Multistage simulation by an adaptive finite element approach using structured grids

This paper presents the application of a three-dimensional Navier-Stokes fi nite element code (NS3D) in the context of turbomachinery rotor-stator mult istage interaction. A mixing-plane approach is used, in which boundary cond itions at a common interface plane between adjacent blade rows are iterativ ely adjusted to yield a flow satisfying the continuity, momentum and energy conservation equations, in an average sense. To further improve the soluti ons, a mesh adaptation technique then redistributes the mesh points of the structured grid within each component, according to an a posteriori edge-ba sed error estimate based on the Hessian of the local flow solution. This ma trix of second derivatives controls both the magnitude and direction of the required mesh movement at each node, is then implemented using an edge-bas ed spring analogy. The methodology is demonstrated for two test cases with two types of data: a well-instrumented experimental large-scale rotating ri g for a second stage compressor at UTRC and an actual engine. The latter, a two-stage compressor of a turboprop, has been only rested as a single-stag e configuration, because of the qualify of the experimental data available. All results compare well to the data and demonstrate the utility of the ap proach. In particular, the mesh adaptation shows large improvements in agre ement between the calculations and the experimental data.