The Magnus vertical axis wind turbine harnesses the principle of the Magnus effect in conjunction with a vertical axis orientation. This mechanism is based on the lift and drag produced by rotating cylinders to propel the rotor and generate power. The proposed method involved installing a flat plate near each rotating cylinder to generate a higher unidirectional torque. As the configuration of the plate affects both the flow pattern and the forces exerted on the blade, the current study aims to identify an optimal blade configuration consisting of a rotating cylinder and a flat plate. A numerical model of the direct-forcing immersed boundary method was used to simulate the flow past a single blade using the static rotor simulation approach, and the Box–Behnken design for the response surface methodology (RSM) was applied to find an optimized flat plate arrangement that would produce the highest mean torque coefficient (CT¯). Three design parameters were examined, specifically the length of the plate (L/D), the gap between the plate and the cylinder (g/D), and the plate's shift angle with respect to the cylinder axis (β). The Reynolds number was 5000, and the cylinder spin ratio (α) was 3. The optimum configuration to achieve a maximum CT¯ was identified at L/D=0.53, g/D=0.1, and β=0°. Validating this optimal CT¯ yielded a value of 0.290, indicating an increase in torque of almost 70% compared to the central design. Furthermore, this value corresponds closely to the predicted result obtained through the RSM optimization method. Considering the flow analysis at various positions, it is crucial to emphasize a critical scenario where the potential for countertorque emerges due to excessive drag at ψ=0° and ψ=315°.

中文翻译：

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使用响应面法和直接强迫浸没边界法对马格努斯 VAWT 叶片被动流动增强的参数研究

马格努斯垂直轴风力涡轮机利用马格努斯效应与垂直轴方向相结合的原理。该机构基于旋转气缸产生的升力和阻力来推动转子并产生动力。所提出的方法包括在每个旋转圆柱体附近安装一块平板，以产生更高的单向扭矩。由于板的配置会影响流动模式和施加在叶片上的力，因此当前的研究旨在确定由旋转圆柱体和平板组成的最佳叶片配置。使用直接强制浸没边界法的数值模型，使用静态转子模拟方法来模拟经过单个叶片的流动，并应用响应面方法 (RSM) 的 Box-Behnken 设计来寻找优化的平板会产生最高平均扭矩系数 (CT´) 的布置。检查了三个设计参数，特别是板的长度 (L/D)、板与圆柱体之间的间隙 (g/D) 以及板相对于圆柱体轴线的偏移角 (β)。雷诺数为 5000，气缸旋转比 (α) 为 3。实现最大 CT 的最佳配置确定为 L/D=0.53、g/D=0.1 和 β=0°。验证此最佳 CT 得出的值为 0.290，表明与中心设计相比，扭矩增加了近 70%。此外，该值与通过RSM优化方法获得的预测结果密切对应。考虑到不同位置的流动分析，强调关键场景至关重要，在该场景中，由于 ψ=0° 和 ψ=315° 处的过大阻力，可能会出现反扭矩。