On non-Oberbeck–Boussinesq effects in Rayleigh–Bénard convection of air for large temperature differences

Abstract

We present direct numerical simulations of non-Oberbeck–Boussinesq (NOB) Rayleigh–Benard (RB) convection due to large temperature differences in two-dimensional (2-D) and three-dimensional (3-D) cells. Perfect air is chosen as the operating fluid and the Prandtl number ( ) is fixed to 0.71 for the reference state . In the present system, we consider large temperature differences ranging from 60 K to 240 K, and relatively strong NOB effects are induced at moderate Rayleigh numbers ( ) in the range . The large temperature difference also induces the turbulence system with large density variation. Due to top-down symmetry breaking under NOB conditions, an increase of the centre temperature is found compared to the arithmetic mean temperature of the top and bottom plates, and the shift of is strongly dependent on Rayleigh number and temperature differential . The NOB effects on the Nusselt number ( ) are quite small ( ). The power-law scalings of versus are robust against NOB effects, even for the extremely large temperature difference 240 K, which has never been reached in previous experiments and simulations. The Reynolds numbers , as well as the scalings of versus , are also insensitive to NOB effects. It is noteworthy that the influence of NOB effects on and in 3-D RB flow are weaker than its 2-D counterpart. Furthermore, the extended laminar boundary layer (BL) equations are developed based on the low-Mach-number Navier–Stokes equations, which qualitatively predicts the NOB effects on velocity profiles. Direct numerical simulation results indicate that the top and bottom thermal BLs can compensate each other much better than the velocity BLs under NOB conditions, which contribute to the robustness of .