微尺度剪切驱动流滑移膜阻尼的有效多松弛时间格子Boltzmann模拟（英文）
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摘要
采用Knudsen边界层模型将壁面效应与稀薄效应引入松弛时间的修正中,通过修正后的有效多松弛时间-格子Boltzmann模型(MRT-LBM)进一步研究微尺度剪切驱动流滑移膜阻尼的物理特性.对比MRTLBM模型与蒙特卡洛模型、高阶格子Boltzmann模型的板间速度分布的吻合度;将切向动量调节系数r对板间速度分布的影响与高阶格子Boltzmann模型的数据进行分析对比,验证了MRT-LBM模型用于分析微尺度非平衡剪切驱动流滑移膜阻尼时的有效性.最后利用该模型研究努森数Kn、斯托克斯数β和板间间隙对微尺度剪切驱动流滑移膜阻尼的影响.结果表明:在过渡区,对于平板剪切振荡驱动流,随着努森数或板间间隙的增大,上平板下表面的滑移膜阻尼逐渐减小;斯托克斯数越大,滑移膜阻尼越大.
To investigate the slide film damping in the micro-scale shear-driven rarefied gas flows, an effective multi-relaxation-time lattice Boltzmann method(MRT-LBM) is proposed. Through the Knudsen boundary layer model, the effects of wall and rarefaction are considered in the correction of relaxation time. The results of gas velocity distributions are compared among the MRT, Monte Carlo model(DSMC) and high-order LBM, and the effects of the tangential momentum accommodation coefficient on the gas velocity distributions are also compared between the MRT and the high-order LBM. It is indicated that the amendatory MRT-LBM can unlock the dilemma of simulation of micro-scale non-equilibrium. Finally, the effects of the Knudsen number, the Stokes number, and the gap between the plates on the damping are researched. The results show that by decreasing the Knudsen number or increasing the Stokes number, the slide film damping increases in the transition regime; however, as the size of the gap increases, the slide film damping decreases substantially.
To investigate the slide film damping in the micro-scale shear-driven rarefied gas flows, an effective multi-relaxation-time lattice Boltzmann method(MRT-LBM) is proposed. Through the Knudsen boundary layer model, the effects of wall and rarefaction are considered in the correction of relaxation time. The results of gas velocity distributions are compared among the MRT, Monte Carlo model(DSMC) and high-order LBM, and the effects of the tangential momentum accommodation coefficient on the gas velocity distributions are also compared between the MRT and the high-order LBM. It is indicated that the amendatory MRT-LBM can unlock the dilemma of simulation of micro-scale non-equilibrium. Finally, the effects of the Knudsen number, the Stokes number, and the gap between the plates on the damping are researched. The results show that by decreasing the Knudsen number or increasing the Stokes number, the slide film damping increases in the transition regime; however, as the size of the gap increases, the slide film damping decreases substantially.
引文
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[13] Park J H, Bahukudumbi P, Beskok A. Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime[J]. Physics of Fluids, 2004, 16(2): 317-330. DOI:10.1063/1.1634563.
[14] Tang G H, Gu X J, Barber R W, et al. Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow[J]. Physical ReviewE, 2008, 78(2): 026706. DOI:10.1103/physreve.78.026706.
[15] Guo Z. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow[J]. Physical ReviewE Statistical Nonlinear & Soft Matter Physics, 2008, 77(3): 036707. DOI:10.1103/PhysRevE.77.036707.
[16] Hadjiconstantinou N G. Oscillatory shear-driven gas flows in the transition and free-molecular-flowregimes[J]. Physics of Fluids, 2005, 17(10): 100611. DOI:10.1063/1.1874193.
[2] Li Dongqing. Encyclopedia of microfluidics and nanofluidics [M]. 2nd ed. NewYork: Springer-Verlag, 2015: 681-693.
[3] Wu L, Reese J M, Zhang Y H. Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows[J]. Journal of Fluid Mechanics, 2014, 746: 53-84. DOI:10.1017/jfm.2014.79.
[4] Pfeiffer M, Nizenkov P, Mirza A, et al. Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases[J]. Physics of Fluids, 2016, 28(2): 027103. DOI:10.1063/1.4940989.
[5] Bakhshan Y, Omidvar A. Calculation of friction coefficient and analysis of fluid flowin a stepped micro-channel for wide range of Knudsen number using Lattice Boltzmann (MRT) method[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 440: 161-175. DOI:10.1016/j.physa.2015.08.012.
[6] Yang D Y, Wang M. Lattice Boltzmann method[M]. Beijing: Publishing House of Electronics Industry, 2015: 69-70. (in Chinese)
[7] Nie X B, Doolen G D, Chen S Y. Lattice-Boltzmann simulations of fluid flows in MEMS[J].Journal of Statistical Physics, 2002, 107(1/2): 279-289. DOI:10.1023/a:1014523007427.
[8] Kim S H, Pitsch H, Boyd I D. Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows[J]. Physical ReviewE, 2008, 77(2): 026704. DOI:10.1103/physreve.77.026704.
[9] Succi S. Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis[J]. Physical ReviewLetters, 2002, 89(6): 064502. DOI:10.1103/physrevlett.89.064502.
[10] Ansumali S, Karlin I V. Kinetic boundary conditions in the lattice Boltzmann method[J]. Physical ReviewE, 2002, 66(2): 026311. DOI:10.1103/physreve.66.026311.
[11] Tang G H, Tao W Q, He Y L. Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions[J]. Physics of Fluids, 2005, 17(5): 058101. DOI:10.1063/1.1897010.
[12] Meng X H, Guo Z L. Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flowwith large viscosity ratio and high Péclet number[J]. Physical ReviewE, 2015, 92(4): 043305. DOI:10.1103/physreve.92.043305.
[13] Park J H, Bahukudumbi P, Beskok A. Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime[J]. Physics of Fluids, 2004, 16(2): 317-330. DOI:10.1063/1.1634563.
[14] Tang G H, Gu X J, Barber R W, et al. Lattice Boltzmann simulation of nonequilibrium effects in oscillatory gas flow[J]. Physical ReviewE, 2008, 78(2): 026706. DOI:10.1103/physreve.78.026706.
[15] Guo Z. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow[J]. Physical ReviewE Statistical Nonlinear & Soft Matter Physics, 2008, 77(3): 036707. DOI:10.1103/PhysRevE.77.036707.
[16] Hadjiconstantinou N G. Oscillatory shear-driven gas flows in the transition and free-molecular-flowregimes[J]. Physics of Fluids, 2005, 17(10): 100611. DOI:10.1063/1.1874193.