Periodic flow at airway bifurcations. III. Energy dissipation

We measured the energy dissipation associated with large-amplitude periodic flow through airway bifurcation models. Each model consisted of a single asymmetric bifurcation with a different branching angle and area ratio, with each branch terminated into an identical elastic load. Sinusoidal volumetric oscillations were applied at the parent duct so that the upstream Reynolds number (Re) varied from 30 to 77,000 and the Womersley parameter (alpha) from 4 to 30. Pressures were measured continuously at the parent duct and at both terminals, and instantaneous branch flow rates were calculated. Time-averaged energy dissipation in the bifurcation was computed from an energy budget over a control volume integrated over a cycle and was expressed as a friction factor, F. We found that when tidal volume was small [ratio of tidal volume to resident (dead space) volume, VT/VD less than 1], F was independent of branching angle and fell with increasing alpha and VT/VD. When tidal volume was large (VT/VD greater than 1), F increased with increasing branching angle and varied less strongly with alpha and VT/VD. No simple benchmark flow represented the data well over the entire experimental range. This study demonstrates that only two nondimensional parameters, alpha and VT/VD, are necessary and are sufficient to describe time-averaged energy dissipation in a given bifurcation geometry during sinusoidal flow.