Analysis of Free Oscillating Flow in a U-Shaped Tube

Abstract

A free oscillating flow of a viscous fluid in a U-shaped tube is considered. For the case of laminar flow, an analytical representation for wall shear stress T_w which includes an acceleration term is adopted and the momentum integral equation is solved analytically. By comparing the present results with previous theoretical and experimental ones, it becomes evident that the solution obtained here agrees well with those of Biery and Yasukawa, et al., and that the solutions derived from any other approximate representations for wall shear stress are attributted to a special case of the present one. For the flow in which transition from laminar to turbulent occurs, the turbulent quasi-steady representation for T_w is used and the momentum integral equation is numerically solved by means of Runge-Kutta method. The agreement between the present numerical and experimental results is fairly good. Further, the limits between laminar, transitional, and turbulent regions are determined on the basis of the present experiments.