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Samaras or winged seeds spread themselves by wind. Ash seed, unlike other samaras, has a high aspect ratio wing which can generate enough lift force to slow down descent by rotating about the vertical axis and spinning around its wing span axis simultaneously. This unique kinematics and inherent fluid mechanism are definitely of great interest. Detailed kinematics of free falling ash seeds were measured using high-speed cameras, then corresponding aerodynamic forces and moments were calculated employing computational fluid dynamics. The results show that both rotating and spinning directions are in the same side and the spinning angular velocity is about 6 times of rotating speed. The terminal descending velocity and cone angles are similar to other samaras. Analysis of the forces and moments shows that the lift is enough to balance the weight and the vertical rotation results from a processional motion of total angular moment because the spin-cycle-averaged aer-odynamic moment is perpendicular to the total angular moment and can only change its direction but maintain its magnitude, which is very similar to a spinning top in processional motion except that the total angular moment of ash seed is not along the spin axis but almost normal to it. The flow structures show that both leading and trailing edge vortices contribute to lift generation and the spanwise spinning results in an augmentation of the lift, implying that ash seeds with high aspect ratio wing may evolve in a different way in utilizing fluid mechanisms to facilitate dispersal.

There are two kinds of seeds that dispersed by wind, pappose seeds (parachute type) and winged seeds. Pappose seeds utilized rag force acting on the pappi [

The aerodynamic characteristics of autorotating seeds have been investigated theoretically and experimentally [

Recently, with the rapid development of measurement techniques and equipment, e.g., stereoscopic PIV (Particle Image Velocimetry), tomographic PIV and high-speed cameras, detailed flow field measurement around a rapidly autorotating seed became feasible [

In this paper, aerodynamics and kinematics of free-falling ash seeds were investigated by means of experimental measurement and computational fluid dynamics. Morphological and kinematical data of stable autorotating and descending seed were measured with high temporal-spatial accuracies, following by numerical simulation based on the measured data; hence, the instantaneous flow field induced by the seed was fully resolved. As a whole, numerical results show several distinct flow structure features and their evolving tendencies, which give clear clues in understanding the essences of such unique autorotation, including the force balance, lift mechanism and the coupling between aerodynamic force and kinematics response.

Ash is common English name for Fraxinus genus plants tree, which is widespread across much of Europe, Asia and North America, often planted as shade tree. The seeds used in this paper were collected from the botanical garden of Institute of Botany, Chinese Academy of Sciences, and preserved in sealed bags to keep moisture. Eleven seeds that successfully enter the terminal stable autorotating and descending state in experiment trials were selected for further measurement and analysis. A typical sample of ash seed is shown in

As shown in

A schematic diagram of the experimental apparatus is shown in

to the front and side cameras also make the backlit LED light sources (not shown in

Using the experimental results as kinematic input for numerical simulation, it is possible to further identify the aerodynamic characteristics of the falling seeds, and find the mechanical mechanism from the perspective of lift generation and flow field. This section describes the computational fluid dynamics method and mesh models used and performs independence verification of some of mesh parameters.

The governing equations of the flow around the flapping and rotary wings are the 3D incompressible unstable Navier-Stokes equations. The artificial compressibility method developed by Rogers [

∂ Q ^ ∂ τ = − ∂ ∂ ξ ( E ^ − E ^ v ) − ∂ ∂ η ( F ^ − F ^ v ) − ∂ ∂ ζ ( G ^ − G ^ v ) + H G C L (1)

where Q ^ = 1 / J [ p u v w ] T is the primitive variables, and J is the Jacobian determinant between the Cartesian coordinate system and the curvilinear coordinate system with the transformations ξ = ξ (x, y, z, t), η = η (x, y, z, t), ζ = ζ (x, y, z, t) and τ = t. The symbols E ^ = ( F ^ and G ^ ) and E ^ v = ( F ^ v and G ^ v ) are the convective and viscous fluxes respectively. In the viscous fluxes, Re is defined as u R e = u ¯ c / ν where u ¯ is the reference velocity, which is defined as the mean velocity of seed tip, c is the chord length, and ν is the kinematic viscosity of fluid. For a moving/deforming mesh, the term H G C L is added to the right side of Equation (1) to enforce the geometric conservation law. A pseudo-time derivative of pressure is introduced into the continuity equation to solve Equation (1). This derivative uses the third-order flux-difference splitting technique for convective terms and the second-order central-difference scheme for viscous terms. The time derivatives in the momentum equation are computed using a three-point backward-difference implicit formula. Arithmetic accuracy is in second order for space and time.

Once the fluid field is solved numerically, integrating the pressure and viscous stress over the wing surface provides the total aerodynamic force acting on the wing. The vertical component of the total force is referred to as lift L, and the moment generated by the force component in the direction of the rotation is referred to as rotating moment Q. The dimensionless lift and rotating moment are referred to as lift C_{L} and rotating moment C_{Q} coefficients:

C L = L 0.5 ρ ( u ¯ ) 2 S (2)

C Q = Q 0.5 ρ ( u ¯ ) 2 S c (3)

where ρ is the air density and S is the wing area.

