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.

Analysis of Mixed Convection in a Lid Driven Trapezoidal Cavity

“…Torrance et al [9] investigated mixed convection in driven cavities as early as in 1972. Papaniclaou and Jaluria [10][11][12][13] carried out a series of numerical studies to investigate the combined forced and natural convective cooling of heat dissipating electronic components, located in rectangular enclosures, and cooled by an external through flow of air. The results indicate that flow patterns generally consists of high of low velocity re-circulating cells because of buoyancy forces induced by the heat source.…”

“…Unlike Φ=0º, when the buoyancy is acting only in the y direction, as the rotational angle Φ changes, the flow field changes significantly. In opposing flow condition the shear driven flow opposes the natural convective flow, At low Richardson number (Ri<1)the forced convection is dominating, creating a single circulation at the right corner of the top moving lid [figure [10][11][12]. As the Richardson number increases (Ri>1), natural convection becomes dominating creating a large circulation at the bottom of the cavity.…”

The effect of a baffle on the heat transfer in underground auxiliary ventilation systems

“…In fact, no steady solution was found due to the instability in the physical system for this situation. Other researchers also found the fluctuating results in closed and open cavities and discussed that the Hopf bifurcations lead to oscillating flows [13,14]. In this work, the examination of heat transfer at Ri=100 is based on solving the unsteady equations using dimensionless time step,…”

Numerical Study on Mixed Convection in Ventilated Cavities with Different Aspect Ratios

“…These studies have been applied to the chemical vapor deposition (CVP) technology and in the control of the propagation of fire and smoke. According to Raji and Hasnaoui [2], the use of these studies would lead to profitable results in the design of buildings, associated with their exercise costs, and in heat accumulation systems and solar energy. Many researchers have performed efforts in the analysis of these problems although, for the moment, they are grappled more in numerical that in that experimental ones.…”

“…A numerical study on transition from a steady laminar regime to a period regime in a similar problem analyzed in Papanicolaou and Jaluria [2], which was investigated also in (Papanicolaou and Jaluria [4].…”