Numerical Analysis of Heat Transfer and Flow Stability in an Open Rotating Cavity Using the Maximum Entropy Production Principle

Abstract

The flow field and heat transfer in the internal cooling system of gas turbines can be modelled using rotating-disc systems with axial throughflow. Because of the complexity of these flows, in which buoyancy-induced phenomena are of the utmost importance, numerical studies are notoriously difficult to perform and need extensive experimental validation. J.M. Owen proposed using the Maximum Entropy Production (MEP) Principle as a possible means of simplifying numerical computations for these complex flows. This theory is based on the heat flux out of the cavity. In this numerical study, the Nusselt numbers on the disc walls inside an open rotating cavity with a Rayleigh number of approximately 4.97×108 are evaluated with regard to the computed Nusselt numbers on the disc walls. These can be considered to be representative of the flow inside the cavity. It is shown that, as predicted by Owen, the flow is stable when the heat transfer out of the cavity is maximised, or, conversely, the system is unstable when the heat transfer is minimised. Furthermore, it is proven that the level of the Nusselt number plays an important role for the change between the number of vortex pairs in the flow as well.