International Journal of Aerospace Engineering

Volume 2019, Article ID 5151808, 12 pages

https://doi.org/10.1155/2019/5151808

## The Effect of Damping Coefficient, Spring Coefficient, and Mass Ratio on the Power Extraction Performance of a Semiactive Flapping Wing

^{1}Institute of Robotics and Intelligent Systems, Wuhan University of Science and Technology, Wuhan 430081, China^{2}Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, China

Correspondence should be addressed to Jianyang Zhu; moc.361@20gnaynaijuhz

Received 15 January 2019; Accepted 27 February 2019; Published 16 April 2019

Academic Editor: Gustaaf B. Jacobs

Copyright © 2019 Jianyang Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The effect of varying damping coefficient , spring coefficient , and mass ratio on the semiactive flapping wing power extraction performance was numerically studied in this paper. A numerical code based on Finite Volume method to solve the two-dimensional Navier-Stokes equations and coupled with Finite Center Difference method to solve the passive plunging motion equation is developed. At a Reynolds number of 3400 and the pitching axis at quarter chord from the leading edge of the wing, the power extraction performance of the semiactive flapping wing with different damping coefficient, spring coefficient, and mass ratio is systematically investigated. The optimal set of spring coefficient is found at a value of 1.00. However, the variation of mass ratio cannot increase the maximum mean power coefficient and power efficiency, but it can influence the value of damping coefficient at which the wing achieves the maximum mean power coefficient and power efficiency. Moreover, insensitivity of the mean power coefficient and power efficiency to the variation of damping coefficient is observed for the wing with smaller mass ratio, which indicates the wing with smaller has better working stability.

#### 1. Introduction

The application of flapping wing for energy extraction is inspired by insects and birds, who exhibit excellent aerodynamic performance by extracting wind energy through flapping their wings. Comparing to the conventional rotation energy extraction turbines, flapping wing power generator possesses many advantages, such as simpler design, less construction costs, more efficiency in low stream speeds, and more friendly to the flying creatures in nature [1]. Therefore, more and more recently researches have been focused on this type of power generator [2–5].

Up to now, there are three types of flapping wing power generator, named fully active [6], semiactive, and purely passive system, respectively [7]. Among them, the semiactive flapping wing power generator which has one of the flapping motion (pitching) is actuated and another motion (plunging) is induced by free stream fluid and is considered as a more feasible approach in industry, because it is easy to implement and control [8, 9]. This type of flapping wing power generator is characterized by the interaction coupling of fluid, driven wing pitching, and passive wing plunging, which results the flow around the generator very complex, and the energy extraction performance is still the main research focus of this type of power generator.

To investigate the energy extraction performance of a semiactive flapping wing near solid walls, the mechanical parameters of the wing to achieve power extraction efficiency were optimized by Wu et al. [10]. They concluded that the spring constant at a value of 1.0 and damping coefficient at a value of are an optimal choice to achieve net power extraction efficiency of the wing, when the wing has fixed wing mass at a value of 1.0 and Reynolds number at a value of 1100. Under the same Reynolds number, Zhan et al. [11] performed a similar numerical study to optimize the energy extraction performance of a semiactive flapping wing with fixed wing mass at a value of 1.0 and reduced frequency . It was found that the parameters for the wing that achieved best power extraction are the difference with different pitching amplitude. For the wing with pitching amplitude , the optimal power extraction efficiency is achieved when the wing has the spring constant at a value of 5.0 and damping coefficient at a value of , while for the wing with pitching amplitude , the optimal power extraction efficiency is achieved when the wing has the spring constant at a value of 5.0 and damping coefficient at a value of 0.5*π*. Moreover, based on the numerical study by Zhu et al. [12], the optimal power extraction performance is the system where there is no spring on the plunge motion and the damping coefficient is at a value of .

On the other hand, to explore an inertial effect on the power extraction performance of a semiactive flapping wing, Deng et al. [13] conducted a strong fluid-structure coupling method to study the power extraction performance of a semiactive flapping wing with different mass ratios (ranging from 0.125 to 100), and it was found that the energy harvesting efficiency decreases monotonically with increasing mass ratio. However, the amount of power extraction changes very little when the wing has mass ratio less than 10. While, according to the experiment study on a flapping wing hydroelectric power generation system by Abiru and Yoshitake [14], the wing with lager mass ratio is needed to excite the hydroelastic response; therefore, the wing with lager mass ratio has better power extraction performance.

As discussed above, the effect of damping coefficient, spring constant, and mass ratio on the power extraction performance of the semiactive flapping wing is still not clearly understood. Therefore, in this paper, a numerical code based on Finite Volume method to solve the two-dimensional Navier-Stokes equations and coupled with Finite Center Difference method to solve passive plunging motion equation is employed. The flow around a semiactive flapping wing is simulated with different damping coefficient, spring constant, and mass ratio. The NACA0015 airfoil is employed to represent the two-dimensional section wing, and the power extraction performance as well as the fluid around the wing are studied details in the following.

#### 2. Problem Definition and Methodology

##### 2.1. Problem Definition

In this paper, NACA0015 airfoil with chord length and mass is employed to model the flapping wing. A damper with damping coefficient and spring constant which is attached to the wing is employed to mimic the power extractor. The schematic view of the semiactive flapping wing is shown in Figure 1, where the profile is defined to drive the pitching motion of the wing; the plunging motion is induced by the lift force of the wing. The pitching point is located at the center line of the wing with a distance 0.25*d* from the leading edge. To simplify the problem, a cosine pitching motion mode is employed, and the center of mass of the wing is also designed to coincide with the pitching point . Then, the governing equation of the pitching motion and passive plunging motion can be defined as
where is the pitching amplitude, is the pitching frequency, is the lift force in direction as shown in Figure 1. The left and right sides of equation (2) is divided by the mass, then, it can be described as