The Turbulent Boundary Layer at a Plane of Symmetry in a Three-Dimensional Flow

1960 ◽  
Vol 82 (3) ◽  
pp. 622-628 ◽  
Author(s):  
James P. Johnston
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Factor ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Momentum Thickness ◽  
Three Dimensional Flow ◽  
Dimensional Boundary ◽  
Momentum Integral

Methods for treating a turbulent three-dimensional boundary layer at a plane of symmetry are presented. Reasonable agreement with experiment was achieved by the use of momentum integral techniques in the prediction of momentum thickness, shape factor, wall shear stress, and the location of separation.

scholarly journals An Analysis of the Turbine Endwall Boundary Layer and Aerodynamic Losses

1975 ◽  
Author(s):  
T. C. Booth
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Shape Factor ◽  
Boundary Layer Thickness ◽  
Energy Equation ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Aerodynamic Loss ◽  
Flow Configurations ◽  
Momentum Integral

A momentum-integral analysis of the three-dimensional flow on the turbine endwall is presented. The formulation is for a compressible turbulent boundary layer with a constant streamwise shape factor. The effect of compressibility enters through a coordinate transformation and an assumed energy equation. An aerodynamic loss model is derived using inner and outer expansions. The losses decompose into frictional losses on the annulus and a vortex loss. Results are predicted for four cascade tests. In addition, previously observed trends of loss versus inlet boundary layer thickness, blade height, and blade chord are predicted. To illustrate a possible application, a parametric study is presented showing the effect on losses and heat transfer of various inlet boundary layer thickness distributions, which simulates different secondary flow configurations.

Direct Force Wall Shear Measurements in Pressure-Driven Three-Dimensional Turbulent Boundary Layers

1982 ◽  
Vol 104 (2) ◽  
pp. 150-155 ◽  
Author(s):  
J. E. McAllister ◽  
F. J. Pierce ◽  
M. H. Tennant
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Direct Measurements ◽  
Stress Directions ◽  
Wall Flow ◽  
Wall Shear ◽  
Pressure Driven

Unique, simultaneous direct measurements of the magnitude and direction of the local wall shear stress in a pressure-driven three-dimensional turbulent boundary layer are presented. The flow is also described with an oil streak wall flow pattern, a map of the wall shear stress-wall pressure gradient orientations, a comparison of the wall shear stress directions relative to the directions of the nearest wall velocity as measured with a typical, small boundary layer directionally sensitive claw probe, as well as limiting wall streamline directions from the oil streak patterns, and a comparison of the freestream streamlines and the wall flow streamlines. A review of corrections for direct force sensing shear meters for two-dimensional flows is presented with a brief discussion of their applicability to three-dimensional devices.

scholarly journals THE DEVELOPMENT OF UNDULAR BORES WITH FRICTION

1970 ◽  
Vol 1 (12) ◽  
pp. 28
Author(s):  
O. Hawaleshka ◽  
S.B. Savage
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Wave Profile ◽  
Wall Friction ◽  
Slight Reduction ◽  
Initial Development ◽  
Theoretical Predictions ◽  
Wall Shear ◽  
Momentum Integral

A theoretical and experimental study of the initial development of undular bores in two-dimensional, rectangular channels with and without boundary friction was performed Equations similar to those of Boussmesq, but including higher order and wall friction terms are presented and solved numerically by an implicit finite difference method A Pohlhausentype boundary layer momentum integral method is used to obtain the wall shear stress distribution under a developing long wave from the consideration of the boundary layer underneath it The solution is performed in a quasi-iterative manner proceeding from the friction coefficient calculation for an initially assumed wave profile to the inclusion of this coefficient in the calculation of a new wave profile at an advanced time Comparisons of theoretical and experimental results are given For the initial development of the undular bore with which the present work is concerned, the measurements are found to be m reasonable agreement with the theoretical predictions The effect of the wall shear stress manifests itself mainly in a slight reduction of the wave amplitudes.

