In Silico Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 337

Using this method, it is possible to calculate the velocity distribution through continu-
ous geometries by relating neighboring points. For instance, let us begin our analysis with
a two-dimensional geometry in a sudden expansion ( Figure 13.2 ). In biofluids, we can ide-
alize the flow of blood from the microcirculation (small diameter) into the venous system
(larger diameter) with this geometry. Let us assume that the diameter of the vessel
increases by 2.5 times at the step and the length of interest is 4 times that of the smaller
diameter.
Taking this geometry and meshing it with a total of 5120 square elements, the finite-
difference method can be used to solve for the velocity field throughout the expansion
( Figure 13.3 , solved with FEMLab). It was assumed that the velocity at the inlet had a par-
abolic profile. This simplified geometry can also be analyzed by hand (using 13.7 ), if the
input boundary conditions and the wall boundary conditions are known. In general, the
geometry and the grids do not need to be idealized as shown here. Later in this section,
we will discuss some work that is being conducted using computational fluid dynamics,
and we will see that the geometries and grids can be quite complex.

FIGURE 13.2 Idealized flow in a sudden

expansion from the microcirculation to the
venous system. Clearly, based on the geome-
try, the computational results will differ, but
with simple geometries an idea of the flow
field can be established.

2.5 d

d

4 d

FIGURE 13.3 Computational fluid dynamic solution for the flow conditions in Figure 13.2 . This illustrates

that in a sudden expansion, there will be a stagnation zone in which the fluid becomes trapped.