Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method |
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Authors: | Zhong Cheng-Wen Xie Jian-Fei Zhuo Cong-Shan Xiong Sheng-Wei and Yin Da-Chuan |
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Institution: | Faculty of Life Science, Key Laboratory for Space
Bioscience and Biotechnology, Northwestern Polytechnical
University,
Xi'an 710072, China; National Key Laboratory of Aerodynamic Design and
Research,
Northwestern Polytechnical University, Xi'an 710072, China |
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Abstract: | The thermal lattice Boltzmann method (TLBM), which was proposed by
J. G. M. Eggels and J. A. Somers previously, has been improved in
this paper. The improved method has introduced a new equilibrium
solution for the temperature distribution function on the assumption
that flow is incompressible, and it can correct the effect of
compressibility on the macroscopic temperature computed. Compared to
the previous method, where the half-way bounce back boundary
condition was used for non-slip velocity and temperature, a
non-equilibrium extrapolation scheme has been adopted for both
velocity and temperature boundary conditions in this paper. Its
second-order accuracy coincides with the ensemble accuracy of
lattice Boltzmann method. In order to validate the improved thermal
scheme, the natural convection of air in a square cavity is
simulated by using this method. The results obtained in the
simulation agree very well with the data of other numerical methods
and benchmark data. It is indicated that the improved TLBM is also
successful for the simulations of non-isothermal flows. Moreover,
this thermal scheme can be applied to simulate the natural
convection in a non-uniform high magnetic field. The simulation has
been completed in a square cavity filled with the aqueous solutions
of KCl (11wt%), which is considered as a diamagnetic fluid with
electrically low-conducting, with Grashof number Gr=4.64×
10^4 and Prandtl number Pr=7.0. And three cases, with different
cavity locations in the magnetic field, have been studied. In the
presence of a high magnetic field, the natural convection is quenched
by the body forces exerted on the electrically low-conducting
fluids, such as the magnetization force and the Lorentz force. From the
results obtained, it can be seen that the quenching efficiencies
decrease with the variation of location from left, symmetrical line,
to the right. These phenomena originate from the different
distributions of the magnetic field strengths in the zones of the
symmetrical central line of the magnetic fields. The results are
also compared with those without a magnetic field. Finally, we can
conclude that the improved TLBM will enable effective simulation of the natural
convection under a high magnetic field. |
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Keywords: | thermal lattice Boltzmann
method natural convection magnetization force Lorentz orce |
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