The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge
The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge
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DOI：
10.1017/jfm.2019.134
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发表时间：
2018-01
影响因子：
3.7
通讯作者：
A. DeVoria;K. Mohseni
中科院分区：
文献类型：
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作者：
A. DeVoria;K. Mohseni
本文介绍了一种三维粘性边界层和剪切层模型，称为涡卷积层。层中的涡量用传统的涡片来解释。层中的质量和动量由具有其内部切向流的二维表面来表示。也就是说，薄片具有单位面积的质量密度，使其动态地有别于周围的外部流体，并允许薄片支持压力跳跃。卷吸的机理由横跨薄板的速度的法向分量的不连续性来表示。旋涡卷吸薄层的速度场由复薄层强度的广义Birkhoff-Rott方程给出。将该模型应用于尖端分离的情况。不需要奇点消除形式的补充库塔条件，因为流动通过法向动量的适当平衡而保持有界，压力在薄板上跳跃。边缘的压力跳跃导致新的涡度的产生。当粘合薄片合并形成自由薄片时，剥离角度由粘合薄片内部的本征流动的法向冲量决定。当到处都存在零卷吸时，模型简化为无质量的传统涡片。因此，压力跳跃必须为零，开口角度必须为切线，这样薄板才能简单地对流离开楔形面。最后，用几个算例验证了涡卷积层模型的有效性。
In this paper a model for viscous boundary and shear layers in three dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two-dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid and allowing the sheet to support a pressure jump. The mechanism of entrainment is represented by a discontinuity in the normal component of the velocity across the sheet. The velocity field induced by the vortex-entrainment sheet is given by a generalized Birkhoff–Rott equation with a complex sheet strength. The model was applied to the case of separation at a sharp edge. No supplementary Kutta condition in the form of a singularity removal is required as the flow remains bounded through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model is demonstrated on several example problems.