Доповiдi Нацiональної академiї наук України (Jul 2019)
Three-dimensional flow of a viscous incompressible fluid in a cylindrical duct with two diaphragms
Abstract
The three-dimensional flow of a viscous incompressible fluid in a cylindrical duct with two serial diaphragms (constrictions) is studied by the numerical solution of non–stationary Navier–Stokes equations. The solution algorithm is based on the finite volume method using difference schemes second-order accurate in both space and time. The TVD form of a central-difference scheme with a flow limiter is used for the interpolation of convec tive terms. The combined computation of the velocity and pressure fields is carried out, by using the PISO procedure. It is shown that, in a certain range of Reynolds numbers, the fluid flow in the region between the diaphragms is non-stationary and is characterized by the presence of an unstable shear layer formed by the boundary layer that breaks off from the surface of the first diaphragm. In the cavity between the diaphragms, a circulating motion of the medium is formed, which can be interpreted as a hydrodynamic feedback channel that creates conditions for the occurrence of self-sustained oscillations in the system. A sequential series of ring vortices is for med in the shear layer that cause self-oscillations of the velocity and pressure fields in a vicinity of the orifice of the second diaphragm, as well as pressure oscillations in the whole medium between the diaphragms. These self-sustained oscillations may serve as an acoustic source in the duct. The obtained results are compared with the model of an axisymmetric flow in a cylindrical duct with two diaphragms. The structure of the three–dimensional flow has an azimuthal asymmetry that substantially affects the local features of the flow. There is an asymmetry of the circulating motion of the medium in the cavity between the diaphragms and of the ring vortices in the shear layer. However, the oscillation periods of the velocity and pressure fields coincide with those in the model of axisymmetric flow. Thus, the asymmetry of the flow practically does not affect its integral characteristics.
Keywords
