Scaling Relation of the Scalar Diffusion in a Rotating Mixer

doi:10.1007/s12204-021-2275-7

Abstract

Abstract: Scalar mixing is under the joint control of convection and diffusion. The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number. In the high Schmidt number limit, the scalar scale is much smaller than that of the momentum, which then requires either special treatment or ad hoc models for the scalar quantity in numerical simulations. In order to avoid model uncertainty or unnecessary numerical complexity, the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank. It has been found that in the range of negligible numerical diffusivity,the characteristic scalar mixing time is inversely proportional to the scalar diffusivity. Analysis based on the dimensional argument justifies such scaling relation as well, from which the unaccepted computational time of the mixing process in the high Schmidt number limit can be efficiently determined, without the use of ad hoc models. This scaling idea is also of practical meaningfulness for other similar problems.

Key words: scalar diffusion| Schmidt number| scaling relation| rotating mixer

摘要： Scalar mixing is under the joint control of convection and diffusion. The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number. In the high Schmidt number limit, the scalar scale is much smaller than that of the momentum, which then requires either special treatment or ad hoc models for the scalar quantity in numerical simulations. In order to avoid model uncertainty or unnecessary numerical complexity, the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank. It has been found that in the range of negligible numerical diffusivity,the characteristic scalar mixing time is inversely proportional to the scalar diffusivity. Analysis based on the dimensional argument justifies such scaling relation as well, from which the unaccepted computational time of the mixing process in the high Schmidt number limit can be efficiently determined, without the use of ad hoc models. This scaling idea is also of practical meaningfulness for other similar problems.

关键词: scalar diffusion| Schmidt number| scaling relation| rotating mixer

CLC Number:

O 35

SUN Na (孙娜), WANG Lipo (王利坡), LI Yuanbo (李渊博), LI Lin (李琳), QI Shuaipeng (齐帅鹏), SHEN Yongxing (沈泳星). Scaling Relation of the Scalar Diffusion in a Rotating Mixer[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(2): 170-175.

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