Fully developed intermittent flow in a strongly curved tube
was numerically simulated
using a numerical scheme based on the simpler method. Physiological pulsatile
flow
in the aorta was simulated as intermittent flow, with a waveform consisting
of a
pulse-like systolic flow period followed by a stationary diastolic period.
Numerical
simulations were carried out for the following conditions: Dean number
κ=393, frequency parameter α=4–27, curvature ratio
δ=1/2, 1/3 and 1/7, and intermittency
parameter η=0–1/2, where η is the ratio of a
systolic time to the cycle period. For
α=18 and 27 the axial-flow profile in a systolic period becomes
close to that of
a sinusoidally oscillatory flow. At the end of the systole, a region
of reversed axial
velocity appears in the vicinity of the tube wall, which is caused by
the blocking of
the flow, similar to blocked flow in a straight tube. This area is enlarged
near the
inner wall of the bend by the curvature effect. Circumferential flow
accelerated in a
systole streams into the inner corner and collides at the symmetry line,
which creates
a jet-like secondary flow towards the outer wall. The region of reversed
axial velocity
is extended to the tube centre by the secondary flow. The development of
the flow
continues during the diastolic period for α higher than 8,
and the flow does not completely dissipate, so that a residual
secondary vortex persists until the next systole.
Accordingly, the development of secondary flow in the following systolic
phase is
strongly affected by the residual vortex at the end of the previous diastolic
phase,
especially by stationary diastolic periods. Therefore, intermittent
flow in a curved tube
is strongly affected by the stationary diastolic period. For η=0 and
1/5, the induced
secondary flow in a systole forms additional vortices near the inner
wall, whereas for
η=1/3 and 1/2 additional vortices do not appear. The
characteristics of intermittent
flow in a curved tube are also strongly affected by the length of the
diastolic period, which represents a period of zero flow.