This paper presents the application of a three-dimensional Navier-Stokes finite element code (NS3D) in the context of turbomachinery rotor-stator multistage interaction. A mixing-plane approach is used, in which boundary conditions at a common interface plane between adjacent blade rows are iteratively adjusted to yield a flow satisfying the continuity, momentum, and energy conservation equations, in an average sense. To further improve the solutions, a mesh adaptation technique then redistributes the mesh points of the structured grid within each component, according to an a posteriori edge-based error estimate based on the Hessian of the local flow solution. This matrix of second derivatives controls both the magnitude and direction of the required mesh movement at each node, is then implemented using an edge-based spring analogy. The methodology is demonstrated for two test cases with two types of data: a well-instrumented experimental large-scale rotating rig for a second stage compressor at UTRC and an actual engine. The latter, a two-stage compressor of a turboprop, has been only tested as a single-stage configuration, because of the quality of the experimental data available. All results compare well to the data and demonstrate the utility of the approach. In Particular, the mesh adaptation shows large improvements in agreement between the calculations and the experimental data.

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