Numerical Simulation of Fluid–Structure Interaction Problems with Applications to Flow in Vocal Folds - Fluid-Structure Interaction and Biomedical Applications - page 358

a

1.565 0.00012 0.00025

1.5645 0.0001

0.0002

8e-05

1.564

6e-05

1.5635 0.00015

4e-05

1.563

2e-05 0.0001

1.5625

0

1.562 5e-05

-2e-05

1.5615 -4e-05

0

1.561 -6e-05

-8e-05 -5e-05

1.5605

0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05

0 0.01 0.02 0.03 0.04 0.05

t[s] t[s]

t[s]

b

2.2155 2e-05 5e-05

-2e-05 0

2.215

0

2.2145

-4e-05

-5e-05

2.214 -6e-05

-8e-05

2.2135 -0.0001

-0.0001

2.213 -0.00012

-0.00015

-0.00014

2.2125

-0.00016 -0.0002

2.212

-0.00018

2.2115 -0.0002 -0.00025

0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05

0 0.01 0.02 0.03 0.04 0.05

t[s] t[s]

t[s]

c

3.134

0.00016 0

3.1335

0.00014

-5e-05

3.133 0.00012

0.0001

3.1325

-0.0001

8e-05

3.132

6e-05 -0.00015

3.1315

4e-05

3.131 -0.0002

2e-05

3.1305

-2e-05 0

-0.00025

3.13

3.1295 -4e-05 -0.0003

0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05

0 0.01 0.02 0.03 0.04 0.05

t[s] t[s]

t[s]

Fig. 5.1 3 The m ean inlet velocity oscillations ( left column ) and the aeroelastic response of the
system w 1 .t/, w 2 .t/ ( middle and right columns )for model F and the prescribed inlet pressure
boundary conditions. The inlet pressure was chosen ( a ) p D 800 Pa, ( b ) p D 1;600 Pa, ( c )
p D 3;200 Pa

a

0.003 0.0025

0.0025

0.002

0.002

0.0015

0.0015

0.001

0.001

0.0005

0.0005

0 0

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2

t[s] t[s]

b

0.004 0.003

0.0035

0.0025

0.003

0.002

0.0025

0.002 0.0015

0.0015

0.001

0.001

0.0005

0.0005

0 0

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2

t[s] t[s]

Fig. 5.14 The aeroelasti c resp on se of the aeroelastic system for model F with the prescribed inlet
velocity; the graphs of w 1 .t/, w 2 .t/ in dependence on time t are shown for the different inlet
velocities ( a ) V 0 D 0:45 ms 1 and ( b ) V 0 D 0:55 ms 1

The values of the inlet velocity V 0 were considered in the range 0.2-0.7 m s 1
in order to detect the critical velocity for the flutter type of aeroelastic instability
leading to self-sustained vibrations of the vocal fold. The aeroelastic responses are
shown in Figs. 5.14 and 5.15 for the inlet flow velocities V 0 D 0:45 ms 1 , V 0 D
0:55 ms 1 , V 0 D 0:6 ms 1 and V 0 D 0:65 ms 1 . For the velocities 0:45 ms 1 and