PROJECT SUMMARY REPORT
FLOW SIMULATION OF A MAPLE SEED
Submitted To
The 2013 Academic Year NSF AY-REU Program
Part of
NSF Type 1 STEP Grant
Sponsored By
The National Science Foundation
Grant ID No.: DUE-0756921
College of Engineering and Applied Science
University of Cincinnati
Cincinnati, Ohio
Prepared By
Thomas Caley, Junior, Aerospace Engineering
Jake Holden, Junior, Aerospace Engineering
Report Reviewed By:
Dr. Mark Turner
REU Faculty Mentor
Research Professor
Aerospace Engineering
College of Engineering and Applied Science
University of Cincinnati
September 9 – December 5, 2013
INTRODUCTION
The purpose of a wind turbine is to extract kinetic energy from the air, turning it into
electrical energy. The purpose of the maple seed is to harness power from the air to travel as
far as possible. In this sense, wind turbines, and specifically their blades, are a form of
biomimicry of the maple seeds and other types of samaras (winged-seeds). By assuming
nature has spent eons optimizing the shape of various maple seeds, it stands to reason that
potentially more efficient turbine blades can be developed by analyzing the organic models.
However, little research has been done on the maple seeds beyond analyzing the equations
of motion and experimentally proving them. The flow fields of maple seeds is a topic now
possible using computational fluid dynamic software. From the fields and scalars available
through simulations, conclusions can be drawn about how to create more efficient turbines.
The main goal of the project is to examine flow field simulations of a maple seed to determine
its efficiency as a natural wind turbine. Objectives include gathering data about the maple
seed and its physical properties, creating an accurate simulation, and drawing conclusions
about applications of seed geometry in the aerospace field.
TASKS AND METHODS
The majority of the research was done on various computers using the computational fluid
dynamics solver STAR-CCM+. Training was provided by CD-Adapco, the creator of STARCCM+, and their tutorials were a major reference. A high speed video camera was used to
film a dozen falling maple seeds, from which some aerodynamic properties were calculated.
Maple seeds from several sub-families were used in the process. We obtained 4 CT-scans of
maple seeds from Exact Metrology, and were able to use these CT-scans as the base model
for the maple seeds in STAR-CCM+.
Figure 1: Snapshot from the high-speed video taken of a rotating maple seed.
One of the first steps for the research was gathering accurate physical data about the
maple seeds – chiefly rotational and translational speeds and the axis of rotation. These
values were gathered from the high speed video taken of the maple seeds. By capturing
maple seeds at 300 frames per second in a 6.5 inch by 4.5 inch window, it was determined
that the axis of rotation is about .008133 meters from the base of the seed, for a .04418
meter long seed. The rotational speed was calculated to be 1516.24 rpms, or 158.78 rad/s at
the tip of the seed. This is equivalent to a 5.724 m/s tangential velocity at the tip. Finally, the
vertical velocity was found from the videos to be 1.39 m/s. Because of the very low speeds at
which the seed travels (Mach .019 at the tip, Mach .00467 vertically), we assumed a steady,
incompressible flow for our simulations.
The first simulations we created for this project involved a stagnant seed in a duct. This
allowed us to look at how the air interacts with the seed’s surface, and the resulting flow field.
While not an accurate representation of nature, it was a logical first step. After creating the
duct around the seed in STAR-CCM+, we added a flow with velocities obtained from our
high-speed video. For this non-realistic case, we assumed an ideal flow – a steady, inviscid
flow with air as the fluid. Our mesh for these simulations was a polyhedral prism layer mesh
with .001 meter base size and 5 prism layers. This was high enough mesh density for the
early simulations. Figure 2 below shows the various meshes for the surfaces. The inlets and
walls of the duct had a coarser mesh than the seed, since our focus is on the flow fields
resulting from the seed’s manipulation of the air.
Figure 2: Close up of the surface meshes.
The next set of simulations involved rotating the seed in a cylindrical duct, with air flowing
over the seed at the same speeds as above. The duct created for these simulations initially
had a cross sectional radius of twice the seed’s length. In an effort to reduce the effect of the
side walls, this radius was increased to 4 times the length of the seed. Our duct was set up
with a velocity inlet and pressure outlet for the ends of the duct, with the seed modeled as a
wall and the side of the duct modeled as a pressure outlet. Our Reynolds number was around
13,000 with flow Mach numbers below .1 Mach. Based on these low speeds and values, our
major models and assumptions for the final rotating simulation included constant density,
conservation of mass, conservation of angular momentum, and conservation of energy. As
with previous simulations, we assumed steady flow with K-Epsilon turbulence, and no
structural deflection of our seed. We did not run grid resolution checks for the final simulation,
instead using intuitive “sanity” checks such as mass flow balance through the boundaries for
the velocity inlet (upstream of the seed) and the pressure outlet (downstream of the seed).
Figure 3 below shows the effect the seed has on the flow throughout the duct. It is the
velocity relative to the rotating frame, so we see it as a vortex. The flow is relatively uniform
prior to reaching the rotation plane of the seed. After the plane of the seed, we see a much
greater range of velocities, as well as the turbulence resulting from the tip of the seed. The
diameter of the vortex also increases after the plane of the seed, as a true wind turbine would
do (see figure 4). By defining the tube of the flow duct as a pressure boundary rather than a
slip wall we are able to see the expansion of the flow (i.e. increasing cross-sectional area of
the stream tube), showing the maple seed acting as a wind turbine.
