Flow Pattern and Frictional Losses in Pulsating Pipe Flow : Part 2, Effect of Pulsating Frequency on the Turbulent Frictional Losses

Abstract

The effect of frequency on frictional losses in a pulsating turbulent pipe flow is investigated. The frictional losses estimated from flow pattern diagrams agree well with those obtained experimentally at the time-averaged Reynolds number of about 5.7×10⁴ and over wide ranges of both frequency and velocity amplitude ratio A₁. As is expected, the instantaneous friction factor λ_u(t) and the quasi-steady friction factor λ_q are almost equal in the quasi-steady region indicated in a previous paper. With an increasing dimensionless frequency ω', however, λ_u(t)⪌λ_q in both accelerating and decelerating zones of a pulse cycle. The time average friction factor λ_u, ta, which is a function of ω' and A₁, is always larger than the friction factor λ_s for a steady flow with equivalent mean Reynolds number and increases monotonically with ω' and A₁.