Closure to “Discussions of ‘A Momentum Integral Solution of a Three-Dimensional Turbulent Boundary Layer’” (1972, ASME J. Basic Eng., 94, pp. 800–802)

1972 ◽  
Vol 94 (4) ◽  
pp. 802-803
Author(s):  
F. J. Pierce ◽  
W. F. Klinksiek
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Integral Solution ◽  
Momentum Integral

A Momentum Integral Solution of a Three-Dimensional Turbulent Boundary Layer

1972 ◽  
Vol 94 (4) ◽  
pp. 795-800
Author(s):  
F. J. Pierce ◽  
W. F. Klinksiek
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Integral Solution ◽  
Edge Condition ◽  
Integral Methods ◽  
Flow Parameters ◽  
Layer Flow ◽  
Momentum Integral

The results of a momentum integral solution of the three-dimensional turbulent boundary layer on the confining wall of an impinging jet are presented. This geometry provides a boundary layer where large gradients in the streamwise and especially the transverse direction occur and hence is a severe test of momentum integral methods. The solution utilizes the Head entrainment function and the Ludwieg and Tillmann wall shear law, with no restriction on cross flows. An extensive comparison with experimental results show good to moderate agreement in the integrated flow parameters, with a strong dependence on the free-stream or edge condition to the boundary layer flow.

Turbulent Boundary Layer Flow on the End Wall of a Cylindrical Vortex Chamber

1975 ◽  
Vol 189 (1) ◽  
pp. 305-315 ◽  
Author(s):  
T. J. Kotas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Vortex Chamber ◽  
Cylindrical Vortex ◽  
Layer Flow ◽  
Momentum Integral ◽  
End Wall

A presentation of some measurements of velocities in the turbulent boundary layer on the end wall of a vortex chamber. These show that the boundary layer flow is three-dimensional with large inward radial velocities. Consequently, most of the fluid entering the vortex chamber passes into the central region through the boundary layers on the end walls rather than the main space of the vortex chamber. A momentum integral solution is used to obtain an estimate of the radial flow through the end-wall boundary layers. A comparison of the theoretical curves with the experimental results gives support to the main assumptions used in the solutions.

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part II: Attachment-Line Flow on an Infinite Swept Wing

1967 ◽  
Vol 18 (2) ◽  
pp. 150-164 ◽  
Author(s):  
N. A. Cumpsty ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Cross Flow ◽  
Swept Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow ◽  
Momentum Integral ◽  
Attachment Line

SummaryAn earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.

On the Three-Dimensional Turbulent Boundary Layer Generated by Secondary Flow

1960 ◽  
Vol 82 (1) ◽  
pp. 233-246 ◽  
Author(s):  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Cross Flow ◽  
Problem Solution ◽  
Boundary Layer Problem ◽  
Flow Components ◽  
Momentum Integral ◽  
The Relationship

A study of the secondary flow type of three-dimensional turbulent boundary layer is presented. Two objectives are achieved: (a) A mathematical model of the relationship between the cross-flow and main-flow components of the velocity vectors of the layer is established. (b) By utilization of the model some of the relationships required to carry out a boundary-layer problem solution by the use of the momentum-integral equations are developed.

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