多边形绕流问题有广泛的应用背景。目前缺乏任意边数下多边形绕流规律研究。本文我们重点研究绕二维正多边形的势流流动和低雷诺数粘性流动，考虑了流动特性随多边形边数的变化规律，并与圆柱绕流的相应特性进行了比较。我们借助 Schwarz-Christoffel变换，推导得到了多边形绕流所满足的一般方程，其中包括纯势流理论解，二维粘性条件下映象（圆）平面内的流函数方程，二维粘性流动中扰动发展的特征方程。接下来从方程的角度，比较了多边形绕流与圆柱绕流的一般性差异。对于势流流动，我们利用纯势流理论解，研究了不同来流方向时，多边形的边数对流场参数和顶点处奇异性的影响规律。我们还对多边形外点涡系运动规律、点涡对的静止位置及其稳定性规律进行了研究。发现了多边形外存在多条与圆柱不同的点涡对静止位置曲线，以及多边形的边数与方向对点涡对稳定性规律的影响。对于粘性流动，我们利用流函数在映像（圆）平面内的方程，二维粘性流动中扰动发展的特征方程，并结合 CFD方法，分析了临界雷诺数与 Strouhal数随边数的变化规律。在定常流动开始出现分离时，我们分析了多边形的第一临界雷诺数（流动刚刚出现分离的雷诺数）随边数的变化，多边形出现分离后的流动拓扑结构及其与圆柱的差别。当顶点与后驻点重合时，第一临界雷诺数比圆柱大，并且随边数 N的增加而逐渐递减。当 N →∞时向圆柱逼进。分岔点（流动刚刚出现分离的位置）在后驻点（对应于圆柱的情况）之前。当棱边中点与后驻点重合时，第一临界雷诺数比圆柱小，并且随边数 N的增加而逐渐递增。当 N →∞时向圆柱的情况逼进。分岔点与后驻点重合。在流动开始出现非定常效应时，我们分析了第二临界雷诺数（流动刚刚出现非定常的雷诺数）和 Strouhal数随边数的变化关系。发现第二临界雷诺数和 Strouhal数比圆柱大，并且随边数 N的增加而逐渐递减。当 N →∞时，向圆柱的情况逼近。

Flow past polygons is widely applied. It is rare to consider the polygon with an arbitrary edge number. In this paper we focus on the two-dimensional flow around regular polygons, with comparison to circular cylinder flow. Both potential flow and low-Reynolds number viscous flows are addressed. With the aid of Schwarz-Christoffel mapping, we obtained the general equation for flow past polygons, e.g. exact solution for pure potential, the equation of stream function in the mapped (circle) domain, eigen functions for disturbance evolution. Based on which we studied the general differences of flow features between polygons and circles.For potential flow, we studied the pure potential flow details and the singularity at apices varying with the edge number, N, at different flow directions. We also studied the behavior, stationary lines and stability, of vortex-pair and found new stationary lines for vortex pairs compared to circular cylinder, and different stabilities corresponding to the edge number and direction.For viscous flow we obtain critical Reynolds numbers and Strouhal numbers, with the aid of the equation of stream function in the mapped (circle) domain, eigen functions for disturbance evolution and CFD methods.For the steady flow when separation first occurs, we obtained the 1st critical Reynolds numbers varying with N, and different streamlines topologies compared with the circular situation. With one apex locating on the rear stagnation point, the 1st critical Reynolds number is a monotonically decreasing function of N, while N →∞ corresponds to that for circular cylinder. The bifurcation point is ahead of the bifurcation point for circular cylinder. With one mid-point of the edge locating on the rear stagnation point, the 1st critical Reynolds number is a monotonically increasing function of N, while N →∞ corresponds to that for circular cylinder. The bifurcation point is just the rear stagnation point. For unsteady flow, the 2nd critical Reynolds number for vortex shedding and the Strouhal number are both monotonically decreasing functions of N.