Applied mathematics

Determination of the line separating domains of vortical flows

A. V. Vasin

Saint Petersburg Water Communications University, Faculty of Information Technology

Abstract: In the framework of Lavrentiev–Shabat's model of separated flows a vorticity area under ideal fluid flow in a circular chamber with a ledge is proved and numerically simulated. The work has direct application to the study of the kinematic pattern of velocity distribution in bypass galleries of lock chambers. Fluid flow in a circular chamber is of vortex character, presence of a ledge leads to another area of vortex flow. The problem of gluing (pairing) of two vortex flows is a generalization of Goldshtik problem of separated vortex flows in areas with potential flow. We prove the existence of solution of generalized Goldshtik problem. The proposed proof essentially uses potential theory. The method of proof is based on approximation of problem solutions with discontinuous nonlinearity by discontinuous solutions of linear problems of Poisson equation type. The possibility of approximating by linear problems is used in the numerical implementation. In the second part of the paper the zone of flow separation in a circular chamber with a ledge is numerically simulated. The results obtained from numerical simulation are compatible with experimental measurements. Bibliogr. 9. Il. 4.

Keywords: ideal fluid flow, fluid with constant vorticity, harmonic functions, Dirichlet problem.

UDC: 519.6


Accepted: October 25, 2012