环形螺旋桨几何形状的数学表达方法

Mathematical expression method for geometric shape of toroidal propeller

[目的]环形螺旋桨因其独特的外形,可有效减少梢涡泄出,有利于降低水动力噪声,提高推进效率,但同时也因其复杂的外形,难以采用常规螺旋桨的数学表达方法来对其几何外形进行建模,因此,需研究新型环形螺旋桨几何形状的数学表达。[方法]首先,详细介绍环形螺旋桨的结构特点和优势;然后,在参考常规螺旋桨几何形状数学表达的基础上,引入轴距、外侧角、侧倾角和竖直角等几何参数,以几何型值参数沿轴距方向分布的方式,详细推导环形螺旋桨的三维坐标数学公式,从而建立环形螺旋桨的数学表达方法;最后,以某一环形螺旋桨的型值为例,验证所提环形螺旋桨数学表达方法的可行性。[结果]结果显示,采用所提方法能够光顺地建立环形螺旋桨的几何外形。[结论]所提方法可用于快速进行环形螺旋桨的三维建模,能为进一步研究环形螺旋桨的物理特性和科学问题奠定坚实的基础。

[Objectives]The toroidal propeller can effectively reduce tip vortex leakage due to its unique shape,which is beneficial for reducing hydrodynamic noise and improving propulsion efficiency.However,its complex shape also makes it challenging to model its geometric shape using conventional mathematical ex-pression methods.Therefore,it is necessary to study the mathematical expression of the toroidal propeller.[Methods]First,the structural characteristics and advantages of the toroidal propeller are introduced in de-tail.Next,by referring to the mathematical expression of conventional propeller geometry,geometric paramet-ers such as axis span,lateral angle,roll angle and vertical angle are introduced,and a detailed 3D coordinate formula for the toroidal propeller is derived by distributing the geometric parameters in the axis span direction,thereby establishing the mathematical expression method for toroidal propellers.Finally,taking the offset of a certain toroidal propeller as an example,the feasibility of the proposed mathematical expression method for toroidal propellers is verified.[Results]The results show that the proposed method can smoothly establish the geometric shape of a toroidal propeller.[Conclusions]The proposed method can facilitate the rapid 3D modeling of toroidal propellers,laying a solid foundation for further research on the physical characteristics and scientific problems associated with toroidal propellers.