Biomedical Engineering Reference
In-Depth Information
Table 8.1
Summary of viscous model and flow setup for selected human nasal cavity simulations
Researcher
L/min
Viscous
Steady/
Heat
Mesh
(peak)
model
Unsteady
transfer
size
Pless et al. (2004)
30
Turbulent
Steady
Yes
360,000
Weinhold and Mlynski (2004)
12-84
Turbulent
Steady
No
Not reported
Zhao et al. (2006)
14-55
Both
Steady
No
Not reported
Lindemann et al. (2005)
18
Turbulent
Steady
Yes
360,000
Naftali et al. (2005)
15
Laminar
Unsteady
Yes
300,000
Schroeter et al. (2006)
15
Laminar
Steady
No
156,000
Croce et al. (2006)
21
Laminar
Steady
No
1.3 million
Garcia et al. (2007b)
15
Laminar
Steady
Yes
1.3 million
Xiong et al. (2008)
21
Laminar
Steady
No
1.8 million
Doorly et al. (2008)
6
Not reported
Steady
No
3.6 million
Lee et al. (2010)
35 (peak)
Turbulent
Unsteady
No
2.9 million
Liu et al. (2010a)
30-90
Turbulent
Steady
No
4.0 million
Horschler et al. (2010)
9-47
Not reported
Both
No
4.5 million
Zhu et al. (2011)
10
Laminar
Steady
No
3.9 million
Xi et al. (2011)
20
Turbulent
Steady
No
1.75 million
(transitional)
Inthavong et al. (2011)
20
Turbulent
Steady
No
3.5 million
(transitional)
observed reflected local flow regimes that have little effect on the bulk flow through
the nose. The average flow rate at which flow switched from transitional to turbulent
for the ten cast replicates was 11 L/min. To give the reader a feel for which flow
regime setup to use, Table
8.1
summarises work from the literature in regard to the
choices the researchers made. The survey of work in Table
8.1
shows a consensus
among researchers in choosing a laminar flow for flow rates less than 20 L/min. In
this study, flow rates of 7.5 and 15 L/min were used with a prescribed laminar flow
regime. These flow rates represent the combined total volume inhaled from both
nostrils per minute; thus each nostril will experience half the total flow rates (3.75
and 7.5 L/min respectively).
Steady or Unsteady
The inhalation process is clearly unsteady with an oscillatory
motion. In order to assess the importance of the unsteadiness on the mean or average
flow characteristics obtained through a steady solution, we make use of the Wom-
ersley number
α
and the Strouhal number
S
. The Womersley number is a ratio of
unsteady forces to viscous forces named after John R. Womersley (1907-1958) and
is defined as
ω
v
g
0
.
5
D
2
α
=
(8.1)
where
D
is the characteristic length which is taken as the inlet hydraulic diameter of
the nostrils equals 0.01 m:
ν
g
is the kinematic viscosity of air, and
ω
is the breathing
1
.
57 s
−
1
; and
u
ave
is the average velocity through the
nasal passage under the flow rate of 15 L/min which is equal to 0.9 m/s. When
α
is
small (1 or less), the oscillatory effects are sufficiently low that the inlet conditions,
=
=
frequency equal to
ω
2
πf
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