液膜表面波在切应力作用下的线性稳定性  

Linear stability of surface waves of a liquid-film under shear

作　　者：叶学民[1] 张润盘[1] 王松岭[1] 

机构地区：[1]华北电力大学电站设备状态监测与控制教育部重点实验室,河北保定071003

出　　处：《华北电力大学学报（自然科学版）》2007年第5期53-56,共4页Journal of North China Electric Power University：Natural Science Edition

基　　金：高等学校博士学科点专向科研基金项目(20040079004)

摘　　要：基于液膜表面的力平衡方程和边界条件,建立了在切应力作用下表征沿倾斜壁面下降液膜流动特性的O-S方程。利用摄动方法,求得了液膜表面波扰动的无量纲流函数扰动和波速表达式,分析了切应力、雷诺数和波数对稳定性的影响。研究表明:切应力是影响液膜稳定性的重要因素之一,同向切应力起不稳定性作用,反向切应力起稳定性用;液膜表面波的稳定性随雷诺数增大逐渐减弱;反向切应力使临界雷诺数增大、扰动增长率减小,同向切应力则起相反作用;表面波扰动的传播速度与波数有关,长波的传播速度低于短波,同向切应力使其传播速度增大,反向切应力使其减小。Based on the force balance on the interface and boundary conditions, the Orr-Sommerfeld equation is established under the shear stress for a falling liquid film draining down an inclined wall. The perturbation method is used to calculate the expressions of perturbation of the dimensionless stream function and the velocity of perturbation, and the effects of shear, Reynolds number and wave number are investigated in this paper. The re.suits show that the shear on the surface is of imtx^rtance for flow stability, and the flow stability tends to be unstable with cocurrent shear and to be unstable with countercurrent shear. The growth rate increases with Reynolds number. The countercurrent shear has the effects of increasing the critical Reynolds number and decreasing the growth rate, and the cocurrent shear has the adverse roles. Furthermore, the wave velocity is dependent on wave number and different shear, and the velocity of long waves is smaller than that of short waves. The wave velocity tends to incream with cocurrent shear and to decrease with countercurrent.

关 键 词：液膜 表面波 流动稳定性 气流切应力 

分 类 号：O352[理学—流体力学]