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
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11472004)
Received Date:24 July 2020
Accepted Date:31 August 2020
Available Online:13 January 2021
Published Online:20 January 2021
Abstract:With the rapid development of micro-nano technology and aerospace technology, researches related to rarefied gas flows have received more and more attention. For micro-/nanoscale systems and spacecraft in a rarefied environment, the reduction in the frequency of intermolecular collisions in the flow field makes the interaction between gas molecules and the solid surface develop into a major factor affecting the flow state. However, the mechanism of gas-surface interaction in rarefied flow has not been fully revealed due to its microscopic nature and physical complexity, and the existing simulation methods cannot accurately reflect the effect of this process on the flow state. In this paper, molecular beam method is adopted to simulate the scattering process of argon molecules on platinum surface, and the impacts of incident velocity, angle and wall roughness on the momentum and energy conversion mechanism are explored. By simulating the molecular scattering process under the two incident angles of $ 5^{\circ} $ and $ 75^{\circ}$, the following conclusions are obtained. When colliding with the wall at an angle close to vertical, both components of the momentum of the gas molecules are lost. The normal energy transfers to the tangential direction, and when the molecular velocity is not less than 2.0, the transfer rate is not significantly affected by the incident energy of the molecule and the surface roughness. The total energy loss of gas molecules after scattering becomes significant with the increase of incident velocity, and it is not sensitive to changes of surface roughness. When the gas molecules are incident at $ 75^{\circ} $, the roughness of the surface has a significant impact on the conversion mechanism of molecular momentum and energy. After colliding with a smooth wall, the momentum and energy values of the gas molecules remain basically unchanged, only the direction of the momentum is reversed. The motion state of molecules is close to the mirror reflection, and the conversion between momentum and energy components is not obvious. The introduction of roughness enhances the degree of accommodation between gas molecules and metal surface, and promotes the transfer of molecular tangential momentum and kinetic energy to the normal direction. When incident at a large polar angle, as opposed to the small-angle cases, the total energy loss of molecules is not sensitive to changes of incident velocity, it goes up significantly with the surface roughness increasing. The research in this article not only explores the gas-surface interaction mechanism, but also provides a useful reference for the high-fidelity simulation of rare gas flow and the development of appropriate gas-surface interaction models. Keywords:gas-surface interaction/ molecular dynamics/ momentum and energy conversion
表1入射极角为$ 5^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量 Table1.When the incident polar angle is $ 5^{\circ}$, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.
表2入射极角为$ 75^{\circ}$时, 不同速度的气体分子在不同表面上散射后的平均速度和能量 Table2.When the incident polar angle is $ 75^{\circ} $, the mean velocity and energy of gas molecules that with different velocities after scattering on different surfaces.
图 3 入射角为$ 5^{\circ}$时, 气体分子与光滑表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化 Figure3. When the incident angle is $ 5^{\circ} $, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.
为了考察与壁面的相互作用过程中, 气体分子法向动量的损失及其与表面的适应程度, 进一步对分子束的法向动量适应系数(NMAC)进行研究, 结果如图4所示. NMAC的定义如(2)式所示, 式中P表示分子的平均动量, 下标“i”和“r”分别代表入射和反射, $ {P_{{\rm{wn}}}} = \sqrt {({m_{{\rm{Ar}}}}\pi {k_{\rm{B}}}{T_{\rm{w}}})/2} $, $ {T_{\rm{w}}} $表示壁温. 图 4 以$ 5^{\circ}$极角入射时, 气体分子在不同粗糙表面的法向动量适应系数(NMAC) Figure4. Normal momentum accommodation coefficient (NMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.
从图4可以看出, 对于不同的表面, $ {V_{\rm{i}}} = 1.0 $时, 气体分子的NMAC都保持在了一个较大的数值, 说明此时气体分子的法向动量基本上与表面达到了完全适应, 法向动量的损失明显. 随着入射速度的进一步增加, 分子束的NMAC发生了明显降低, 并会随着速度的增加而缓慢增大. 同时还可以发现, 相同入射条件下, 金属表面的粗糙对气体分子的法向动量适应系数的数值影响不大. 图5为不同粗糙表面条件下, 动能的损失率随入射速度的变化, 整体来看, 动能的损失率会随入射速度的增加而增大. 这是因为, 当气体分子的入射速度增加时, 分子进入表面力场的深度就更深, 因此气体-表面之间的适应程度会更高, 这也就导致了气体分子的能量损失率的增大. 而粗糙度的增加会使分子在金属表面的吸附概率增加[32], 尤其是分子的速度较低时吸附会变得明显. 所以当$ {V_{\rm{i}}} = 1.0 $, R = 1.0 ?时, 气体分子的能量损失较大, 导致了此时的变化规律与整体趋势不一致. 随着入射速度的增大, 气体分子在金属表面的吸附不再是影响其能量损失的主要因素. 从图5还可以看出, 在速度较高时, 表面粗糙度对能量损失率的影响并不明显. 图 5 以$ 5^{\circ} $极角入射时, 气体分子在不同粗糙表面的能量损失率 Figure5. Energy loss rate of gas molecules on different rough surfaces when the incident polar angle is $ 5^{\circ} $.
