Case Studies in the Human Respiratory System - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 236

where E is the energy term from Eq. 5.16 and is related to the sensible enthalpy ( h ),
pressure, and kinetic energy. The mass transfer equation for water vapour can be
written as

∂ ( ρYu i )
∂x i

∂J i
∂x i

=− (8.4)

where Y is the vapour mass fraction and J is the vapour diffusion flux which arises
due to concentration gradients. For a laminar flow,

ρD ∂Y
∂x i

J i =− (8.5)

where D is the diffusivity which varies with temperature and is expressed by the
semi-empirical correlation from Vargaftik (1975):

2 . 16 e − 5 T
273 . 15

1 . 8

D = (8.6)

Equations (8.3) to (8.5) are usually defined automatically within the CFD software
package. Eq. (8.6) is a fluid property and is usually defined with a constant value. In
this case, the diffusivity varies with temperature, and therefore a customised function
is needed.

8.2.3 Geometry Comparisons

Fourteen cross-sections evenly spaced apart in the x -direction were created to be
used for geometry and flow analysis. The cross-sectional areas versus distance from
the anterior tip of the nose of the left and right cavities are compared in Fig. 8.3 .
In the anterior region of the nasal cavity ( x< 26 mm) and the posterior turbinate
region ( x> 44 mm), the cross-sectional area of the right cavity is larger than that of
the left, while in the middle region the right side is smaller than the left.
The developed computational model was also compared with other nasal cavities
of which existing data were available. Although inter-subject variations in the nasal
cavity geometries exist, a general trend can be observed on a macro level. For exam-
ple, a local minimum is found for all profiles just after the inlet where the nasal valve
region exists. The nasal valve is the narrowest region where the cross-sectional area
was found to be 1.4 cm 2 which compares with 1.6, 1.9 and 2.0 cm 2 in the models
by Subramanian et al. (1998); Cheng et al. (1996) and Keyhani et al. (1995), re-
spectively. At the anterior turbinate region, the airway expands to accommodate the
olfactory sensors and the turbinate bone projections. This is reflected by an increase
in the cross-sectional profiles which is observed immediately after the nasal valve
region. For the current geometry, the nasal valve region is located about 2.0 cm from
the anterior tip of the nose, which compares with the other models that are all located
around 3.0 cm away from the anterior tip of nose (Fig. 8.3 ).