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

Abstract

As shown in earlier work ͓Ahlers et al., J. Fluid Mech. 569, 409 ͑2006͔͒, non-Oberbeck-Boussinesq ͑NOB͒ 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 coefficient ␤͑T͒. More precisely, it is the nonlinear T dependence of the density ͑T͒ 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 ␤͑T͒ is significant. The measurements reported here cover the ranges 2.1Շ PrՇ 3.9 and 5 ϫ 10 9 Շ RaՇ 2 ϫ 10 12 and are for cylindrical samples of aspect ratios 1.0 and 0.5.

Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh-Bénard convection

“…As the GL theory is based on the assumption that the BL thickness scales inversely proportional to the square root of the Reynolds number according to Prandtl's 1904 theory, the validity of Prandtl-Blasius BL flow needs to be tested also locally. Note that comparison of the mean bulk temperature calculated using the Prandtl-Blasius theory with that measured in both liquid and gaseous nonOberbeck-Boussinesq RB convection shows very good agreement [16][17][18] . In addition, the kinematic BL thickness evaluated by solving the laminar Prandtl-Blasius BL equations was found to agree well with that obtained in the direct numerical simulation (DNS) 19 .…”

New perspectives in turbulent Rayleigh-Bénard convection

“…They have a square cross-section and Γ = 1/2 and 1/4. The Nusselt number is determined from the injected power into the flow and the direct measurement of the temperature gradient inside the channel as given in (60). The experiment showed a particular largescale flow organization.…”

“…Several gases have been used at ambient temperatures: argon Ar [56,57], nitrogen N 2 [56][57][58], helium He [56,59], ethane C 2 H 6 [60], sulfur hexafluoride SF 6 [56,58,61,62], and air [63]. Globally, the range 60 < Ra < 10 15 of Rayleigh numbers has been spanned with gases.…”

“…The approach worked however less well for cases with very strong temperature dependence of the material parameters such as for α(T ) in ethane [60] or all material parameters in glycerol [175].…”

Limits of the Oberbeck–Boussinesq approximation in a tall differentially heated cavity filled with water

“…In these cases NOB effects are mainly due to variations of the viscosity with temperature. However, Ahlers et al [24] also studied NOB effects caused by the strong dependence of the thermal expansion coefficient on the temperature for ethane near its critical point.…”