Unstructured periodic grid generation around 2D turbine cascades

Abstract

A novel grid generation algorithm for periodic unstructured grid around two-dimensional highly-staggered turbine cascades, including multiply connected blade geometries, is presented. The idea is to generate the mesh in a transformed space in which the periodic boundaries are coincident and internal to the computational domain so that no special treatment along these curves is required. The mesh in the transformed u-v space is computed by means of front-advancing/Delaunay technique and the resulting grid is transformed back into the x-y space of physical variables after introducing a suitable cut, which translates to periodic boundaries in the x-y plane. The cut is not arbitrary and it is automatically managed by the algorithm. The proposed transformation is conformal and therefore no elements are distorted in the process. In this way, the prescribed element size and mesh quality are easily attained and the uniqueness of the periodic nodes is guaranteed by the fact that they are indeed coincident in the space u-v. Numerical simulations of a VKI LS-89 turbine blade are presented to support the present approach.