23.2.大极角入射时的动量、能量转化机制分析 -->
3.2.大极角入射时的动量、能量转化机制分析
气体分子以$ 5^{\circ} $入射时, 动量和能量的法向分量占主导地位, 为了进一步研究切向动量和能量向法向的转移机制, 本节中将气体分子的入射极角设置为$ 75^{\circ} $. 表2列出了入射角为$ 75^{\circ} $时气体分子散射前后速度和能量的变化. 可以看出, 与垂直入射时不同, 大极角入射时粗糙度对动量和能量转移的影响变得明显了. 例如, 当速度为4.0的粒子入射到光滑平面时, 反射后的切向和法向动量的绝对值都与入射前很接近, 只是法向动量的方向发生了改变, 切向、法向能量的变化和总能量的损失也维持在2.5%—4.0%以内. 而当表面的粗糙度为0.5 ?时, 切向动量和能量的减小、法向动量和能量的增加以及总能量的损失就不能忽略了. 当粗糙度继续增加到1.0 ?时, 切向动量的损失达到了90%以上, 法向能量几乎增加了4倍, 总能量的损失也达到了34.5%. 上述结果表明, 表面粗糙度会促进切向动量和能量向法向的转移. 为了进一步探究气体分子各个动量和能量分量之间的转化关系, 分别对速度为2.0的气体分子与光滑(R = 0 ?)和粗糙(R = 1.0 ?)表面碰撞过程中速度和能量随时间的变化进行研究, 结果分别如图6和图7所示(由于大角度入射时, 在整个壁面力场气体分子的能量都会有较为明显的波动, 只显示碰撞前后一小段能量变化的方式已不再适应, 因此本节给出的都是气体分子在整个壁面力作用区域速度和能量的变化). 从图6可以看出, 当气体分子以大极角入射到光滑壁面时, 散射规律非常接近于Maxwell[39]所假设的镜面反射, 具体表现为入射前后切向速度和能量的变化都很小, 并且这种可以维持入射前切向动量、能量的现象会随着入射速度的增加而更加明显. 结合表2中数据可以发现, 当$ {V_{\rm{i}}} = 8.0 $时, 入射气体分子的切向速度和切向动能分别为$ 17.293\sigma /\tau $和$ 149.53\varepsilon,$ 在光滑表面反射后, 气体分子的切向速度和切向动能分别为$ 16.988\sigma /\tau $和$ 146.57\varepsilon $. 同时, 气体分子的法向速度和法向能量在反射前后也变化不大, 只是法向速度的方向发生了改变, 这说明对于光滑表面, 入射速度的增大基本不会对动量、能量分量之间的转化产生影响, 气体分子的法向速度和能量变化只能依靠与壁面的热交换. 与图6中气体分子速度和能量的变化基本保持独立的现象不同, 表面粗糙度的出现会改变气体分子与表面之间的动量、能量交换模式. 如图7所示, 当金属表面粗糙时, 在与表面碰撞之后, 分子的切向速度和能量会减小, 而法向速度和能量会增加, 说明粗糙度的存在促进了分子切向动量和能量向法向的转移. 图 6 入射角为$ 75^{\circ} $时, 气体分子与光滑表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化 Figure6. When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a smooth surface: (a) Variation of molecular velocity; (b) variation of molecular energy.
图 7 入射角为$ 75^{\circ} $时, 气体分子与粗糙表面碰撞中速度和能量随时间的变化 (a)速度随时间的变化; (b)能量随时间的变化 Figure7. When the incident angle is $ 75^{\circ}$, the variations of molecular velocity and energy in the collision with a rough surface: (a) Variation of molecular velocity; (b) variation of molecular energy.
为了研究不同入射条件下, 气体分子切向动量与表面的适应情况, 按照(3)式对大角度入射时的切向动量适应系数(TMAC)进行了计算, 结果如图8所示, (3)式中$ {P_{{\rm{it}}}} $和$ {P_{{\rm{rt}}}} $分别为气体分子的入射切向动量和反射切向动量的平均值. 图 8 以$ 75^{\circ}$极角入射时, 气体分子在不同粗糙表面的的切向动量适应系数(TMAC) Figure8. Tangential momentum accommodation coefficient (TMAC) of gas molecules on different rough surfaces when the incident polar angle is $ 75^{\circ}$.
图 1 三种表面粗糙度构型
图 2 气体分子的入射极角
图 3 入射角为
图 4 以
图 5 以
图 6 入射角为
图 7 入射角为
图 8 以
图 9 以
