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 ...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 KC1 （llwt%）, 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.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10772150)the Aeronautical Science Fund of China (Grant No 20061453020)Foundation for Basic Research of Northwestern Polytechnical University
文摘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 KC1 （llwt%）, 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.
