Computational Fluid Structure Interaction - Computational Hemodynamics: Theory, Modelling and Applications - page 96

Fig. 5.2 Main artery bifurcations in the body which include a carotid arteries b coronary arteries,
and c abdominal aorta artery

5.2.1.1 Artery Bifurcation Example

Throughout the circulatory network, many parts of the arteries bifurcate into subse-
quent smaller branches. The major bifurcations include the carotid artery, coronary
artery, and abdominal aorta bifurcation (Fig. 5.2 ). There are two common carotid
arteries, the left and right, which sub divide in the neck to form the external and
internal carotid arteries to deliver oxygenated blood to the head. Both the left and
right main coronary arteries bifurcate into smaller branches which in turn bifurcate
again into even smaller branches to surround the heart with a network of branches.
The abdominal aorta is the largest artery in the abdominal cavity and is a continu-
ation the aorta in the heart. It bifurcates at the fourth lumbar vertebrae into the left
and right common iliac arteries.
In these geometries the main flow is divided into two separate streams, and
therefore its mass flow rate is divided, and in the case of the main coronary artery,
subsequent bifurcation continues. Subdivision of the flow rate is dependent on the
resistance to flow and this is determined by the branch diameters and its alignment
with the main branch. Nevertheless the mass flow must be conserved throughout the
entire branch network. Figure 5.3 demonstrates the mass conservation through an
idealised bifurcation network. If we consider the mass flow rate at the inlet as m 1 ,
then the sum of all the mass flow rates through the outlets must equal to m . 1 ,

          

m mm mmmmmm m m =+=+++++++

1 2 3 4 5 6 7 8 9 10 11

5.2.1.2 One-Dimensional Vessel Flow Example

In Chap. 4 we saw that from the inlet, the velocity profile changes from a constant
velocity profile 1 uU at the pipe entrance to a parabolic profile in the fully devel-
oped region (Fig. 5.4 ).
The mass flow rates at the inlet and the fully developed region must equal, for
mass conservation. The velocity profiles are different but the cross-sectional areas