长微圆管道气体流动的简化计算

Simplified Computation of Gas Flows in a Long Microtube

从N S方程出发 ,考虑稀薄气体效应 ,推导出长微圆管道中压力驱动的可压缩气体流动的简化控制方程组 ;采用迭代方法求解此方程组 ,得到了流动的速度分布、密度分布、质量流量 ;

For the gas flow in a long microtube, the Knudsen nu mber (Kn=λ/L) is large (>10 -3 ) due to the small characteristic size (L), even for small molecular mean free path (λ) of gas with moderate d ensity. The rarefied gas effect becomes significant. For pressure driven gas flo w in the tube, the mean streamwise velocity is typically in the very low subsoni c range (<1 m/s). The general numerical methods, such as DSMC, encounter difficu lties because of the enormous length diameter ratio of the tube and the low spe ed of the flow. Based on the theory of Berg et al.(1993), a simplified system of control equations is derived from the N S equations for such kind of gas flow. Iterative method is used to solve the equations combined with slip boundary con ditions. The distribution of flow velocity, density, and the mass flow rate are given. The result reveals that the flow is compressible even though the Mach nu mber is very small(<0.01 in general). The slip velocity at wall is visible, the streamwise velocity increasng due to the rarefied gas effect. The density does n ot decrease linearly along streamwise direction as in typical creeping flows bec ause of the compressible effect and the rarefied gas effect. The mass flow rates are higher than those based on no slip boundary conditions, which agree quite w ell with Beskok's(1996) empirical formula. The factors affecting the mass flow r ates include the tube length,diameter, density and pressure at the outlet and in let of the tube.