Multi-scale analysis of turbulent thermal boundary layer with zero pressure gradient

Abstract

In the present study, a numerical approach using finite element method has been employed to investigate fully developed turbulent flow and forced convection heat transfer over an isothermally heated horizontal flat plate. Seven different turbulence models, namely low Re k-ε, shear stress transport (SST), Spalart-Allmaras, standard k- ε, k- ε, Length VELocity (L-VEL), and Algebraic yPlus are selected along with Reynolds Averaged Navier-Stokes (RANS) and thermal energy equations for numerical simulation. The numerical results are compared with direct numerical simulation (DNS) and experimental data for different momentum thickness Reynolds numbers, Reθ = 400, 1500, 2154, and 2239 and Prandtl number, Pr = 0.71. From the comparative study, it is found that Spalart-Allmaras model has good agreement with both DNS and experimental results and can be used to predict mean turbulent flow and heat transfer characteristics for higher Reynolds and Prandtl numbers within reasonable accuracy. At first, the influence of different Reynolds and Prandtl numbers on the mean properties of the turbulent thermal boundary layer is studied. It is observed that both the magnitude and the distribution of these mean properties are strongly influenced by the variation of the governing nondimensional numbers under traditional inner and outer normalizations. Prandtl number effects are more prominent in the thermal field than the Reynolds number and Reynolds number has more dominance over the momentum field than the Prandtl number. The visualizations of these effects are also presented. Both local and average Nusselt number correlations have been developed for 5×105 ≤ ReL ≤ 1.3×106 and Pr = 0.71, 2, 3, 4, and 5. The new correlations show maximum ±15% deviations when compared with existing correlations which are based on a large range of 5×105 ≤ ReL ≤ 1.3×108 and 0.6 ≤ Pr ≤ 60. A multi-scale analysis of the turbulent thermal boundary layer with zero pressure gradient over an isothermal flat plate has been carried out considering both the four vii layer structure scheme and the asymptotic matched expansion theory. The study is performed for various Reθ = 400, 1432, 2154, 2239, 2522 and 3332 and Pr = 0.71, 2, 3, 4, 5. Scaling of both the mean momentum and thermal field reveal the existence of an intermediate or mesolayer with its own characteristics logarithmic nature. The multi-scaling of the flow field exhibits more agreement to the considered scaling variables as it explicitly depends on only Reynolds number. The energy field scaling shows convincing results in the inner layer, intermediate layer and with little discrepancies in the outer layer for the present scaling variables. The inner and outer scaling of both flow and thermal field shows similar results for both theories. The intermediate layer scaling properties