Numerical simulation of turbulent mercury natural convection in a heat-ed-from-below cylinder with zero and non-zero thickness of the horizontal walls


Аuthors

Smirnov S. I.*, Smirnovskii A. A.

Peter the Great Saint-Petersburg Polytechnic University, 29, Polytechnicheskaya str., St. Petersburg, 195251, Russia

*e-mail: sergeysmirnov92@mail.ru

Abstract

The results of direct numerical simulation of mercury natural convection (Prandtl number Pr = 0.025) in a cylindrical container, with the height-to-diameter ratio equal to 1.0, heated from below are presented. The effect of heat transfer in the solid (steel) horizontal walls of finite thickness on the flow structure and integral heat transfer is being studied. The thickness of the vertical cylindrical wall is assumed infinitesimal. The effective Rayleigh number computed over the averaged temperature difference between the horizontal media interfaces ranges from 106 to 108. At that, the corresponding scale Rayleigh number, constructed over the difference between the temperatures of the specified outer surfaces of horizontal walls, varies from 3∙106 to 7∙108. Besides the Rayleigh and Prandtl numbers, the convection is determined also by ratios of the specific heat capacities and the thermal conductivities of the liquid and solid media, which are adopted close to unity in the present paper. All calculations have been performed employing the SINF/Flag-S finite-volume in-house program code. The Navier–Stokes equations, written with the Boussinesq approximation, were solved using the fractional-step method with second order accuracy of spatial and temporal discretization. It was shown, that in the examined range of Rayleigh numbers a mostly characteristic flow structure was the so-called large-scale circulation. The vertical velocity component time variations analysis points to the presence of random low-frequency oscillations of the convective cell that were observed earlier in experimental studies. Integral Nusselt numbers calculated at zero wall thickness are in a good agreement with computational data reported by other authors. Quantitative difference between the Nusselt numbers obtained in cases of zero and non-zero thickness of the horizontal walls has been determined, namely, in the case of the finite wall thickness the integral heat transfer through the layer is 5-10% higher.

Keywords:

Rayleigh-Bénard convection, liquid metal, conjugate heat transfer

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