Numerical investigation of different modes of internal circulation in spherical drops: Fluid dynamics and mass/heat transfer

Abstract The results of detailed, three-dimensional numerical simulations of fixed spherical drops in a uniform flow are presented. The fluid dynamics outside and inside of the drops as well as the internal problem of mass (or heat) transfer are studied. Liquid drops in both a liquid and a gaseous ambient phase are considered. Special emphasis is put on the investigation of different modes of internal circulation. At low Reynolds numbers of the inner fluid, the flow field inside the drop resembles the well known Hill’s vortex solution. However, at higher internal Reynolds numbers, stable steady or quasi-steady alternative modes of internal circulation are found. As these modes are not cylindrical symmetric around the streamwise axis, the often applied assumption of a two-dimensional, axisymmetric flow field is not justified in these cases. Thus, major discrepancies to previous numerical studies are obtained. However, it is shown that experimental results support our findings. For liquid drops surrounded by a liquid, a major influence of the state of internal circulation on the drag is discovered, whereas the drag is nearly unaltered in the case of a liquid drop in gas. Concerning the internal problem of mass/heat transfer, the various internal flow modes show different characteristics. At low internal Peclet numbers, higher Sherwood numbers are reached for the Hill’s vortex-like cases, whereas at higher Peclet numbers, the transfer is faster for the alternative modes. For cases with a Hill’s vortex-like solution, asymptotic Sherwood numbers for very high Peclet numbers of around 20 are found, whereas no upper limit for cases with alternative modes can be determined. In the present study a maximum internal Sherwood number of 130 is reached, more than six times the maximum value for a case with a Hill’s vortex-like internal solution.