (1681) ◽  
pp. 225-238 ◽  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Boundary Layer Equations

A numerical method is presented for calculating unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity. The method used an eddy-viscosity formulation to model the Reynolds shear stress term appropriate to turbulent flow and an efficient two-point finite-difference method to solve the governing boundary-layer equations. The method is used to calculate phase angles between the wall shear stress and an oscillating external laminar boundary layer over a flat plate. The results are in excellent agreement with the analytic solutions of Lighthill for the high- and low-frequency limits and provide information in the region between. Similar calculations for turbulent flows are compared with experimental data and the method shown to be more precise than previously described attempts to represent flows of this type. The agreement between calculations and measurements is imperfect but probably within the resolution of the experiments and adequate for engineering purposes.

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.

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]

High Freestream Turbulence Effects on Turbulent Boundary Layers

1996 ◽  
Vol 118 (2) ◽  
pp. 276-284 ◽  
Author(s):  
K. A. Thole ◽  
D. G. Bogard
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Outer Region ◽  
Power Spectra ◽  
Turbulent Boundary Layers ◽  
Freestream Turbulence ◽  
Length Scales ◽  
Turbulent Eddies ◽  
Viscous Shear

High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.

A Procedure for Computation of Fully Stalled Flows in Two-Dimensional Passages

1978 ◽  
Vol 100 (2) ◽  
pp. 180-186 ◽  
Author(s):  
R. L. Woolley ◽  
S. J. Kline
Keyword(s):  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Separated Flows ◽  
Two Dimensional ◽  
Design Problems ◽  
Zonal Model ◽  
Pressure Distributions ◽  
Insight Into ◽  
Critical Aspects ◽  
Two Dimensional Flows

A procedure is described for computation of incompressible, steady, two-dimensional flows in fully-stalled diffusers with plenum exit. The procedure is successful in predicting pressure distributions and patterns to the accuracy of the data. The procedure employs a zonal model; this maintains close connections between the modeling and the physics thereby providing insight into critical aspects of modeling separated flows. The procedure presented is also convenient for computing unstalled flows in passages with turbulent boundary layers for either direct or indirect design problems. Computing times are well within engineering feasibility. The concepts developed can be extended to other classes of separated flows; some of these extensions have already been completed and are referenced.

An Approximate Method for the Calculation of Turbulent Boundary Layers in Diffusers

1957 ◽  
Vol 8 (1) ◽  
pp. 58-77 ◽  
Author(s):  
J. F. Norbury
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Approximate Method ◽  
Boundary Layers ◽  
Stress Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Form Parameter ◽  
Parameter Equation

SummaryAn approximate method is described for the calculation of turbulent boundary layers in which the turbulence is developed before the commencement of the adverse pressure gradient, as in most diffuser layers. It is based on a method due to Spence which has been modified and also extended to the calculation of three-dimensional diverging layers such as occur in ducts whose breadth is increasing. The velocity profiles occurring in a diverging layer are examined and it is shown that the inner part obeys the universal logarithmic law, as in two-dimensional layers. This result is used to obtain an equation for the form parameter in diverging layers, by substitution in the equation of motion and incorporation of the equations of momentum and continuity for diverging flow. The form parameter equation contains a term involving the gradient of shear stress at y = θ and values of this term are obtained by the analysis of experimental data and the substitution of known values for all the other terms in the form parameter equation. Values of the term involving shear stress gradient are then correlated in terms of known boundary layer quantities, and the resulting correlation allows the formulation of a step-by-step method for the solution of the form parameter equation. This may be used in conjunction with the momentum equation to predict the boundary layer growth. It was not found possible to effect a satisfactory correlation for boundary layers on lifting aerofoils, in which the turbulence develops within the adverse pressure gradient, and the method cannot be used for the prediction of such layers. The results of a number of calculations are given.

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.

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