Proper Orthogonal Decomposition of Turbine Rotor-Stator Interaction

Abstract

Numerical simulations of the flow in a one-stage turbine are carried out to investigate the feasibility of constructing a reduced-order model via Galerkin methods. The flow in the turbine is modeled by the unsteady Reynolds-averaged Navier-Stokes equations. The governing equations are written in the strong conservation form and solved using a fully implicit, finite difference approximation. By the use of the proper orthogonal decomposition (POD), spatial dominant features, also known as POD modes or eigenfunctions, are identified and separated from the spatiotemporal dynamics of the turbine flow. The POD reconstructed solutions indicate that a significant portion of the original dynamics is captured by a few modes. The solution reconstructed using the first 40 modes captures more than 99% of the energy spectrum, whereas the error of the energy variable is less than 0.6%, and the error of skin friction is less than 1.5%. Phase-space plots further indicate the existence of low-dimensional dynamics, which supports the validity of a reduced-order model for turbine flow.