Abstract
Three-dimensional direct numerical simulations are used to characterize turbulent buoyant convection in a box-shaped Rayleigh–Bénard cavity with a rough bottom plate made of a series of square based blocks separated by valleys. The cavity is filled with water. The Rayleigh number varies over five decades up to $10^{10}$ . As mentioned in the literature, three successive heat transfer regimes are identified: from inactive roughness (I) to a regime (III) where the heat transfer increase is larger than that expected from only surface increase due to roughness. The heat transfers of the transitional regime II are particularly intense. After validation against experimental and numerical data from the literature, we highlight the role of the fluid retained within valleys (the inner fluid). It is shown that only the heat transfer across the fluid interface between the cavity bulk and the inner fluid is responsible for changes in the overall heat transfer at the rough plate, with an exponent of the heat transfer scaling law close to $1/2$ in regime II. The valley flow typifies the limits of this regime: the blocks protrude from the thermal boundary layer while remaining within the kinetic boundary layer. As compared with regimes I and III, regime II is characterized by larger temperature fluctuations, especially near the rough plate, and a larger friction coefficient. A fluctuating rough fluid layer overlaying both blocks and valleys appears in regime III, in addition to the classic boundary layers formed along the plate geometry.
Highlights
The addition of wall roughness to thermal systems involving turbulent convection is a common strategy to enhance the heat transfer of industrial systems
Taking advantage of the full three-dimensional information obtained from direct numerical simulations (DNS), this paper aims at describing the evolution of the fluid dynamics around the roughness blocks for the three heat transfer regimes and to explain how it contributes to enhancing heat transfer
We note in regime I that the heat transfer is slightly reduced by the addition of roughness in the asymmetric cavity (R/S) when compared with the S/S cavity, as previously shown by Tisserand et al (2011); Shishkina & Wagner (2011)
Summary
The addition of wall roughness to thermal systems involving turbulent convection is a common strategy to enhance the heat transfer of industrial systems. The corresponding flow depends on the following main control parameters: the Rayleigh number, Ra, the Prandtl number, Pr, and the cavity aspect ratio, Γ , while the main response of the system can be expressed in terms of a dimensionless heat transfer i.e. by means of the Nusselt number, Nu. The dependence of the Nusselt number on the control parameters (Nu ∼ αRaβ Prζ ) has been widely investigated (see Ahlers, Grossmann & Lohse 2009; Chillà & Schumacher 2012 for reviews), and the unifying theory of Grossmann & Lohse (2000, 2001) has been proposed to describe the multiple scaling laws of the Nusselt number in the (Ra − Pr) parameter space. Some experimental studies have reported this regime, such as Chavanne et al (1997) (see Roche (2020) for a review)
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