Abstract
Turbulent forced convection in a channel with one planar wall and one wall of sinusoidal shape is investigated by Direct Numerical Simulation. The flow is fully developed and the Reynolds number based on the mean bulk velocity and the average hydraulic diameter is Re ≈ 18,900; in this weakly turbulent flow regime three different Prandtl number values are investigated, Pr = 0.025, 0.20, 0.71. The fluid is in contact with the colder channel walls at an equal, uniform temperature. The main statistical quantities, like the root-mean-square of temperature fluctuations and the turbulent heat fluxes, the local heat transfer coefficient and turbulent Prandtl number values are reported. Effects of flow separation and reattachment on the local heat transfer rate and turbulent Prandtl number distribution are also presented and discussed.An a priori analysis of the behavior of the simple gradient diffusion model of turbulent heat fluxes is performed in the low Prandtl number, separated flow conditions of the present work. While the low Prandtl number effect can be accounted for by an appropriate selection of the turbulent Prandtl number value to be provided to the model, deviations form the expected behavior of turbulent heat fluxes are seen to occur in the flow separation region and downstream reattachment.
Highlights
5 Results5.2.1 Heat transfer effectiveness at different Prandtl numbers 20
Studies dealing with the turbulent convection of heat at low Prandtl number consider in most cases the flat channel configuration
The authors observe that the effect of Re on the turbulent Prandtl number is stronger at low Pr
Summary
Nu f Nusselt Number for a flat channel Nul local Nusselt number, calculated using Eq (14) at the lower wall. Nuu Nuu P local Nusselt number, calculated using Eq (14) at the upper wall space averaged Nusselt number at the upper wall pressure field p periodic part of the pressure field. Qs time-averaged volume flow rate per unit spanwise width Pe Peclet number Pe = RePr. Peτ friction Peclet number, Peτ = Reτ Pr Re∗ total drag Reynolds number Re∗ = u∗δ/ν. Greek letters α thermal diffusion coefficient αt turbulent diffusivity β pressure drop assigned along x δ half the average channel height δ = Hav/2 η wall-normal coordinate λ wavelength ΛL space and time-averaged temperature decay rate along the axial direction ν kinematic viscosity νt turbulent viscosity ρ density τ shear stress θ dimensionless, normalized temperature, see equation (7)
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