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该文对二维不可压缩无黏流场中多个圆柱体之间的水动力相互作用问题进行了理论研究。提出了用一个构造方法求解一类平面多圆外Neumann问题,这是一类复平面上的Riemann-Hilbert边值问题。此方法需要先采用连续补函数方法,并结合新的“广义循环排序”方法依次满足物体上的边界条件,从而得出含有N个二维运动圆柱体的流场复势,此复势可以表示为幂级数形式的N个奇点之和,并用此可得到这N个圆柱体的附加质量,然后根据Hamilton系统的变分原理得出了这N个圆柱体运动的矢量动力学方程。研究表明:N个物体局部能量的平衡性和全息性;该系统中N个物体的加速度是耦合的,不能单独确定,且耦合系数是附加质量。此研究结果证明了能量型Lagrange框架和动量型框架的等价性,同时也显示出附加质量在流固Hamilton系统中的重要性。
In this paper, the hydrodynamic interaction between two cylinders in a two-dimensional incompressible non-stick flow field is theoretically studied. A construction method is proposed to solve a class of planar multi-circular Neumann problems, which is a kind of Riemann-Hilbert boundary value problem on the complex plane. In this method, we first need to use the continuous complement function method and combine the new “generalized cyclic ordering ” method to satisfy the boundary conditions on the object one by one so as to obtain the complex potential of the flow field containing N two-dimensional moving cylinders Can be expressed as the sum of N singular points in the form of power series, and can be used to obtain the additional mass of these N cylinders. Then based on the Hamilton system variational principle, the vector dynamics equations of the N cylinders are derived . The results show that the local energy of N objects is balanced and holographic. The acceleration of N objects in this system is coupled and can not be determined separately, and the coupling coefficient is additional mass. The result of this study proves the equivalence of the energy Lagrangian framework and the momentum framework, and also shows the importance of the additional mass in the fluid-solid Hamiltonian system.