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.