不可压湍流平均流与拟序流的各向异性模式理论及其数值验证

使用侧偏统计平均方法理性推导了不可压湍流的封闭方程组。侧偏统计平均提供了湍流脉动量的一阶统计信息,在引入加权漂移速度对称性及正交各向异性后,导出了漂移流的连续方程、动量方程及能量方程,最后依据湍流物理的唯象论,使用动量传输链概念模化封闭了整个方程组。方程组不含任何经验系数,保留了N- S方程的均化的非线性特性。其级数形式的能量方程与非线性现象多尺度层次现象相对应,具备了描述湍流统计平均流动及拟序结构流动的双重功能。 

The United Modeling Theory for both of Mean Flow and Coherent Flow of Incompressible Turbulence

A unilateral statistical average scheme is used to derive a new set of closed equations of incompressible turbulent flows,which is capable of describing both of statistical mean flow and intermittent coherent flow without introducing any empirical treatments and coefficients.Besides the special average scheme,the concepts of symmetic drift flows,orthotropic trubulence and the chain of momentum transference are also used in the original derivation.More important,the obtained energy equation of series form suggests that the infinite terms in the equation are corresponding to infinite layers of structures of trubulence.If all the terms of the series are taken for determining the length scale,one obtains statistical mean results.On the other hand,if only parts of terms are taken,coherent flows would appear.To verify the adaptablity of the equations,three benchmark flows,i.e.free shear flow,boundary layer transition flow and separated flow,are numerically simulated on PC computers.Both of accurate results of statistical mean flows and vivid structures of coherent flows are obtained.