宏观速度对适应系数的影响规律研究

张烨; 张冉; 赖剑奇; 李桦

doi:10.7498/aps.68.20190987

摘要

适应系数是稀薄气体动力学中的重要参数, 反映了气体分子与固体表面的动量和能量适应程度, 常常用于稀薄气体数值模拟的边界条件中. 本文构建了单个气体分子Ar与金属Pt表面相互作用的物理模型, 通过Phontom模型来构造固体壁面以反映真实物理特性. 采用分子动力学方法模拟了气体分子在固体表面的碰撞过程, 通过速度抽样使得入射气体具有宏观速度特征, 根据入射前和反射后气体分子的平均动量和能量计算出切向动量适应系数、法向动量适应系数和能量适应系数, 分别在光滑和粗糙表面下分析了适应系数随宏观切向速度和宏观法向速度的变化规律. 结果显示, 适应系数对于气体的宏观速度和表面粗糙度均表现出了很强的相关性. 切向速度的增大使得气体分子与表面的作用时间缩短, 适应系数减小, 对于气固适应有消极的作用. 当切向速度较大时会发生动量由切向向法向转移的情况. 法向速度的增大对于光滑表面而言有助于气体分子与表面的动量和能量适应, 对于粗糙表面而言却呈现相反的规律.

关键词:

Abstract

The accommodation coefficient is an important parameter in the field of rarefied gas dynamics, representing the adaptation level of the momentum and energy between gas molecules and solid surfaces, which is frequently used in the boundary conditions of numerical simulation of rarefied gas flow. In this paper, a physical model of the interaction between a single gas molecule Ar and the metal Pt surface is constructed, which greatly saves computational resources by omitting the collision between gas molecules in the bulk flow. The Pt surface is constructed by the Phontom model to reflect real physical properties. The surface roughness is modeled by a typical pyramid model, which is physically realistic and stable in structure. The molecular dynamics method is used to simulate the collision process of the gas molecules on the solid surface. The velocity sampling method is used so that the incident gas molecules possess the characteristics of macroscopic velocity. According to the average momentum and energy of the gas molecules before incidence and after reflection, the tangential momentum accommodation coefficients (TMACs), the normal momentum accommodation coefficients (NMACs) and the energy accommodation coefficients (EACs) are obtained. Moreover, the variation regularities of the accommodation coefficients with the macroscopic tangential velocity and the macroscopic normal velocity are analyzed under the smooth and rough surface, respectively. The results indicate that the accommodation coefficients have a strong correlation to macroscopic velocity and roughness. The increase of tangential velocity shortens the interaction time of gas molecules with solid surface, which results in the decrease of TMAC, NMAC and EAC of gas molecules, indicating that the tangential velocity has a negative effect on gas-solid adaptation. In addition, the momentum is found to be transformed from the tangential direction to the normal direction at a large tangential velocity, and this transformation tendency becomes more apparent as the tangential velocity increases. However, the influence of normal velocity on the momentum and energy accommodation coefficient is different. With regard to the smooth surface, the increase of normal velocity contributes to the tangential momentum and energy adaptation of gas molecules with the surface. While for the rough surface, the adaptation level of tangential momentum and energy between gas molecules and the surface is weakened as the normal velocity increases. This paper reveals the mechanism of gas molecules scattering on the surface from a microscopic point of view, which is quite different from the macroscopic phenomena. The conclusions of this paper indicate the irrationality of traditional scattering kernel models to represent the degree of accommodation through constant values, which is of great significance for the improvement of boundary conditions in rarefied gas flows.

Keywords:

作者及机构信息

1.
国防科技大学空天科学学院, 长沙　410073

2.
西北核技术研究院, 激光与物质相互作用国家重点实验室, 西安　710024

通信作者: 张冉, zr07024221@126.com

基金项目: 国家自然科学基金(批准号：11472004)资助的课题

Authors and contacts

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

2.
State Key Laboratory of Laser Interaction with Matter, Northwest Institute of Nuclear Technology, Xi’an 710024, China

Corresponding author: Zhang Ran, zr07024221@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11472004)

