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 λ_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, √(ω') and oscillation amplitude, A_1 are 2.72 ≤ √(ω') ≤ 28 and 0.05 ≤ A_1≤ 0.96 respectively. A multiplication element is defined as Mel = Re_ta×√(ω^'). A modified friction multiplier, λ_(Mel ) which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( λ_Mel = λ_(u,ta)/λ ) is also referred. The correlation of λ_Mel = λ_Mel (Mel) is dependent on flow regime and the magnitude of Re_ta for the range of √(ω^') > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of λ_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 λ_Mel varies in 0.589 ≤ λ_Mel ≤ 28.125 for Re_(ta ) ≤ 5000 while λ_Mel = 1 is obtained for Re_(ta ) > 5000. The graphical representation of λ_Mel = λ_Mel (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.

Keywords

• Time-Average Friction Factor,Time-Average Reynolds Number,Womersley Number,Multiplication Element,Modified Friction Multiplier = C

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