## 3 Results and Discussions  
### Combined Non-Sinusoidal Plunging and Sinusoidal Pitching Motion  
In this research, the energy extraction performance of parallel foils at combined non-sinusoidal plunging and sinusoidal pitching motion is investigated firstly. Five different plunging motions,  
Figure 5: The variations of \(C_{P}\) under different mesh strategies and time steps. which are controlled by the non-sinusoidal plunging parameter \(K_{h}\) (\(K_{h}\) is set as \(-1\), \(-0.5\), \(0\), \(1\) and \(2\) respectively), are simulated. As shown in Figure 6, when \(K_{h}\) is \(-0.5\), \(0\) and \(1\), the average power coefficient \(C_{Pm}\) ascends firstly and then decreases with the increasing \(k\), showing a stable trend in general. At these three motions, all peak values of \(C_{Pm}\) appear at \(k=0.8\). Additionally, the maximal \(C_{Pm}\) is achieved when \(K_{h}=-0.5\), which is \(0.375\). When \(k<1.0\), the best energy extraction performance of foil is observed at \(K_{h}=-0.5\) under different \(k\). Additionally, the optimal performance is gained at \(K_{h}=1\) when \(k>1.0\). It is found from Figure 6 that \(C_{Pm}\) decreases obviously and becomes a negative value gradually with the increase in \(k\) when \(K_{h}=-1\) and \(K_{h}=2\). This means these two oscillation motions are in the energy consumption situation and not the energy extraction situation in the range of frequency considered in this paper. It can be concluded from Figures 4 and 6 that, at the same frequency, the more the plunging motion is similar to the sinusoidal motion, the more the energy that can be extracted by parallel foils. At the same time, the extraction efficiency \(\eta\) shows a similar trend with the \(C_{Pm}\) curves at the non-sinusoidal plunging motion. When \(k=0.8\) and \(K_{h}=-0.5\), the maximal extraction efficiency \(\eta\) is observed, which is \(0.188\). Parallel foils in this paper oscillate as the combined plunging and pitching motion. Thus, to further investigate the effect factors and change law of energy extraction performance, the average power coefficient \(C_{Pm}\) is divided into the one caused by the plunging motion \(C_{Phm}\) and the one caused by pitching motion \(C_{Phm}\). In general, the plunging motion is the process that extracting energy and the pitching motion is the process that consuming energy. However, as shown in Figure 7, when \(K_{h}=-1\), the plunging motion converts the energy extraction situation into the energy consumption situation with increasing \(k\). While the \(C_{Phm}\) increases gradually with the increasing \(k\) at the other four non-sinusoidal plunging motions. It indicates that the plunging motion with \(K_{h}=-1\) is not appropriate to the energy extraction of the foil. For the pitching motion, they are all sinusoidal motion in different cases. In the figure, the little difference of \(C_{Phm}\) at the same frequency is from the difference of the flow field caused by non-sinusoidal plunging motion. With the rise in \(k\), \(C_{Phm}\) declines obviously, which means the energy consumption increases. This is because the foil oscillates faster at high frequencies and the angular velocity of the adjusting process of the foil near the plunging limited position is higher, consuming more energy. In summary, the difference of \(C_{Pm}\) curves in Figure 6 is mainly from the different non-sinusoidal plunging motion. Figure 6: The \(C_{Pm}\) and \(\eta\) of parallel foils at different \(K_{h}\): (**a**) \(C_{Pm}\) curves under different \(k\); (**b**) \(\eta\) curves under different \(k\). The amount of energy extracted during the plunging oscillation process is related to the synchronicity between the lift coefficient \(C_{l}\) and the plunging velocity \(V_{y}\). The \(C_{l}\) curves of the upper foil at \(K_{h}=0\) and \(K_{h}=2\) with \(k=0.8\) are shown in Figure 8. By comparing these two cases, it is concluded that the synchronicity of \(C_{l}\) and \(V_{y}\) is better at \(K_{h}=0\).