Effect of circumferential wave number on stability of suspension flow

Abstract

The linear stability analysis is carried out for the suspension flow of spherical particles between a rotating inner cylinder and a stationary concentric outer cylinder. The mass conservation equation and Navier-Stokes equation are applied to the continuous fluid phase and the particle phase. Results of stability analysis show that the increase of wave number in the circumferential direction attenuates the effect of the axial wave number on the amplification factor. The ratio of particle density to fluid density increasing above 0.1 amplifies the flow instability, while it can be weakened with higher circumferential direction wave number. Effect of the critical Taylor number on the amplification factor is reduced by increasing the circumferential direction wave number. The flow stability is affected by the geometry of flow field (the radius ratio) at non-zero circumferential direction wave numbers.