A numerical model has been developed to reproduce the effects of complex casing treatments (CT) in steady RANS simulations of multistage compressors. While some CTs, such as circumferential grooves, can be described by a rotation surface and can thus easily be included in conventional steady simulations, the CFD analysis of other casing treatments like axial slot or recessed vanes, currently requires a time-resolving analysis of the interaction between such structures and rotating parts. At present unsteady simulations are still too time consuming to be used in the early phase of a compressor design. In the presented study a numerical model was developed for casing treatment applications, to introduce the unsteady effects caused by such casing treatments into steady CFD-simulations. With the help of the model, non-axisymmetric elements can be eliminated from the geometry allowing a steady simulation to be used. The flow acceleration and redirection caused by these geometrical elements is replaced with adequate source terms introduced into the three-dimensional Navier-Stokes equations. These source terms, derived from a consecutive time- and circumferential averaging of the three-dimensional unsteady Reynolds-averaged Navier-Stokes-equations, arise from the momentum and energy equations. Using these additional terms, the CT-model simulates both the pressure forces that the walls of the real casing treatment exert on the flow, and the effects of the mean blockage induced by the omitted geometry. Furthermore, the deterministic stresses, caused by a circumferentially inhomogeneous flow within the CT-structure, are modeled. The source terms consist of geometrical data that can be derived directly from the real geometry of the casing treatment as well as physical quantities of the time-averaged flow in the real casing treatment. The latter terms can be obtained from a reference unsteady simulation. In the presented case one unsteady simulation was sufficient to set up the model for a complete speed line. The model was implemented into the three-dimensional Navier-Stokes-code TRACE [5][12]. By using steady instead of unsteady CFD simulations, the time required for a speedline computation was reduced by a factor of 10. At the same time, the numerical results of the CT-model showed good alignment with the reference data. The model was evaluated for several different styles of compressors. In this paper various results are presented, including speedlines as well as radial inflow- and outflow-profiles.
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