Conditionally Sampled Turbulent Prandtl Number in the Outer Region of a Turbulent Boundary Layer

1996 ◽  
Vol 118 (2) ◽  
pp. 480-482 ◽  
Author(s):  
D. E. Wroblewski
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Outer Region ◽  
Turbulent Prandtl Number

Effect of small roughness elements on thermal statistics of a turbulent boundary layer at moderate Reynolds number

2015 ◽  
Vol 787 ◽  
pp. 84-115 ◽  
Author(s):  
Ali Doosttalab ◽  
Guillermo Araya ◽  
Jensen Newman ◽  
Ronald J. Adrian ◽  
Kenneth Jansen ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Rough Surface ◽  
Surface Flow ◽  
Unit Mass ◽  
Turbulent Prandtl Number ◽  
Reynolds Analogy ◽  
Moderate Reynolds Number

A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with$k^{+}\approx 11$and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number$Pr=0.71$is simulated. The dynamic multiscale approach developed by Arayaet al.(J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for$y^{+}<9$. In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region the Reynolds analogy is only approximately valid, with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth-wall case, the turbulent transport of heat per unit mass,$\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$, towards the wall is enhanced in the buffer layer, but the transport of$\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass,$\overline{v^{\prime }u^{\prime }v^{\prime }}$. Above the roughness sublayer (3$k$–5$k$) it is found that most of the temperature field statistics, including higher-order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend’s Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and$k^{+}$considered in this study.

Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer

1981 ◽  
Vol 103 (1) ◽  
pp. 153-158 ◽  
Author(s):  
H. W. Coleman ◽  
R. J. Moffat ◽  
W. M. Kays
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Turbulent Heat Flux ◽  
Test Surface ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number

Heat transfer behavior of a fully rough turbulent boundary layer subjected to favorable pressure gradients was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Stanton numbers and profiles of mean temperature, turbulent Prandtl number, and turbulent heat flux are reported. Three equilibrium acceleration cases (one with blowing) and one non-equilibrium acceleration case were studied. For each acceleration case of this study, Stanton number increased over zero pressure gradient values at the same position or enthalpy thickness. Turbulent Prandtl number was found to be approximately constant at 0.7–0.8 across the layer, and profiles of the non-dimensional turbulent heat flux showed close agreement with those previously reported for both smooth and rough wall zero pressure gradient layers.

Determination of the turbulent Prandtl number in an asymptotic boundary layer with suction

1981 ◽  
Vol 16 (1) ◽  
pp. 57-61
Author(s):  
M. A. Gol'dshtik ◽  
S. S. Kutateladze ◽  
A. M. Lifshits
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Turbulent Prandtl Number ◽  
Asymptotic Boundary
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