# Theoretical Modelling of Flow in Rotor-Stator Systems

• Izzi Mear-Stone

Student thesis: Doctoral ThesisPhD

### Abstract

The prevention of hot gas ingress between rotating and stationary discs in gas turbines is big business, with experimental and computational research being common in the sector. Experimental rigs, operating at a fraction of the engine size and in simulated fluid dynamic conditions, model the engine environment. Computational Fluid Dynamics (CFD) is used in both academia and industry to model the flow and heat transfer in a turbine. CFD is expensive, time consuming and requires detailed experimental validation. The engine designer has a need for simpler, faster mathematical modelling methods, ultimately to be used in 1D design codes. The research in this thesis stems from this need for the industrial engine designers to be able to predict the flow, pressure and temperatures in the secondary-air-system. Momentum-integral equations are known to model flow over rotating and stationary discs in isolation. This thesis shows that the momentum-integral equations can be solved together, to successfully model the flow inside a rotor and stator cavity. New momentum-integral equations are derived, free of the incorrect assumption that swirl ratio inside a rotor-stator cavity does not vary with radius. Two cavity models are described based upon the momentum-integral equations: one for a closed cavity and one for a cavity with sealing flow and no ingress. Both are computationally fast and are shown to give good agreement with experimental measurements and CFD results. Detailed flow structures are given for a range of rotor-stator cavity cases and the results of the models allow conclusions about the flow structure to be drawn. It is found that the outer region, where flow leaves the rotor and is entrained by the stator, is not affected by sealing flow. As well as complete cavity models, two other models for specific rotor-stator phenomenon have been derived. The effect of ingress on the swirl ratio in the cavity has been modelled, using a momentum balance approach. The buffer ratio and buffering effect, which quantify how the rotor is protected from ingress, have been defined, modelled and validated against measurements of adiabatic effectiveness for four different seal geometries. The model has allowed the calculation of Φ′min,r, the sealing flow rate where the effectiveness on the rotor reaches 95%.
Date of Award 20 Oct 2015 English University of Bath Siemens plc & Engineering and Physical Sciences Research Council Gary Lock (Supervisor) & Michael Wilson (Supervisor)

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