Jet impingement on a wall of arbitrary configuration

The problem of jet impingement on a wall of arbitrary configuration is studied. A curvilinear wall is approximated by a polygonal line with a fairly large number of links and a method based on the classical approach of Joukowski and Michell is applied to solve the problem. By successive displacement of the jet it is established that at a certain wall configuration the problem can have two solutions, one of which is multivalent. The limiting flow regimes characterized by the total disappearance of one of the jets formed after the division of the main impinging jet are revealed. An attempt to model the well-known experiment on the stable position of a small sphere lying on the horizontal bottom, when a slender water jet falls on it, is made. In the modeling the sphere is replaced by a circular cylinder in a separationless flow. It is numerically shown that any jet displacement to the right or to the left from the position corresponding to zero horizontal force acting on the cylinder leads to the generation of an oppositely directed nonzero force which indicates the absolute instability of the cylinder in the separationless jet flow.