A COMMENT ON UNSTEADY-PERIODIC FLOW FRICTION FACTOR: AN ANALYSIS ON EXPERIMENTAL DATA GATHERED IN PULSATILE PIPE FLOWS

In 1940's, Schultz- Grunow proposed that time-average value of friction factor, lambda(u,ta) was similar to its corresponding steady state value, lambda 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 lambda(u,ta) in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 <= Re-ta <= 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, root omega' and oscillation amplitude, A(1) are 2.72 <= root omega' <= 28 and 0.05 <= A(1) <= 0.96 respectively. A multiplication element is defined as Mel = Re-ta x root omega'. A modified friction multiplier, lambda(Mel) which is similar to the conceptual parameter of Zhuang et al's friction factor ratio C (lambda(Mel) =lambda(u,ta)/lambda) is also referred. The correlation of lambda(Mel) = lambda(Mel) (Mel) is dependent on flow regime and the magnitude of Re-ta for the range of root omega' > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of lambda(Mel) = 1 is observed for turbulent flow cases with Re-ta >= 35000. In laminar regime the magnitude of Re-ta is governing the fact. The magnitude of lambda(Mel) varies in 0.589 <= lambda(Mel) <= 28.125 for Re-ta <= 5000 while lambda(Mel) = 1 is obtained for Re-ta > 5000. The graphical representation of lambda(Mel) = lambda(Mel) (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.