Pulsatile developing channel flows in low Reynolds Number regime

In this study, comprehensive numerical simulations were conducted to examine laminar pulsatile developing flows through flat channels. The developing velocity fields and the hydrodynamic entry length were explored for the Reynolds numbers from 20 to 200, and the low and intermediate non-dimensional pulsation frequency or the Womersley number (1.08 ≤Wo≤ 8.86). For all simulations, the pulsating amplification factor was considered from zero to one, (0 ≤A≤ 1), and to achieve more practical and relevant outcomes, time-dependent parabolic inlet velocity profiles were applied. The outcomes reveal that for the higher values of the pulsation frequency or the Womersley number (6 ≤ Wo ≤ 8.66), the maximum pulsatile entranced length during a cycle is close to the inlet length of the mean component of the flow. On the other hand, for the rest of the Womersley number range (1.08 ≤ Wo < 6), and high amplification factor (0.5 ≤ A), the value of the entrance length increases and is significantly different from the development length of the steady component. Moreover, the results demonstrate that the entry length correlates with the Womersley number through a power-law function, whilst it has linear correlations with the Reynolds number and the amplification factor. Further, using the result of the accomplished numerical study, a practical correlation of the entrance length is offered to be used in the design phase for any type of pulsatile flow through the flat channels.