Biomedical Engineering Reference
In-Depth Information
Secondary flow arises because of a lateral (centripetal) acceleration, which
causes a radial pressure gradient that drives slower moving fluid near the vessel
wall towards the center, while faster moving fluid in the vessel core is swept out-
wards. The strength of the secondary flow is characterised by the Dean number
De
.
For a unifromly curved vessel with slight curvature, the Dean number is defined as:
1/ 2
2
aU
a
1/ 2
De
=
=
2
δ
Re
(4.23)
ν
R
where
δ
is the ratio of the vessel radius (
a
) to the radius of curvature (
R
) ,
U
is the
mean axial velocity in the vessel. Therefore, the Dean number is the ratio of the
square root of the product of the inertial and centrifugal forces to the viscous forces,
and equals to the Reynolds number modified by the vessel curvature.
Although the arotic arch geometry used here is much more complex than a uni-
formly bent pipe, some conculsions regarding the secondary flow motion can be
drawn using the above concept. At the distal descending thoracic arota (Fig.
4.21c
),
plane C-C, the Dean number is relatively large and the blood flow experiences a
strong radial acceleration, which pushed the symmetirc pair of counter-rotating vor-
tices towards the outer wall of the bend. At plane D-D, as a comparison, the vessel
curvature is reduced. Its corresponding Dean numer becomes small. Consequently,
a single vortex is obsevred close to the vessel center and the maximum circumfer-
ential velocity is attained in the center of the vessel.
4.7.4
Aneursym in Abdominal Aorta
Using the same anatomical model, the haemodynamics of the abdominal aortic an-
eurysm is investigated here. Abdominal aortic aneurysm (AAA) is an irreversible,
localized growth, typically in the infra-renal region of the aorta. The causes and
details of an aneurysm were discussed in Chap. 2, but essentially an aneurysm is
a balloon-like swelling extending out from an artery. Artery walls can withstand
normal blood pressure. However certain medical problems or trauma and injury can
weaken its walls, leading to a growth of an aneurysm.
Fluid dynamics has been found to play an important role in understanding
and predicting the initiation, growth, and rupture of aneurysms. Computational
modelling allows for the investigation of flow patterns and drag forces on stent-
grafts, which may influence stent-graft migration after its implantation. In this sec-
tion, an AAA model with a diameter of 36 mm (Fig.
4.22a
) is used to investigate the
basic intra-aneurysmal flow characteristics.
The fluid domain is first meshed with hexahedral cells, and a near wall refine-
ment is imposed at the wall to improve the grid resolution (Fig.
4.22b
). Using the
same CFD modelling strategy, the inlet of the interest fluid domain is set as a ve-
locity inlet, and the velocity value is determined according to the same Reynolds
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