A Direct Numerical Simulation of Early Transition Phenomena in a Buoyancy-Opposed Vertical Channel Flow

Abstract

The early transition phenomena in a buoyancy-opposed vertical channel flow have been investigated. The spectral method with a weak formulation is employed in the direct numerical simulation to solve the coupled transient 3-D momentum and energy equations. Initial perturbation includes a finite-amplitude 2-D TS wave and a pair of 3-D oblique waves in a K-type disturbance. The results show that after a period of transition time, small-sized vortical structures appear in the central regions of the channel. The subsequent development and breakdown of the vortical structures take place in the central regions of the channel where the shear stress of the laminar base velocity for the buoyancy-opposed flow is significantly larger than that of the isothermal flow. The patterns of the vortical structures in the wall region are almost unchanged during the transition. These transition phenomena are different from those in the buoyancy-assisted and isothermal flows, where the formation and development of the vortical structures initiate from the walls. The simulation results such as the local temperature fluctuations and harmonic energy carried by the different wave modes, are consistent in pointing out a general trend of sudden change from the laminar regime to a different state for the buoyancy-opposed flow, which agrees with the experimental observations obtained for pipe and annulus flows.