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A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux‐corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady‐state examples are solved to illustrate the performance of the algorithm.

SUMMARYWe present the extension of flux-corrected transport ( F a ) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, we have chosen triangular elements in two dimensions. The limiting procedure is based on Zalesak's extension to more than one dimension of the FCT schemes developed by Boris and Book. The resulting scheme, FEM-FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.

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In this two-part paper the phenomenon of part span rotating stall is studied. The objective is to improve understanding of the physics by which stable and persistent rotating stall occurs within high speed axial flow compressors. This phenomenon is studied both experimentally (Part I) and numerically (Part II). The experimental observations reported in Part I are now explored through the use of 3D unsteady Reynolds-averaged Navier–Stokes (RANS) simulation. The objective is to both validate the computational model and, where possible, explore some physical aspects of the phenomena. Unsteady simulations are presented, performed at a fixed speed with the three rows of variable stator vanes adjusted to deliberately mismatch the front stages and provoke stall. Two families of rotating stall are identified by the model, consistent with experimental observations from Part I. The first family of rotating stall originates from hub corner separations developing on the stage 1 stator vanes. These gradually coalesce into a multicell rotating stall pattern confined to the hub region of the stator and its downstream rotor. The second family originates from regions of blockage associated with tip clearance flow over the stage 1 rotor blade. These also coalesce into a multicell rotating stall pattern of shorter length scale confined to the leading edge tip region. Some features of each of these two patterns are then explored as the variable stator vanes (VSVs) are mismatched further, pushing each region deeper into stall. The numerical predictions show a credible match with the experimental findings of Part I. This suggests that a RANS modeling approach is sufficient to capture some important aspects of part span rotating stall behavior.