圆柱形谐振管内非线性驻波的有限体积计算方法.pdf

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第48卷第16期
机槭工程学报
Vol 48 No 16
2012年8月
JOURNAL OF MECHANICAL ENGINEERING
A
2012
DOI:10390/JME.2012.16.116
员柱形谐振管内非线性驻波的有限体积计算方法
宁方立张文治董梁
(西北工业大学机电学院西安710072)
摘要: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。诸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 SIMIPLEC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
皆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対压力波形、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寞定了良好基础。
关键词:谐振管非线性驻波有限体积法强声密封
中图分类号:TH1130429
Finite Volume Algorithm for Nonlinear Standing Waves in Cylindrical
Acoustic Resonators
NING Fangli ZHANG Wenzhi DONG Liang
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072
Abstract: A finite olume al o m for solving nonlinear standin waves n cylindical acoustic resonator is presented. The fluid i
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 for
solving nonlinear standing waves for the macrosonic seal
Key words: Resonator Nonlinear standing wave Finite volume algorithm Macrosonic seal
动力学方程对谐振管内的速度势建立了一个一维模
型方程,并用有限傅里叶级数表示该速度势,获得
了描述诺振管外加激振力幅值与谐振管内声场固有
近些年,国内外学者对谐振管内非线性驻波的频率之问关系的软特性与硬特性,并揭示了软使特
数值仿真方法进行了研究。 ILINSKI等通过气体性与谐振管形状的关系。与 LAWRENSONL的试验
研究相对比,LI等刚通过数值优化方法将谐振管内
国家自然科学基金(51075329)、因家留学基金委青年骨干教师出国研
修、西北工业大学基础研究基金(NPU-FR-JC200932)和西北工业大学
压比提高了240%。 ERICKSON等对于同样的模
研究生创业种子基金(22011077资助项月。20120208收到初稿,
型方程,利用伽辽金方法对一维谐振管内的非线性
20120622收到修改稿