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首页> 外文期刊>International journal of computational fluid dynamics >Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves
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Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

机译：涡流密度与激波和膨胀波相互作用的数值研究

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We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different form that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave result in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation #GAMMA#_1 as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for #GAMMA# are derived and their accuracy is discussed. The splitting of VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.
机译：我们研究了涡旋密度不均匀性（VDI）与激波和膨胀波的相互作用。我们称VDI为集中涡度（涡旋）区域，其密度与周围环境的密度形式不同。垂直于VDI表面的密度梯度的非平行方向以及冲击波上的压力梯度会导致额外的涡旋。数值研究了初始圆形VDI向非对称形状的累积。通过二维Euler代码执行此交互的数值建模。自适应非结构​​化数值网格的使用使得可以获得高精度，并捕获具有适中总数的网格点的诱发涡度区域。为了验证代码，将计算结果与可用的实验结果进行比较，并获得良好的一致性。研究了VDI与传播的冲击波之间的相互作用，包括一系列初始循环和诱导循环，并给出了获得的流动模式。 VDI的分裂发展成非对称涡流对的形成，而不是形成一组涡流。提出了一种由于运动的VDI与许多波相互作用而对整体诱导环流＃GAMMA＃_1进行解析计算的方法。推导了＃GAMMA＃的简化近似表达式，并讨论了其准确性。数值研究了通过Prandtl-Meyer扩展波的VDI分裂。对于相同的初始循环和诱导循环，将获得的VDI模式与VDI与传播的冲击波相互作用的模式进行比较。这些模式在相应的时刻具有相似的形状。

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