The flow inside cavities between corotating compressor disks of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the disks, and the disk temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anticyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady, and unstable, and it is a challenge to compute and measure the heat transfer from the disks to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both disks in a rotating cavity of the Bath compressor-cavity rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disk temperature were collected under carefully controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disk temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disk increase as the buoyancy forces increase. At high rotational speeds, the temperature rise in the core, created by compressibility effects in the air, attenuates the heat transfer, and there is a critical rotational Reynolds number for which the Nusselt number is a maximum. In the cavity, there is an inner region dominated by forced convection and an outer region dominated by buoyancy-induced flow. The inner region is a mixing region, in which entrained cold throughflow encounters hot flow from the Ekman layers on the disks. Consequently, the Nusselt numbers on the downstream disk in the inner region tend to be higher than those on the upstream disk.

The change in compressor blade-tip clearance across the flight cycle depends on the expansion of the rotor, which in turn depends on the temperature and stress in the disks. The radial distribution of temperature is directly coupled to the buoyancy-driven flow and heat transfer in the rotating disk cavities. This paper describes a new test rig specifically designed to investigate this conjugate phenomenon. The rig test section includes four rotating disks enclosing three cavities. Two disks in the central cavity are instrumented with thermocouples to provide the radial distribution of temperature; the two outer cavities are thermally insulated to create appropriate boundary conditions for the heat transfer analysis. An axial throughflow of air is supplied between a stationary shaft and the bore of the disks. The temperature of the throughflow air is measured by thermocouples in rakes upstream and downstream of the central cavity. For a cold throughflow, the outer shroud of the central cavity is heated. Two independently controlled radiant heaters allow differential shroud temperatures for the upstream and downstream disks, as found in aero-engine compressors. Alternatively, the throughflow can be heated above the shroud temperature to simulate the transient conditions during engine operation where stratified flow can occur inside the cavity. The rig is designed to operate in conditions where both convective and radiative heat transfer dominate; all internal surfaces of the cavity are painted matt black to allow the accurate calculation of the radiant heat transfer. Separate attachments can be fitted to the cobs of both central disks; the attachments reduce the axial gap between the cobs—reducing the gap to zero creates a closed cavity, which can occur in some compressor designs. Other instrumentation includes heat-flux gages on the shroud and high-frequency pressure transducers embedded into the disk diaphragm to capture unsteady flow structures. Attention has been given to experimental uncertainty, including the computation of the thermal-disturbance errors, caused by thermocouples embedded in the rotating disks; a Bayesian statistical model is used to reduce the effect of uncertainties in temperature measurements on the calculation of the Nusselt number. The effect of relevant nondimensional parameters on the radial distribution of the disk and throughflow temperatures has been shown for some typical cases.