Buoyancy-Induced Heat Transfer inside Compressor Rotors: Overview of Theoretical Models

Abstract

Increasing pressures in gas-turbine compressors, particularly in aeroengines where the pressure ratios can be above 50:1, require smaller compressor blades and an increasing focus on blade-clearance control. The blade clearance depends on the radial growth of the compressor discs, which in turn depends on the temperature and stress in the discs. As the flow inside the disc cavities is buoyancy-driven, calculation of the disc temperature is a conjugate problem: the heat transfer from the disc is coupled with the air temperature inside the cavity. The flow inside the cavity is three-dimensional, unsteady and unstable, so computational fluid dynamics is not only expensive and time-consuming, it is also unable to achieve accurate solutions at the high Grashof numbers found in modern compressors. Many designers rely on empirical equations based on inappropriate physical models, and recently the authors have produced a series of papers on physically-based theoretical modelling of buoyancy-induced heat transfer in the rotating cavities found inside compressor rotors. Predictions from these models, all of which are for laminar flow, have been validated using measurements made in open and closed compressor rigs for a range of flow parameters representative of those found inside compressor rotors. (The fact that laminar buoyancy models can be used for large Grashof numbers (up to 10 12 ), where most engineers expect the flow to be turbulent, is attributed to the large Coriolis accelerations in the fluid core and to the fact that there is only a small difference between the rotational speed of the core and that of the discs.) As many as 223 separate tests were analysed in the validation of the models, and good agreement between the predictions and measurements was achieved for most of these cases. This overview paper has collected together the equations from these papers, which should be helpful to designers and research workers. The paper also points out the limitations of the models, all of which are for steady flow, and shows where further experimental evidence is needed.

Measurement and Analysis of Buoyancy-Induced Heat Transfer in Aero-Engine Compressor Rotors

“…Some engine designers use empirical formulae which are not always based on appropriate physical models. The authors have recently produced a series of publications on physicallybased theoretical modelling; an overview is presented by Owen et al [9].…”

Conjugate Modeling of a Closed Co-Rotating Compressor Cavity

“…The unstable phenomena in the fluid present a challenge for Computational Fluid Dynamics (CFD). Successful application of CFD as a design tool requires experimental validation and can be supplemented by physically-based theoretical modelling as documented in Owen et al [6]. The practical application of this research is to improve the predictive capability of industrial conjugate models, including fatigue and component-life applications.…”

A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem

“…This state suffers transitions as the value of R is further increased. Some industrial setups concerning the use of Rayleigh-Bénard convection equations can be found in [33][34][35][36][37][38][39][40]. Reduced-order models based on POD usually operate in two phases: (1) an off-line phase, where proper bases for the problem unknowns are computed from snapshots, and (2) an on-line phase, where the original partial differential equations are projected over the aforementioned bases.…”