Continuum-based slip model and its validity for micro-channel flows  

作　　者：ZHANG Genxuan LIU Minghou ZHANG Xianfeng YE Taohong CHEN Yiliang WANG Lu 

机构地区：[1]Thermal Science & Energy Engineering Department, University of Science & Technology of China, Hefei 230027, China [2]The 38th Research Institute of CETC, Hefei 230031, China

出　　处：《Chinese Science Bulletin》2006年第9期1130-1137,共8页

基　　金：This work was supported by the National Natural Science Foundation of China （Grant Nos. 50376060 and 10372099）.

摘　　要：In this paper, the low Mach number he- lium and nitrogen flows in micro-channels are inves- tigated numerically with variations of inlet to outlet pressure ratios, aspect ratios, out pressures and fluid mediums by using different continuum-based slip models. Theoretical solutions based on perturbation expansions of the Navier-Stokes equations have been developed under different order slip conditions. The validity of slip models has been examined by the corresponding experiments and the DSMC method at different Knudsen numbers. Simulations have shown good predictions of the compressibility, rarefaction and thermal creep effects on micro-channel flows with the present slip models. The higher order slip models relatively decrease the rarefaction effects comparing with a first-order slip model. Both of the Knudsen number and the Reynolds number have been identified as key parameters, which govern the rarefaction effects and thermal creep effects, respec- tively. The present slip models have been also dem- onstrated to be appropriate for micro-channel nitro- gen flows with the Knudsen number less than 0.15, and the higher order slip conditions improve the Na- vier-Stokes predictions in the slip flow regime with Kn<0.08. However, the continuum-based slip models significantly under-predict the rarefaction effects in the transitional flow regime as the Knudsen number exceeds 0.2.In this paper, the low Mach number helium and nitrogen flows in micro-channels are investigated numerically with variations of inlet to outlet pressure ratios, aspect ratios, out pressures and fluid mediums by using different continuum-based slip models. Theoretical solutions based on perturbation expansions of the Navier-Stokes equations have been developed under different order slip conditions. The validity of slip models has been examined by the corresponding experiments and the DSMC method at different Knudsen numbers. Simulations have shown good predictions of the compressibility, rarefaction and thermal creep effects on micro-channel flows with the present slip models. The higher order slip models relatively decrease the rarefaction effects comparing with a first-order slip model. Both of the Knudsen number and the Reynolds number have been identified as key parameters, which govern the rarefaction effects and thermal creep effects, respectively. The present slip models have been also demonstrated to be appropriate for micro-channel nitrogen flows with the Knudsen number less than 0.15, and the higher order slip conditions improve the Navier-Stokes predictions in the slip flow regime with Kn〈0.08. However, the continuum-based slip models significantly under-predict the rarefaction effects in the transitional flow regime as the Knudsen number exceeds 0.2.

关 键 词：微通道 滑移模型 扰动分析 稀疏效应 克努森数 

分 类 号：TK12[动力工程及工程热物理—工程热物理]