Comparison of Transitional Turbulence Models for Numerical Simulation of Flow Past a Sphere in a Pipe

Abstract

Abstract To develop a novel passive valve with a spherical disc for reactors, it is necessary to find a suitable numerical model to study the flow characteristics of flow past a sphere in confined spaces. The problem of flow past a sphere arises in many fields, and the phenomenon of drag crisis of a sphere in external flow, in which the drag coefficient of the sphere drops off suddenly as the Reynolds number increases, still occurs in internal flows. With the rapid development of transitional turbulence models in the past decade, we try to improve the drag coefficient prediction of flow past a sphere in a pipe with a wide range of Reynolds numbers using transitional turbulence models. In this study, we numerically investigated the flow past a sphere in a pipe with a blockage ratio (the ratio of sphere diameter to pipe diameter) of 0.667 with three transitional turbulence models. The SST k-ω turbulence model without transition effects was also employed for comparison purposes. The studied Reynolds numbers ranged from subcritical region to supercritical region (5E+3 ⩽ Re ⩽ 3E+5). The skin friction coefficients and pressure coefficients of the sphere were calculated and compared for the four turbulence models. Compared to the measured drag coefficient data of a sphere in a pipe with a similar blockage ratio in the literature, the Intermittency transition model performs best in predicting the drag coefficient than the other turbulence models. None of the four turbulence models can adequately capture the drag crisis phenomenon, i.e., the calculated drag coefficients drop smoothly near the critical region of Reynolds numbers for all four turbulence models. The pipe wall effect is not neglectable in the estimation of the sphere drag coefficient by the pressure drop between the ends of the pipe.