Similarity Analysis in Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

2004 ◽  
Author(s):  
Raul Bayoan Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Forced Convection ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
External Pressure ◽  
Similarity Analysis ◽  
Pressure Gradients

Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Xia Wang ◽  
Luciano Castillo ◽  
Guillermo Araya
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Forced Convection ◽  
Boundary Layers ◽  
Heat Mass Transfer ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis

Based on the theory of similarity analysis and the analogy between momentum and energy transport equations, the temperature scalings have been derived for forced convection turbulent boundary layers. These scalings are shown to be able to remove the effects of Reynolds number and the pressure gradient on the temperature profile. Furthermore, using the near-asymptotic method and the scalings from the similarity analysis, a power law solution is obtained for the temperature profile in the overlap region. Subsequently, a composite temperature profile is found by further introducing the functions in the wake region and in the near-the-wall region. The proposed composite temperature profile can describe the entire boundary layer from the wall all the way to the outer edge of the turbulent boundary layer at finite Re number. The experimental data and direct numerical simulation (DNS) data with zero pressure gradient and adverse pressure gradient are used to confirm the accuracy of the scalings and the proposed composite temperature profiles. Comparison with the theoretical profiles by Kader (1981, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 24, pp. 1541–1544; 1991, “Heat and Mass Transfer in Pressure-Gradient Boundary Layers,” Int. J. Heat Mass Transfer, 34, pp. 2837–2857) shows that the current theory yields a higher accuracy. The error in the mean temperature profile is within 5% when the present theory is compared to the experimental data. Meanwhile, the Stanton number is calculated using the energy and momentum integral equations and the newly proposed composite temperature profile. The calculated Stanton number is consistent with previous experimental results and the DNS data, and the error of the present prediction is less than 5%. In addition, the growth of the thermal boundary layer is obtained from the theory and the average error is less than 5% for the range of Reynolds numbers between 5×105 and 5×106 when compared with the empirical correlation for the experimental data of isothermal boundary layer conditions.

Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

2005 ◽  
Vol 127 (2) ◽  
pp. 194-198 ◽  
Author(s):  
Rau´l Bayoa´n Cal, ◽  
Xia Wang, ◽  
Luciano Castillo
Keyword(s):  
Pressure Gradient ◽  
Forced Convection ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
External Pressure ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
Outer Flow ◽  
The Mean ◽  
Blowing Parameter

The problem of forced convection transpired turbulent boundary layers with external pressure gradient has been studied by using different scalings proposed by various researchers. Three major results were obtained: First, for adverse pressure gradient boundary layers with suction, the mean deficit profiles collapse with the free stream velocity, U∞, but into different curves depending on the strength of the blowing parameter and the upstream conditions. Second, the dependencies on the blowing parameter, the Reynolds number, and the strength of pressure gradient are removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits [Zagarola, M. V., and Smits, A. J., 1998, “Mean-Flow Scaling of Turbulent Pipe Flow,” J. Fluid Mech., 373, 33–79] scaling, U∞δ*/δ. Third, the temperature profiles collapse into a single curve using the new inner and outer scalings proposed by Wang and Castillo [Wang, X., and Castillo, L., 2003, “Asymptotic Solutions in Forced Convection Turbulent Boundary Layers,” J. Turbulence, 4(006)], which produce the true asymptotic profiles even at finite Pe´clet number.

Similarity Analysis for Nonequilibrium Turbulent Boundary Layers*

2004 ◽  
Vol 126 (5) ◽  
pp. 827-834 ◽  
Author(s):  
Luciano Castillo ◽  
Xia Wang
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Turbulent Boundary Layers ◽  
External Pressure ◽  
Navier Stokes ◽  
Similarity Analysis ◽  
Classical Paper ◽  
Nonequilibrium Flows

In his now classical paper on pressure gradient turbulent boundary layers, Clauser concluded that equilibrium flows were very special flows difficult to achieve experimentally and that few flows were actually in equilibrium [1]. However, using similarity analysis of the Navier–Stokes equations, Castillo and George [2] defined an equilibrium flow as one where the pressure parameter, Λ=[δ/ρU∞2dδ/dx]dP∞/dx, was a constant. They further showed that most flows were in equilibrium and the exceptions were nonequilibrium flows where Λ≠constant. Using the equations of motion and similarity analysis, it will be shown that even nonequilibrium flows, as those over airfoils or with sudden changes on the external pressure gradient, are in equilibrium state, but only locally. Moreover, in the case of airfoils where the external pressure gradient changes from favorable to zero then to adverse, three distinctive regions are identified. Each region is given by a constant value of Λθ, and each region remains in equilibrium with Λθ=constant, respectively.

The Asymptotic Temperature Profile for Forced Convection Turbulent Boundary Layers With and Without Pressure Gradient

2003 ◽  
Author(s):  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Forced Convection ◽  
Boundary Layers ◽  
Power Law ◽  
Equations Of Motion ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis ◽  
Temperature Profiles

Similarity analysis of the equations of motion is used in order to study forced convection turbulent boundary layers with and without pressure gradient. New scalings are found for both the inner and the outer temperature profiles, respectively. It is shown that by normalizing the temperature profiles using the new scalings, the effects from the Pe´clet number and pressure gradient can be removed completely from the profiles. Therefore, the asymptotic solutions can be obtained even at the finite Pe´clet number. Moreover, using the Near-Asymptotic principle, a power law solution is derived for the temperature profile in the overlap region. This power law solution is a consequence of the fact that the boundary layer depends on two different temperature scalings.

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

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.

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