PROJECT SUMMARY REPORT

FLOW SIMULATION OF A MAPLE SEED

Submitted To

The 2013 Academic Year NSF AY-REU ProgramPart of

NSF Type 1 STEP Grant

Sponsored ByThe National Science FoundationGrant ID No.: DUE-0756921

College of Engineering and Applied Science University of Cincinnati

Cincinnati, Ohio

Prepared By

Thomas Caley, Junior, Aerospace EngineeringJake Holden, Junior, Aerospace Engineering

Report Reviewed By:

Dr. Mark TurnerREU Faculty MentorResearch Professor

Aerospace EngineeringCollege 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 STAR-CCM+, 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 seed1.

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 cross-sectional area of the streamtube (as it was confined by the wall).

Table 1: Performance analysis of a rotating maple seed with pressure boundary walls.

Inlet Velocity [m/s] 1.5Outlet Velocity Avg. (m/s) 0.999Inlet Total Pressure (Pa.g.) 67.588Outlet Total Pressure (Pa.g) 67.271Work/Mass [J*s/kg] 401.4062025Work (surface avg mass) [J] 0.007063545Lift [N] 0.001685G Forces [N] 0.00098Difference of Lift and G [N] 0.000705Angular Momentum [J*s] 3.34E-06Axial Induction Factor 0.167

Performance Analysis

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.