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.

The prediction of the temperature distribution in a gas turbine rotor containing closed, gas-filled cavities, for example in between two discs, 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 non-uniform 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 axis. The experimental set-up is designed to establish a pure centripedal 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 (1007 < 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° sections and the heat transfer increases considerably. A computer programme to simulate flow and heat transfer in closed rotating cavities has been developed and tested successfully for annuli with isotherm side walls with different temperatures giving an axial heat flux. For the centripedal 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 Bénard problem in the gravitational field.

The prediction of the temperature distribution in a gas turbine rotor containing gasfilled closed cavities, for example between two disks, has to account for the heat transfer conditions encountered inside these cavities. In an entirely closed annulus no forced convection is present, but a strong natural convection flow occurs induced by a nonuniform density distribution in the centrifugal force field. A computer code has been developed and applied to a rotating annulus with square cross section as a base case. The co-axial heat flux from one side wall to the other was modeled assuming constant temperature distribution at each wall but at different temperature levels. Additionally the inner and outer walls were assumed to be adiabatic. The code was first verified for the annulus approaching the plane square cavity in the gravitational field, i.e., the ratio of the radius r over the distance h between outer and inner cylindrical wall was set very large. The results obtained agree with De Vahl Davis’ benchmark solution. By reducing the inner radius to zero, the results could be compared with Chew’s computation of a closed rotating cylinder, and again good agreement was found. Parametric studies were carried out varying the Grashof number Gr, the rotational Reynolds number Re, and the r/h ratio, i.e., the curvature of the annulus. A decrease of this ratio at constant Gr and Re number results in a decrease of heat transfer due to the Coriolis forces attenuating the relative gas velocity. The same effect can be obtained by increasing the Re number with the h/r ratio and the Gr number being constant. By inserting radial walls into the cavity the influence of the Coriolis forces is reduced, resulting in an increase of heat transfer.

The prediction of the temperature distribution in a gas turbine rotor containing gas filled closed cavities, for example in between two discs, has to account for the heat transfer conditions encountered inside these cavities. In an entirely closed annulus no forced convection is present, but a strong natural convection flow occurs induced by a non-uniform density distribution in the centrifugal force field. A computer code has been developed and applied to a rotating annulus with square cross section as a base case. A co-axial heat flux from one side wall to the other was modelled assuming the temperatures at this walls being different but uniformly distributed, while both the outer and inner cylindrical surfaces were assumed to be adiabatic. The code was first verified for the annulus approaching the plane square cavity in the gravitational field, i.e. the ratio of the radius r over the distance h between outer and inner cylindrical wall was set very large. The results obtained agree with De Vahl Davis’ benchmark solution. By reducing the inner radius to zero, the results could be compared with Chew’s computation of a closed rotating cylinder, and again good agreement was found. Parametric studies were carried out varying the Grashof number Gr, the rotational Reynolds number Re and the r/h-ratio, i.e. the curvature of the annulus. A decrease of this ratio at constant Gr and Re number results in a decrease of heat transfer due to the Coriolis forces attenuating the relative gas velocity. The same effect can be obtained by increasing the Re number with the h/r-ratio and the Gr number being constant. By inserting radial walls into the cavity the influence of the Coriolis forces is reduced resulting in an increase of heat transfer.