中等Reynolds数平板绕流的动理论分析  

KINETIC ANALYSIS OF THE FLOW PAST A FLAT PLATE AT MODERATE REYNOLDS NUMBERS

作　　者：樊菁[1] 吴晨曦[1] 孙泉华[1] 蒋建政[1] 

机构地区：[1]中国科学院力学研究所高温气体动力学重点实验室,北京100190

出　　处：《力学进展》2009年第4期421-425,共5页Advances in Mechanics

基　　金：国家自然科学基金(90205024;10425211;10621202)资助项目~~

摘　　要：郭永怀先生1953年给出的中等Reynolds数下、不可压缩流体有限长平板绕流的解析解是边界层理论中的经典工作,许多研究者对平板绕流阻力系数的郭永怀公式以及后续工作进行了评估,评估的依据是Janour与Schaaf和Sherman的实验数据,本文的动理论分析和计算表明:Schaaf和Sherman在低亚声速条件下(0.16<M<0.21)获得的实验数据,当Reynolds数(Re)介于1和10之间时,由于稀薄气体效应显著(所对应的Knudsen数约在0.03和0.3之间),不宜作为不可压缩理论解的依据,而其它满足不可压缩假设的实验数据都支持郭永怀解;计及稀薄气体效应时,低速或亚声速情况下平板绕流的阻力系数C_D=C_(D,c)×C_(D,FM)/(C_(D,c)+C_(D,FM)),其中C_(D,c)和C_(D,FM)分别为连续介质和自由分子流极限情况下的理论解;平板绕流速度分布的郭永怀解,与基于动理论的信息保存方法(IP)的数值解定性相符,差别表现在稀薄气体效应显著的前缘;与速度分布的Blasius解相比,当Re<100时,郭永怀修正变得重要。An analytical solution given by Y.H. Kuo in 1953 for the incompressible flow past a flat plate at moderate Reynolds numbers was a classical work of boundary layer theory. Many researchers, based on experimental data given respectively by Janour and Schaaf and Sherman, made an assessment of Kuo＇s formula and carried out follow-up studies for determining the drag coefficient around a fiat plate. Kinetic analyses in the present paper show that the experimental data of Schaaf ＆ Sherman in low subsonic situations （0.16 〈 M 〈 0.21） is not suitable to serve as a standard to assess an incompressible theory when the Reynolds number （Re） ranges from 1 to 10, because the corresponding Knudsen numbers under the experimental conditions are about between 0.03 and 0.3, indicating significant rarefied gas effects, while other experimental data satisfying the incompressible assumption support Kuo＇s formula. When rarefied gas effects are taken into account, the drag coefficient around a flat plate in low-speed or subsonic situations may be expressed as CD = CD,c × CD,FM/（CD,c ×CD,FM）, where CD,c and CD,FM are the theoretical solutions at continuum and free molecular limits, respectively. Kuo＇s solution for the velocity distribution past a flat plate is in qualitative agreement with the numerical results given by the information preservation （IP） method based on kinetic theory, with some difference occurring at the leading edge where rarefied gas effects become significant. Compared with Blasius solution to the velocity distribution, Kuo＇s correction becomes important when Re 〈 100.

关 键 词：平板绕流 郭永怀解 稀薄气体效应 动理论分析 IP方法 

分 类 号：O357[理学—流体力学] O357.1[理学—力学]