Acta Scientiarum Naturalium Universitatis Pekinensis

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Numerical Studies of Scaling Exponents in Compressible

HU Kaiheng, CHEN Kai1, SHE Zhensu   

  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871; 1Corresponding Author,
  • Received:2006-05-18 Online:2007-05-20 Published:2007-05-20



  1. 北京大学工学院,湍流与复杂系统国家重点实验室,北京,100871; 1通讯作者,

Abstract: Compressible turbulent channel flows at two Mach numbers (M = 0.8 and 1.3 ) are simulated by the numerical integration of the Navier, Stokes equations with a high, order compact finite difference scheme. The comparative studies of incompressible and compressible flows indicate that the effect of compressibility on the scaling exponents is small in the region near y+ = 20 and in the center while it is significant in the viscous sublayer (y+=5.5) and the log, law region (y+≈120). Further studies on the variation of the relative scaling exponent show that the channel can be divided into four distinct zones according to their scaling behavior: viscous sublayer and lower edge of buffer layer (Ⅰ); the outer part of the buffer layer and lower part of log region (Ⅱ); the major part of the log region and lower edge of the center region (Ⅲ); and finally the other part of the center region (Ⅳ). The variation of the scaling exponents with the compressibility is the most remarkable in the zone Ⅰ and Ⅲ. Finally, it is found that the most intermittent region exactly coincides with the location of the maximum Reynolds shear stress.

Key words: scaling law, direct numeric simulation, compressible channel flow, extended self similarity

摘要: 使用高精度的有限差分格式直接数值模拟了Mach数等于0.8和1.3两种条件下的槽道湍流。根据数值模拟得到的速度差的概率密度分布,计算了两个方向的速度结构函数的相对标度指数。与不可压的标度指数的对比表明在y+=20附近和槽道中心区,压缩性对标度律的影响很小;而在粘性底层(y+=5.5)和对数区内(y+≈120),压缩性对标度指数有显著影响。对六阶标度指数沿壁面距离变化的进一步分析表明,槽道可以分为4个不同行为区,在不同行为区间歇性的变化规律具有不同的特征,其中最大雷诺剪应力所在的那个区域间歇性最强。

关键词: 标度律, 直接数值模拟, 可压缩槽道湍流, 扩展自相似模型

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