A General Finite Difference Technique for the Compressible Flow in the Meridional Plane of Centrifugal Turbomachinery

There has been an increased concentration of effort recently in the understanding of the complex flow in centrifugal turbomachines, especially industrial machines. Although it is impossible at this time, to model all the phenomena existing in a real machine, it is felt that a systematic approach which makes use of recent advances in computational fluid dynamics, and extends these as further developments occur, will significantly improve our understanding of the flow, and our ability to predict performance and improve efficiency. In this paper, a new general finite difference technique for solving the flow field in the hub-to-shroud plane of any component of a centrifugal turbomachine is described. The technique uses a quasi-orthogonal finite-difference net, and solves the resulting system of equations using a matrix method. Thus the technique offers a stable, accurate computational method, combined with a fixed grid which may be simply applied to the most complex annular passage shape. The results for three numerical examples are presented, a radial to axial inlet, a vaneless radial diffuser and an interstage return bend.