Flow Rectification in Loopy Network Models of Bird Lungs

We demonstrate flow rectification, valveless pumping, or alternating to direct current (AC-to-DC) conversion in macroscale fluidic networks with loops. Inspired by the unique anatomy of bird lungs and the phenomenon of directed airflow throughout the respiration cycle, we hypothesize, test, and validate that multiloop networks exhibit persistent circulation or DC flows when subject to oscillatory or AC forcing at high Reynolds numbers. Experiments reveal that disproportionately stronger circulation is generated for higher frequencies and amplitudes of the imposed oscillations, and this nonlinear response is corroborated by numerical simulations. Visualizations show that flow separation and vortex shedding at network junctions serve the valving function of directing current with appropriate timing in the oscillation cycle. These findings suggest strategies for controlling inertial flows through network topology and junction connectivity.

Figure 1

Loopy network models of bird lungs. (a) Schematic of anatomy modified from Ref. [11]. Reciprocal expansion and contraction of air sacs (AS) drives oscillatory inhalation and exhalation flows in the primary bronchus (P). Directed flow is observed in dorso-, para-, ventrobronchi (DPV) that span the mesobronchus (M). (b) A “spherical bird” simplification with a single AS and DPV. (c) A closed network formed by connecting P to AS, the latter replaced by a reciprocating piston. (d) A symmetrized network that modifies conduit lengths while preserving the connectivity of the $T$ junctions.

Figure 2

Experimental system for characterizing flows in a forced fluidic network. (a) Rigid tubing of inner diameter $D=1.6\mathrm{cm}$ is formed and connected via $T$ junctions, and the network is filled with water seeded with microparticles. Oscillatory flow in the AC branch is driven by a motorized piston that oscillates with amplitude $A$ and frequency $f$, and the resulting flow field in a DC branch is measured via PIV. (b) Flow profiles in the DC branch measured at different times in the cycle for $A=7.2\mathrm{cm}$ and $f=2.0\mathrm{Hz}$ ($A/D=4.5$, ${\mathrm{Wo}}^2=900$, and $\mathrm{Re}=2500$). Rectification is evident as the positive bias in the time-averaged profile (dashed curve). (c) Imposed oscillatory flow in the AC branch (top) and measured section-averaged flow in a DC branch (bottom); the time average $U$ of the latter characterizes the pump rate.

Figure 3

Experimental characterization of AC-to-DC conversion in the symmetric circuit of Fig. 2. (a) Dependence of DC flow speed $U$ on AC driving parameters $A$ and $f$. Multiple data points represent independent trials, Bezier curves are shown as guides to the eye, and values of $f$ are indicated on the color bar. Inset: magnified view of low-$A$ data. (b) Effectiveness $E=U/2Af$ as a dimensionless measure of AC-to-DC conversion. (c) Map of $E$ across normalized amplitude $A/D$ and frequency ${\mathrm{Wo}}^2\propto f$. Markers indicate where measurements are performed, and the map is generated by linear interpolation or extrapolation and smoothing via moving-window averaging.

Figure 4

Simulation of the asymmetric circuit. (a) The domain and spatial grid near a $T$ junction (inset). Color indicates flow speed normalized by $2\pi fA$ and at the moment the piston is moving rightward at peak velocity. Here $D=0.5\mathrm{cm}$, $A=2.5\mathrm{cm}$, and $f=1\mathrm{Hz}$. (b) Effectiveness $E$ across $A/D$ and ${\mathrm{Wo}}^2\propto f$. (c) Streamlines and vorticity near one junction at four equally spaced phases in the cycle and for the parameters circled in (b). Arrows indicate the phase of the imposed flow from the primary bronchus ($P$). Vorticity is normalized by ${\pi }^{2}f(A/D{)}^2$, a scale appropriate for vortex shedding from a sharp edge in oscillatory flow [41, 42].