Biomedical Engineering Reference
In-Depth Information
6
5
4
3
2
1
0
0
2
4
6
x [mm]
Fig. 5.9
The considered geometry of the vocal folds for the female model F (
left
) and example of
the vocal fold in displaced position (
right
)
5.7
Numerical Examples
5.7.1
Interaction of Incompressible Flow with Rigid Body
Models of Vocal Folds
For the numerical analysis the following parameters were used. The distance of the
masses m
1
and m
2
from the center was l D L=2 (see Fig.
5.4
b). The total mass
m of the vocal folds, the inertia moment I, and the eccentricity e were computed
using the vocal fold shape a.x/ and the material density
s
D 1;020 kg m
3
, length
(depth of the channel) h
s
D 18mm and thickness L D 6:8mm, see [
39
] for details.
D 1:2 kg m
3
and the dynamic viscosity D 1:896
The fluid density was
f
10
5
kg m
1
s
1
.
The geometry of vocal folds depends on the tension in the vocal folds and varies
with the fundamental vibration frequency, loudness, and mode of phonation. For
the purposes of numerical analysis in this paper the geometry of the vocal folds
was chosen as linear function according to [
40
]asa
f
.x/ D 0:77120x [m] (linear
shape, approximation of the vocal fold for female—model F) or the vocal fold with
intermediate bulging a
m
.x/ D 1:858x 159:861x
2
[m] (parabolic shape, approx-
imation of the vocal fold for male—model M), see Figs.
5.9
and
5.10
, respectively.
The channel half-height (at time t D 0) is chosen as H
0
D max
x
2
Œ0;L
a.x/ C g
0
,
where g
0
is the initial half-gap, i.e., g.0/ D 2g
0
. The considered initial half-gap was
chosen g
0
D 0:25mm and g
0
D 0:3 mm for model F and model M, respectively.
In all computations the subglottal length L
0
D 1:5L and the supra-glottal length
L
2
D 5Lwere used. The computations were performed in the domains
t
shown
in Fig.
5.11
with H
0
D 5:54416mm and H
0
D 5:7 mm for model F and model M,
respectively.
Aeroelastic Simulations for Model F with Inlet Pressure Condition
First, the problem of interaction of air flow with aeroelastic model F was considered
with the inlet pressure boundary condition. The structural parameters and the
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