[en] Following our previous two-dimensional (2D) studies of flows in differentially heated cavities filled with air, we studied the stability of 2D natural convection flows in these cavities with respect to 3D periodic perturbations. The basis of the numerical methods is a time-stepping code using the Chebyshev spectral collocation method and the direct Uzawa method for velocity–pressure coupling. Newton's iteration, Arnoldi's method and the continuation method have been used in order to, respectively, compute the 2D steady-state base solution, estimate the leading eigenmodes of the Jacobian and perform linear stability analysis. Differentially heated air-filled cavities of aspect ratios from 1 to 7 were investigated. Neutral curves (Rayleigh number versus wave number) have been obtained. It turned out that only for aspect ratio 7, 3D stationary instability occurs at slightly higher Rayleigh numbers than the onset of 2D time-dependent flow and that for other aspect ratios 3D instability always takes place before 2D time-dependent flows. 3D unstable modes are stationary and anti-centro-symmetric. 3D nonlinear simulations revealed that the corresponding pitchfork bifurcations are supercritical and that 3D instability leads only to weak flow in the third direction. Further 3D computations are also performed at higher Rayleigh number in order to understand the effects of the weak 3D fluid motion on the onset of time-dependent flow. 3D flow structures are responsible for the onset of time-dependent flow for aspect ratios 1, 2 and 3, while for larger aspect ratios they do not alter the transition scenario, which was observed in the 2D cases and that vertical boundary layers become unstable to traveling waves. (paper)

[en] Transient and steady free convection around a line heat source is studied experimentally and numerically. Experiments are performed with a thin platinum wire of 50 μm in radius immersed in water and heated by Joule effect. Time evolution of velocity and temperature fields are measured by PIV (Particle Image Velocimetry) and micro-thermocouple for three different heating rates. Numerical simulations are done using a time-stepping algorithm based on a velocity-pressure formulation. The equations are discretized on a domain of limited extension, using spectral type approximations and a domain decomposition technique, and a pressure condition is imposed at the outer boundary. A three-stage scenario is proposed for the development of transient free convection around a thin wire, and, at each stage, the numerical approach is assessed through detailed comparison between numerical and experimental results. Previously established scaling laws for the onset of convective motion are checked for long time behavior. Numerical and experimental results confirm that these laws remain meaningful at long time and a qualitative similarity is observed for the transients. In addition, a steady case of a heated wire in air is studied and compared with the experimental study of Brodowicz and Kierkus [Brodowicz, K., Kierkus, W., 1966. Experimental investigation of free-convection in air above horizontal wire with constant flux. Int. J. Heat Mass Trans. 9, 81-94]. Despite a wire superheat of 210 K, good agreement is observed between the experiment and numerical simulations performed under the Boussinesq assumption. In particular, numerical simulations match with the scaling laws of the far-field above the wire

[en] Highlights: ► Turbulent natural convection is studied numerically and experimentally. ► DNS of full conduction–convection–radiation coupling is performed. ► Spectral methods are combined with domain decomposition. ► Considering surface radiation improves strongly numerical results. ► Surface radiation is responsible for the weak stratification. -- Abstract: The present study concerns an air-filled differentially heated cavity of 1 m × 0.32 m × 1 m (width × depth × height) subject to a temperature difference of 15 K and is motivated by the need to understand the persistent discrepancy observed between numerical and experimental results on thermal stratification in the cavity core. An improved experiment with enhanced metrology was set up and experimental data have been obtained along with the characteristics of the surfaces and materials used. Experimental temperature distributions on the passive walls have been introduced in numerical simulations in order to provide a faithful prediction of experimental data. By means of DNS using spectral methods, heat conduction in the insulating material is first coupled with natural convection in the cavity. As heat conduction influences only the temperature distribution on the top and bottom surfaces and in the near wall regions, surface radiation is added to the coupling of natural convection with heat conduction. The temperature distribution in the cavity is strongly affected by the polycarbonate front and rear walls of the cavity, which are almost black surfaces for low temperature radiation, and also other low emissivity walls. The thermal stratification is considerably weakened by surface radiation. Good agreement between numerical simulations and experiments is observed on both time-averaged fields and turbulent statistics. Treating the full conduction–convection–radiation coupling allowed to confirm that experimental wall temperatures resulted from the coupled phenomena and this is another way to predict correctly the experimental results in the cavity