圆柱形谐振管内非线性驻波的有限体积计算方法

Finite Volume Algorithm for Nonlinear Standing Waves in Cylindrical Acoustic Resonators

提出一种用于求解圆柱形谐振管内非线性驻波的有限体积计算方法。谐振管内初始为自由状态的流体被整体谐振激励,当激励频率与谐振管内声场固有频率一致时,谐振管内将产生非线性驻波。建立整体振动条件下谐振管内瞬态可压缩热粘性牛顿流体的一维Navier-Stokes模型方程的积分方程;在时域上,通过SIMPLEC方法(以压力为基础的有限体积法)和交错网格技术推导出离散化代数方程组,并进行求解。当谐振管内的流体为R-12气体,在整体振动的条件下,利用提出的方法对谐振管内的非线性驻波进行求解,通过与现有文献中伽辽金方法的计算结果进行对比,所得到的非线性驻波声压在波形和幅值方面都与这些结果非常吻合,从而验证了该方法的可行性。得到谐振管左端处的绝对压力波形、温度波形和声压频谱响应等物理特性分布;同时得到谐振管内不同位置处的速度变化,发现在谐振管两端出现了速度钉状波形;有限体积计算方法为解决强声密封的非线性驻波的数值计算奠定了良好基础。

A finite volume algorithm for solving nonlinear standing waves in cylindrical acoustic resonator is presented. The fluid is initially at rest and excited by the harmonic motion at the entire resonator, when excitation frequency is in accord with natural frequency of acoustic field in the resonator, nonlinear standing acoustic waves can be generated. The final discretized equations are built based on SIMPLEC scheme that is one pressure based finite volume method and a staggered grid manner in the time domain by integrating the one-dimensional Navier-Stokes model equations for an unsteady compressible thermoviscous Newtonian fluid. The cylindrical resonator excited by harmonic motion is filled＇with R-12. The nonlinear standing waves in resonators are solved with the finite volume algorithm. The numerical simulation results are excellent agreement with the Galerkin method. So the feasibility of this method is verified. The physical properties, including The absolute pressure wave, temperature wave and a frequency pressure spectrum et al, are displayed. Meanwhile, the velocity waves in the different positions in resonator are obtained. It is shown that the sharp velocity spikes appear at the two ends of the cylindrical resonator. The Numerical Algorithm will provide a solid foundation tbr solving nonlinear standing waves for the macrosonic seal.