Vortical flow of incompressible viscous fluid in finite cylinder

Abstract

The effective use of vortex energy in production of strong velocity fields by different devices is one of the modern areas of applications, developed during the last decade. In this paper the distribution of velocity field for viscous incompressible fluid in a pipe with a system of finite number of circular vortex lines, positioned on the inner surface of the finite cylinder is calculated. The approximation of the corresponding boundary value problem for the Navier‐Stokes equations is based on the finite difference method. This procedure allows us to reduce the 2D problem decribed by the system of Navier‐ Stokes PDEs to the monotonous difference equations. Calculations are done using the computer program Matlab and the following regimes are calculated: a) the flow in a smooth pipe; b) the flow, poured inside a pipe through the circle; c) the flow, poured inside a pipe through the ring. The model is investigated for different values of parameters Re (Reynolds number), G (swirl number) and A (vortex intensity).

Key words:

• 2D problem
• finite difference method
• monotonous finite difference
• Navier ‐ Stokes equations
• viscous fluid
• monotonous finite difference schemes