Thermal convection in inclined cylindrical containers

Abstract

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle β, 0 β π/2, of a Rayleigh-Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number Nu and Reynolds number Re. The considered Rayleigh numbers Ra range from 10 6 to 10 8 , the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the Nu (β)/Nu(0) dependence is not universal and is strongly influenced by a combination of Ra and Pr. Thus, with a small inclination β of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small Pr, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to β = π/2, Nu and Re decrease with increasing β in all considered cases. Generally, the Nu(β)/Nu(0) dependence is a complicated, non-monotonic function of β.

Robustness of heat transfer in confined inclined convection at high Prandtl number

“…Notice however that the Re l at large β could not be estimated in the experiments for the laminar regime due to the extreme weakness of the flow. Let us remark that the curves of Re is again different from the experimental results at smaller Prandtl number, where it is generally observed a peak occurring also at β ≃ 10 ± 2 o but followed by a linear decrease till the largest inclinations [19,21,22] we report also the local Reynolds number Re l from experiments is (red diamonds). In the insets: the superposed graphs for Re(β)/Re(0) (squares) and Nu(β)/Nu(0) (triangles) from DNS.…”

“…While the first studies (water and silicon-oil) revealed a weak monotonous decrease of the heat flux, with a maximal reduction of 20% with respect to the RBC value, the second group of studies displayed always an overall increase of Nu with the existence of an optimal inclination around β ≃ 65 o − 70 o for which the increment was 20% in the Γ = 1, and remarkably as high as 1100% in the Γ = 1/20 system. On the numerical side a thorough series of studies in Γ = 1 cylindrical setting have been conducted for 0.1 ≤ Pr ≤ 100 and 10 6 ≤ Ra ≤ 10 8 [19]. This highlighted that the relative variation of Nu (with respect to the RBC case) is always moderate < 25%.…”

Towards parallel-in-time simulations of turbulent Rayleigh-Bénard convection

“…To calculate the velocity and temperature at the surfaces of each finite volume, it uses higher-order discretization schemes in space, up to the fourth order in the case of equidistant meshes. Goldfish has been used to study thermal convective flows in different configurations [152,153,155], in cylindrical and parallelepiped domains. For the time integration, the leapfrog scheme is used for the convective term and the explicit Euler scheme for the viscous term.…”

“…In Chapter 3, we compare four of these codes based on different discretization techniques: (1) a second-order finite difference method (AFID/RBflow [163,165,174,179,180]); (2) a fourth-order finite volume method (Goldfish [153,155,152]); (3) an eighth-order spectral element method (Nek5000 [24,48,75,97,148]); (4) a second-order finite volume method (OpenFOAM [183]). The first two codes are dedicated to RB convection in simple geometries, whereas the latter two codes are designed for general problems also in complex geometries.…”

“…For the cylindrical simulations we use the latest version of RBflow, which is an optimized version of the code used by Stevens et al [165,163]. The second code is Goldfish by Shishkina et al [153,155,152], which is based on a finite-volume approach and uses discretization schemes of the fourth-order in space. Goldfish can be used to study turbulent thermal convection in cylindrical and parallelepiped domains.…”