Linear ODE Based Geometric Modelling for Compressor Blades

Abstract

Abstract-Geometric modeling based on physical environment of the objects has been emerging as a powerful modeling technique and started to gain popularity for surface modeling and design. These methods usually allow the geometric objects to be defined and governed by a set of differential equations. In this paper, we focus on the geometric modeling for compressor blades, upon which the flow is governed by Navier-Stokes (NS) equations. As we cannot use NS equations directly due to its essential complexity, linear ODE systems are used to describe the elementary blade types of the blade surface. Then, we use the homotopy based method to reconstruct the full surface. A specific blade surface represented as data scatter is used to verify our method. According to the properties of the original data, different parametrization methods are discussed. Numerical results show that our method offers a nice representation for the blade surface.