A generalized interpolative interface is developed to provide an axisymmetric boundary condition for multielement unstructured field solvers, including those that require highly stretched anisotropic meshes. The method centers around an extruded interpolative interface that does not require matched unstructured grids on the corresponding axisymmetric surfaces. Arc-based mesh extrusions are constructed from each periodic interface, which allow for closure and the solution of control volumes that lie on the interface. For each extruded point, a corresponding virtual point is created in order to control the exact location at which the client data interpolations are performed; for axisymmetric surfaces, the virtual points are rotated and placed inside of the opposite side of the domain. Special procedures, such as utilization of surface projections and parallel boundary layer displacement algorithms, are required for support of highly stretched anisotropic grids commonly used in the resolution of boundary layers in fluid flow solvers. All algorithms used to extrude the interpolative surface, place virtual points, and interpolate for the client data must be parallelized for compatibility with modern parallel field solvers. No restrictions are to be placed on the subdomain decomposition. To this end, fully general parallel mechanisms are implemented in order to transport data from its native storage to a possibly remote location. This overall axisymmetric boundary condition scheme is implemented in the Tenasi code for testing. Interpolation requires a parallel unstructured multielement search algorithm, which is a concerted effort by itself, and is the subject of an upcoming paper. This axisymmetric interface scheme is validated on an empty rotor passage, as well as on a Rotor 37 standard test case at full design speed. For these simulations, the two equation Menter SST  turbulence model is utilized. Profiles of the relative Mach number aft of the blade and pressure ratio data match very well with experimental results, demonstrating the validity of the proposed approach.
A Generalized Axisymmetric Boundary Condition Method for Parallel Unstructured Field Solvers
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Hyams, DG, Webster, R, & Sreenivas, K. "A Generalized Axisymmetric Boundary Condition Method for Parallel Unstructured Field Solvers." Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air. Volume 7: Turbomachinery, Parts A, B, and C. Glasgow, UK. June 14–18, 2010. pp. 981-995. ASME. https://doi.org/10.1115/GT2010-23414
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