文章全文 : translate this paragraph

参考文献

[1]	Verbridge S S, Craighead H G, Parpia J M 2008 Appl. Phys. Lett. 92 013112 Google Scholar
[2]	Zhang Z Q, Zhang H W, Ye H F 2009 Appl. Phys. Lett. 95 154101 Google Scholar
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[4]	Rovenskaya O I 2015 Int. J. Heat Mass Tran. 89 1024 Google Scholar
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[14]	Agrawal A, Prabhu S V 2008 J. Vac. Sci. Technol. A 26 634
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[29]	Prabha S K, Sathian S P 2012 Comput. Fluids 68 47
[30]	Pham T T, To Q D, Lauriat G, Leonard C 2012 Phys. Rev. E 86 051201 Google Scholar
[31]	Liang Z, Keblinski P 2014 Int. J. Heat Mass Tran. 78 161 Google Scholar
[32]	Reinhold J, Veltzke T, Wells B, Schneider J, Meierhofer F, Colombi Ciacchi L, Chaffee A 2014 Comput. Fluids 97 31 Google Scholar
[33]	Lim W W, Suaning G J, McKenzie D R 2016 Phys. Fluids 28 097101 Google Scholar
[34]	Yamaguchi H, Matsuda Y, Niimi T 2017 Phys. Rev. E 96 013116 Google Scholar
[35]	张冉, 谢文佳, 常青, 李桦 2018 物理学报 67 084701 Google Scholar Zhang R, Xie W J, Chang Q, Li H 2018 Acta Phys. Sin. 67 084701 Google Scholar
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[41]	Wu L, Bogy D B 2002 J. Tribol.-T. ASME 124 562 Google Scholar

施引文献

图 1 气体分子在固体表面散射的物理模型

Fig. 1. Physical model for scattering gas molecules on solid surfaces.

下载: 全尺寸图片幻灯片

图 2 表面粗糙度的纳米构型

Fig. 2. Schematic diagram of the roughness geometry.

下载: 全尺寸图片幻灯片

图 3 不同宏观切向速度下的切向动量适应系数

Fig. 3. TMAC values of gas molecular under different macroscopic tangential velocities.

下载: 全尺寸图片幻灯片

图 4 不同宏观切向速度下气体分子与表面作用时间

Fig. 4. Time of gas-solid interaction under different macroscopic tangential velocities.

下载: 全尺寸图片幻灯片

图 5 不同宏观切向速度及法向速度下的切向动量适应系数

Fig. 5. TMAC values of gas molecular under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 6 不同宏观切向速度及法向速度下的法向动量适应系数

Fig. 6. NMAC values of gas molecular under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 7 不同宏观切向及法向速度下的法向能量适应系数

Fig. 7. EAC values of gas molecular under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 8 粗糙度为0.5 A的粗糙表面下, 不同宏观切向速度及法向速度下的切向动量适应系数

Fig. 8. TMAC values of gas molecular on rough surfaces of 0.5 A under different macroscopic tangential and normal velocities

下载: 全尺寸图片幻灯片

图 9 粗糙度为0.5 A的粗糙表面下, 不同宏观切向速度及法向速度下的气体分子吸附概率

Fig. 9. Sticking probability of gas molecular on rough surfaces of 0.5 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 10 粗糙度为0.5 A的粗糙表面下, 不同宏观切向速度及法向速度下的法向动量适应系数

Fig. 10. NMAC values of gas molecular on rough surfaces of 0.5 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 11 粗糙度为0.5 A的粗糙表面下, 不同宏观切向速度及法向速度下的能量适应系数

Fig. 11. EAC values of gas molecular on rough surfaces of 0.5 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 12 粗糙度为1.0 A的粗糙表面下, 不同宏观切向速度及法向速度下的切向动量适应系数

Fig. 12. TMAC values of gas molecular on rough surfaces of 1.0 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 13 粗糙度为1.0 A的粗糙表面下, 不同宏观切向速度及法向速度下的气体分子吸附概率

Fig. 13. Sticking probability of gas molecular on rough surfaces of 1.0 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 14 粗糙度为1.0 A的粗糙表面下, 不同宏观切向速度及法向速度下的法向动量适应系数

Fig. 14. NMAC values of gas molecular on rough surfaces of 1.0 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

图 15 粗糙度为1.0 A的粗糙表面下, 不同宏观切向速度及法向速度下的能量适应系数

Fig. 15. EAC values of gas molecular on rough surfaces of 1.0 A under different macroscopic tangential and normal velocities.

下载: 全尺寸图片幻灯片

表 1 分子动力学模拟中的参数

Table 1. Parametersin the MD simulations.

相互作用	$\sigma {\rm{/nm}}$	$\varepsilon {\rm{/J}}$	mass/kg
Ar-Ar	0.3405	$1.670 \times {10^{-{\rm{21}}}}$	$6.633 \times {10^{-{\rm{26}}}}$
Pt-Pt	0.2770	$52.07 \times {10^{ -{\rm{21}}}}$	$32.36 \times {10^{-{\rm{26}}}}$
Ar-Pt	0.3085	$0.894 \times {10^{ - {\rm{21}}}}$	—

