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.

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.

Boundary Layer Effects in the Turbulent Spiral Vortex Flow of a Compressible Fluid

1968 ◽  
Vol 183 (1) ◽  
pp. 179-188 ◽  
Author(s):  
B. F. Scott
Keyword(s):  
Boundary Layer ◽  
Vortex Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Radial Pressure ◽  
Vortex Chamber ◽  
Adiabatic Wall ◽  
Spiral Vortex ◽  
Momentum Integral

Because of the characteristically narrow impeller tip width in a proposed supersonic centrifugal compressor design, boundary layer effects in the vortex chamber are likely to be significant. The radial pressure gradient in the chambers sweeps retarded fluid towards the centre of curvature of the streamlines, thereby creating a ‘cross-flow’ in the boundary layer which is three-dimensional. Although the flow geometry has axial symmetry, the cross-flow is not independent of the streamwise flow. The momentum—integral method is adopted, together with assumptions concerning the velocity profiles; the energy equation is solved with the assumption of an adiabatic wall. Simultaneous solution of the free stream and boundary layer equations yields results emphasizing the critical dependence of the transverse deflection and growth of the boundary layer on the whirl component of the velocity. Separation cannot be predicted, but effects in the free stream can be estimated when the perturbations are small. Although the results are related to compressor performance, the method is generally applicable in situations where the idealizing assumption of spiral vortex flow is acceptable.

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 Turbulent Boundary Layer on a Rotating Nose-Body

1971 ◽  
Vol 22 (4) ◽  
pp. 389-402 ◽  
Author(s):  
T-S. Cham ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coordinate System ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Rotation Parameter ◽  
Method Of Solution ◽  
Flow Directions ◽  
Momentum Integral

SummaryEarlier papers described a method of calculating three-dimensional turbulent boundary layers based on the use of momentum-integral equations in the streamwise and cross-flow directions. Here the method is applied to a problem which is initially formulated in a coordinate system appropriate to the somewhat complex body geometry. Transformation to a streamline coordinate system is then made before the application of a rapidly converging iterative method of solution. The calculations, which are confined to single Reynolds number and a particular value of the rotation parameter, show the very large increases in drag and torque that accompany early transition.

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