High-Frequency Pulsatile Pipe Flows Encompassing All Flow Regimes

Abstract

Time-varying pipe flows driven by a harmonically pulsating inlet velocity and spanning all flow regimes have been investigated by means of numerical simulations. The Reynolds number varied from 1000 to 5000 in response to the inlet velocity oscillations. The frequency of the pulsations was varied from 1 to 10 Hz. These frequencies are markedly higher than those previously studied (maximum value of 0.025 Hz). The motivation for the use of the elevated frequency range was engendered by practical applications such as cardiovascular and respiratory systems of mammals in addition to numerous industrial applications. The simulations made use of the modified Menter transitional model. The key conclusion found here is that the use of a quasi-steady model for the prediction of fully developed friction factors is not applicable for the higher frequencies considered here. The deviations between the actual and quasi-steady friction factor values increase markedly with increasing frequency. Backflow occurs near the wall as the flow transists from deceleration to acceleration. This transition gives rise to a change in the sign of the axial pressure gradient. The amplitudes of the pressure oscillations generated by the imposed velocity variations increase markedly with increasing frequency and diminish with increasing downstream distance from the pipe inlet. The effect of modifications of the Menter model was assessed by carrying out separate numerical solutions for the unmodified and modified models. The pressure oscillations corresponding to the respective models were compared, and it was found that the deviations are insignificant.