Case Studies in the Human Respiratory System - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 234

such as a parabolic velocity profile, have time to develop during each cycle, and the
flow will be very nearly in phase with the pressure gradient. When α is large (10 or
more), the oscillation effects are sufficiently large that the velocity profile does not
develop in time and the mean flow characteristics lag the pressure gradient by about
90 ◦ , Womersley (1955). The Strouhal number is a ratio of the unsteady forces to the
inertial forces named after Vincenc Strouhal (1850-1922) and is defined as

ωD
u ave

=

S (8.2)

where u ave is the mean airflow velocity. For large S ( > 1), the oscillations become
important. For low S ( 1), the contribution of the velocity dominates the oscillations.

The calculated α and S numbers for the nasal cavity in this case study are 1.68 and
0.01, respectively. Although α is greater than 1, it is not much greater, while the
low value for S suggests that the flow may be assumed to be quasi-steady. It has,
however, been shown experimentally that the oscillatory effects are not present until
α> 4 (Isabey and Chang 1981). Other studies have also concluded that under most
conditions, especially low flow rates, the nasal airflow can be considered quasi-steady
(Chang 1989; Hahn et al. 1993; Sullivan and Chang 1991).
Inlet/Outlet Conditions Boundary conditions for the computational surfaces need to
be defined. While the surface walls are easily understood in terms of their definition
as a rigid wall boundary (see Sect. 9.2 for dealing with elastic walls), the nostril
inlets and the nasopharynx outlet provide the user with more options for definition.
In this case study, a uniform flow perpendicular to the nostril inlet was specified. This
assumption is based on the data of Keyhani et al. (1997) which showed that a velocity
profile at the nostrils for a given flow rate did not show significant differences on the
downstream flow field when compared with experimental data. In addition, the flow
rates of the left and right nostrils are assumed to be the same. This does not simulate
real breathing perfectly since the flow is induced from the lungs drawing the air from
the nostrils which are affected by geometrical differences leading to varied flow rates
between the cavities.
However, for this case study, the focus is to present the ability of CFD to capture the
micro-fluid structures that exist in flow patterns within the left and right cavities under
a steady-state solution while being able to compare these results against available
experimental data that are based on a fixed flow rate through a single nasal cavity
side (Keyhani et al. 1995; Subramaniam et al. 1998). Therefore, it is important to
maintain similar settings and to keep the flow rates between the two cavities the
same.
To give the reader a more complete understanding of applying boundary condi-
tions, the pressure boundary condition for modelling the breathing cycle is discussed
here. The breathing cycle is caused by the pressure difference induced by the di-
aphragm flattening/contracting to increase/decrease the volume of the pleural cavity.
Therefore it is natural to assign the nostril inlets and the nasopharynx outlet as
pressure conditions. The inlet pressure condition is used to define the total pressure
and other scalar quantities at flow inlets. It is an ideal condition to use when the