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Influence of background gas on two-dimensional metal evaporation

Lu Xiao-Yong Zhang Xiao-Zhang

Influence of background gas on two-dimensional metal evaporation

Lu Xiao-Yong, Zhang Xiao-Zhang
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  • The spatial distributions of macroscopic parameters such as density, bulk velocity and temperature of the metal vapor have influences on the photo ionization yield of target isotope and the utilization ratio of material, which is related to the separation efficiency and the cost of atomic vapor laser isotope separation. To study this problem more practically, a system of binary gas Bhatnagar-Gross-Krook (BGK) model equations, which describe both the metal vapor and the background gas, is established. The physical characteristics are dealt with by dimensionless method for simplifying the calculations. The model equations are discretized by one-order upwind difference and then are solved by iteration method for obtaining stable results. The computational grids are adjusted to the flow field in order to acquire modest computational cost and accurate result simultaneously. Non-uniform grids in the phase space and in the velocity space are constructed to match the macroscopic parameter gradient and the form of the velocity distribution, respectively. The macroscopic parameters in the cases of different background gas densities, temperatures of tail plate and absorptivities are obtained for studying the influence of the background gas. The results show that with the increase of density of the background gas, the density and temperature of the metal vapor increase, the bulk velocities in the x and z$ direction decrease obviously in the domain far from the evaporation source, while the macroscopic parameters that are close to the evaporation source hardly change. As a result, the evaporation rate is not affected. Meanwhile, a circulation of the background gas is driven by the metal vapor, which in turn affects the diffusion of the metal vapor. Besides, as the temperature of tailing plate rises, the influence of the background gas on the macroscopic parameters of the metal vapor weakens. However, the rise of the temperature of tail plate leads the absorptivity of metal vapor to decrease, which enlarges the influence of the background gas. Therefore, it is appropriate to adjust the temperature of the tail plate based on the relationship between the absorptivity of metal vapor and the temperature. The results of theoretical calculation can serve as a reference for designing the vacuum and laser spot of the separation device.
      Corresponding author: Zhang Xiao-Zhang, zhangxzh@mail.tsinghua.edu.cn
    [1]

    Waichman K 1996 Phys. Fluids 8 1321

    [2]

    Wang D W 1999 Theory and Application of Laser Isotope Separation (Beijing: Atomic Energy Press) pp382-390 (in Chinese) [王德武 1999 激光分离同位素理论及其应用 (北京: 原子能出版社) 第382390页]

    [3]

    Xiao J X, Wang D W 1999 J. Tsinghua Univ. (Sci. Tech.) 39 52 (in Chinese) [肖踞雄, 王德武 1999 清华大学学报(自然科学版) 39 52]

    [4]

    Xiao J X, Wang D W 2000 Atom. Energ. Sci. Tech. 34 244 (in Chinese) [肖踞雄, 王德武 2000 原子能科学技术 34 244]

    [5]

    Graur I, Polikarpov A P, Sharipov F 2011 Comput. Fluids 49 87

    [6]

    Pantazis S, Valougeorgis D 2013 Eur. J. Mech. B: Fluid. 38 114

    [7]

    Scherer C S 2015 Z. Angew. Math. Phys. 66 1821

    [8]

    Das R M, Chatterjee S, Iwasaki M, Nakajima T 2015 J. Opt. Soc. Am. B 32 1237

    [9]

    Lu X Y, Zhang X Z, Zhang Z Z 2017 Acta Phys. Sin. 66 193201 (in Chinese) [卢肖勇, 张小章, 张志忠 2017 物理学报 66 193201]

    [10]

    Bo Y, Bao C Y, Zhu Y H, Wang D W, Yu Y H 2000 J. Tsinghua Univ. (Sci. Tech.) 40 16 (in Chinese) [薄湧, 包成玉, 诸渔泓, 王德武, 余耀辉 2000 清华大学学报 (自然科学版) 40 16]

    [11]

