Theoretical models of Buoyancy-induced flow in Rotating cavities

Student thesis: Doctoral ThesisPhD


Calculation of the blade tip clearances of the high-pressure-compressor rotors in aeroengines involves calculating the radial growth of the corotating compressor discs. This requires the calculation of the thermal growth of the discs, which in turn requires a knowledge of the disc temperatures and Nusselt numbers for the buoyancy-induced flow in the cavity between the discs. This is a strongly conjugate problem in which the equations for the fluid flow and the disc temperature are coupled.In this thesis, the buoyancy-induced flow and heat transfer inside the compressor rotors is modelled assuming laminar Ekman-layer flow on the discs and compressible flow in the fluid core between the Ekman layers; conduction in the discs is modelled using a one-dimensional fin equation. The theoretical predictions are compared with Nusselt numbers and temperatures obtained from two independent sets of temperature measurements, obtained on a multi-cavity compressor rig, and the ‘experimental’ Nusselt numbers were calculated using a Bayesian model for the inverse solution of the fin equation. For most of the experimental cases, with Grashof numbers up to 1012, mainly good agreement was achieved between the theoretical predictions and experimental values of the disc temperatures and Nusselt numbers. As predicted by the model, increasing the rotational Reynolds number can, under certain conditions, cause a decrease in the Nusselt numbers. Importantly, the results suggest that laminar Ekman-layer flow could occur even at the high Grashof numbers found in the compressor rotors of aeroengines.An extension of the buoyancy model included empirical correlations for the Nusselt numbers for the compressor shroud and disc cobs. This extended model was used to predict the temperature rise of the axial throughflow of cooling air in the compressor rotor, and reasonable agreement was achieved between the predicted and measured throughflow temperatures. This is the first time a theoretical model (rather than CFD) has been used to predict the temperatures of a compressor disc and the axial throughflow, and the model takes only seconds to predict the temperatures that would take days or even weeks to predict using CFD. Some suggestions are made for future research to improve the extent and accuracy of the model.
Date of Award11 Jan 2017
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJ. Michael Owen (Supervisor), Gary Lock (Supervisor) & Michael Wilson (Supervisor)


  • Buoyancy-Induced flow
  • Heat transfer
  • Theoretical model

Cite this