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Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method 下载免费PDF全文
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. 相似文献
2.
对Eggels和Somers提出的热格子Boltzmann格式进行了改进. 在不可压缩流动的假设下,提出了一种新的温度平衡分布函数,可以克服压缩性对温度统计的影响,并且相应地修正了统计宏观温度的方法. Eggels和Somers的方法对速度和温度均采用半步长反弹格式边界条件,适合无滑移的速度边界条件.但是对温度采用该边界条件在物理本质上显得不够准确,所以在边界上对二者统一采取算法既简单又容易实现的非平衡态外推格式,同时可以与Boltzmann格式的整体二阶精度保持一致. 最后,利用改进的热格子Boltzmann方法(TLBM)模拟了Ra=10^6和Pr=0.71(空气)的方腔中的自然对流,模拟得到的流动参数与其它数值方法的结果吻合得很好,表明改进的热格子Boltzmann方法可以有效准确地模拟非等温流动. 相似文献
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