    Du Q, Zhu L Z, Li S F, Xiong X X, Zhou Z Y, Lin F C 1990 Chin J. Laser 17 726 (in Chinese) [杜清, 朱利洲, 李世芳, 熊夏幸, 周志尧, 林福成 1990 中国激光 17 726]

    [12]

    Wang L J, Zhao L M 2002 J. Tsinghua Univ. (Sci. Tech.) 42 576 (in Chinese) [王立军, 赵鹭明 2002 清华大学学报 (自然科学版) 42 576]

    [13]

    Xie G F, Wang D W, Ying C T 2002 Acta Phys. Sin. 51 584 (in Chinese) [谢国锋, 王德武, 应纯同 2002 物理学报 51 584]

    [14]

    Xie G F, Wang D W, Ying C T 2002 Atom. Energ. Sci. Tech. 36 147 (in Chinese) [谢国锋, 王德武, 应纯同 2002 原子能科学技术 36 147]

    [15]

    Morse T F 1964 Phys. Fluids 7 2012

    [16]

    Ying C T 1990 Theory and Application of Gas Transport (Beijing: Tsinghua University Press) pp258-260 (in Chinese) [应纯同 1990 气体输运理论及应用 (北京: 清华大学出版社) 第258260页]

    [17]

    Brull S, Schneider J, Pavan V 2014 Acta Appl. Math. 132 117

    [18]

    Arcidiacono S, Ansumali S, Karlin I V, Mantzaras J, Boulouchos K B 2006 Math. Comput. Simulat. 72 79

    [19]

    Aimi A, Diligenti M, Groppi M, Guardasoni C 2007 Eur. J. Mech. B: Fluid. 26 455

    [20]

    Frezzotti A, Ghiroldi G P, Gibelli L 2012 Vacuum 86 1731

    [21]

    Shen Q 2003 Rarefied Gas Dynamics (Beijing: National Defense Industry Press) pp210-216 (in Chinese) [沈青 2003 稀薄气体动力学(北京: 国防工业出版社) 第210216页]

  • [1]

    Waichman K 1996 Phys. Fluids 8 1321

    [2]

    Wang D W 1999 Theory and Application of Laser Isotope Separation (Beijing: Atomic Energy Press) pp382-390 (in Chinese) [王德武 1999 激光分离同位素理论及其应用 (北京: 原子能出版社) 第382390页]

    [3]

    Xiao J X, Wang D W 1999 J. Tsinghua Univ. (Sci. Tech.) 39 52 (in Chinese) [肖踞雄, 王德武 1999 清华大学学报(自然科学版) 39 52]

    [4]

    Xiao J X, Wang D W 2000 Atom. Energ. Sci. Tech. 34 244 (in Chinese) [肖踞雄, 王德武 2000 原子能科学技术 34 244]

    [5]

    Graur I, Polikarpov A P, Sharipov F 2011 Comput. Fluids 49 87

    [6]

    Pantazis S, Valougeorgis D 2013 Eur. J. Mech. B: Fluid. 38 114

    [7]

    Scherer C S 2015 Z. Angew. Math. Phys. 66 1821

    [8]

    Das R M, Chatterjee S, Iwasaki M, Nakajima T 2015 J. Opt. Soc. Am. B 32 1237

    [9]

    Lu X Y, Zhang X Z, Zhang Z Z 2017 Acta Phys. Sin. 66 193201 (in Chinese) [卢肖勇, 张小章, 张志忠 2017 物理学报 66 193201]

    [10]

    Bo Y, Bao C Y, Zhu Y H, Wang D W, Yu Y H 2000 J. Tsinghua Univ. (Sci. Tech.) 40 16 (in Chinese) [薄湧, 包成玉, 诸渔泓, 王德武, 余耀辉 2000 清华大学学报 (自然科学版) 40 16]

    [11]

    Du Q, Zhu L Z, Li S F, Xiong X X, Zhou Z Y, Lin F C 1990 Chin J. Laser 17 726 (in Chinese) [杜清, 朱利洲, 李世芳, 熊夏幸, 周志尧, 林福成 1990 中国激光 17 726]

