碟式离心机层流边界层方程的对称性和不变解

为运用边界层理论进行碟式离心机的碟片型线设计,首先对于碟式离心机内部多个碟片浅层固液两相界面流动模型,从流体力学基本的N-S方程组出发,得出碟片间隙斜窄流二维层流边界层方程;其次,采用李群演绎算法,推导出系统偏微分方程组允许的无穷小对称和不变解,更重要的是给出了其详细的解析表达式和有关性质。结果发现,碟式离心机层流边界层厚度与碟片结构(如碟片尺寸和间距、转速)以及流体物性(如液相粘性系数)密切相关。本文研究为考虑边界和初始条件的流场边界层精确解析解提供了有效途径,也为边界层分离控制模型的各种数值算法提供了验证。

The symmetries and invariant solutions for laminar boundary layer of disc centrifuge

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.