An unsteady point vortex method for coupled fluid–solid problems
An unsteady point vortex method for coupled fluid–solid problems
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DOI：
10.1007/s00162-009-0096-7
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发表时间：
2009-05
影响因子：
3.4
通讯作者：
S. Michelin;Stefan G. Llewellyn Smith
中科院分区：
文献类型：
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作者：
S. Michelin;Stefan G. Llewellyn Smith
提出了一种研究一般尖边固体与周围无粘流二维耦合运动的方法。物体边缘涡量的形成是由点涡在每个拐角处的脱落来解释的，每个点涡的强度在每个时间步被调整，以满足生成拐角处流动的规律性条件。通过要求旋涡强度随时间单调变化，模型考虑了旋涡脱落的不可逆性。给出了这些点涡的运动方程(Brown-Michael方程)的线性动量守恒。作用在固体上的力和力矩被计算为固体速度以及涡旋的位置和强度的显式函数，从而将涡固耦合问题显式地表示为一组非线性常微分方程组。然后用这种方法研究了流体中初始静止的下落卡的例子。分析了侧向下落的稳定性，并证明了从两个板块边缘脱落的涡量使这一位置不稳定，这与实验研究和数值模拟相一致。流体运动的点涡降阶表示被用来理解这种失稳的物理根源。
A method is proposed for the study of the two-dimensional coupled motion of a general sharp-edged solid body and a surrounding inviscid flow. The formation of vorticity at the body’s edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices’ intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown–Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices’ position and intensity, thereby providing an explicit formulation of the vortex–solid coupled problem as a set of non-linear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadside-on fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reduced-order representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.