Sublayer-Stanton numbers of heat and matter for aerodynamically smooth surfaces: basic considerations and evaluation

Summary

Sublayer-Stanton numbers, B_i, of heat and matter for the interfacial sublayer over aerodynamically smooth surfaces determined for forced convective conditions by elementary and numerical integration are reviewed and evaluated. The results are based on Roth’s modified Heisenberg model for the spectral energy transfer in the equilibrium range under locally isotropic conditions and the approaches of Reichardt, Elser, Deissler, van Driest, Rannie, Sheppard, and Spalding for the normalized eddy diffusivity K_m/v. The results substantiate that with the exception of Sheppard’s K_m/v-approach all formulations are appropriate to provide sublayer-Stanton numbers with a sufficient degree of accuracy. From a theoretical point of view the K_m/v-relationships of Roth, Reichardt, van Driest, and Spalding are to be preferred, when a turbulent Prandtl number Pr_t = 1 is presumed.

Since within the framework of mesoscale meteorological modelling numerical integration techniques would consume too much CPU-time because of the large number of near-wall grid points, a parameterization formula for the sublayer-Stanton number is proposed and evaluated. Compared to the B_i ⁻¹-results obtained by numerical integration, this kind of parameterization leads to a relative error of less than 5 percent for roughness Reynolds numbers, η_r, ranging from 30 to 600.