Simplified Lumped Parameter Model for Oscillatory Flow in an Elastic Tube: A Hierarchical Approach

Abstract

In this article, the significant characteristics of wave transmission and boundary layer influence are studied for an incompressible fluid flowing through a long elastic tube using lumped parameter model. An ameliorated version of the lumped parameter model is derived, where the flow impedance is linked with Womersley number to understand the phenomena of fluid wall interaction, especially in human airways. To analyze the flow phenomena through tubes, the flow governing equations are transformed through the Bessel series. We have observed that for the low value of Womersley number, there is a phase difference between pressure and flowrate, which produces a frequency-dependent flow impedance. The physiological relevance of this result is especially shown in the nasal-pharynx during breathing. The results are validated by ansys-based numerical simulation as well as by experimental results.