Integral Methods for Turbulent Boundary Layers in Pressure Gradients

1972 ◽  
Vol 16 (03) ◽  
pp. 191-204
Author(s):  
Paul S. Granville
Keyword(s):  
Shear Stress ◽  
Boundary Layers ◽  
Shape Parameter ◽  
Turbulent Boundary Layers ◽  
Stress Factors ◽  
Quasi Equilibrium ◽  
Pressure Gradients ◽  
Equilibrium Conditions ◽  
Integral Methods ◽  
Two Parameter

Shape parameter differential equations are developed for turbulent boundary layers in pressure gradients incorporating two-parameter velocity profiles. Energy and entrainment methods are included. Shear stress factors are explicitly developed for equilibrium and quasi-equilibrium conditions.

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.

Effects of Three-Dimensional Pressure Gradients on High-Speed Turbulent Boundary Layers

2021 ◽  
Author(s):  
Scott J. Peltier ◽  
Brian E. Rice ◽  
Ethan Johnson ◽  
Venkateswaran Narayanaswamy ◽  
Marvin E. Sellers
Keyword(s):  
Boundary Layers ◽  
High Speed ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

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.

Sign in / Sign up

Export Citation Format

Share Document