Automated Construction of Airfoils Lattice Based on Cassini Oval

When developing turbomachines for various purposes, designing a blade apparatus (constructing aerodynamically smooth airfoils) is a time-consuming multifactorial task. A promising method for designing airfoils uses the properties of Cremona transformations of a plane with coincident F-points, while the transformation object is the Cassini oval. The results of analytical construction of airfoils lattice by Hirst transformation methods are presented. To implement the proposed mathematical model, an algorithm and a package of applied programs (based on it), which are in fact an automated design system, have been developed. Some calculation formulas are given, the influence of the Cassini oval position relative to the origin of coordinates on the shape of the designed airfoil is described, the main geometric characteristics of the airfoils are calculated, examples of the midline construction and the design of the airfoil leading edge are presented. The proposed mathematical model can be an independent calculation system, a CAD subsystem (software module) or a page of an electronic airfoil catalogue.