Flow Characteristics and Stability Analysis of Variable-Density Rotating Flows in Compressor-Disk Cavities

Previous heat transfer experiments showed that significant differences in the flow and heat transfer characteristics can occur in models of aircraft gas-turbine, high-compressor drums. Experiments with heated disks and colder flow show large-scale instabilities that cause mixing between the cooling flow and the flow in the trapped cavities. The general result of this mixing is relatively high heat flux on the disks. Other heat transfer experiments, simulating the aircraft take-off condition with cold disks and hotter coolant, show decreased heat transfer due to the stabilizing effects of positive radial density gradients. A stability analysis for inviscid, variable-density flow was developed to quantify the effects of axial velocity, tangential velocity, and density profiles in the bore region of the disk cavities on the stabilizing or destabilizing characteristics of the flow. The criteria from the stability analysis were used to evaluate the axial velocity and density profile conditions required to stabilize three tangential-velocity profiles, obtained from previous experiments and analyses. The results from the parametric study showed that for Rossby numbers, the ratio of axial velocity to disk bore velocity, less than 0.1, the flow can be stabilized with ratios of cavity density to coolant density of less than 1.1. However, for Rossby numbers greater than 1, the flow in the bore region is unlikely to be stabilized with a positive radial density gradient. For Rossby numbers between 0.1 and 1.0, the flow stability is a more complex relationship between the velocity and density profiles. Results from the analysis can be used to guide the correlation of experimental heat transfer data for design systems.