An O-H type mesh is used for numerical simulation (

Eleven free falling trails in stable autorotation were filmed successfully. For each trail, about 3 whole cycles of rotation around vertical axis were recorded and digitalized to obtain all kinematics parameters needed. As an example, snapshoots of one seed in free falling are overlapped and given in

To describe wing kinematics, two coordinate systems are introduced here (see _{w}y_{w}z_{w}). The z_{w} axis is along wing span and the x_{w} axis is along the chord line pointing to leading edge. The kinematic parameters are the descending velocity (v_{d}), rotational speed about vertical axis (ω), spinning speed around wing span axis (ω_{f}) and

coning angle (θ). The coning angle (θ) is defined as the angle between the wing span axis (z_{w}) and the horizontal plane (xz), the pitch angle (α) is the angle between the chord line of the seed (x_{w}z_{w}) and the horizontal plane (xz).

The time history of the lift coefficient is shown in _{L} reaches about 1.5. The cycle-averaged lift coefficient (C_{Lavg} = 0.889) is about 10% larger than the seed non-dimensional weight ( G * = m g / 0.5 ρ ( u ¯ ) 2 S = 0.806 ), which indicates that the seed weight is balanced by the aerodynamic force pretty well, enabling the ash seed to descend at a relative low speed (see _{d} = 1.114 m/s).

_{1}, the wing generates maximum lift and the leading-edge vortex (LEV) is formed and remains attached to its upper surface, while the trailing edge vortex is also quite strong but separates from the wing surface. At time t_{2}, the wing pitches up and the LEV starts to separate from the wing surface, correlating with a dramatic decrease in lift. When the wing pitches

almost upright ( α = 84 ∘ ), the lift decreases to its minimum value. It is obvious that from t_{1} to t_{3} the horizontal component of aerodynamic force (F) is drag, meaning its direction is opposite to rotating motion. On the other hand, while from t_{3} to t_{5}the horizontal component of aero dynamic force is thrust. As a result, the cycle-averaged moment C_{Qavg} is almost zero due to its periodical essence.

As aforementioned, due to rotations about vertical axis and span axis, the seed can generate enough aerodynamic force to balance its weight, which allowing a low speed descent. However, the lift is not through the center of mass, therefore there exist aerodynamic moments acting on the mass of center. To explain this, another frame ( o x ′ y ′ z ′ ) has to be introduced, whose z ′ axis is in the same direction as the z w axis and x ′ axis always in horizontal, thus the frame ( o x ′ y ′ z ′ ) only rotates about y axis as the wing rotates. As a result, the spin-cycle-averaged aerodynamic moment will be parallel to x ′ axis. And the spin-cycle-averaged total angular moment ( L ) will be in o y ′ z ′ plane (see

L = I z ( ω 1 + ω f ) + I y ω 2 (4)

where I y and I z are moment of inertia about y ′ and z ′ , ω 1 and ω 2 are the components of ω in z ′ and y ′ , ω f is the Euler angle rate ( α ˙ ) about z ′ . Therefore, the z ′ component of angular moment ( L 1 = I z ( ω 1 + ω f ) ) is much smaller than that of y ′ component of angular moment ( L 2 = I y ω 2 ), because I y is about two order larger than I z while ω 1 , ω 2 and ω f in same order. Therefore, the total angular moment ( L ) is almost perpendicular to axis z ′ in o y ′ z ′ plane (see

d L / d t = ω × L (5)

which is pointing to the same direction of the aerodynamic moment. This processional movement about vertical axis is very similar to the processional movement of a spinning top on a table whose moment is caused by gravity, except that the total angular moment of ash seed is not along the spin axis but almost normal to it (

The contour plots of z w component of vorticity at different spanwise position from non-dimensional time t 1 to t 4 are given in

Detailed kinematics of free falling ash seeds were measured using high-speed cameras, then corresponding aerodynamic forces and moments were calculated employing computational fluid dynamics. The results show that both rotating and spinning directions are in the same side and the spinning angular velocity is about 6 times of the rotating speed. The terminal descending velocity and cone angles are similar to other samaras. Analysis of the forces and moments shows that the lift is enough to balance the weight and the vertical rotation results from a processional motion of total angular moment because the spin-cycle-averaged aerodynamic moment is perpendicular to the total angular moment and can only change its direction but maintain its magnitude, which is very similar to a spinning top in processional motion except that the total angular moment of ash seed is not along the spin axis but almost normal to it. The flow structures show that both leading and trailing edge vortices contribute to lift generation and the spanwise spinning results in an augmentation of the lift, implying that ash seeds with high aspect ratio wing may evolve in a different way in utilizing fluid mechanisms to facilitate dispersal.

This research was primarily supported by the National Natural Science Foundation of China (No. 11672028).

Fang, R., Zhang, Y.L. and Liu, Y.P. (2017) Aerodynamics and Flight Dynamics of Free-Falling Ash Seeds. World Journal of Engineering and Technology, 5, 105-116. https://doi.org/10.4236/wjet.2017.54B012