An approach for transition correlation of laminar pulsatile pipe flows via frictional field characteristics

Abstract

Transition of laminar pulsatile pipe flow into turbulence is one of the current research topics in flow dynamics. Despite the existence of a considerable number of theoretical and experimental studies, the physical mechanism of transition is not well defined. Furthermore, there is almost no information on the start and the end of the transition in terms of pulsatile flow parameters. In this paper, an approach which consists of attempts to correlate the governing flow parameters is presented to reveal the transition process with particular emphasis on the frictional field. The experimental data collected in slightly compressible, Newtonian, one-dimensional laminar pulsatile pipe flow without a flow reversal were compiled for this purpose. The common oscillation parameters, dimensionless frequency parameter ω′ and velocity amplitude ratio A 1 were the main variables of the experimental study covering the ranges of 7≤ ω′ ≤28 and 0.05≤ A 1≤0.8. The time history of local static pressure gradient and axial velocity field were accumulated and the data were expressed through pulsatile flow, instantaneous λ u( t) and time-averaged λ u, ta friction factors using momentum-integral equation. A reference friction factor ratio λ R, whose definition was based on the concept of steady flow friction was introduced. The start and the end of transition were predicted through the functional relationships of λ R with time-averaged and oscillating Reynolds numbers, Re ta and Re os by means of a trial–error procedure. The proposed correlations and determined approximate critical limits of transition are only valid in the corresponding ranges of 2000≤ Re ta ≤60 000 , 620≤ Re os ≤18 800 and the analysis is open to discussion.