Transition to a periodic regime in mixed convection in a square cavity

Abstract

The numerical study presented in this work describes the transition from a steady, laminar regime to a periodic regime in an air-filled, two-dimensional cavity subjected to localized heating. The cavity lies at the bottom of a horizontal channel through which a cold air stream flows. The heating is provided by a constant heat input source, located on one of the vertical walls of the cavity and this generates a buoyancy-driven recirculating flow in the cavity. The interaction of this recirculating flow with the cold through-flow leads to steady flow and thermal fields as long as the value of the Grashof number, associated with the heat input from the source, remains below a certain critical value. As this value is exceeded, an unstable situation arises and, after an initial transient, the results show a very regular, periodic, almost sinusoidal behaviour. Similar previous works on natural convective flows in cavities have discovered such a periodic behaviour, as a form of travelling wave instability, having the characteristics of a Hopf bifurcation. These characteristics were also found to be present in this mixed convective situation, where the amplitudes of the oscillating quantities, like the thermal energy outflow, vary with the square root of the Grashof number. However, the present problem is also governed by the value of the Reynolds number, and its effect on the results is studied. The observed instability is of thermal origin, with small fluid cells at the centre of the cavity being subjected to periodic cooling and heating and, therefore, to a circulatory motion due to the density change.