A direct numerical simulation of K- and H-type flow transition in a heated vertical channel

Abstract

In this study, the transition of a low Reynolds number mixed convection flow in a vertical channel is investigated by direct numerical simulations. Both K-type and H-type disturbances are investigated. For the K-type transition, it is found that the kinetic energy generated by the thermal buoyant force is the main driving force and the rate of vorticity generation is largely enhanced in the very early transition stage. The most significant characteristics during this period are that the large and high-strength vortex structures develop rapidly, large-scale temperature fields are found in the central region of the channel, and the Nusselt number increases quickly. For the H-type transition, it shares most of the characteristics with those of the K-type flow. One important exception is that the vortex structures in the H-type flow are positioned in a staggered pattern instead of an ordered pattern found in the K-type flow. The streamwise period is double that in the K-type flow. For both types, the flow field bifurcates to a new quasisteady nonlinear state after the initial transient period. The flow structure of this bifurcated state consists of many medium-scale and weak vortices, which are distributed relatively uniformly in the entire flow domain. These vortex structures do not change significantly with time. The important characteristics of the new state are that the vortex structures are still relatively regular as time progresses and the shear production of kinetic energy reaches to a small but finite magnitude and it changes very slightly with time. For a typical case, the average Nusselt number of the new state is about 32% above that of the laminar flow and the temperature fluctuations are low-frequency and small-scale oscillations. Those characteristics agree well with the experimental observations.