Simulation and Visualization of Air Flow Around Bat Wings During Flight

Abstract

This paper presents a case study of interdisciplinary collaboration in building a set of tools to simulate and visualize airflow
around bat wings during flight. A motion capture system is used to generate 3D coordinates of infrared markers attached to
the wings of a bat flying in a wind tunnel. Marker positions that cannot be determined due to high wing deformation are reconstructed
on the basis of the proper orthogonal decomposition (POD). The geometry obtained for the wings is used to generate a sequence
of unstructured tetrahedral meshes. The incompressible Navier-Stokes equations in arbitrary Lagrangian-Eulerian formulation
are solved using the hybrid spectral/hp element solver Nektar. Preliminary simulation results are visualized in the CAVE,
an immersive, 3D, stereo display environment.

Full text

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V.S. Sunderam et al. (Eds.): ICCS 2005, LNCS 3515, pp. 689 – 694, 2005.
© Springer-Verlag Berlin Heidelberg 2005
Simulation and Visualization of Air Flow
Around Bat Wings During Flight
I.V. Pivkin1, E. Hueso2, R. Weinstein2,
D.H. Laidlaw2, S. Swartz3, and G.E. Karniadakis1
1 Division of Applied Mathematics
2 Department of Computer Science
3 Department of Ecology and Evolutionary Biology,
Brown University, Providence, RI 02912, USA
Abstract. This paper presents a case study of interdisciplinary collaboration in
building a set of tools to simulate and visualize airflow around bat wings during
flight. A motion capture system is used to generate 3D coordinates of infrared
markers attached to the wings of a bat flying in a wind tunnel. Marker positions
that cannot be determined due to high wing deformation are reconstructed on
the basis of the proper orthogonal decomposition (POD). The geometry
obtained for the wings is used to generate a sequence of unstructured tetrahedral
meshes. The incompressible Navier-Stokes equations in arbitrary Lagrangian-
Eulerian formulation are solved using the hybrid spectral/hp element solver
Nektar. Preliminary simulation results are visualized in the CAVE, an
immersive, 3D, stereo display environment.
1 Introduction
Fluid dynamics approaches have revolutionized our understanding of insect flight,
revealing aerodynamic mechanisms almost unimaginable only 25 years ago [1–9].
Although bat and bird flight is also likely to yield insights of use in future
technological application, such as the development of unmanned micro-air vehicles
[10,11], researchers of vertebrate flight are just beginning to incorporate in their work
sophisticated methodologies drawn from the physical and mathematical sciences
[12−14]. The unique features of bats – their specialized skeletal anatomy, high
muscular control over wing conformation, and highly deformable wing-membrane
skin – yield wings that undergo large changes in 3D geometry with every wing-beat
cycle, and consequently produce highly maneuverable and energetically efficient
flight [15−18].
To date, however, bat flight has not been studied from the quantitative perspective
of unsteady aerodynamics. In particular, there is no rigorous understanding of the
mechanisms by which the bat generates the high aerodynamic coefficients necessary
for its flight capabilities, or of the vortex structure associated with the bat’s exquisite
aerodynamic control. Simulation of airflow around wings that not only flap but also
undergo enormous shape changes in each wing-beat poses significant technical
challenges, as does visualizing the complex 3D data such studies necessitate.

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690 I.V. Pivkin et al.

This paper describes our interdisciplinary collaboration to build a set of tools for
simulation and visualization of airflow around bat wings during flight. The next
section gives a brief overview of our data acquisition techniques. In section 3 we
discuss data preprocessing, which is necessary to provide input for the numerical
simulations described in section 4. Finally, the visualization of preliminary simulation
results is presented in section 5.
2 Data Acquisition
The motion-capture data of bat flight were acquired by flying more than 20
individuals of several species through a wind tunnel [18]. Two high-speed digital
cameras tracked infrared markers attached to the bat wings. We chose to study the
flight of a Pteropus Policephalus because of its large size and relatively slow motion.
After selecting 160 video frames where the motion of the bat is close to one
complete wing beat, the Peak [19] motion capture system was used to extract the 3D
coordinates of markers. These data are utilized to animate a simple 3D polygonal
model of the surface of the bat’s wings [20] (Fig. 1). Due to high wing deformations
during flight, the 3D coordinates of a few markers cannot be determined in some
frames. At the heart of generating polygonal bat wing model is the ability to
reconstruct accurately the positions of these markers.

