Numerical study of thermally developing turbulent internal flows

Abstract

The effect of fluid Prandtl number on the thermal characteristics of the flow at the thermal-entry region of a hydrodynamically fully developed turbulent channel flow at a friction Reynolds number of Reτ=180 is investigated using direct numerical simulation. Four test cases with molecular Prandtl numbers of Pr = 0.71, 1, 3, 7 are considered. The numerical results confirm that in contrast to laminar flows, where the thermal entry length increases with the increase of the Prandtl number, for turbulent flows the increase of the Prandtl number accelerates the thermal development of the flow toward its asymptotic fully developed state. The variations of the Nusselt number, and the mean and rms temperature profiles are reported in the streamwise direction. It is shown that at highest Prandtl number considered in this study (Pr =7 ), while the mean temperature profile in the logarithmic region is still developing, the temperature profile in the conductive sublayer and the Nusselt number approach their fully developed values, confirming the dependence of the Nusselt number of turbulent flows to the development of the conductive sublayer. The development of the rms temperature profiles in the streamwise direction is also shown to be a good indicator for the flow reaching its thermally fully developed condition. The temperature-velocity correlations, temperature variance budgets, and contours of temperature are also reported at different streamwise locations for different Prandtl numbers.