上昇気泡からの高シュミット数条件下における物質輸送の数値解析手法の開発

Abstract

Under a high Schmidt number condition, concentration boundary layers get much thinner than momentum boundary layers. Resolution requirement to numerically capture the steep concentration gradient near an interface is therefore significantly high. This article presents a novel VOF-based method to predict mass transfer from gas-liquid interfaces using a computational grid of a marginal resolution required for the solution of the Navier-Stokes equation. The solution procedure to the mass conservation equation is divided into two steps: the dissolution and diffusion step and the advection step. The concentration profiles near gas-liquid interfaces, which are identified as segments (in case of two-dimensional computations) in each computational cell, are reconstructed in terms of the complementary error function by virtue of the boundary layer approximation to the solution of the unsteady advection-diffusion equation of mass. The amount of dissolution from the interfaces and diffusion in the vicinity of the interfaces is obtained by taking advantage of the reconstructed concentration profile on each interface segment. In the advection step, the un-smoothness of concentration profiles in the interface cells is explicitly taken into consideration by taking full advantage of a VOF advection scheme. The present method is validated in two-dimensional test problems with the Schmidt number of 100 which cover a pure diffusion problem and a mass transfer problem from a freely rising buoyant bubble. The validation shows the present method is capable of resolving a concentration boundary layer which is as thin as a computational cell. The reduction rate in the overall computational cost is O(10-3) compared to one of the conventional methods (Ezu et al., 2011) without the subgrid-scale resolution.