中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4083-4093.doi: 10.1088/1674-1056/18/10/004

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Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method

尹大川1, 钟诚文2, 解建飞2, 卓从山2, 熊生伟2   

  1. (1)Faculty of Life Science, Key Laboratory for Space Bioscience and Biotechnology, Northwestern Polytechnical University, Xi'an 710072, China; (2)National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
  • 收稿日期:2008-10-09 修回日期:2009-06-13 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10772150), the Aeronautical Science Fund of China (Grant No 20061453020) and Foundation for Basic Research of Northwestern Polytechnical University.

Simulation of natural convection under high magnetic field by means of the thermal lattice Boltzmann method

Zhong Cheng-Wen(钟诚文)a)‡, Xie Jian-Fei(解建飞)a)†, Zhuo Cong-Shan(卓从山)a), Xiong Sheng-Wei(熊生伟)a), and Yin Da-Chuan(尹大川)b)   

  1. a National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China; b Faculty of Life Science, Key Laboratory for Space Bioscience and Biotechnology, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2008-10-09 Revised:2009-06-13 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10772150), the Aeronautical Science Fund of China (Grant No 20061453020) and Foundation for Basic Research of Northwestern Polytechnical University.

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摘要： 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.

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=4.64×104 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.

Key words: thermal lattice Boltzmann method, natural convection, magnetization force, Lorentz orce

中图分类号:  (Turbulent convective heat transfer)

  • 47.27.te
05.60.-k (Transport processes) 47.11.-j (Computational methods in fluid dynamics) 47.65.Cb (Magnetic fluids and ferrofluids) 75.50.Mm (Magnetic liquids) 75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects)