Identification of the Onset of Bifurcations in a Trapezoidal Cavity Receiver Open at the Top

Abstract

Stability analysis of buoyancy-driven convective flow in the trapezoidal cavities is essential for efficient heat transfer in solar evaporators. In the present analysis, the symmetry breakdown pitchfork and Hopf bifurcations' phenomena have been identified for different aspects of the trapezoidal cavity, which is heated at the bottom and open at the top. The system loses stability through pitchfork bifurcation, and as a result, symmetry breakdown of the temperature contour occurs beyond a threshold value of Rayleigh number (Ra). Further, increases in Ra cause instability in the form of Hopf bifurcation at the aspect ratio of 1.5 and for different cavity internal angles. Hopf bifurcation emerges by the sudden change in the streamwise velocity component, shifting from a decaying state to a continuously fluctuating magnitude at a particular location within the cavity. Through this, we predict the threshold value of Ra corresponding to Hopf bifurcation at different obtuse and acute cavity angles for an aspect ratio of 1.5. The flow's stable transient and unstable states are also identified and discussed for different values of the cavity internal angle for an aspect ratio of 1.5.