流体-结构相互作用下用微分求积法求弹性板上的动水压力场

Numerical simulation of hydrodynamic pressure on vibrating plates through differential quadrature method with fluid-structure interaction

采用微分求积法(DQ)在流体-结构相互作用(FSI)框架下求解原变量形式的Navier-Stokes(N-S)方程和板的弯曲振动方程,获取作用在弹性板上的动水压力场。分析对象是4块矩形板组成的箱型流道,其中两块为弹性薄板,另外两块为刚性板。为比较FSI对动水压力场的影响,数值结果给出了1.5 m×0.5 m×0.2 m流道、来流雷诺数分别为7 000和10 000、相应DQ网格为25×25×25和29×29×29考虑FSI与否的压力分布。数值计算结果表明,所建立的考虑FSI的DQ法数值求解原变量形式N-S方程和弹性板振动方程,获取弹性板上的动水压力场是可行的,FSI效应对动水压力场的影响是明显的。

The differential quadrature （DQ） method is firstly applied to solve three-dimensional incompressible Navier-Stokes equations in primitive variable form with the fluid-structure interaction （FSI）. The flow passage used in the present paper consists of four rectangular plates, two of which are elastic and others rigid, and the elastic plates are vibrating while the fluid are flowing. To compare the influences of FSI on the pressure fields, the size of the flow passage is designated to 1.5 m × 0.5 m × 0.2 m as a working example. The DQ mesh sizes of 25 × 25 × 25 and 29 × 29 × 29 were used for Reynolds numbers of 7000 and 10 000, with and without FSI, respectively. The numerical results show that the developed DQ method with FSI is a suitable tool to analyze hydrodynamic pressure on a vibrating plate, and the effects of FSI on the flow fields are significant.