We investigate the steady expiratory and the oscillatory flow in a planar double bifurcation model with geometric proportions relevant to the respiratory human airways. Expanding on a previous study focused on steady inspiration [Jalal et al., Exp. Fluids 57, 148 (2016)10.1007/s00348-016-2234-5], we use magnetic resonance velocimetry to characterize the three-dimensional velocity field for a range of Reynolds (Re) and Womersley (Wo) numbers. During expiration the velocity profiles are flatter than in inspiration, due to stronger secondary motions. The latter are characterized by counter-rotating streamwise vortices induced by curvature at the branch junctions. With increasing Re, the vortices gain strength, and for Re≥1000 they propagate through successive branching generations, profoundly changing the secondary flow pattern. Under oscillatory conditions, as long as the ventilation frequency is in the normal respiration range, the flow topology for both inhalation and exhalation phases is similar to the corresponding steady cases over most of the breathing cycle. On the other hand, in the high-frequency ventilation regime (Wo=12), the acceleration part of both inhalation and exhalation phases show signature features of oscillatory flows, with high-momentum regions located close to the walls. The phenomenon of counterflow is found to be prominent at Wo≥6, with reverse flow pockets marking the velocity field especially during the inhalation-exhalation inversion. With increasing oscillation frequency, the secondary motions become more intense during the inhalation phase but are attenuated during the exhalation phase of the cycle. The cycle-averaged drift is found to be significant at low Wo but decreases with increasing ventilation frequency, suggesting that steady streaming is not the main transport mechanism during high-frequency ventilation.
Bibliographical noteFunding Information:
We gratefully acknowledge the support from the National Science Foundation (Chemical, Bioengineering, Environmental, and Transport Systems, Grant No. 1453538) and the National Institutes of Health (Grants No. NHLBI-R21HL129906 and 1S10OD017974-01).