下载: 导出CSV

[1]	Verbridge S S, Craighead H G, Parpia J M 2008 Appl. Phys. Lett. 92 013112 Google Scholar
[2]	Zhang Z Q, Zhang H W, Ye H F 2009 Appl. Phys. Lett. 95 154101 Google Scholar
[3]	Song H Q, Yu M X, Zhu W Y, Zhang Y, Jiang S X 2013 Chin. Phys. Lett. 30 014701 Google Scholar
[4]	Rovenskaya O I 2015 Int. J. Heat Mass Tran. 89 1024 Google Scholar
[5]	Bao F B, Huang Y L, Zhang Y H, Lin J Z 2015 Microfluid Nanofluid 18 1075 Google Scholar
[6]	Cao B Y, Sun J, Chen M, Guo Z Y 2009 Int. J. Mol. Sci. 10 4638 Google Scholar
[7]	Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford: Oxford University Press) pp199−206
[8]	Fan J, Shen C 2001 J. Comput. Phys. 167 393
[9]	Yuan Y D, Rahman S 2016 Physica A 463 25 Google Scholar
[10]	Verbeek M G 2018 Microfluid. Nanofluid. 22 34 Google Scholar
[11]	Maxwell J C 1879 Phil. Trans. R. Soc. Lond. 170 231 Google Scholar
[12]	Cercignani C, Lampis M 1971 Transp. Theory Stat. Phys. 1 101 Google Scholar
[13]	Lord R G 1991 Phys. Fluids 3 706 Google Scholar
[14]	Agrawal A, Prabhu S V 2008 J. Vac. Sci. Technol. A 26 634
[15]	Yakunchikov A N, Kovalev V L, Utyuzhnikov S V 2012 Chem. Phys. Lett. 554 225 Google Scholar
[16]	Zhang W, Meng G, Wei X 2012 Microfluid. Nanofluid. 13 845 Google Scholar
[17]	Zhang H W, Zhang Z Q, Zheng Y G, Ye H F 2010 Phys. Rev. E 81 066303 Google Scholar
[18]	Rapaport D C 2004 The Art of Molecular Dynamics Simulation (New York: Cambridge University Press) pp4−5
[19]	Bao F B, Huang Y L, Qiu L M, Lin J Z 2015 Mol. Phys. 113 561 Google Scholar
[20]	Spijker P, Markvoort A J, Nedea S V, Hilbers P A 2010 Phys. Rev. E 81 011203 Google Scholar
[21]	Bruno D, Cacciatore M, Longo S, Rutigliano M 2000 Chem. Phys. Lett. 320 245 Google Scholar
[22]	Kovalev V, Yakunchikov A, Li F 2011 Acta Astronaut. 69 744 Google Scholar
[23]	Dongari N, Zhang Y H, Reese J M 2012 AIP Conf. Proc. 1501 895
[24]	Cao B Y, Chen M, Guo Z Y 2005 Appl. Phys. Lett. 86 091905 Google Scholar
[25]	Finger G W, Kapat J S, Bhattacharya A 2007 J. Fluids Eng. 129 31
[26]	Sun J, Li Z X 2008 Mol. Phys. 106 2325 Google Scholar
[27]	Sun J, Li Z X 2009 Mol. Simul. 35 228 Google Scholar
[28]	Sun J, Li Z X 2010 Comput. Fluids 39 1345 Google Scholar
[29]	Prabha S K, Sathian S P 2012 Comput. Fluids 68 47
[30]	Pham T T, To Q D, Lauriat G, Leonard C 2012 Phys. Rev. E 86 051201 Google Scholar
[31]	Liang Z, Keblinski P 2014 Int. J. Heat Mass Tran. 78 161 Google Scholar
[32]	Reinhold J, Veltzke T, Wells B, Schneider J, Meierhofer F, Colombi Ciacchi L, Chaffee A 2014 Comput. Fluids 97 31 Google Scholar
[33]	Lim W W, Suaning G J, McKenzie D R 2016 Phys. Fluids 28 097101 Google Scholar
[34]	Yamaguchi H, Matsuda Y, Niimi T 2017 Phys. Rev. E 96 013116 Google Scholar
[35]	张冉, 谢文佳, 常青, 李桦 2018 物理学报 67 084701 Google Scholar Zhang R, Xie W J, Chang Q, Li H 2018 Acta Phys. Sin. 67 084701 Google Scholar
[36]	Cao B Y, Chen M, Guo Z Y 2006 Int. J. Eng. Sci. 44 927 Google Scholar
[37]	Xie J F, Cao B Y 2016 Mol. Simul. 43 65
[38]	张冉, 常青, 李桦 2018 物理学报 67 223401 Google Scholar Zhang R, Chang Q, Li H 2018 Acta Phys. Sin. 67 223401 Google Scholar
[39]	Maruyama S 2000 Advances in Numerical Heat Transfer (Vol.2) (Boca Raton : CRC Press) pp189
[40]	张烨, 张冉, 常青, 李桦 2019 物理学报 68 124702 Google Scholar Zhang Y, Zhang R, Chang Q, Li H 2019 Acta Phys. Sin. 68 124702 Google Scholar
[41]	Wu L, Bogy D B 2002 J. Tribol.-T. ASME 124 562 Google Scholar

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