This research presents high-fidelity numerical modelling of flow and heat transfer related to turbomachinery internal air systems. Code_Saturne, an open-source computational fluid dynamics (CFD) code, has been selected due to its favourable capabilities, noticeably high parallel performance. First, the code is validated against the previous experimental, numerical and theoretical solutions available in several representative disc cavity flow types, including closed rotor-stator cavity flows and co-rotating cavity with radial throughflows. Subsequently, the code is developed to model gravitational and centrifugal buoyancy-induced flows. The developed code is validated in a differential heated enclosure and rotating cavities, either sealed or with an axial throughflow, with careful justifications. The wall-modelled large-eddy simulation (WMLES) method shows a good balance between computational accuracy and cost, with clear advantages over the unsteady Reynolds-averaged Navier-Stokes (URANS) method under some conditions.

For the sealed rotating cavity flow, attention is focused on different heat convection types, including axial, radial and mixed, emphasising the effect of the axial temperature gradient. LES is implemented in a Rayleigh number range from 10⁷ to 10⁹. Axial convection gives lower core turbulence but axial core temperature gradient and flow circulation, with thicker boundary layers. Mixed convection shows flow features superimposed from radial and axial convections, with higher wall heat transfer. A low-order elementary model is proposed and validated for predicting wall heat transfer and cavity core temperature.

For the rotating cavity with an axial throughflow, WMLES is applied within a Reynolds number range from 3.2×10⁵ to 10⁷. Critical validations are conducted up to the highest Reynolds number of 3.0×10⁶ in the recent experiments available. Encouraging agreement with the experiment is achieved, with significant speed-up from previous calculations. At the highest Reynolds number of 10⁷, shroud heat transfer follows the scaling of lower Reynolds number results expected for natural convection. However, disc heat transfer is enhanced due to the flow transition from laminar to turbulent within the disc Ekman layer. This transition is found to be delayed by a positive inflow swirl.

Parametric studies for the rotating cavity with an axial throughflow are conducted. The effects of inlet and outlet flow reversal and buoyancy treatment are considered. Furthermore, based on the comparisons between the test rig and a modern civil aero engine high-pressure compressor, the effects of cavity geometry, disc temperature distribution and inflow swirl are considered. Engine representative cavity geometry, disc temperature distribution and inflow swirl all result in higher shroud heat transfer, but only the positive inflow swirl changes the flow structure in the cavity. These differences are associated with the exchange rates between throughflow and cavity flow. WMLES is recommended for further exploring aero engine operating conditions in support of lower-order thermal modelling and design in industry.