Journal of Applied Physiology, Vol 67, Issue 1 147-159, Copyright © 1989 by American Physiological Society
Some features of oscillatory flow in a model bifurcation
D. L. Jan, A. H. Shapiro and R. D. Kamm
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge 02139.
Oscillatory flow in the lung is studied using an order-of-magnitude
analysis and flow visualization experiments in a single bifurcation with
lung-like geometry. The results are used to obtain a classification scheme
that identifies three major flow regimes, distinguished on the basis of
whether the flow is dominated by unsteadiness, viscous effects, or the
effects of convective acceleration. The unsteady regime is found to exist
for values of a dimensionless stroke length (L/a, i.e., stroke volume/local
cross-sectional area) less than or equal to 3 and for values of a
dimensionless frequency (alpha 2 = alpha 2 omega/nu, where alpha is airway
radius, omega the oscillatory frequency, and nu the kinematic viscosity)
less than or equal to 10 in basic agreement with previous studies. The
viscous regime is found when alpha 2(L/a)(a/R)1/2 less than 10 and alpha 2
less than 10 where R is the local radius of curvature in the bifurcation;
the convective regime is found when alpha 2(L/a)(a/R)1/2 greater than 10
and L/a greater than 3. This same approach yields scaling laws for the
magnitude of secondary flow velocities and shows that the ratio of
secondary-to-axial velocity is small everywhere outside of the convective
regime where it scales with (a/R)1/2. Comparison of these results to
related simple flows shows that many of the features observed can be
attributed to the effects of curvature, suggesting that the influence of
the flow divider and of area change may be of lesser importance than
previously thought.
