In Silico Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 354

What happens if complete dynamic similarity is not achievable, because there are
too many parameters to match between the real scenario and the model? In some
instances, by solving the dimensionless groups simultaneously, it can be found that no
fluid exists that can match the properties needed.Forinstance,ifonewasmodelingthe
flow around an airplane wing, you may want to make a 1/10 or 1/50 model, which
would then dictate the other properties of the fluid and the experimental conditions.
By matching as many parameters as possible (velocity, wave frequency), it is typical
that the fluid viscosity or density is what needs to be modified to make the solution
dynamically similar. What happens when there is no known fluid that exists that can
match the required parameters? Should some of the other parameters be altered to find
a suitable fluid? If there is an incomplete dynamic similarity, then the only way to
achieve a similar model is to use a full-scaled model, which may not be reasonable
(what if it is a nuclear submarine or a single cell?). However, studies have shown that
some of the data that are obtained from incomplete dynamically similar solutions are
still useful. Therefore, it is best to match as many parameters as possible when model-
ing a real scenario, but if all of the parameters cannot be matched, then this must be
accounted for when analyzing the data.

END OF CHAPTER SUMMARY
13.1 Computational fluid dynamics is a method that can be used to solve the coupled governing

equations of biofluid flow, without making many simplifying assumptions. The most com-
mon method to solve CFD simulations is to mesh a realistic geometry and then by using
either the forward difference method or the backward difference method, the fluid proper-
ties can be obtained at subsequent grid points. The equation takes the form of

i 5

@f
@x

f i 1 1 2 f i 1 1
2 Δx 1H:O:T:

Under these simulations, it is also possible to incorporate turbulent flow properties into the
simulations. The most commonly used models are either the k -

ε or the k - ω turbulent mod-

els, which are defined by

1
2 u i u i

k5

ð

t 1Δt

1
Δt

ε5u i;j u i;j 5ν u i;j u i;j dt

t

ε5 kω

A second useful tool that is incorporated into many CFD commercial software packages is
the ability to solve for the discrete movement of particles within the fluid. By coupling
Newton's laws to the fluid dynamics laws, equations can be composed that determine the