Flow Simulation of a Maple Seed

Flow Simulation of a Maple Seed

Thomas Caley1 and Jake Holden2

1 Undergraduate Student, University of Cincinnati, Cincinnati, OH 45221

2 Undergraduate Student, University of Cincinnati, Cincinnati, OH 45221

Dr. Mark Turner3

3 Faculty of Aerospace Engineering, University of Cincinnati, Cincinnati, OH 45221

ABSTRACT: An analysis of the flow field around a maple seed as it rotates and subsequent comparison to wind turbine blades will be presented. Maple seeds are simulated with and without rotation with various fluid effects to mirror nature. Numerical values were determined experimentally from a real maple seed sample while fluid values for simulations consisted of accepted values for air. An accurate simulation of the falling maple seed has been achieved. Expected behaviors have been witnessed and potential for higher accuracy has been discovered. Further analysis of derived values shows areas for future research with biomimicry in aerospace design.

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 field of a maple seed can now be modeled and examined thoroughly using modern computational fluid dynamic software. From the fields and scalars available through simulations, conclusions can be drawn about how to create more efficient turbines.

The analysis that many of the papers on samaras draw from dates back to Norberg (1973), which examines the seeds aerodynamic characteristics and the governing equations of a seed’s falling motion. The orientation of the seed as it falls, which varies greatly between different species with samara seeds, has a profound effect on the angular and translational speeds, and the distance traveled horizontally. The shape of the wings planform, the angle of the samara as it falls, and the location and weight of the actual seed relative to the wing are a few of the characteristics studied by Norberg. Samara seeds are incredibly stable when rotating as they fall. Using the basic experimental values and equations from previous research will hopefully allow the creation of biologically inspired aircraft with stable and controllable flight.

Figure 1: Autorotation of a maple seed Figure 2: A mature maple seed

Since the rotation of the samara as it falls is what leads to its stable nature, analysis such as that of Rosen & Seter (1991) is valuable to the field. The authors present theoretical and experimental results for their analysis of the vertical autorotation of the seeds. By accurately deriving the equations of motion including all dynamic effects, basic theories surrounding the unique flight of samaras were developed. Due to the nature of the flight, mechanical control requires complex algorithms requiring further development.

Much of the research on samaras is in an effort to create monocopters and other flying vehicles with wings and propellers based off of the seeds. Collaborative efforts between DARPA, Lockheed Martin and other professionals have yielded promising results in monocopter designs. Many small propellers involve two identical blades, similar to a samara on the tree. Youngren (2011) showed that lessons from analysis of samara seeds using fluid dynamic software such as XFOIL and OVERFLOW lead to more efficient propeller designs.

Two biologically inspired Mirco-UAV projects from Youngren (2008) and Youngren (2012) involved pulsejet aircrafts with a body shape similar to a samara. Like a samara, these aircraft relied on rotation around the center of mass for flight. Through wind-tunnel testing and fluid dynamic simulations, early models for monocopter unibody vehicles have been developed and flight-tested. Several university projects have also lead to stable samara-inspired vehicles. Houghton & Hoburg (2008) and Kellas (2005) present design techniques based off of computational analysis of various samaras and the experimental results when designing controllable vehicles imitating samaras in flight.

Sairam (2013) presents analysis of wind turbine blades using computational fluid dynamics software in an effort to relate the planform characteristics and wing orientation to the efficiency of the blade with current turbine designs. This provides good comparisons for any samara analysis and allows for future research in the area.

The purpose of this paper is to present the results of computational analysis of a specific type of samara – the maple seed – based off of highly accurate CAD models of the seeds. The flow fields in particular are an area of interest for both stagnant and autorotation cases. Through the analysis of the flow fields and other scalars, the question of whether the maple seed has evolved to an optimum shape for low-speed rotational lift generation will be answered. The method of creating simulations will be discussed, followed by analysis of the results and comparisons with turbine blades.

MATERIALS AND METHODS

The majority of the research was done on various computers using the computational fluid dynamics solver STAR-CCM+. A high-speed video camera was used to film a dozen falling maple seeds, from which some dynamic 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+.

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 3000 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.

NON-ROTATIONAL SIMULATIONS

The first simulations we created for this project involved a fixed seed in a duct. This allowed us to look at how the air interacts with the seed’s surface as a blunt body, 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 and 5 prism layers to accurately capture boundary layer effects. This was high enough mesh density for the early simulations. Figure 3 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 3: Close up of the surface meshes.

Once the mesh and the non-rotational case were established, it was clear that the code was running as expected and the next phase could begin. It became necessary to rotate the fluid volume to simulate the fluid velocities and incidences that the seed experiences in reality.

ROTATIONAL SIMULATIONS

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 an adiabatic, no-slip wall and the side of the duct modeled as a pressure outlet. Our calculated Reynolds number was 13,161 with a flow Mach number of .018 at the blade tip. 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 modeling, 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 4: The above is a screen shot of the models used in STAR-CCM+ for this case

Figure 5 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 6). 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 5: Relative velocity streamlines before and after the seed.

Figure 6: Stream tube boundary diagram for a wind turbine and maple seed from Sairam5

In addition to the stream tube showing turbine-like behavior, our streamlines are similar to that of a wind turbine. Looking at previous simulations of the NREL wind turbine (Sairam, 54), we see similar turbulence in the streamlines after the flow passes over the tip. Figure 7 shows our simulation, while figure 8 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 7: Relative velocity streamlines over the tip of a maple seed.

Figure 8: NREL velocity streamtubes over the tip of the blade from Sairam5

Static pressure is also a feature we checked; applying our “sanity” check to help verify our seed was indeed rotating. Looking at figure 10, we can see 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).

Figure 9: Static pressure on the Pressure (right) and Suction (left) sides of the maple seed.

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

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, but a more impressive figure is the 401.4 Joules of energy it generates each second for every kilogram of air flowing over it. 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. 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

Figure 10: Above is Riva Calzoni M33 Single Bladed Wind Turbine

A major goal of this research was to accurately 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.