Fig. 1. Video capture of bat wing shape changes
3 Missing Data Reconstruction
Here we follow an approach based on proper orthogonal decomposition (POD)
combined with the least-squares approach first proposed in [21] for image
reconstruction. Let us consider a vector of data points
frame t, where N is the number of markers attached to the bat wings. We assume that
we have available a finite number P of frames. We then look for a representation of
u(t) in the form
N
t
)(
ℜ ℜ
)(
3
∈ ∈
u
given for each

,)(
1
0
∑ ∑
= =
k
+ += =
N
kk
t
φφ
u
α

(1)

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Simulation and Visualization of Air Flow Around Bat Wings During Flight 691

where
∑ ∑
= =
= =
P
t
t
1
0
)(
u
φ
is a mean (time-averaged) position of the markers and
k
φ

are the orthonormal spatial modes. The unknown functions
k
φ can be calculated by
minimizing an energy functional, producing a POD or Karhunen-Loeve
decomposition.
The formulation assumes the completeness of the data; modifications are required
if there exist a space-time regions in which components of u(t) are missing or
corrupted. The procedure proposed in [21] completes the missing data iteratively
starting from the average value at missing data location as the initial guess for the
unknowns.
In order to make the bat motion cyclic, as is desirable for numerical simulations,
we enforce periodicity on the POD mode coefficients
)(t
k
α
.
4 Numerical Simulations
The animated polygonal model is the basis for a sequence of tetrahedral meshes of the
volume of 10 by 10 by 20 around the bat geometry, which has a wing span of
approximately two non-dimensional units at its widest. Wings are represented by an
infinitely thin tessellation of triangles (Fig. 2). An arbitrary Lagrangian-Eulerian
(ALE) formulation of the incompressible Navier-Stokes equations is employed to
solve for the flow field. This allow us to run simulations with changing geometry
without remeshing each time step. A single tetrahedral mesh can be deformed to fit a
number of frames, typically between 7 and 15 depending of the rate of deformation.
When the deformation of the mesh becomes too extreme, elements degenerate and a
new tetrahedral mesh must be created. As a result, multiple meshes are necessary and
must be interpolated together in order to simulate an entire wing-beat. The mesh
generator Gridgen [22] is used to generate up to 15 meshes for one wing-beat. Each
mesh has approximately 6000 spectral tetrahedral elements. The governing equations
are solved using the hybrid spectral/hp element solver Nektar [23].
Preliminary simulations were performed using third-order polynomial expansion in
each element. The Reynolds number was set to 100, greatly reducing computational


Fig. 2. Some of the meshes used in simulations

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692 I.V. Pivkin et al.

effort and time. The solver produced 40 snapshots over one periodic motion cycle that
describe the fluid velocity and the pressure distribution around the animated bat
wings.
5 Visualization
The size and complexity of the time varying fields generated by the simulation makes
them unfit for real-time visualization. To overcome this limitation, we pre-compute
and store sets of pathlines and streamlines that can later be visualized interactively.
The line sampling and visualization methods used on the bat flow data is a variation
of the one presented in [24] for the visualization of blood flow in a coronary artery.
We visualize the flow data in the CAVE [25], an immersive 3D stereo display
environment that scientists find more engaging than our less sophisticated desktop
displays. One of our visualizations shows massless particles flowing down pre-
computed pathlines that resemble eels of variable length, color and opacity. A second
visualization relies on animated streamlines, represented with lines of variable color
and opacity. The user has interactive control over the number of lines displayed, how
randomly they are distributed in space, and the mapping of opacity to flow quantities.
These controls allow users to explore a continuum between localized visualization of
detected vortices and the contextual flow around them [26] (Fig. 3).
Fig. 3. Three different visualization methods are used to show different characteristics of the
structure of the simulated flow around a motion-captured bat: (left to right) particle eels display
pathlines, time-varying streamlines show vortices atop the wing during a down beat, and white
dots capture structures in the wake
6 Discussion and Conclusions
Our studies differ from previous studies of bat flight in an important way: we do not
treat the wings as simple oscillating plates, but instead explicitly characterize the
changing intrinsic wing structure of potentially great aerodynamics importance. This
makes realistic Reynolds number simulations challenging. The preliminary results
reported here were obtained for Re=100, too low to make judgments about the
mechanisms by which the bat executes its flight capabilities. Even with higher
Reynolds number simulations, the results would ideally be compared with

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Simulation and Visualization of Air Flow Around Bat Wings During Flight 693
experimental measurements to validate our process. Our current simulation results let
us develop prototype visualization techniques that we believe can be extended to the
flows with higher, more realistic Reynolds numbers. However, we have found that the
preprocessing time and complexity of the visualization tools make them difficult to
use on an everyday basis. Initial feedback does show that these tools help
significantly in the exploration of complex time-dependent flow data.
In conclusion, we have completed a full iteration of simulation and visualization of
unsteady flow around the bat wings during the flight. We believe that progress in
understanding the relationship among wing shape, movement, and airflow during bat
flight benefits significantly from the kind of interdisciplinary collaboration presented
in this paper.
Acknowledgements
This work was supported in part by NSF (CCR-0086065 and CNS-0427374).
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