A Comment on Unsteady–periodic Flow Friction Factor: An Analysis on Experimental Data Gathered in Pulsatile Pipe Flows

Abstract

In 1940's, Schultz-Grunow proposed that time-average value of friction factor, λ u,ta was similar to its corresponding steady state value, λ for the presence of gradual and slow oscillations in pulsatile flows. A recent approach was available for low frequency pulsatile flows through narrow channels in transitional and turbulent regimes by Zhuang et al, in 2016 and 2017. In this analysis; extensive experimental data of , in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 ≤ ≤ 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, √ ′ and oscillation amplitude, 1 are 2. 72 ≤ √ ′ ≤ 28 and 0.05 ≤ 1 ≤ 0.96 respectively. A

A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

“…Figure 5 shows the velocity comparisons between the Womersley velocity profile (shown in solid line) and the Poiseuille function profile (indicated with dots) in different sections (denoted with A, B, C, D, and E) for different times relating to the cardiac cycle defined with Equation (8). Based on pure observation, the results clearly show that there is no evident difference between the two studied velocity profiles.…”

“…Figure 5 shows the velocity comparisons between t (shown in solid line) and the Poiseuille function profile (in sections (denoted with A, B, C, D, and E) for different tim defined with Equation (8). Based on pure observation, the is no evident difference between the two studied velocity p Second-order numerical schemes for spatial and temporal discretization have been selected.…”

“…Since then, the Womersley function has been widely used in hemodynamics. In the context of computational fluid dynamics modelization of arteries and blood vessels, several works employ the Womersley function in the inlet velocity boundary condition (see [2][3][4][5][6][7][8][9]).…”