Figure 3: Relative velocity streamlines before and after the seed.
Figure 4: Stream tube boundary diagram for a wind turbine and maple seed 1.
In addition to the stream tube showing turbine-like behavior, our streamlines are similar to
that for a wind turbine. Looking at previous simulations of the NREL wind turbine (Sairam,
54), we see similar turbulence in the stream lines after the flow passes over the tip. Figure 5
shows our simulation, while figure 6 contains the data for the NREL case. Both figures are
showing relative velocity streams, and in both cases we see a swirling vortex in the wake of
the blades.
Figure 5: Relative velocity streamlines over the tip of a maple seed.
Figure 6: NREL velocity streamtubes over the tip of the blade1.
Static pressure is also a feature we checked, applying our “sanity” check to help verify our
seed was indeed rotating. Looking at the static pressure on the seed, we saw the static
pressure is highest on the leading edge near the tip, decreasing along both the chord and the
span. It is also smallest near our rotation axis. This was as expected based on our knowledge
of fluid dynamics, and verified not only the rotation, but the positive effect the pressure
boundary of the tube had on the simulation. A previous simulation with a slip wall (also
rotating) had produced a strange pressure spread, and showed no increase in the crosssectional area of the streamtube (as it was confined by the wall).
Table 1: Performance analysis of a rotating maple seed with pressure boundary walls.
Performance Analysis
Inlet Velocity [m/s]
1.5
Outlet Velocity Avg. (m/s)
0.999
Inlet Total Pressure (Pa.g.)
67.588
Outlet Total Pressure (Pa.g)
67.271
Work/Mass [J*s/kg]
401.4062025
Work (surface avg mass) [J]
0.007063545
Lift [N]
0.001685
G Forces [N]
0.00098
Difference of Lift and G [N]
0.000705
Angular Momentum [J*s]
3.34E-06
Axial Induction Factor
0.167
Table 1 above holds some of the most important values we tabulated and calculated from our
final simulation. From the data, we see a drop in both velocity and total pressure, which is
required if the seed is going to do any work and harness any kinetic energy from the flow.
The maple seed produces around .007 Joules of energy. For such a low speed flow, the
maple seed is able to harness a large amount of energy. We also notice a discrepancy
between the lift and drag forces. They should theoretically be equal, if the maple seed is
falling with no acceleration. However, we have 41% difference between our values. This is
due to inaccurate mass estimations for the weight (G forces). While this does not affect the
quality of the simulation, it does decrease the accuracy of our lift vs. drag analysis. The final
value in the table is the axial induction factor. This is the percentage of the upstream kinetic
energy that our seed has converted into work. The theoretical limit for the axial induction
factor is .593, although most wind turbines are much lower. The optimal induction factor for
the NREL turbine was around .33 (Sairam 32), although some theoretical designs are
approaching the limit defined in blade element-momentum theory. Our .167 induction factor
means that only 16.7% of the kinetic energy was harnessed by the maple seed. This is where
modification of the seed geometry could be explored, in an effort to increase the factor.
APPLICATIONS & CONCLUSIONS
A major goal of this research was to simulate the aerodynamics of a natural body, which we
successfully reached by simulating a rotating maple seed with a reasonable level of
accuracy. Biomimicry is a field with great potential, and in aerospace much of the research
will focus on the aerodynamics and geometry of natural objects. The geometry of the maple
seed has been shown to be effective at harnessing the energy from a fluid, allowing a slow
descent through rotation. This could have effects not only on wind turbine design but also the
design decelerators, for example providing a cheap and simple way to airdrop supplies or
return rocket stages safely to Earth. This research, while successfully simulating the
autorotation of a maple seed, has many avenues that could be further explored. A first step
would be improving the accuracy of both the seed geometry and the physical properties we
calculated for it, such as velocity and mass. This would have a positive effect on the accuracy
of the simulation, and creates a solid base for further simulations. Also, recreating the shape
of the maple seed using airfoils in a blade geometry software such as 3DBGB would allow us
to see how variations in the chord and area of the “blade” affect the flow field and the values
in Table 1. While most turbine blades currently have a relatively uniform lift distribution along
there span, the large variations in the maple seed’s geometry lead to extremes in pressure
and lift forces. Whether or not this is advantageous to energy harnessing is a tie in with
biomimicry with potential for further research.
ACTION PHOTOGRAPHS
Figure 7: Jake Holden working with a non-rotating case in STAR-CCM+
Figure 8: Thomas Caley working with streamlines for a non-rotating case in STAR-CCM+
Figure 9: Jake Holden presenting early research at the OAI Annual Industry Forum
Jake Holden working on the final simulation in STAR-CCM+
ACKNOWLEDGEMENTS
Funding for this research was provided by the NSF CEAS AY REU Program, Part of NSF
Type 1 STEP Grant, Grant ID No.: DUE-0756921.
Thanks are also given to the support team at CD-Adapco for their assistance in providing a
STAR-CCM+ student license, training, and support for the research.
Thanks to Rob Odgen for licensing and hardware support.
Thanks to Kedhamath Sairam for his thesis, which was a valuable source for wind turbine
theory and analysis.
Thanks to Exact Metrology for their assistance with scanning maple seed samples and
creating the 3D CAD files that were the basis of our research.
REFERENCES
1Sairam,
K. (2013). “The Influence of Radial Area Variation on Wind Turbines to the Axial Induction.”
Master’s Thesis, University of Cincinnati, Cincinnati, Ohio.