Stratified and Buoyancy-Induced Flow in Closed Compressor Rotors

Abstract

The radial growth of compressor discs is strongly influenced by conjugate heat transfer between conduction in the co-rotating discs and buoyancy-driven convection in the rotating fluid core between the discs. An accurate prediction of metal temperatures of these discs is an important issue in thermo-mechanical design, where blade-tip clearances must be controlled carefully to ensure safety and efficiency under all operating conditions. This paper presents an experimental study of the fluid dynamics and heat transfer in a closed rotating cavity, comparing results with theoretical models and introducing a new compressibility parameter χ. At large values of χ, where compressibility effects are significant, the air temperature approaches that of the shroud; such conditions suppress buoyancy effects and the flow in the rotating cavity becomes stratified, with convection replaced by conduction inside the fluid core. There are important practical consequences of stratification with significant differences in temperature distributions and stresses inside compressor discs. The influence of χ is also shown on the radial temperature distributions for the discs and on the shroud heat transfer correlations, which are compared qualitatively with previously published data collected where the effects of compressibility are relatively small. The experiments reveal that there is a critical value of χ where the convective heat flux to the shroud is zero. The radial distribution of disc temperature was that expected from pure conduction in a cylinder. A new heat transfer correlation based on measured shroud heat flux and the theoretical core temperature is presented. The unsteady flow characteristics in the cavity were also investigated, identifying coherent rotating structures across a range of experimental conditions. These cyclonic / anti-cyclonic vortex pairs generate the non-dimensional circumferential pressure difference necessary for the radial outflow (of cold fluid) and inflow (of hot fluid) through the rotating core. The experiments show the magnitude of these pressure variations can be correlated against Grashof number and that at high values of χ the structures do not exist. The combined experimental and theoretical results will be of practical interest to engine designers and for the validation of computational models.

Plume Model for Buoyancy-Induced Flow and Heat Transfer in Closed Rotating Cavities

“…It can be seen that although the disc flux increases with radius, the flux ratio is positive (indicating heat transfer from the disc to the core) in the outer part of the cavity and negative in the inner part. This flux reversal, which is consistent with the difference between the disc and core temperatures in Figure 6, was observed from experimental measurements in [14].…”

“…As 𝑚̇𝑝 ̂ is invariant with r, eq. ( 52) implies that Δ𝑝 must also be invariant with r. This equation is used for the correlation for 𝑚̇𝑝 ̂ obtained in the companion paper [14].…”

“…There is no accepted correlation for 𝐶 𝑤 , the mass flow rate in the plumes, and so the equation used to correlate the data in [14] of this paper is used here, where 𝐶 𝑤 = 1.0(Gr 𝑠 Pr) 0.61 (74)…”

“…The practical effects will also depend on the assumptions made for the heat flux from the shroud and hub and on the geometry of the cavity. In [14], the theoretical values of the temperature distributions are compared with measurements made in an experimental rig. The principal assumptions are that the convective heat transfer from the hot shroud to the cold hub is via plumes of fluid in which the cold fluid moves radially outward, and the hot fluid inward, inside an inviscid quasi-axisymmetric core of rotating fluid in which there are radial and circumferential distributions of pressure.…”

“…A companion paper [14] includes experimental measurements in a closed-cavity rig and compares these with predictions from the plume model.…”