Numerical simulation of turbulent Rayleigh-Bénard mercury convection in a circular cylinder with introducing small deviations from the axisymmetric formulation

Abstract

Results of DNS are reported for turbulent Rayleigh-Bénard mercury convection (Pr = 0.025) in a cylindrical container with the aspect ratio of unity at the Rayleigh number of Ra = 106. The main goal of the study is to estimate the influence of small deviations from the axisymmetric formulation on the behavior of large-scale circulation (LSC) developing in the container. The deviations examined are a small tilt of the cylinder or prescribed sinusoidal disturbances of the bottom wall temperature. The effects of the computational grid structure in the central region of the flow are investigated as well. It has been shown that the azimuthal low-frequency reorientations of the LSC, which are typical for the axisymmetric problem setting, can be fully suppressed by imposing relatively small non-axisymmetric disturbances of various kinds. Time-averaged 3D velocity and temperature fields, as well as spatial non-uniformities of local heat transfer are analyzed for a “locked” LSC case.

The Emergence and Identification of Large-Scale Coherent Structures in Free Convective Flows of the Rayleigh-Bénard Type

“…Thus for both cases the cell size exceeded the minimum turbulence scale only within the restricted areas of the regions, and at the most by factor 2. In our previous studies [37,38], it was shown that such degree of resolution of the turbulent content is sufficient to obtain grid-independent fields of average velocity and temperature, as well as pulsation values characterizing small-scale turbulence (this will also be illustrated in the present study).…”

“…The coordinate system has its origin in a center of the cylinder. Some details on the problem definition, as well as preliminary results, were reported by us in [37,38]. No-slip conditions are imposed on all boundaries.…”

“…The situation is improved if some stabilizing external factor is artificially introduced, by means of which the large-scale circulation is "fixed" in a certain azimuthal position. For example, in a number of experimental [28,[34][35][36] and numerical [37][38][39] works, it was shown that the tilt of the container by a small angle almost completely "fixes" the CS in a certain position. In the paper, we show the results of our numerical simulation of the Rayleigh-Bénard convection in a cylinder, both tilted and non-tiled, and perform the AIM analysis of the large-scale coherent structure.…”