Multi-scaling analysis of turbulent boundary layers over an isothermally heated flat plate with zero pressure gradient

Abstract

A meticulous investigation into turbulent boundary layers over an isothermally heated flat plate with zero pressure gradient has been conducted. Eight distinct turbulence models, including algebraic yPlus, standard k-ω, standard k-ε, length-velocity, Spalart-Allmaras, low Reynolds number k-ε, shear stress transport, and v2-f turbulence models, are carefully chosen for numerical simulation alongside thermal energy and Reynolds-Averaged Navier-Stokes equations. A comparative analysis has determined that the Spalart-Allmaras model exhibits remarkable agreement with the results from direct numerical simulation, making it a reliable tool for predicting turbulent heat transfer and fluid flow, particularly at higher Prandtl and Reynolds numbers. Subsequently, a multi-scale investigation employs a comprehensive four-layer structure scheme and encompasses various momentum thickness Reynolds numbers of 1432, 2522, and 4000, and Prandtl numbers of 0.71, 2, and 5. The subsequent investigation reveals the governing non-dimensional numbers' substantial impact on the distribution and magnitude of mean thermal and flow characteristics. Notably, the scaling of mean thermal and momentum fields discloses the existence of a meso or intermediate layer characterized by a logarithmic nature unique to itself. The multi-scaling analysis of the flow field demonstrates greater conformity with the selected scaling variables primarily relying on the Reynolds number. Furthermore, the scaling of the energy field yields compelling outcomes within the inner and intermediate layers. However, according to the four-layer theory, minor discrepancies are observed in the outer layer when using the current scaling.

Keywords

• Turbulent boundary layers
• RANS models
• Multi-scale analysis
• Zero pressure gradient
• Reynolds shear stress
• Meso scaling