Direct measurements of the thermal dissipation rate in turbulent Rayleigh–Bénard convection

Anna Hertlein,Ronald Du Puits

doi:10.1063/5.0033746

Abstract

We report measurements of the thermal dissipation rate in turbulent Rayleigh-Bénard convection using a four-thermistor temperature gradient probe. The measurements have been undertaken in a Rayleigh-Bénard cell filled with air (Prandtl number Pr=0.7). The focus of this work is on large aspect ratios Γ (ratio between the horizontal and vertical extension of the cell), for which reason four datasets in the range of Rayleigh number Ra=3.9×106 to Ra=1.8×109 were taken at Γ≥8. In order to extend the range toward higher Rayleigh numbers, two smaller aspect ratios were also investigated (Γ=4 with Ra=1.7×1010 and Γ=2 with Ra=1.6×1011). We present highly resolved, vertical profiles of the thermal dissipation rate in the central vertical axis and discuss how these profiles change with the Rayleigh number. With its maximum near the wall and at the highest Rayleigh number, the thermal dissipation rate decreases monotonically with the distance from the plate. Moreover, the normalized, volume-averaged thermal dissipation rate, which effectively results in the Nusselt number Nu, scales with an exponent of about 0.29 with the Rayleigh number. In the Rayleigh number range investigated here, the dissipation is always higher in the boundary layer than in the bulk region. However, by means of an extrapolation of the considered Rayleigh number range to larger Rayleigh numbers, the intersection point between the dissipation in the boundary layer and the bulk region can be estimated as Ra≈3×1012.

Highlights

The understanding of the reciprocal transfer between kinetic and thermal energies is very important for the understanding of complex flow fields
We found the measured mean thermal dissipation rate to be larger in the boundary layer and to become smaller toward the midplane
We have executed our measurements at six different Rayleigh numbers 3:9 Â 106 < Ra < 1:6 Â 1011 at a Prandtl number Pr 1⁄4 0:7, whereas for the two highest Rayleigh numbers Ra 1⁄4 1:7 Â 1010 and Ra 1⁄4 1:6 Â 1011, the aspect ratios were C 1⁄4 4 and C 1⁄4 2, respectively

Summary

Introduction

The understanding of the reciprocal transfer between kinetic and thermal energies is very important for the understanding of complex flow fields. The transition from kinetic to thermal energy is called thermal dissipation and can be described by the thermal dissipation rate. We study this quantity by direct measurements in thermal convection. A very common setup to study thermal convection is the Rayleigh-Benard setup, where a fluid layer is cooled from above and heated from below. The temperature gradient generates a complex fluid flow, which transports heat from the warm bottom to the cold top plate. This setup is characterized by a set of five dimensionless parameters. As shown in Eq (1), it depends on the thermal expansion coefficient b, the gravitational acceleration g, the temperature difference DT, the distance H between heating and cooling plates, the thermal diffusivity j, and the kinematic viscosity , Ra

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Conclusion