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

摘要

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 multiplication element is defined as ???????????? = ???????????????? × √????′ . A modified friction multiplier, ???????????????? which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( ???????????????? = ????????,???????? ???? ) is also referred. The correlation of ???????????????? = ????????????????(????????????) is dependent on flow regime and the magnitude of ???????????????? for the range of √????′ 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of ???????????????? = 1 is observed for turbulent flow cases with ???????????????? ≥ 35000. In laminar regime the magnitude of ???????????????? is governing the fact. The magnitude of ???????????????? varies in 0.589 ≤ ???????????????? ≤ 28.125 for ???????????????? ≤ 5000 while ???????????????? = 1 is obtained for ???????????????? 5000. The graphical representation of ???????????????? = ????????????????(????????????) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.