Experimental and Theoretical Investigations of Heat Transfer in Closed Gas-Filled Rotating Annuli

The prediction of the temperature distribution in a gas turbine rotor containing closed, gas-filled cavities, for example in between two disks, has to account for the heat transfer conditions encountered inside these cavities. In an entirely closed annulus, forced convection is not present, but a strong natural convection flow exists, induced by a nonuniform density distribution in the centrifugal force field. Experimental investigations have been made to analyze the convective heat transfer in closed, gas-filled annuli rotating around their horizontal axes. The experimental setup is designed to establish a pure centripetal heat flux inside these annular cavities (hot outer, and cold inner cylindrical wall, thermally insulated side walls). The experimental investigations have been carried out for several geometries varying the Rayleigh number in a range usually encountered in cavities of turbine rotors (10⁷ < Ra < 10¹²). The convective heat flux induced for Ra =10¹² was found to be a hundred times larger compared to the only conductive heat flux. By inserting radial walls the annulus is divided into 45 deg sections and the heat transfer increases considerably. A computer program to simulate flow and heat transfer in closed rotating cavities has been developed and tested successfully for annuli with isothermal side walls with different temperatures giving an axial heat flux. For the centripetal heat flux configuration, three-dimensional steady-state calculations of the sectored annulus were found to be consistent with the experimental results. Nevertheless, analysis of unsteady calculations show that the flow can become unstable. This is analogous to the Be´nard problem in the gravitational field.