Theoretical and Experimental Reflection Coefficients in Flexible Tubes as a Function of the Mach Number

Abstract

© 2018 Creative Commons Attribution. The standard formulation of Wave Intensity Analysis (WIA) assumes that the flow velocity (U) in the conduit is ll the velocity of propagation of waves (c) in the system, and Mach number, M=U/c, is negligible. However, in the large conduit arteries, U is relatively high due to ventricular contraction and c is relatively low due to the large compliance; thus M is > 0, and may not be ignored. Therefore, the aim of this study is to identify experimentally the relationship between M and the reflection coefficient in vitro. Combinations of flexible tubes, of 2 m in length with isotropic and uniform circular cross sectional area along their longitudinal axes, were used to present mother and daughter tubes to produce a range of reflection coefficients. An approximately semi-sinusoidal pulse was generated at the inlet of the mother tube using a syringe pump, first in the condition of initial velocity, U0=0, and when U0>0 with steady flow to superimpose the pulse. Pressure (P) and Velocity (U) were measured in the mother tube, wave speed was determined using the foot to foot and PU-loops methods. The theoretical reflection coefficient, Rt at M=0, has been compared to the experimental reflection coefficient, R at M>0, which was determined as dP-/dP+ as calculated using WIA. The function R(M) changes significantly with the geometrical and mechanical features of the connected tubes. In our experiments, R increased significantly with small values of M In the range of M=0-0.02, R increased by 4-36%. Therefore, we conclude that M significantly affects the magnitude of reflections.