Evaluation of the Momentum Integral Equation for Turbulent Boundary Layers

1953 ◽  
Vol 20 (7) ◽  
pp. 502-502 ◽  
Author(s):  
Donald Ross
Keyword(s):  
Integral Equation ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Momentum Integral

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.

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 Generalized Integral Computation Technique for Nonequilibrium Compressible Turbulent Boundary Layers Using Moment Equations

1972 ◽  
Vol 39 (3) ◽  
pp. 667-672 ◽  
Author(s):  
J. P. Lamb ◽  
L. J. Hesler ◽  
J. H. Smith
Keyword(s):  
Boundary Layers ◽  
Mechanical Energy ◽  
Moment Equation ◽  
Turbulent Boundary Layers ◽  
Moment Equations ◽  
Governing Equations ◽  
Starting Conditions ◽  
The Moment ◽  
Momentum Integral ◽  
Layer Concept

Computation of nonequilibrium compressible turbulent boundary layers using Coles’ three-parameter representation for the layer (cf, δ, Π) is discussed. Governing equations include momentum integral, skin friction, and an integral moment equation. It is shown that the hypothetical equilibrium layer concept employed by Alber to determine the dissipation integral of the mechanical energy equation can be utilized to estimate similar auxiliary parameters in the entrainment and moment-of-momentum integral equations. A series of comparisons of experimental data and predictions, using each of the moment equations shows that all combinations yield very similar results which are in general agreement with measurements. Some sensitivity to starting conditions was observed with the moment-of-momentum and entrainment relations.

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.

Prediction of the Development of Non-Equilibrium Turbulent Boundary Layers Based on Modified Log-Wake Law

2014 ◽  
Vol 620 ◽  
pp. 39-43
Author(s):  
Tao Zhang ◽  
Xiao Jun Zhu ◽  
Fei Peng ◽  
Shao Song Min
Keyword(s):  
Dynamical System ◽  
Boundary Layers ◽  
System Approach ◽  
Reasonable Agreement ◽  
Nonlinear Dynamical System ◽  
Turbulent Boundary Layers ◽  
Experiment Data ◽  
Nonlinear Dynamical ◽  
Momentum Integral ◽  
Non Equilibrium

The properties of non-equilibrium turbulent boundary layers are substantially more complicated than that of equilibrium ones, and current understanding and predictive capabilities of the former are less well developed than of the latter. This paper proposed a nonlinear dynamical system approach to predict streamwise development of non-equilibrium turbulent boundary layers by means of realizing the closure of the momentum integral equation with aid of the modified log-wake law and the entrainment equation. The example calculation showed the results were in reasonable agreement with the experiment data, and demonstrated the proposed method could predict the streamwise evolution of the layers accurately and simply. Moreover, the method would be conveniently extended to the flows over rough surfaces.

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.

Sign in / Sign up

Export Citation Format

Share Document