## 1 Introduction  
As a new energy extraction device using clean energy, foil is thought to have a bright prospect, especially in the current situation of energy shortages and environmental pollution. Since the combined plunging and pitching motion was put forward and realized to extract energy in 1981 [1], plenty of researchers have discussed the energy extraction characteristics of foil by numerical and experimental methods. According to the laminar computation model, [PERSON] et al. [2] simulated the energy extraction performance of foil at a low-velocity flow field with \(Re=1100\). It was found that the energy extraction efficiency can achieve 35% and the deep stall of airfoil has a positive effect on efficiency. [PERSON] [3] discussed the energy extraction performance and the effect factors (such as the plunging and pitching amplitude, frequency and the free stream velocity) by experiments. The results showed that the power coefficient and efficiency increase with the increase in the amplitude. The experiment system efficiency is observed to be at least 32%. A wind energy extraction device was designed by [PERSON] et al. [4], which is based on the flutter mechanism of foil. The device worked under a low frequency and gained a high extraction performance and efficiency. [PERSON] et al. [5] established a quasi-stable state model and a semi-empirical model of dynamic stall, optimizing the aerodynamic force and energy extraction performance of foil. They observed that the semi-empirical model of the dynamic stall is effective in predicting the aerodynamic force and efficiency. The numerical research on the extraction performance of foil discusses the potential effect factors like the oscillation motion, the motion parameter, the \(Re\) number and the profile of foil by the control variable method and the traditional optimization algorithm, aiming at finding a higher power output and extraction efficiency [6; 7; 8; 9; 10; 11; 12; 13]. The oscillation process always adopts the sinusoidal motion, however, some researchers tried to use non-sinusoidal motion on foil for further investigations. [PERSON] et al. [14; 15; 16] designed a foil device extracting energy in non-sinusoidal motion and conducted numerical simulations on the power output, the extraction efficiency and the feasibility of this device. [PERSON] et al. [17; 18] carried out an analysis of different non-sinusoidal pitching motions which are similar to trapezoidal ones, their research revealed that foil under non-sinusoidal motions like trapezoid motion has a higher power output and extraction efficiency at some \(St\) number. [PERSON] [19] discussed the effect of different non-sinusoidal motions on the flow field around the foil. They found that the power coefficient of non-sinusoidal motions improved by 17% compared to sinusoidal motion. Recently, research about the effect factors of foil extraction performance has been becoming more and more perfect and complete. However, most research focused on single foil and only a few of the researchers analyzed the extraction characteristics of foils under parallel configuration. According to our previous research [20], the flow field around two parallel foils will affect each other during the oscillation motions, which results in a better performance than that around the single foil. Therefore, it is necessary to further explore the influence of non-sinusoidal motion to the energy extraction performance of parallel foils. In this paper, two oscillation motions are considered, which are the combined non-sinusoidal plunging and sinusoidal pitching motion, as well as the combined non-sinusoidal pitching and sinusoidal plunging motion. The numerical analysis of energy extraction characteristics is conducted. The rest of this paper is introduced as follows. Firstly, the computation model, the numerical method and the oscillation control equations of parallel foils are described. Then, the energy extraction characteristics of parallel foils under two different combined motions are analyzed in detail.