KINETIC ANALYSIS OF THE FLOW PAST A FLAT PLATE AT MODERATE REYNOLDS NUMBERS
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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$C_D= C_{D,c} \timesC_{D,FM}/ (C_{D,c} + C_{D,FM} )$, 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.Abstract: An analytical solutiongiven by Y.H. Kuo in 1953 for the incompressible flow past a flatplate at moderate Reynolds numbers was a classical work ofboundary layer theory. Many researchers, based on experimentaldata given respectively by Janour and Schaaf and Sherman, made anassessment of Kuo's formula and carried out follow-up studies fordetermining the drag coefficient around a flat plate. Kineticanalyses in the present paper show that the experimental data ofSchaaf {\&} Sherman in low subsonic situations ($0.16 < M < 0.21)$is not suitable to serve as a standard to assess an incompressibletheory when the Reynolds number ($Re$) ranges from 1 to 10,because the corresponding Knudsen numbers under the experimentalconditions are about between 0.03 and 0.3, indicating significantrarefied gas effects, while other experimental data satisfying theincompressible assumption support Kuo's formula. When rarefied gaseffects are taken into account, the drag coefficient around a flatplate in low-speed or subsonic situations may be expressed as $C_D= C_{D,c} \times C_{D,FM} /(C_{D,c} + C_{D,FM} )$, where $C_{D,c}$and $C_{D,FM} $ are the theoretical solutions at continuum andfree molecular limits, respectively. Kuo's solution for thevelocity distribution past a flat plate is in qualitativeagreement with the numerical results given by the informationpreservation (IP) method based on kinetic theory, with somedifference occurring at the leading edge where rarefied gaseffects become significant. Compared with Blasius solution to thevelocity distribution, Kuo's correction becomes important when$Re< 100$.
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