TY - JOUR

T1 - Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point

AU - Ahlers, Günter

AU - Calzavarini, Enrico

AU - Fontenele Araujo, Francisco

AU - Funfschilling, Denis

AU - Grossmann, Siegfried

AU - Lohse, Detlef

AU - Sugiyama, Kazuyasu

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - IR-58977

KW - METIS-247309

U2 - 10.1103/PhysRevE.77.046302

DO - 10.1103/PhysRevE.77.046302

M3 - Article

VL - 77

JO - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

JF - Physical review E: covering statistical, nonlinear, biological, and soft matter physics

SN - 2470-0045

IS - 4

M1 - 046302

ER -