The flow of a liquid in a cylindrical duct with diaphragms of a rectangular profile

Abstract

The flow of a viscous incompressible liquid in a cylindrical duct with two serial diaphragms of a rectangular profile is studied by the numerical solution of the unsteady Navier-Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is non-stationary and is characterized by the presence of an unstable shear layer under the certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity field in the vicinity of the orifice of the second diaphragm. In comparison with the case of rounded diaphragms, an increase in the maximum jet velocity is observed, which in turn leads to an increase in the frequency of self-sustained oscillations and a decrease in the Reynolds numbers at which quasi-periodic oscillations are excited.