Scale law analysis of the curved boundary layer evolving around a horizontal cylinder at Pr > 1

Abstract

The convective boundary layer flow on the external surface of an isothermally heated horizontal cylinder is investigated in this study. Numerical simulations are first carried out for a wide range of flow parameters, i.e., Rayleigh and Prandtl numbers, and scale relations quantifying the boundary layer flow are then determined from the simulation data. The numerical results suggest that the curved boundary layer experiences an initial growth state, a transitional state, and a developed state, which are essentially identical to the extensively studied flat boundary layers. Scale relations quantifying the local flow variables are obtained, and the proposed scale laws indicate that during the initial growth, the present curved boundary layer flow follows a two-dimensional growth rather than the well-known one-dimensional startup of flat boundary layers. It is further demonstrated that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, however, the maximum streamwise velocity of the boundary layer shifts to approximately 7π/9 and the thickness consistently increases with the circumferential location. It is also shown that the thickness of the inner viscous boundary layer could be obtained by properly considering the Prandtl number effect, i.e., by the term (1 + Pr−1/2)−1. The proposed scale relations could reasonably describe the curved boundary layer flow, and all regression constants are above 0.99.