Strong symmetrical non-Oberbeck–Boussinesq turbulent convection and the role of compressibility

Abstract

Strong non-Oberbeck–Boussinesq (OB) effects in turbulent convection were investigated experimentally in SF6 in the vicinity of its gas-liquid critical point (CP). The temperature and density dependencies of the thermodynamic and kinetic properties of SF6 near its CP and at the average critical density lead to strong but symmetric vertical variations of the main physical properties, which enter into the control parameters of turbulent convection. This produces an up-down symmetry in the temperature drops across the upper and lower half of the cell, while the temperature in the middle of the cell remains equal to the average value. Thus, in spite of the strong variations of the fluid properties across the cell height, the up-down symmetry remains like in the OB case. The distinctive feature of the symmetric non-OB turbulent convection is that the heat transport scales with the Rayleigh number Ra like in the OB turbulent convection. At the same time, it shows a much stronger dependence on the Prandtl number Pr. We singled out the influence of the non-OB effect on the heat transport and found that, for the same Pr, an eightfold larger non-OB effect does not alter either the value of the Nusselt number, Nu, nor its scaling with respect to the Rayleigh number, Nu∝Raγ. The conclusion is that the strong symmetric non-OB effect by itself is not responsible for the strong Pr dependence of the heat transport near CP. The possible source of this Pr dependence is the strongly enhanced isothermal compressibility in the vicinity of CP, which can affect the dynamics of plumes and so the heat transport close to the CP, and manifests itself in a dependence of Nu on Pr much steeper than in the OB case.

New perspectives in turbulent Rayleigh-Bénard convection

“…While in [171,172] the deviation of the centre temperature from the algebraic mean, T ref = (T bottom + T top )/2, is observed, Burnishev et al [61] report a high-Rayleigh-number NOB convection with symmetric temperature profiles and a scaling Nu ∼ Ra β which is comparable to the experiments in the OB limit at same Ra (see sect. 6).…”

“…Complete mixing is obtained when the aspect ratio is decreased as in [144]. They also found a scaling (61) showing that the lateral boundary layers at the side walls do not affect the heat transfer. All data which are reported in fig.…”

“…The latter experiment by Burnishev and Steinberg [61] is of particular interest since it reports the absence of a property that is usually assigned with NOB convection -the breaking of the up-down-symmetry. While in [171,172] the deviation of the centre temperature from the algebraic mean, T ref = (T bottom + T top )/2, is observed, Burnishev et al [61] report a high-Rayleigh-number NOB convection with symmetric temperature profiles and a scaling Nu ∼ Ra β which is comparable to the experiments in the OB limit at same Ra (see sect.…”

“…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 anelastic approximation (5) is a first weak compressibility effect which is for example incorporated in atmospheric convection that exceeds layers of height H ≈ 2 km. Stronger compressibility effects and thus large variations of the fluid properties can arise when the working fluids are operated in the vicinity of their critical points as done in helium [171], in ethane [172], or in SF 6 [61].…”