Numerical study of a laminar flow in an expanding round pipe with a backward facing step

Abstract

A numerical study of a laminar flow in an expanding round pipe with a backward facing step is conducted. Uniform and parabolic velocity profiles are used at the inlet just before the abrupt expansion. Reynolds number used in the simulations was in range between 100 and 1000 and based on the small pipe diameter. The aspect ratio D/d was systematically varied between 2, 3 and 4. The pipe was maintained under a constant surface temperature of 310K. Two types of fluid were used in the numerical simulations with Prandtl equal to 0.7 and 7. Due to the expansion, a flow separation region known as the recirculation region was observed. The increase in Reynolds number led to an increase in the reattachment and the fully developed lengths of the flow, the same behavior was observed when the aspect ratio was increased. The reattachment and fully developed lengths of the parabolic velocity profile are both greater than these lengths corresponding to the uniform velocity profile. A linear correlation is obtained for the reattachment length as a function of Reynolds number for the different values D/d and for both velocity profiles. Similar linear correlations were obtained for the fully developed length for all considered cases. The thermal analysis of this problem focused mainly on the local Nusselt number distribution. It was noticed that the parameters that affected the reattachment length also affected the local Nusselt number behavior. The Nusselt number distribution in the large pipe increased when Reynolds number and the aspect ratio decreased and was higher for the case of the uniform velocity profile at the inlet.