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为了扩展谐振管内非线性驻波在工程中的应用, 以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题. 根据变截面的非稳态可压缩热黏性流体Navier-Stokes方程和空间守恒方程, 并基于求解压力速度耦合方程的半隐式算法和交错网格技术, 构建一种能够计算任意形状轴对称谐振管受活塞驱动时内部非线性驻波的有限体积算法. 分别对圆柱形、指数形和圆锥形谐振管内的非线性驻波进行仿真计算. 通过与现有试验结果以及数值仿真结果的对比, 验证了该方法的正确性.并获得除驻波声压之外的另外一些新的物理结果, 包括速度、密度、温度的瞬时变化.在直圆柱形谐振管内产生冲击声压波, 速度波形中出现钉状结构.而在指数形和圆锥形谐振管内产生高声压幅值的驻波, 没有出现冲击波, 速度波形中均未发现钉状结构. 计算结果表明谐振管内非线性驻波的物理属性与谐振管形状之间有密切关系.In order to expand the engineering application area of nonlinear standing waves in acoustic resonators, a new numerical algorithm is proposed for simulating nonlinear standing waves in resonators. It also can be used to overcome the shortages of the existing numerical methods, which restrict the solution to the nonlinear standing waves in cylindrical resonators and exponential resonators. The numerical algorithm is constructed based on the Navier-Stokes equations in the resonators with variable cross-section for an unsteady compressible thermoviscous fluid without truncation, and the space conservation law. The numerical algorithm-finite volume method for solving the nonlinear standing waves in acoustic resonators by piston driving is built based on the semi-implicit method for pressure-linked equations-consistent algorithm and staggered grid technique. Simulations for solving the nonlinear standing waves in cylindrical resonators, exponential resonators and conical resonators are carried out. By comparison with the existing experimental results and numerical simulation results, the accuracy of the developed finite volume algorithm is verified. Some new physical results are obtained, including unsteady velocity, density and temperature. The shock-like pressure wave shapes are found in cylindrical resonators, simultaneously, and the results show that the sharp velocity spikes appear in the cylindrical resonators. High amplitude acoustic pressures are generated in exponential resonators and conical resonators. Shock-like pressure waves and the sharp velocity spikes are not found. The strong dependence of the physical properties of nonlinear standing waves on resonator shape is demonstrated through the simulative results.
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Keywords:
- pistons /
- resonators /
- nonlinear standing waves /
- finite volume method
[1] Nguyen N T, Huang X Y, Chuan T K 2002 J. Fluids Eng. 124 384
[2] Wang S S, Jiao Z J, Huang X Y, Yang C, Nguyen N T 2009 Microfluid. and Nanofluid. 6 847
[3] Coppens A B, Sanders J V 1968 J. Acoust. Soc. Am. 43 516
[4] Keck W, Beyer R T 1960 Phys. Fluids. 3 346
[5] Saenger R A, Hudson G E 1960 J. Acoust. Soc. Am. 32 961
[6] Van Buren A L 1975 J. Sound Vibration 42 273
[7] Yano T 1999 J. Acoust. Soc. Am. 106 L7
[8] Vanhille C, Campos-Pozuelo C 2001 J. Acoust. Soc. Am. 109 2660
[9] Lawrenson C C, Lipkens B, Lucas T S, Perkins D K, Van Doren T W 1998 J. Acoust. Soc. Am. 104 623
[10] Ilinskii Y A, Lipkens B, Lucas T S, Van Doren T W, Zabolotskaya E A 1998 J. Acoust. Soc. Am. 104 2664
[11] Luo C, Huang X Y, Nguyen N T 2007 J. Acoust. Soc. Am. 121 2515
[12] Patankar S V 1980 Numerical heat transfer and fluid flow (New York: McGraw-Hill) p90-92.
[13] Erickon R R, Zinn B T 2003 J. Acoust. Soc. Am. 113 1863
[14] Chun Y D, Kim Y H 2000 J. Acoust. Soc. Am. 108 2765
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[1] Nguyen N T, Huang X Y, Chuan T K 2002 J. Fluids Eng. 124 384
[2] Wang S S, Jiao Z J, Huang X Y, Yang C, Nguyen N T 2009 Microfluid. and Nanofluid. 6 847
[3] Coppens A B, Sanders J V 1968 J. Acoust. Soc. Am. 43 516
[4] Keck W, Beyer R T 1960 Phys. Fluids. 3 346
[5] Saenger R A, Hudson G E 1960 J. Acoust. Soc. Am. 32 961
[6] Van Buren A L 1975 J. Sound Vibration 42 273
[7] Yano T 1999 J. Acoust. Soc. Am. 106 L7
[8] Vanhille C, Campos-Pozuelo C 2001 J. Acoust. Soc. Am. 109 2660
[9] Lawrenson C C, Lipkens B, Lucas T S, Perkins D K, Van Doren T W 1998 J. Acoust. Soc. Am. 104 623
[10] Ilinskii Y A, Lipkens B, Lucas T S, Van Doren T W, Zabolotskaya E A 1998 J. Acoust. Soc. Am. 104 2664
[11] Luo C, Huang X Y, Nguyen N T 2007 J. Acoust. Soc. Am. 121 2515
[12] Patankar S V 1980 Numerical heat transfer and fluid flow (New York: McGraw-Hill) p90-92.
[13] Erickon R R, Zinn B T 2003 J. Acoust. Soc. Am. 113 1863
[14] Chun Y D, Kim Y H 2000 J. Acoust. Soc. Am. 108 2765
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