M.Sc Thesis
M.Sc Student Ramus Artem Laminar Flow in a Curved Pipe with a Sudden Expansion Department of Mechanical Engineering Assistant Professor Michael Shusser Professor Oleg Gendelman

Abstract

Flow in a curved pipe with a sudden expansion is often encountered in practice, for example in piping or blood vessels. While it is well known that in laminar flow in a curved pipe there is a secondary flow in the bend consisting of two symmetric azimuthal vortices, there is some data that suggests that the secondary flow will be different in the presence of a sudden expansion upstream of the bend. The purpose of this study was to find and figure out these differences and to study this flow in a curved pipe with a sudden expansion.

The flow through an axisymmetric sudden expansion followed by a curved pipe was solved numerically using the CFD software Fluent. The validity of numerical calculations was proven by computing the flow in a straight pipe with a sudden expansion and the flow in a curved with these found in literature.

Most of the calculations were done for the steady flow. The influence of the expansion ratio and the Reynolds number on the vortex pair in the bend and on the recirculating flow caused by the sudden expansion was studied. A correlation for the length of the recirculating flow was obtained. It was found that the reattachment length is a logarithmic function of the Reynolds number and a linear function of the expansion ratio. This result differs from the flow in the straight pipe with an axisymmetric sudden expansion, where the reattachment length is a linear function of both Reynolds number and expansion ratio.

During the simulations of this flow it was found that for one specific combination of the expansion ratio and the Reynolds number the solution is periodic for the steady state boundary conditions. This unstable flow was studied in order to find the reason for the origin of the instability. Comparison of the flow with a sudden expansion followed by a bend with the flow in a straight pipe with a sudden expansion and with the flow in the bend for the same mass flow rate was performed. In addition, the flows with a sudden expansion followed by a bend with different expansion ratios but the same mass flow rate were compared. It was found that the possible reason for this instability could be the sharp velocity gradient near the outer bend at the beginning of the pipe turn.