Approximate mathematical models in high-speed hydrodynamics
Approximate mathematical models in high-speed hydrodynamics
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DOI：
10.1007/s10665-005-9026-x
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发表时间：
2006-07
影响因子：
1.3
通讯作者：
E. V. Paryshev
中科院分区：
文献类型：
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作者：
E. V. Paryshev
给出了高速流体动力学中某些问题的近似解，这些解是基于著名的方法，如空腔膨胀独立原理（Logvinovich）、固体轮廓浸入液体问题的公式化（瓦格纳）、尾部空腔闭合的各种模型等。腔体的数学模型以非线性延时微分方程组的形式获得。发展了适用于各种腔型的腔稳定性和振荡的线性理论。考虑了气泡分离的非线性空腔振荡机制，并给出了大量的数值实验结果。空腔闭合的理论模型，提出了发展著名的Efros方法与再入射流。对模型进行了近似分析。用瓦格纳公式求解了一个具有变半径自由表面的膨胀圆柱体在液体中的撞击和浸没问题。
Approximate solutions of some problems in high-speed hydrodynamics are given, the solutions being based upon well-known approaches, such as the principle of independence of cavity expansion (Logvinovich), formulation of the problem of the immersion of a solid contour into liquid (Wagner), various models of cavity closure in its tail, etc. Theoretical studies of the dynamic properties of slender ventilated cavities are performed. The mathematical model of a cavity is obtained in the form of a system of nonlinear time-delay differential equations. The linear theory of cavity stability and oscillations is developed for various cavity types. The mechanism of nonlinear cavity oscillations accounting for gas-bubble detachment is considered, and the results of extensive numerical experimentation are presented. A theoretical model of cavity closure is proposed that develops the well-known Efros approach with a re-entrant jet. An approximate analysis of the model has been performed. A planar problem of the impact and immersion of an expanding cylinder into liquid with a cylindrical free surface of variable radius is solved in Wagner’s formulation.