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, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard 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 coefficientB(T). More precisely, it is the nonlinear T dependence of the density P(T) in the buoyancy force that causes another type of NOB effect. We demonstrate this through a combination of experimental, numerical, and theoretical work, the last in the framework of the extended Prandtl-Blasius boundary-layer theory developed by Ahlers et al. as cited above. The theory comes to its limits if the temperature dependence of the thermal expension coefficient B(T) is significant. The measurements reported here cover the ranges 2.1 < PR < 3.9 and 5×109 < Ra < 2×1012 and are for cylindrical samples of aspect ratios 1.0 and 0.5.