1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Simulation of an inhomogeneous elastic filament falling in a flowing viscous fluid
Rent:
Rent this article for
USD
10.1063/1.2433127
/content/aip/journal/pof2/19/1/10.1063/1.2433127
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/1/10.1063/1.2433127

Figures

Image of FIG. 1.
FIG. 1.

The typical trajectories of the filament with no or small external disturbances. The left figure corresponds to no external disturbances and the right figure corresponds to small magnitude disturbances. The filament falling motion is stable when no external disturbances or instantaneous external disturbances of small magnitude are imposed.

Image of FIG. 2.
FIG. 2.

The trajectories of the filament subjected to large disturbances. Each figure corresponds to a different bending rigidity and/or a different mass density. See Figs. 3 and 4 for details of density and rigidity distributions. The disturbances are imposed on the center portion of the filament for all cases on the bottom panel. For the top panel, disturbances on the right portion for the first and third cases, and on the left portion for the second case. We see that the large disturbances bring the filament motion into a totally different state than the stable state.

Image of FIG. 3.
FIG. 3.

The filament bending rigidity as a function of filament length for each case in Fig. 2. Each figure corresponds to the case at the corresponding location in Fig. 2, respectively. The axis is the filament length (dimensionless), the axis is the dimensionless bending rigidity. The values of the dimensionless mean bending rigidity are from top left to bottom right, respectively.

Image of FIG. 4.
FIG. 4.

The filament mass density as a function of filament length for each case in Fig. 2. The axis is the filament length (dimensionless), the axis is the dimensionless mass density. The curved line corresponds to the second case on the top of Fig. 2. The straight line corresponds to all of the other cases. The values of the dimensionless mean mass density are 0.9778, 0.9756, 0.9778, 0.9778, 0.9778, 0.9778, from top left to bottom right, respectively.

Image of FIG. 5.
FIG. 5.

The visualization of the flow field for the third case on the upper panel of Fig. 2. The top group is the instantaneous fluid marker positions, and the bottom group is the vorticity contours. The dark line represents the filament. The four dimensionless instants from the left to the right are 2.0, 3.0, 4.0, 5.0, respectively.

Image of FIG. 6.
FIG. 6.

The visualization of the flow field for the first case on the lower panel of Fig. 2. The top group is the instantaneous fluid marker positions, and the bottom group is the vorticity contours. The dark line represents the filament. The four dimensionless instants from the left to the right are 2.0, 3.0, 4.0, 5.0, respectively.

Image of FIG. 7.
FIG. 7.

Comparison of trajectories for homogeneous (dashed curves) and inhomogeneous (solid curves) filaments. The three figures correspond to three different loading locations of external disturbances: on the left portion (left figure), on the right portion (middle figure), and on the middle portion (right figure). All the other parameters are the same for the three figures. For each figure, two simulation results were plotted together. The only difference between the two simulations is the mass density distribution: one is linearly distributed (see Fig. 8) the other is uniformly distributed (taken as the mean value of the linear distribution). The dimensionless bending modulus is a constant (0.00926).

Image of FIG. 8.
FIG. 8.

The mass distribution over the filament arc-length for the inhomogeneous filament in Fig. 7.

Image of FIG. 9.
FIG. 9.

Comparison of trajectories for homogeneous (shadowed curves) and inhomogeneous (solid curves) filaments. The only difference for the two results in each figure is the bending modulus. See Fig. 11 for bending modulus distribution of the inhomogeneous filament. The bending modulus of the homogeneous one is a constant (the mean value of the inhomogeneous distribution). Three figures correspond to three different loading locations of external disturbances. Counting from the left to the right, the disturbance was loaded on the left, right and middle portion of the filament, respectively.

Image of FIG. 10.
FIG. 10.

The trajectories of the filament subjected to initial large external disturbances on different locations. The disturbance is imposed on the left, right, and center portions of the filament from the left to the right, respectively. As a consequence the filament falls in significantly different ways. This indicates the complexity of the filament motion in a flowing viscous fluid because of the interaction of elasticity and hydrodynamics.

Image of FIG. 11.
FIG. 11.

The bending rigidity distribution for the case in Fig. 10. The axis is the filament length (dimensionless), the axis is the dimensionless bending rigidity. The mean bending rigidity is 0.0046, and the dimensionless mass density is 0.9017.

Image of FIG. 12.
FIG. 12.

The flow and filament visualization for the first case in Fig. 10 for ten different time instants (continued in Fig. 13). The top figures are instantaneous positions of fluid markers and the lower figures are corresponding vorticity contours at the same time instant. The dimensionless time instants are 0.667, 1.200, 1, 733, 2.267, 2.800, from the left to the right, respectively.

Image of FIG. 13.
FIG. 13.

Continued from Fig. 12. The dimensionless time instants are 3.333, 3.867, 4.400, 4.933, 5.467, from the left to the right, respectively.

Image of FIG. 14.
FIG. 14.

The flow and filament visualization for the third case in Fig. 10 for ten different time instants (continued in Fig. 15). The top figures are instantaneous positions of fluid markers and the lower figures are corresponding vorticity contours at the same time instant. The dimensionless time instants are 0.667, 1.200, 1.733, 2.267, 2.800, from the left to the right, respectively.

Image of FIG. 15.
FIG. 15.

Continued from Fig. 14. The dimensionless time instants are 3.333, 3.867, 4.400, 4.933, 5.333, from the left to the right, respectively.

Tables

Generic image for table
Table I.

Parameters used in the simulations.

Generic image for table
Table II.

Nondimensional parameters used in the simulations. For the meanings of the symbols used in the definition of the nondimensional parameters, see Table I.

Loading

Article metrics loading...

/content/aip/journal/pof2/19/1/10.1063/1.2433127
2007-01-18
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simulation of an inhomogeneous elastic filament falling in a flowing viscous fluid
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/1/10.1063/1.2433127
10.1063/1.2433127
SEARCH_EXPAND_ITEM