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

The onset of transition in laminar pulsatile pipe flow can be retarded up to Reta,crit = 4817 at ω′ = 3.85 in the covered experimental range. No more effect of A1 on Reta,crit is seen for ω′ > 8.61 although there is a considerable effect of A1 on Reos,crit. The effect of ω′ on Reta,crit and Reos,crit is not observed for A1 < 0.30. The interactive influences of ω′ and A1 are also investigated on Reta,crit as functions of Reta,crit = Reta,crit (A1ω′) and Reta,crit = Reta,crit (ω′/A1). The interactive influences of ω′ and A1 are not seen on Reta,crit for ω′ > 8.61. This shows that the time-periodicity (ω′, A1) 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, Ios=ω′/A1 is proposed. According to this non-dimensional number, the pulsatile flow at the onset of transition can be subclassified such as quasi-steady for Ios < 5, intermediate for 5 ⩽ Ios ⩽ 30 and inertia dominant regions of pulsatile pipe flows for Ios > 30 considering the effects of both ω′ and A1 on contrary to the classifications available in the literature.