非定常分离流动的Lagrange方法数值模拟

Numerical Simulation of Unsteady Flow Separation Using Lagrange Method

本文对Ｌａｇｒａｎｇｅ坐标系下的边界层方程进行了数值模拟。研究了静止流场中的线涡诱导的非定常边界层流动。数值结果表明，随着边界层接近分离，确实出现了有限时间奇性。流动在驻定点附近很窄的区域内堆积，并在垂直壁面方向迅速增长，形成一脉冲似的突跃。基于此现象讨论了非定常分离的性质和三种分离模式。采用Ｌａｇｒａｎｇｅ方法能很好地说明有限时间奇性，便干精确地给出分离的定义和判据，而且物理常清楚。Ｌａｇｒａｎｇｅ方法有着明显的解析和计算上的优点。

The unsteady boundary layer due to a rectilinear vortexabove a plane wall in a stagnant fluid are considered using the classicalboundary layer equations in Lagrange coordinates.The calculated re-sults show that as thc boundary-layer flow evolves toward eruption,the spon-taneous generation of a finite time singularity does indeed occur, and theflow focuses into a narrow band near the stationary point in the stream-wise direction,but which grows explosively in the direction normal tothe wall.This developing spike is formed.On the basis of this phenom-enon,we discusscd three kinds of the physical picture of unsteady separa-tion. It is clear that the Lagrangce method is best suited to show thesingularity developed at finite time. It convenient to determine the un-steady separation definitely and to provide a clear and unambiguous cri-terion for the evolution of the separation point physical implication ofthem is very clear.The Lagrange method may have significant analytialand computational advantages.