Efficient Computational Model for Nonaxisymmetric Flow and Heat Transfer in Rotating Cavity

Abstract

Existence of large scale unsteady flow structures manifested in contrarotating vortex pairs has been previously identified in rotor disk cavities. The nonaxisymmetric nature with an unknown number of vortices presents a computational challenge, as a full 360 deg circumferential domain will be needed, requiring significant computational resources. A novel circumferential spatial Fourier spectral technique is adopted in the present work to facilitate efficient computational predictions of the nonaxisymmetric flows. Given that the flow nonuniformities in the circumferential direction are of large length scales, only a few circumferential Fourier harmonics would be needed, resulting in a drastic reduction in number of circumferential mesh points to be required. The modeling formulations and implementation aspects will be described. Computational examples will be presented to demonstrate the validity and effectiveness of the present modeling approach. The computational results show that the nonaxisymmetric flow patterns, in terms of the number of vortex pairs, are sensitive to small scale external disturbances. It is also indicated that the occurrence of a nonaxisymmetric flow might be captured by the present Fourier solution with even one harmonic.