Numerical Analysis of Flow in a Collapsible Vessel Based on Unsteady and Quasi-Steady Flow Theories

Abstract

This chapter summarizes the unsteady one-dimensional (1-D) separable flow theory recently proposed by the first author and his co-worker, comparing it to the quasi-steady theory. Numerical analysis was carried out on the self-excited oscillation of the flow in a two-dimensional (2-D) flexible channel to examine the effectiveness of the unsteady flow theory and to compare it with the quasi-steady flow theory. In the unsteady flow theory, the unsteadiness is represented by an additional term in the flow velocity downstream of the flow separation point, whereas this term is not included in the quasi-steady flow theory. The higher frequency components of the flow velocities, the pressures, and the motion of the separation point, therefore, can more accurately be accounted for in the unsteady flow theory. The variances of the velocitiexs and pressures are numerically predicted to be much larger by the unsteady theory than by the quasi-steady theory. On the other hand, the frequency of the higher mode calculated by the latter is about twice that of the former. The introduction of the unsteadiness in the analysis is very important for an accurate prediction of the dynamic features of the flow-channel behavior.