A Computational Study of Chaotic Flow and Heat Transfer within a Trapezoidal Cavity

Abstract

Numerical findings of natural convection flows in a trapezoidal cavity are reported in this study. This study focuses on the shift from symmetric steady to chaotic flow within the cavity. This cavity has a heated bottom wall, a cooled top wall, and adiabatic inclined sidewalls. The unsteady natural convection flows occurring within the cavity are numerically simulated using the finite volume (FV) method. The fluid used in the study is air, and the calculations are performed for different dimensionless parameters, including the Prandtl number (Pr), which is kept constant at 0.71, while varying the Rayleigh numbers (Ra) from 100 to 108 and using a fixed aspect ratio (AR) of 0.5. This study focuses on the effect of the Rayleigh numbers on the transition to chaos. In the transition to chaos, a number of bifurcations occur. The first primary transition is found from the steady symmetric to the steady asymmetric stage, known as a pitchfork bifurcation. The second leading transition is found from a steady asymmetric to an unsteady periodic stage, known as Hopf bifurcation. Another prominent bifurcation happens on the changeover of the unsteady flow from the periodic to the chaotic stage. The attractor bifurcates from a stable fixed point to a limit cycle for the Rayleigh numbers between 4 × 106 and 5 × 106. A spectral analysis and the largest Lyapunov exponents are analyzed to investigate the natural convection flows during the shift from periodic to chaos. Moreover, the cavity’s heat transfers are computed for various regimes. The cavity’s flow phenomena are measured and verified.