WIND TUNNEL INVESTIGATION OF THE AERODYNAMIC CHARACTERISTICS OF PURPLE WISTERIA COMPOUND LEAVES

doi:10.6052/0459-1879-18-140

Abstract

Abstract:

The capability of reconfiguration of tree leaves is of significance in the designs of solar panel, aerofoil, bionic antenna, and wind power generation tree. The leaf was clamped at the base end of the rachis and vertically suspended in the center of wind tunnel test section, and tested with its front and back surface facing on-coming stream respectively at step-by-step increasing wind speed from 0 to 25 m/s. Results show that the changing process of the leaf can be divided into three stages: earlier steady, intermediate transition, and later steady, and critical wind speeds are observed. In earlier stage, the downstream bending curvature of the rachis increases rapidly with wind speed, and multi-layer wing steady and multi-layer multi-shape steady states exist. In intermediate stage, large amplitude low frequency rachis vibration, and small amplitude high frequency lobules vibration are observed. In later steady stage, two-layer structure or single streamlined body of conic, or wedge or U-shape cross section can be found. As wind speed increasing, the number of lobule layers and the width of the compound leaf $b$ decrease, until the single streamlined body formed. As $Re$ increasing, the drag coefficient of the leaf decreases rapidly at first, then slowly approaching to a constant. The absolute value of the negative Vogel component $\vert \alpha \vert$ decreases with the increase of lobule number of the leaf. $\vert \alpha \vert $ of the leaf with its back surface is larger than that with its front surface facing wind, but they tend to converge with the increase of lobule number. Rachis vibration occurs if the frequency of vortex shedding from the leaf is close to the natural frequency of the rachis. The second critical wind speed $V_2/\sqrt{E/\rho}$, at which the rachis vibration begins, is shown to be the function of $b/l$ and $d/l$, where $E, \rho , d, $and $l$ are respectively elastic module, mass density, diameter and length of the rachis, $b$ is width of the deformed leaf, and a figure about this function is drawn using experimental data.

CLC Number:

V211.74

Yu Kejie, Shao Chuanping. WIND TUNNEL INVESTIGATION OF THE AERODYNAMIC CHARACTERISTICS OF PURPLE WISTERIA COMPOUND LEAVES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 245-262.

Figures/Tables 21

Fig. 1 Tree leaves and their components: (a) single leaf, (b) imparipinnate leaf, (c) paripinnate leaf...

Fig. 2 The purple wisteria compound leaf in test: (a) side view,\\ (b) upward view

Table 1 Tested compound leaves in groups divided according to their lobule number

Fig. 3 State variation of a compound leaf with itsfront side facing wind: (a) initial state, (b) multi-layer wingsteady, (c) multi-layer wing-cone steady,(d$_1$) and (d$_2$) rachis in vibration, (e) intermediate steady, ($f_1$) and ($f_2$) lobules in vibration, (g) cone steady

Fig. 4 Various steady states of a compound leaf: (a$_1$)U-shape, side view; (a$_2$) U-shape, upward view;(b$_1$) wedge, side view; (b$_2$) wedge, upward view; (c$_1$) cone, side view; (c$_2$) cone, upward view; (d) multi-layer structure, side view

Fig. 5 The Change of lobule layer number with wind speed, the lobule number of the compound leaf is seven

Table 2 Existence probability of each state at different stages

Earlier steady stage		Intermediate stage			Later steady stage
multi-layer wing steady	multi-layer varied shape Steady	multi-layer varied rachis vibration shape steady	lobules vibration	two-layer steady	cone steady U-shape steady wedge steady
61.2%	43.8%	60% 32.5%	36.2%	48.8%	28.2% 11.2%	5%

Fig. 6 Vibration process of the rachis in aperiod, wind speed 9.2 m/s.(a$_1$) and (a$_2$), $t=0$, side and upward view; (b$_2$) and (b$_2$), $t=T/4$, side and upward view; (c$_1$) and (c$_2$), $t= 2T/4$, side and upward view

Fig. 7 Changes of attitude angles of the rachis and lobuleswith wind speed, the lobule number of the leaf is seven. (a)Rachis inclined angle,(b) rachis yaw angle, (c) averaged laterallobule inclined angle, (d) averaged lateral lobule azimuth angle,(e) apical lobule inclined angle,(f) apical lobule yaw angle

Fig. 8 Statistical relation between projected width $b/b_0$ of the compound leaf and Reynolds number $Re=Ub_0/v$...

Fig. 9 Statistical relation between rachis inclined angle$\theta$ and Reynolds number $Re=Ub_0/v$

Fig. 10 Changes of vibration frequencies of the rachis and lobules with parameter $V_\infty b^{-1}$

Table 3 Critical wind speeds for the leaves of different lobules

The surface to face wind	Lobules per leaf	V1	V2	V3	V4	V5
	5	3.7	7.1	11.3	12.8	17.1
front	7	3.6	6.9	9.3	11.0	14.4
	9	3.5	7.0	8.1	10.0	13.4
	5	4.4	7.6	11.8	13.4	17.0
back	7	3.9	7.6	9.4	13.2	15.7
	9	3.5	7.3	8.7	11.2	14.9
front	weighted average	3.6	7.0	9.9	11.2	15.2
back		4.1	7.5	10.0	12.7	15.9

Fig. 11 Probability density distribution of every critical wind speed

Fig. 12 The statistical relation between compound leaf drag coefficient and Reynolds number

Fig. 13 The logarithmic relation between compound leaf drag coefficient $C_{ D}$ and wind speed $V_\infty$

Table 4 Statistical values of Vogel coefficient for the compound leaves of different lobule number n

n	5	7	9	Average
aF	-0.40	—0.51	—0.54	—0.48
aB	—0.50	—0.60	—0.54	—0.55

Fig. 14 The influence of lobule number $n$

Fig. 15 The second critical wind speed similarity curve

Fig. 16 The 4th critical wind speed $U^\ast_4$ vs. mass ratio $M^\ast$

Fig. A1 The 4th critical wind speed $U^\ast_4$ vs. mass ratio $M^\ast$

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