Modeling of hydrodynamics and heat transfer at the upward flow of liquid metal in a channel of rectangular cross section under influence of coplanar magnetic field

Аuthors

Kostichev P. V.¹, Pyatnitskaya N. Y.^{1, 2}, Razuvanov N. G.^{1, 2*}, Sviridov E. V.¹

1. National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya str., Moscow, 111250 Russia
2. Joint Institute for High Temperatures of the Russian Academy of Sciences, 13, Izhorskaya str., Moscow, 125412, Russia

*e-mail: nikita.razuvanov@mail.ru

Abstract

The studies of hydrodynamics and heat transfer while the liquid metal upward flow in a rectangular channel of about 3/1 aspect ratio under the impact of coplanar magnetic field under condition of non-uniform (one-sided) channel heating were performed. The flow configuration is close to the heat exchange channel of the liquid metal cooling system module of the tokamak-type fusion reactor blanket. The experiments were conducted based on a mercury magneto-hydrodynamic test bench, being a part of the MEI-JIHT RAS MHD-complex. Under conditions of upward flow, a significant impact of thermo-gravitational convection (TGC) was found, which interaction with an external magnetic field leads, in some regimes, to the instabilities occurrence and evolution in a laminar flow. The averaged speed profiles, temperature, and the channel wall temperature are represented. The detailed measurements were made in the channel cross section, remote fr om the heating start in the area of the uniform magnetic field, and along the channel length. Magnetic field leads to the suppression of turbulent transfer, and, as a result, the temperature of the heated wall increases.

The authors suggest a model for numerical modeling of the studied values in conditions consistent with the experiment. A system of differential equations was being solved while numerical simulation: the continuity equation, the equation of motion for the three velocity components, and the energy equation. The buoyancy force (free convection) and electromagnetic force were being accounted for in the equation of motion. The electric field potential was introduced for electromagnetic force computing, and the corresponding equation was being solved. The Reichardt model adapted to the rectangular channel was employed to account for the turbulence. The turbulent viscosity was assumed as zero in magnetic field.

Computational and experimental results are being compared within the range of the regime parameters by Reynolds numbers Re = 10 000–55 000, Hartmann numbers Ha = 0–800, Grashof numbers Gr_q = 0–6 × 10⁸.Computational results are in satisfactory agreement with the experimental data in the flow regimes wh ere the effect, associated with instabilities evolution caused by thermo-gravitational convection is absent or relatively small.

Keywords:

magneto-hydrodynamics, heat transfer, thermo-gravitational convection, velocity and temperature profiles, heat transfer coefficients, numerical simulation

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