Numerical study of the flow around a hyperbolic cylinder at Reynolds number 3900

Abstract

In this paper, a numerical computation method combining a high-order compact difference scheme and immersed boundary method is used to simulate the flow around a hyperbolic cylinder with different aspect ratios and eccentricity. It is found that compared to the circular cylinder, the vortex-separation point in the wake of the hyperbolic cylinder moves backward, and the corresponding drag coefficient decreases by 27.6%. More interestingly, the time-averaged drag coefficient of hyperbolic cylinder behaviors parabolic relationship with cross-section aspect ratio and hyperboloid eccentricity, respectively. As the aspect ratio decreases from 1 to 0.6, the flow drag parallel to the long-axis reduces dramatically to 42.9%. Especially, there is no obviously low pressure region behind the hyperbolic cylinder when r = 0.4, which leads to the drag coefficient is only 0.0249 and close to zero. Besides, the average drag coefficient diminishes in a parabolic trend with the eccentricity that has a monotonously positive correlation with two parameters, and an increase in eccentricity e by varying a or c will also reduce the drag, but the effect of parameter a is more obvious than parameter c. The results presented here are expected to suggest a strategy for drag reduction in flow around the cylinder and provide theoretical guidance for the design and optimization of hyperbolic structures in flowing fluid.