Transient natural convection flows and heat transfer in a thermally stratified air-filled trapezoidal cavity

Abstract

This paper focuses on studying the transient behavior of natural convective heat and fluid flow in a two-dimensional trapezoidal cavity subjected to a heated bottom surface, cooling from the top, and thermally stratified inclined surfaces. The Finite Volume (FV) method is employed to numerically simulate the transient flow. The study considers a thermally stratified environment with a Prandtl number of Pr set to 0.71 (for stratified air), an aspect ratio (A) of 0.5, and a large array of Rayleigh numbers (Ra) ranging from 100 to 108. The research examines how the Rayleigh numbers affect the flow structures, transient phenomena, and heat transfer (HT) characteristics within the cavity. The transitional flow reveals several supercritical bifurcations. These include a changeover from symmetric to asymmetric states known as a Pitchfork bifurcation, as well as a shift from a steady-state to a periodic state referred to as a Hopf bifurcation. The Pitchfork bifurcation happens between Ra values of 105 and 2 × 105, while the Hopf bifurcation happens within the range of the Ra values from 4.7 × 105 to 4.8 × 105. Moreover, another bifurcation from a periodic to a chaotic state is observed between Ra of 3 × 107 and 4 × 107. To examine the transient flows during the changeover to chaos, various techniques such as power spectral density (PSD), limit points, limit cycles, trajectory in phase space, and the largest Lyapunov exponent (LLE) are used. Furthermore, convective heat transfer is computed, and its corresponding impact on the Ra values is explained. The flow phenomena within the cavity are measured and verified.