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 Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration

1995 ◽  
Vol 117 (3) ◽  
pp. 535-538 ◽  
Author(s):  
James Sucec
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Integral Solution ◽  
Good Agreement

The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

Equilibrium-Turbulent Boundary Layer Prediction for a Proposed Prandtl Mixing Length Distribution

1968 ◽  
Vol 10 (5) ◽  
pp. 426-433 ◽  
Author(s):  
F. C. Lockwood
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Length Distribution ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Good Agreement

The momentum equation is solved numerically for a suggested ramp variation of the Prandtl mixing length across an equilibrium-turbulent boundary layer. The predictions of several important boundary-layer functions are compared with the equilibrium experimental data. Comparisons are also made with some recent universal recommendations for turbulent boundary layers since the equilibrium experimental data are limited. Good agreement is found between the predictions, the experimental data, and the recommendations.

Turbulent Boundary Layers With Mass Transfer by the Dorodnitsyn Finite Element Method

1987 ◽  
Vol 54 (1) ◽  
pp. 197-202 ◽  
Author(s):  
C. A. J. Fletcher ◽  
R. W. Fleet
Keyword(s):  
Mass Transfer ◽  
Finite Element ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Element Formulation ◽  
Surface Mass ◽  
Surface Mass Transfer ◽  
Good Agreement

The Dorodnitsyn finite element formulation is extended to cover incompressible, two-dimensional turbulent boundary layers with surface mass transfer in the normal direction. The method is shown to give accurate and economical answers with only eleven points spanning the boundary layer. Good agreement is obtained when the computational solutions are compared with the experimental results of McQuaid [13] for skin friction coefficient, displacement and momentum thickness and velocity profiles. Zero and adverse pressure gradient and discontinuous injection cases have been considered.

Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

2007 ◽  
Vol 365 (1852) ◽  
pp. 755-770 ◽  
Author(s):  
Hassan M Nagib ◽  
Kapil A Chauhan ◽  
Peter A Monkewitz
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Classical Theory ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Careful Examination ◽  
Mean Velocity ◽  
Logarithmic Law

Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations accurately describe the local C f behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, H , shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of Δ and δ asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter, Π , is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.

Correction for Streamline Curvature and Coriolis Force in a Boundary Layer Integral Method

1981 ◽  
Author(s):  
R. A. Van Den Braembussche ◽  
P. Zunino
Keyword(s):  
Experimental Data ◽  
Integral Method ◽  
Theoretical Calculations ◽  
Correction Term ◽  
Dissipation Factor ◽  
Coriolis Forces ◽  
Streamline Curvature ◽  
Rotation Numbers ◽  
Wide Range ◽  
Good Agreement

The influence of Coriolis forces and streamwise curvature on boundary layers has been introduced into an integral method by adding a correction term to the dissipation factor. This correction term is related to Coriolis forces and streamline curvature in terms of a parameter 13 which was determined using existing experimental data. Theoretical calculations using this value of show good agreement with experimental results for a wide range of curvature and rotation numbers representing realistic conditions for turbomachinery applications.

scholarly journals Calculation of some turbulent wall currents

2021 ◽  
Vol 1 (101) ◽  
pp. 89-93
Author(s):  
Vitalii Mamchuk ◽  
Leonid Romaniuk
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Model ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Positive Pressure ◽  
Pressure Gradients ◽  
Turbulent Wall

A mathematical model for the calculation of turbulent boundary layers and wall stream has been developed. The results of calculations are compared with the results of other authors on the compliance of the calculated values with the experimental data. The currents that are formed under the influence of positive pressure gradients and lead to the phenomenon of separation of the turbulent boundary layer are studied.

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