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

Abstract

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, U 0 =0, and when U 0 >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, R t 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.