Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data.

中文翻译：

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边界层对空腔流动的影响

考虑在流入涡流的情况下经过障碍物的腔流。所提出的解决问题的方法是基于用离散形式代替连续涡流，其中离散涡流沿着与流线重合的涡流线集中。流线之间的流动没有涡流。问题是确定流线的形状和空腔边界。空腔边界上的压力是恒定的，等于液体的蒸气压。流水线上的压力是连续的。复变量理论用于确定通过其边界条件耦合的以下子区域中的流动：带有弯曲壁的通道中的流动，射流中的空腔流动以及沿着弯曲壁的无限流动。数值方法基于逐次逼近法。考虑具有尖锐边缘的物体的数值过程得到了验证，对于该物体，空腔分离点是固定的。对于光滑物体，根据布里渊准则确定腔体脱离。发现流入的涡流延迟了腔的分离并减小了腔的长度。将获得的结果与实验数据进行比较。