Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point
As shown in earlier work (Ahlers et al., J. Fluid Mech. 569, p.409 (2006)), non-Oberbeck Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Benard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient. If the working fluid is ethane close to the critical point the origin of non-Oberbeck-Boussinesq corrections is very different, as will be shown in the present paper. Namely, the main origin of NOB corrections then lies in the strong temperature dependence of the isobaric thermal expansion coefficient β(T). More precisely, it is the nonlinear T-dependence of the density ρ(T) in the buoyancy force which causes another type of NOB effect. We demonstrate that through a combination of experimental, numerical, and theoretical work, the latter in the framework of the extended Prandtl-Blasius boundary layer theory developed in Ahlers et al., J. Fluid Mech. 569, p.409 (2006). The latter comes to its limits, if the temperature dependence of the thermal expension coefficient β(T) is significant.