Abstract
The sand-driven flow is studied from the continuum viewpoint in this paper. The crux of this work is how to model the stresses of the particle phase properly. By analysing the two-fluid model which usually works in solving gas-particle two-phase flow, we find that this model has many deficiencies for studying the sand-driven flow, even for the simplest case — the steady, two-dimensional fully-developed flow.
Considering this, we have proposed the three-fluid model in which the upward-particles and the downward-particles are regarded as two kinds of fluids respectively. It is shown that the three-fluid model is better than the two-fluid model in reflecting the internal structure of the flow region and the influence of the boundary situations on the flow, and it is advantageous to find an approximate solution in that the main components of the particle phase stresses can be explicitly expressed by those variables in the three-fluid model.
In the end, the governing equations as well as the boundary conditions for the three-fluid model are provided with a discussion.
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Communicated by Li Jiachun
Project supported by the National Natural Science Foundation of China
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Dayou, L., Fei, D. A three-fluid model of the sand-driven flow. Appl Math Mech 17, 647–657 (1996). https://doi.org/10.1007/BF00123108
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DOI: https://doi.org/10.1007/BF00123108