Inlet swirl decay and mixing in a laminar micro-pipe flow with wall slip

Abstract

In this work, the decaying laminar inlet swirl flow in a straight circular micro-pipe with wall slip is solved analytically and the solution is verified numerically. Based on a fully developed parabolic axial velocity profile, the swirl velocity equation is solved by the separation of variables technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within the circular micro-pipe from the inlet, the wall slip, and the inlet swirl velocity profile. The effects of the parameters on the swirl velocity distribution and the swirl decay are analyzed along the flow. The addition of swirling velocity to the flow of a fluid in a pipe is of great importance in the enhancement of transport characteristics. The current results offer analytical equations to estimate the swirl velocity distribution with slip at the walls for the design of swirl flow devices. Furthermore, to quantify mixing, the change in the average distance traveled by fluid particles from the inlet in a swirl flow is compared with the average distance traveled by the fluid particles in the case of no swirl. A clear enhancement of the average distance traveled is obtained for flows with the interaction of both swirl and slip effects. In our opinion, the present work is useful to researchers looking for the enhancement of transport characteristics in circular micro-pipes.