A non-dimensional oscillation parameter describing interactive influence of oscillation frequency and velocity amplitude ratio for use in pulsatile flows

Abstract

Abstract The interactive influences of oscillation frequency and velocity amplitude ratio on onset of transition in pulsatile pipe flow are investigated experimentally in the ranges of time-averaged and oscillating Reynolds numbers of 1019 ± 35 ⩽ Re ta ⩽ 4817 ± 164 and 107 ± 4 ⩽ Re os ⩽ 4261 ± 145 with velocity amplitude ratio of 0.05 ± 0.0017 ⩽ A 1 ⩽ 0.96 ± 0.03 for 227 runs. Oscillation frequency is in the range of 0.1 Hz ⩽ f ⩽ 14 Hz corresponding to Womersley number range of 2.72 ⩽ ω ′ ⩽ 32.21 covering quasi-steady, intermediate and beginning of inertia dominant regimes of pulsatile laminar flow. The onset of transition in laminar pulsatile pipe flow can be retarded up to Re ta , crit = 4817 at ω ′ = 3.85 in the covered experimental range. No more effect of A 1 on Re ta , crit is seen for ω ′ > 8.61 although there is a considerable effect of A 1 on Re os , crit . The effect of ω ′ on Re ta , crit and Re os , crit is not observed for A 1 ω ′ and A 1 are also investigated on Re ta , crit as functions of Re ta , crit = Re ta , crit ( A 1 ω ′ ) and Re ta , crit = Re ta , crit ( ω ′ / A 1 ). The interactive influences of ω ′ and A 1 are not seen on Re ta , crit for ω ′ > 8.61. This shows that the time-periodicity ( ω ′ , A 1 ) does not affect significantly the onset of transition at the beginning of inertia dominant region of pulsatile laminar flow ( ω ′ > 8.61) when compared with their interactive effects in the quasi-steady and intermediate regions ( ω ′ ⩽ 8.61). For flow classification of pulsatile flow at the onset of transition, a new non-dimensional interactive oscillation number, I os = ω ′ / A 1 is proposed. According to this non-dimensional number, the pulsatile flow at the onset of transition can be subclassified such as quasi-steady for I os I os ⩽ 30 and inertia dominant regions of pulsatile pipe flows for I os > 30 considering the effects of both ω ′ and A 1 on contrary to the classifications available in the literature.