A recent study by Fluent Inc. engineers (Weiss et al., 1999) demonstrated how CFD simulations of a multi-stage turbine configuration using the mixing plane model compared to published data for an AGARD E/TU-4 turbine at both "design" and "off-design" conditions. While the mixing plane approach itself is not new, its use with fully unstructured mesh systems is only now being exploited. The principal advantage this combination offers the analyst or designer is the ability to rapidly generate meshes for complex geometries using the robust automated meshing tools that are available for unstructured tetrahedral and hybrid meshes. Hybrid meshes permit very accurate boundary layer resolution and solution-based adaption in order to resolve the varying length-scales of an evolving flowfield. This approach significantly reduces mesh generation time to provide results that can be used in a design environment.

In the mixing plane model, the flowfields within adjacent blade rows are solved in a steady state fashion, despite the fact that one row rotates relative to the next. At the interface between blade row regions, circumferentially averaged or "mixed" profiles of dependent variables are passed back and forth. These boundary profiles are updated at each iteration as the calculation converges.

The study examined both a "design" condition and an "off-design" condition involving two of the turbine's four stages. The rotor and stator meshes do not have to be conformal within FLUENT's mixing plane model and can be of different element types. The results agreed well with both static and total pressure profiles. Reasonably good agreement was obtained for the total temperature predictions. This study illustrates the mixing plane model's suitability for design studies, where quantities, such as overall pressure ratio and stage efficiency, depend upon the spanwise average total pressure and temperature.

Contours of static pressure through the multi-stage turbine

Following the two-stage analysis, a numerical study was conducted for the entire four-stage turbine. The figure below illustrates the mesh used, which includes seven mixing planes. The figure above shows the static pressure contours on the stator, rotor, and hub surfaces for the entire stage. This calculation demonstrates that the mixing plane model can be applied to problems involving a large number of blade rows.

Geometry and surface mesh of the four-stage turbine

Reference:

1. Weiss, J.M and Kelecy, F.J. "Numerical Simulation of Steady-State Flow Through a Multi-Stage Turbine Using Unstructured Meshes", Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, California, July 18-23, 1999.

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