    [12]

    Wang L J, Zhao L M 2002 J. Tsinghua Univ. (Sci. Tech.) 42 576 (in Chinese) [王立军, 赵鹭明 2002 清华大学学报 (自然科学版) 42 576]

    [13]

    Xie G F, Wang D W, Ying C T 2002 Acta Phys. Sin. 51 584 (in Chinese) [谢国锋, 王德武, 应纯同 2002 物理学报 51 584]

    [14]

    Xie G F, Wang D W, Ying C T 2002 Atom. Energ. Sci. Tech. 36 147 (in Chinese) [谢国锋, 王德武, 应纯同 2002 原子能科学技术 36 147]

    [15]

    Morse T F 1964 Phys. Fluids 7 2012

    [16]

    Ying C T 1990 Theory and Application of Gas Transport (Beijing: Tsinghua University Press) pp258-260 (in Chinese) [应纯同 1990 气体输运理论及应用 (北京: 清华大学出版社) 第258260页]

    [17]

    Brull S, Schneider J, Pavan V 2014 Acta Appl. Math. 132 117

    [18]

    Arcidiacono S, Ansumali S, Karlin I V, Mantzaras J, Boulouchos K B 2006 Math. Comput. Simulat. 72 79

    [19]

    Aimi A, Diligenti M, Groppi M, Guardasoni C 2007 Eur. J. Mech. B: Fluid. 26 455

    [20]

    Frezzotti A, Ghiroldi G P, Gibelli L 2012 Vacuum 86 1731

    [21]

    Shen Q 2003 Rarefied Gas Dynamics (Beijing: National Defense Industry Press) pp210-216 (in Chinese) [沈青 2003 稀薄气体动力学(北京: 国防工业出版社) 第210216页]

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  • Received Date:  09 January 2018
  • Accepted Date:  20 February 2018
  • Published Online:  05 August 2018

Influence of background gas on two-dimensional metal evaporation

    Corresponding author: Zhang Xiao-Zhang, zhangxzh@mail.tsinghua.edu.cn
  • 1. Department Engineering of Physics, Tsinghua University, Beijing 100084, China

Abstract: The spatial distributions of macroscopic parameters such as density, bulk velocity and temperature of the metal vapor have influences on the photo ionization yield of target isotope and the utilization ratio of material, which is related to the separation efficiency and the cost of atomic vapor laser isotope separation. To study this problem more practically, a system of binary gas Bhatnagar-Gross-Krook (BGK) model equations, which describe both the metal vapor and the background gas, is established. The physical characteristics are dealt with by dimensionless method for simplifying the calculations. The model equations are discretized by one-order upwind difference and then are solved by iteration method for obtaining stable results. The computational grids are adjusted to the flow field in order to acquire modest computational cost and accurate result simultaneously. Non-uniform grids in the phase space and in the velocity space are constructed to match the macroscopic parameter gradient and the form of the velocity distribution, respectively. The macroscopic parameters in the cases of different background gas densities, temperatures of tail plate and absorptivities are obtained for studying the influence of the background gas. The results show that with the increase of density of the background gas, the density and temperature of the metal vapor increase, the bulk velocities in the x and z$ direction decrease obviously in the domain far from the evaporation source, while the macroscopic parameters that are close to the evaporation source hardly change. As a result, the evaporation rate is not affected. Meanwhile, a circulation of the background gas is driven by the metal vapor, which in turn affects the diffusion of the metal vapor. Besides, as the temperature of tailing plate rises, the influence of the background gas on the macroscopic parameters of the metal vapor weakens. However, the rise of the temperature of tail plate leads the absorptivity of metal vapor to decrease, which enlarges the influence of the background gas. Therefore, it is appropriate to adjust the temperature of the tail plate based on the relationship between the absorptivity of metal vapor and the temperature. The results of theoretical calculation can serve as a reference for designing the vacuum and laser spot of the separation device.

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