The hydrodynamics of two oscillating foils in side-by-side configuration is numerically investigated for in-phase and out-of-phase pitching at Reynolds number of 4000 and Strouhal numbers of $\text{St}=0.25\text{–}0.5$. The effects of phase difference (in-phase and out-of-phase) and Strouhal number on symmetric attributes of the wake and unsteady propulsive performance of the foils are studied in detail. At lower Strouhal numbers, there is a quasisteady performance in both thrust generation and power consumption, which coincides with persistence of the wake symmetry. As Strouhal number increases, however, in-phase and out-of-phase pitching display unsteady cycle-averaged behavior with very different wake characteristics. The asymmetric wake of in-phase pitching foils at high Strouhal numbers transitions to a quasisymmetric wake, when an extensive interaction between the two vortex streets is observed in the wake. This coincides with an improvement on the propulsive performance of the foils. In contrast, the symmetric wake of the out-of-phase pitching foils at a high Strouhal number transitions to an asymmetric wake. The adverse effect of this transition is only observed on the propulsive performance of one foil while the other exploits the wake towards a better performance. The collective performance of the the out-of-phase pitching system, however, remains unchanged. There is also a strong correlation between the wake symmetric characteristics and total nonzero side-force production.

中文翻译：

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尾流对称性对同相和异相振荡期间串联水翼的性能有不同的影响

数值研究了两个并排配置的振荡箔片的流体动力学，以研究雷诺数为4000且斯特劳哈尔数为4000时的同相和异相螺距。 $\text{圣}=0.25\text{–}0.5$。详细研究了相差（同相和异相）和Strouhal数对箔的尾流和非稳态推进性能的对称属性的影响。在较低的Strouhal数下，推力产生和功率消耗都具有准稳态性能，这与尾流对称性的持续存在相吻合。但是，随着Strouhal数的增加，同相和异相俯仰显示出不稳定的周期平均行为，并具有非常不同的唤醒特性。当在尾流中观察到两个涡流道之间存在广泛的相互作用时，高Strouhal数的同相俯仰箔片的不对称尾流转变为准对称尾流。这与箔的推进性能的改善相吻合。相反，在高Strouhal数时，异相沥青箔的对称尾流过渡到不对称尾流。仅在一种箔的推进性能上观察到这种转变的不利影响，而另一种则利用尾流向更好的性能发展。但是，异相俯仰系统的总体性能保持不变。尾流对称特性与总的非零侧力产生之间也有很强的相关性。