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

Abstract

The radial clearance between the rotating blades and stationary casing of a gas turbine compressor depends on the radial growth of the rotating discs, and this growth depends on the buoyancy-induced flow and heat transfer in the air-filled cavities between adjacent discs. A theoretical model has been developed to calculate the radial distribution of the temperature of the disc in a closed rotating cavity. The principal assumptions are that the convective heat transfer from the hot shroud to the cold hub of the cavity 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. The core is surrounded by boundary layers on all rotating surfaces, with free-convection layers on the surfaces of the shroud and hub and laminar Ekman layers on the surface of the discs. In addition to the convection, heat is transferred by one-dimensional radial conduction in the rotating discs. Using the model, equations have been derived to calculate the radial distribution of temperature in the discs and fluid core. These equations reveal that the non-dimensional temperatures for the disc and core, θd and θc, are controlled by three independent non-dimensional parameters: ReΦ, βΔT and x, the rotational Reynolds number, the buoyancy parameter, and the compressibility parameter. The theoretical model predicts radial distributions of temperatures in the discs and fluid core that are in good agreement with the experimentally derived values in a companion paper.

Stratified and Buoyancy-Induced Flow in Closed Compressor Rotors

“…Here the term experimentally-derived values refers to the temperatures and heat fluxes determined using the Bayesian model [19]; theoretical values refer to the temperatures and fluxes predicted from the Tang and Owen model [18]. The Appendix shows good agreement between the theoretical model and experimental measurements over a wide range of Reϕ, βΔT and .…”

“…In a closely-connected paper [18], Tang and Owen developed a quasi-axisymmetric conjugate model for buoyancy-induced flow in a closed rotating cavity; the radial variations of the temperature of the discs and fluid core, and that of the heat flux between the discs and the core, were predicted for compressible flow. The model assumed that radial plumes of fluid in the core convect heat from the hot shroud to the cold hub.…”

“…Tang and Owen [18] have conducted a parametric study to show the theoretical effect of the rotational Reynolds number 𝑅𝑒 𝜙 , the buoyancy parameter βΔT, compressibility parameter , and the thermal conductivity of the discs on the nondimensional core and disc temperatures, θc and θd. The nondimensional parameters and temperatures were defined as follows:…”

“…The nondimensional radius is defined as x = r/b, with xa = 0.45, xi = 0.52 and xo = 0.98see Figure 4. As shown by Tang and Owen [18], the radial distribution of θc is determined by the compressibility parameter , and the disc temperature can be calculated using the non-dimensional form of the circular fin equation:…”

“…where 𝜉 is the parameter used in the plume model to account for the effect of disc heat transfer on core temperatures. More details about the solution technique can be found in [18].…”