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| The symmetries and invariant solutions for laminar boundary layer of disc centrifuge |
| Received:February 10, 2021 Revised:April 25, 2021 |
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| DOI：10.7511/jslx20210210001 |
| KeyWord:disc centrifuge laminar boundary layer symmetries Invariant solution thickness |
| Author | Institution |
| 郑明亮 |
无锡太湖学院 机电学院, 无锡 |
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| Abstract: |
| In order to use the boundary layer theory to design the disc profile of a disc centrifuge firstly,the solid-liquid two-phase interface flow in the shallow layer of the disc centrifuge is considered,in this paper,and the two-dimensional laminar boundary layer equations of oblique narrow flow in disc gap are obtained from the basic N-S equations of hydrodynamics.Secondly,by using the Lie group analytical method,the admissible infinitesimal symmetries and invariant solutions of the partial differential equations are derived.More importantly,their analytical expressions and properties are discussed in detail.It is found that the thickness of the laminar boundary layer is closely related to the structure of the disc and the physical properties of the fluid,such as the disc size,disc spacing,the rotating speed and the viscosity coefficient.The content of this paper provides an effective way for the accurate analytical solution of boundary layers considering the boundary and initial conditions,and also provides a verification for various numerical algorithms of boundary layer separation control models. |
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