Transition to chaotic flow, bifurcation, and entropy generation analysis inside a stratified trapezoidal enclosure for varying aspect ratio

Abstract

In this numerical study, we investigate the effect of aspect ratio (AR) on the natural convection (NC) flow and entropy generation (S_gen) in a stratified fluid confined inside a trapezoidal enclosure with thermally stratified side walls. The bottom of the enclosure is heated, and top of the enclosure is cooled. We use the Finite Volume Method (FVM) for simulating unsteady flows. We consider a Prandtl number (Pr = 0.71 for air) and explore AR of 0.2, 0.5, and 1.0, covering a wide range of Grashof numbers (Gr) from 10 to 10⁸. The outcomes are presented for Grashof numbers and the effect of the AR on fluid flow, rates of heat transfer (HT), and S_gen inside the enclosure. Critical Grashof numbers are identified, marking the shift in flow behavior from being influenced by baroclinic to Rayleigh–Bénard instability, and from a steady to an unsteady state for various AR. In the context of this transition to chaotic flow, several supercritical bifurcations are observed, including a Pitchfork bifurcation from symmetric to asymmetric states and a Hopf bifurcation from a steady state to an unsteady state. Additionally, we analyze the discrepancies in average entropy generation (S_avg) and average Bejan number (Be_avg) across the entire enclosure, considering various AR and Gr values. It is observed that for enclosures with Gr ≥ 10⁵, S_avg increases as AR decreases, indicating an enhancement in HT rate with decreasing AR. Furthermore, a quantitative relationship between S_avg, HT, AR, and Gr is presented. The study concludes that, as AR increases, the ecological coefficient of performance (ECOP) decreases, signifying a reduction in thermodynamics efficiency.