谐振管内非线性驻波的二维有限差分计算方法

Two-dimensional Finite Difference Algorithm for Simulating Nonlinear Standing Waves in Resonators

谐振管内非线性驻波的数值计算方法是目前强声密封研究的关键技术。基于三个气体动力学方程推导得出一个关于无旋可压缩牛顿流体的非线性波动方程,并通过对非线性波动方程进行有限差分离散化处理,提出求解谐振管内非线性驻波的二维有限差分计算方法。通过边界条件的处理,使所推导的二维有限差分计算方法能够在整体谐振激励作用下计算谐振管内非线性驻波。在圆柱形谐振管内部填充Refrigerant-12作为工作媒质以及整体谐振激励的条件下,利用所提出的二维有限差分计算方法对圆柱形谐振管内的非线性驻波进行求解,并得到圆柱形谐振管内绝对压力波形、声压频谱响应以及谐振管内的声压空间分布。通过与现有仿真方法的计算结果和现有试验结果进行对比,所得到的计算结果无论从波形还是数值上都能与这些结果吻合,从而验证了该方法的可行性。该方法为强声密封的非线性驻波计算研究奠定了良好基础。

The research of the nonlinear standing waves in resonators is a key technology for the macrosonic seal which is being studied.A nonlinear wave equation for irrotational and compressible Newtonian fluid is carried out from three gasdynamic equations.Based on the discretized nonlinear wave equation,a two-dimensional finite difference algorithm for simulating nonlinear standing waves in resonators is proposed.Based on the process of boundary conditions of the resonators,the proposed two-dimensional finite difference algorithm can be employed to simulate the nonlinear standing waves in resonators.When the cylindrical resonator filled with Refrigerant-12 as working fluid is excited by harmonic motion,the nonlinear standing wave is solved with the finite difference algorithm.Then the absolute pressure wave and a frequency spectrum for the acoustic pressure are obtained.The space distribution of acoustic pressure in the cylindrical resonator is also displayed.The numerical simulation results are in excellent agreement with the other simulation solutions and experiment.So the feasibility of this method is verified.The two-dimensional finite difference algorithm is a solid foundation for the macrosonic seal.