Biomedical Engineering Reference
In-Depth Information
The governing partial differential equations for the k-ω
turbulent model are
2
0
1
A @ k
@x j
3
@t ðρkÞ 1 @
@
@x j ðρU j kÞ 5ρP2ρωk1 @
μ1 μ t
σ k
4
@
5
@x j
2
0
1
A
@x j
3
ð
13
:
14
Þ
@t ðρωÞ 1 @
@
1 @
@x j
μ1 μ t
σ k
4
@
5
2
@x j ðρU j ωÞ 5αρP2βρω
where
are closure coefficients, which are constants.
In the near-wall regions, a majority of the turbulent kinetic energy is dissipated.
Therefore, by including the dissipation rate within the solution, the k -
α
and
β
turbulent model
delivers a more accurate near-wall solution. Also, by averaging the Navier-Stokes equa-
tions, changes in the turbulent properties are smoothed. A method to calculate the irregu-
lar changes within turbulent flows is the large eddy simulation (or LES), which follows
the development of small turbulent vortices within the fluid. Another method of turbulent
modeling is through the direct coupling of the Navier-Stokes equations and the continuity
equations, which is termed the direct numerical simulation (or DNS) of flow properties.
Many biofluid mechanics labs use computational fluid dynamics to predict regions
within the flow fields that are likely to facilitate cardiovascular disease development,
model the performance of implantable cardiovascular devices, or to just model and predict
the flow profiles within the body. These studies have significantly helped the biofluids
community gain understanding of many of the biofluid mechanics principles discussed
within this textbook. Also, the design of implantable cardiovascular devices can be signifi-
cantly improved with the help of computational fluid dynamics. For instance, mechanical
heart valves tend to disrupt the flow profiles distal to the valve as compared to the native
valves. A few research groups have built numerical models with accurate valve geometries
to investigate how the implantation of an artificial heart valve affects the local flow field
under transient and turbulent flow conditions. Also, these groups have asked, Why do the
mechanical heart valves disrupt blood flow, and how can we minimize the disruption?
With this knowledge, valve designs have been modified and performances of the artificial
valves have been improved.
Studies have also been conducted by many research groups to identify areas in specific
blood vessels (such as coronary arteries) that may induce large-magnitude transient shear
stresses, oscillatory shear stresses, as well as large shear stress gradients. Altered shear
stress in these regions has a higher potential to antagonize endothelial cells, platelets, and
red blood cells to initiate activation and/or inflammatory processes. This tends to lead to
an increased likelihood of cardiovascular disease formation at these areas. With early iden-
tification of these locations, it may be possible to target disease interventions toward these
regions. Computation fluid dynamics modeling can be used to predict disease initiation
and development.
For example, a model of a left coronary artery has been built using CFX (ANSYS 12.0)
( Figure 13.4 ), and a stenosis can be introduced downstream of the bifurcation where the
left main coronary artery divides into the left anterior descending artery and the left cir-
cumflex artery. Using the Wilcox k -
ω
ω
turbulent model, flow fields in the left coronary
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