Use of Surface Fences to Measure Wall Shear Stress in Three-dimensional Boundary Layers

1973 ◽  
Vol 24 (2) ◽  
pp. 87-91 ◽  
Author(s):  
J D Vagt ◽  
H Fernholz
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Skin Friction ◽  
Boundary Layers ◽  
Manufacturing Process ◽  
Three Dimensional ◽  
Calibration Curves ◽  
Dimensional Boundary ◽  
Wall Shear

SummaryIf surface fences are to be applied for measuring skin friction in three-dimensional boundary layers they must be calibrated for both magnitude and direction of the shear stress. Results of the calibration for fences of different height are given. Furthermore, a manufacturing process and a mounting procedure are described to obtain surface fences with identical calibration curves.

Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

1989 ◽  
Vol 202 ◽  
pp. 263-294 ◽  
Author(s):  
Shawn D. Anderson ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Free Stream ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Stress Vector ◽  
Dimensional Boundary ◽  
Cross Wire

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

The Boundary-Layer Velocity Distribution in Turbulent Swirling Pipe Flow

1969 ◽  
Vol 91 (4) ◽  
pp. 728-733 ◽  
Author(s):  
R. G. Backshall ◽  
Fred Landis
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Three Dimensional ◽  
Axial Flow ◽  
Swirl Flow ◽  
Momentum Balance ◽  
Twisted Tape ◽  
Layer Velocity ◽  
Wall Shear

An experimental study was performed to determine the boundary-layer characteristics of an incompressible swirl flow produced by the insertion of a helically twisted tape into a pipe. The resulting flow can be approximated by a uniform axial flow with a superposed forced vortex flow. Boundary-layer velocity measurements indicate that the total velocity in this three-dimensional flow is well approximated by the universal logarithmic velocity profile. Modified axial and tangential logarithmic velocity laws have also been derived and are shown to be in good agreement with the data. The wall shear stress has to be determined either by direct velocity gradient measurements at the wall or by a modified momentum balance since pressure loss measurements do not directly lead to the correct wall shear stress.

Three-Dimensional Turbulent Boundary Layer in a Rotating Helical Channel

1975 ◽  
Vol 97 (2) ◽  
pp. 197-210 ◽  
Author(s):  
A. K. Anand ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Layer Growth ◽  
Viscous Effects ◽  
Helical Channel ◽  
Wall Shear

An analytical and experimental investigation of the characteristics of a three-dimensional turbulent boundary layer in a rotating helical channel is reported in this paper. Expressions are developed for the velocity profiles in the inner layer, where the viscous effects dominate, and the outer layer, where the viscous effects are small. The prediction of boundary layer growth is based on the momentum integral technique. The analysis is valid for incompressible flow through a rotor blade row with small camber. The velocity profiles, wall shear stress and limiting streamline angles are measured inside the passages of a flat plate inducer at various radial and chordwise locations using rotating probes. The measurements are in general agreement with the predictions. Flow near the blade tip is found to be highly complex due to interaction of blade boundary layers and the annulus wall, resulting in appreciable radial inward flow as well as a defect in mainstream velocity near the midpassage. A wall shear stress correlation, which includes the effect of both Reynolds number and rotation parameter, is derived from the measured data.

Study of the Boundary Layer on Ship Forms

1970 ◽  
Vol 14 (03) ◽  
pp. 153-167
Author(s):  
W. C. Webster ◽  
T.T. Huang
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Three Dimensional ◽  
Momentum Thickness ◽  
Flow Conditions ◽  
Integral Boundary ◽  
Outer Flow ◽  
Boundary Layer Equations ◽  
Pressure Distributions ◽  
Layer Flow

This paper presents a theoretical investigation of the development of the boundary layer about a ship. The "outer flow" conditions, including the streamlines and pressure distributions, are found from linearized, thin-ship theory using the method of Guilloton. Linearized, integral boundary-layer equations appropriate for three-dimensional turbulent flow are integrated numerically along the streamlines to determine the momentum thickness, the shape factor, and the angle of the boundary-layer flow to the outer flow. The results of computations for Series 60, block 0.60 and 0.80 are presented for various Froude numbers and ship lengths.

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