A Three-Dimensional Integral Method for Calculating Incompressible Turbulent Skin Friction

1975 ◽  
Vol 97 (4) ◽  
pp. 550-555 ◽  
Author(s):  
F. M. White ◽  
R. C. Lessmann ◽  
G. H. Christoph
Keyword(s):  
Skin Friction ◽  
Integral Method ◽  
Three Dimensional ◽  
Separated Flow ◽  
Turbulent Boundary Layers ◽  
Shape Factors ◽  
Coupled Partial Differential Equations ◽  
Separation Line ◽  
Curved Duct ◽  
Dimensional Integral

A new integral method is proposed for the analysis of three-dimensional incompressible turbulent boundary layers. The method utilizes velocity profile expressions in wall-law form to derive two coupled partial differential equations for the two components of surface skin friction. No shape factors or empirical shear stress correlations are needed in the method. The only requirements are a knowledge of the external velocity and streamline distribution and initial values of skin friction along a starting crossflow line of the flow. The method is insensitive to sidewall conditions and may be continued downstream until the complete three-dimensional separation line of the flow has been computed. Two comparisons with experiment are shown: a curved-duct unseparated flow and a T-shaped-box separated flow. The calculations are very straightforward and agree reasonably well with the data for friction, crossflow angle, and separation line.

Boundary-layer separation of rotating flows past surface-mounted obstacles

1992 ◽  
Vol 237 ◽  
pp. 343-371 ◽  
Author(s):  
K. J. Richards ◽  
D. A. Smeed ◽  
E. J. Hopfinger ◽  
G. Chabert D'Hières
Keyword(s):  
Flow Separation ◽  
Three Dimensional ◽  
Separated Flow ◽  
Boundary Layer Separation ◽  
Critical Value ◽  
Complex Stress ◽  
Rotating Fluid ◽  
Separation Line ◽  
Maximum Value ◽  
The Hill

This paper describes laboratory experiments on the flow over a three-dimensional hill in a rotating fluid. The experiments were carried out in towing tanks, placed on rotating tables. Rotation is found to have a strong influence on the separation behind the hill. The topology of the separation is found to be the same for all the flows examined. The Rossby number R in the experiments is of order 1, the maximum value being 6. The separated flow is dominated by a single trailing vortex. In the majority of cases the surface stress field has a single separation line and there are no singular points. In a few experiments at the highest Rossby numbers the observations suggest more complex stress fields but the results are inconclusive.A criterion for flow separation is sought. For values of D/L > 1, where D is the depth of the flow and L the lengthscale of the hill, separation is found to be primarily dependent on R. At sufficiently small values of R separation is suppressed and the flow remains fully attached.Linear theory is found to give a good estimate for the critical value of R for flow separation. For hills with a moderate slope (slope ≤ 1) this critical value is around 1, decreasing with increasing slope. It is postulated that the existence of a single dominant trailing vortex is due to the uplifting and subsequent turning of transverse vorticity generated by surface pressure forces upstream of the separation line.

A three-dimensional field-integral method for the calculation of transonic flow on complex configurations — theory and preliminary results

1988 ◽  
Vol 92 (916) ◽  
pp. 235-241 ◽  
Author(s):  
P. M. Sinclair
Keyword(s):  
Transonic Flow ◽  
Integral Method ◽  
Three Dimensional ◽  
Full Potential ◽  
Potential Equation ◽  
Direct Extension ◽  
Body Shapes ◽  
Dimensional Integral ◽  
Field Integral ◽  
Good Agreement

Summary A three-dimensional integral formulation for the solution of the full potential equation and the associated numerical algorithm, the field-integral method, are presented. The method is a direct extension of a two-dimensional method and in particular retains the simple grid generation requirements noted in that method. Results are presented for the flow over body shapes and a complex winglet configuration, and are compared with existing transonic methods and experiments with good agreement. The further work necessary to provide a fast, robust method for use in design is outlined.

Prediction of Transpired Turbulent Boundary Layers With Arbitrary Pressure Gradients

1997 ◽  
Vol 119 (3) ◽  
pp. 526-532 ◽  
Author(s):  
Miodrag Oljaca ◽  
James Sucec
Keyword(s):  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Method ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Wide Range ◽  
Better Than ◽  
Good Agreement

An integral method, using Coles combined inner and outer law as the velocity profile, is developed for calculation of turbulent boundary layers with blowing or suction and pressure gradients. The resulting ordinary differential equations are solved numerically for the distribution of skin friction coefficient and integral thickness along the surface. Comparisons of predicted skin friction coefficients with experimental data are made for a wide range of blowing and suction rates and for various pressure gradients, including adverse, zero and a strong favorable gradient. In addition to good agreement with experimental data for constant blowing fractions F, the method is also successfully tested on cases where the blowing fraction is variable with position. Predictions, in general, exhibit satisfactory agreement with the data. The integral method predictions are comparable to, or better than, a number of finite difference procedures in a limited number of cases where comparisons were made.

A Wake and an Eddy in a Rotating, Radial-Flow Passage—Part 2: Flow Model

1973 ◽  
Vol 95 (3) ◽  
pp. 213-219 ◽  
Author(s):  
J. Moore
Keyword(s):  
Boundary Layers ◽  
Channel Flow ◽  
Potential Flow ◽  
Integral Method ◽  
Flow Model ◽  
Radial Flow ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Momentum Transport ◽  
Flow Passage

Rotational and three-dimensional terms are added to a strip-integral method for predicting the behavior of turbulent boundary layers. The secondary flow in the boundary layers is analyzed, and a theory for the momentum transport in the corner regions is used to couple the development of all the boundary layers. Simple assumptions for the potential flow and wake regions complete a model which allows the calculation of the whole channel flow, with only the specification of the inlet boundary layers.

The measurement of skin friction in turbulent boundary layers with adverse pressure gradients

1969 ◽  
Vol 35 (4) ◽  
pp. 737-757 ◽  
Author(s):  
K. C. Brown ◽  
P. N. Joubert
Keyword(s):  
Shear Stress ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Direct Measurements ◽  
Floating Element ◽  
Dimensional Boundary

This paper describes a floating-element skin friction meter which has been designed for use in adverse pressure gradients. The effects of secondary forces on the element, which arise from the pressure gradient, are examined in some detail. The limitations of various methods of measuring wall shear stress are discussed and the results from the floating element device are compared with measurements taken in a two-dimensional boundary layer using Preston tubes and velocity profiles. As it is planned to use the instrument later for direct measurements of the shear stress in three-dimensional boundary layers, the relevance of the instrument to this situation is also discussed.

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