Three-dimensional thermoconvection from a non-uniformly heated plate near the liquid-vapor critical point

Three-dimensional buoyancy-driven convection close to the liquid-vapor critical point is numerically investigated. We consider a supercritical nitrogen-filled rectangular cavity with horizontal/vertical aspect ratios of 3:1 and 2:1, which is heated differentially at the bottom by a constant heat flux of 10 W/m². Dependent on the size of the heating area (covering, namely, the full, a half, and a quarter of the bottom wall, respectively), spatiotemporal descriptions of the development of hydrodynamic instabilities are obtained for both near-critical and weakly-critical fluid conditions based on real-fluid properties, which include the vortex cores educed by the second invariant of the velocity gradient tensor. Direct numerical simulations are performed on a hydrodynamic model modified by the low-Mach-number approximation using a finite volume-based SIMPLE method. In addition, a co-located multigrid strategy is adopted to accelerate the simulation. The results capture the influences of the distance to the critical point on the evolution of the flow pattern and convective heat transfer under increasingly more complex heating arrangements. The strong equivalency among different near-critical fluids is demonstrated by a comparison between Rayleigh-Bénard flows in supercritical nitrogen and CO₂ with comparable degrees of criticality.