Formulation and validation of boundary conditions at a branched junction for nonlinear waves
Formulation and validation of boundary conditions at a branched junction for nonlinear waves
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非线性波分支结点边界条件的制定和验证
DOI：
10.1016/j.jsv.2005.11.023
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发表时间：
2006
影响因子：
4.7
通讯作者：
Duck
中科院分区：
文献类型：
--
作者：
K. Chae;Kyungtae Lee;C. Hwang;Duck
建立了输气管道系统中非线性波通过分叉点的数值计算模型。在一维时域波动动力学分析中，非线性波的行为由管道系统中连接处的准稳态边界条件决定。通过结的准定常处理产生一个非线性平衡方程组。非线性方程组的迭代求解过程会产生发散和多解问题。为了克服这些困难，在不牺牲精度的情况下，建立了一组新的准线性平衡方程。本模型，因此，需要一个非迭代的解决方案的过程，导致在一个独特的解决方案和较小的计算工作量。在每个管道处使用Thompson边界条件。基于Thompson边界条件，给出了一种新的时间导数形式的平衡方程，并给出了一组线性代数方程。当实现新的时间导数形式的平衡方程时，数值上增加了校正项。本数值模型的实施和测试的非线性波的行为在一个分支管和亥姆霍兹共振器的声衰减的计算和预测的内燃机的辐射孔噪声的计算。计算结果表明，与以往的迭代计算和测量数据吻合良好。
A numerical model is presented for the calculation of nonlinear waves through the branched junctions in a gas transmission pipe system. In the one-dimensional time domain analysis of the wave dynamics, the behaviour of the nonlinear waves is determined by quasi-steady boundary conditions at junctions in a pipe system. The quasi-steady treatment through the junction yields a system of nonlinear balance equations. The iterative solution procedure of the system of nonlinear equations causes the problems of divergence and multiple solutions. In order to overcome the difficulties, a new set of quasi-linear balance equations is formulated without a sacrifice of accuracy. The present model, therefore, requires a non-iterative solution procedure that results in a unique solution and a smaller computational effort. Thompson's boundary condition is used at each pipe. A new time-derivative form of balance equations, based Thompson’ boundary condition, gives a set of linear algebraic equations for the balance equations. When implementing the new time-derivative form of the balance equations, corrected terms are added numerically. The present numerical model is implemented and tested for the calculation of behaviour of nonlinear waves in a branched pipe and the calculation of sound attenuation of a Helmholtz resonator and the prediction of radiated orifice noise of an internal combustion engine. Calculation results show good agreements with previous iterative calculations and measurement data.