Unsteady Entrance Flow Development in a Straight Tube

The entrance conditions for pulsatile flow are important in the understanding blood flow out of the heart and in developing regions at branches. The pulsatile entrance flow was solved using a spectral element simulation of the full unsteady Navier- Stokes equations. A mean Reynolds number of 200 and a range of Womersley parameters from 1.8 to 12.5 was used for a sinusoidal inlet flow waveform 1+sin (ωt). Variations in the entrance length were observed during the pulsatile cycle. The amplitude of the entrance length variation decreased with an increase in the Womersley parameter. The phase lag between the entrance length and the inlet flow waveform increased for Womersley parameter α up to 5.0 and decreased for α larger than 5.0. For low α, the maximum entrance length during pulsatile flow was approximately the same as the steady entrance length for the peak flow. For high α, the pulsatile entrance length was more uniform during the cycle and tended to the entrance length for the mean flow. The wall shear rate reached its far downstream value after only about half of the entrance length and also exhibited a dependence on α. The results quantify the entrance conditions typically encountered in studies of the arterial system.