Biomedical Engineering Reference
In-Depth Information
characteristics need to be understood is shown in the form of a flow chart. The
geometry is divided into discrete points that together form polygons that give
the effect of a mesh on the surface of the body. The CFD solver then applies
physical and chemical data to the problem and the resulting equations are
solved to make flow prediction.
The application of CFD presumes a well-posed mathematical model of the
problem, by using conservation laws, boundary conditions, and in the case of
unsteady problems, initial conditions. Therefore, one cannot avoid the issue of
constitutive modelling. Since constitutive models are established by
conducting experiments, CFD cannot eliminate the need for experimental fluid
mechanics. CFD is therefore both a competitor as well as a natural
complement to experimentation. Figure 27 illustrates this relationship
graphically.
Reproduced with permission. Copyright retained by Inderscience Publishers.
Figure 27. CFD along with constitutive modeling gives an effective understanding of
the flow process.
Navier-Stokes' (NS) Equations
The equations of motion for general isothermal laminar flow of a
Newtonian incompressible fluid were originally derived by F. Navier and then
developed further by C. G. Stokes. The complete derivation of these equations
was the culmination of centuries of philosophical, empirical, and scientific
observation and discussion of fluid flow phenomenon. These equations form
the basis for studying most fundamental phenomena in fluid flow. In cartesian
coordinates, V = V(
x, y, z, t
), the equations are given as,
Continuity
∂u/∂x + ∂v/∂y =
0
(7)
u, v
are the components of flow velocity in x and y directions,
respectively. The continuity equation is a mathematical form of the law of
conservation of mass, which implies that the total mass flowing through a
