• 1 Q判据
  • 1.1 计算公式
  • 1.2 物理含义
  • 1.3 相应脚本
    • 1.3.1 Tecplot使用的MCR文件
    • 1.3.2 Fluent使用自定义场函数

1 Q判据

1.1 计算公式

Vortices of an incompressible flow are identified as connected fluid regions with a positive second invariant of the velocity-gradient tensor \(\Delta u\), \(\Delta u = S + \Omega\), \(S\) is the strain-rate tensor, \(\Omega\) is the vorticity tensor. Formula is as follows,¹

\[ \begin{aligned} Q &= \frac{1}{2} ( u^{2}_{i,i} - u_{i,j} u_{j,i} ) \\ &= - \frac{1}{2} u_{i,j} u_{j,i} \\ &= \frac{1}{2} ( \Vert \Omega \Vert^{2} - \Vert S \Vert^{2} ) \\ \end{aligned} \]

1.2 物理含义

• 待补充

1.3 相应脚本

1.3.1 Tecplot使用的MCR文件

• Qcriterion.mcr
  • Using Tecplot’s Specify Equations tool this file calculates the components of the symmetric and antisymmetric parts of the velocity gradient tensor. Using these new tensors the lambda-2 and Q-criterion (Q criterion) is determined.
  • 实际使用中，载入该宏文件后，需要指定X,Y,Z方向的速度在Data Set Info中的序号。
  • 实际运行效率很低，对于三维算例运行时间较长，约半小时。

1.3.2 Fluent使用自定义场函数

• 使用custom field function，按照Q判据定义，计算出新的变量作为Q-Criterion。使用的计算式如下，

    Q-Criterion = 0.5 * ( {Vorticity Magnitude}^2 - {Strain Rate}^2 )

  • 其中Vorticity Magnitude位于Velocity分类下，Strain Rate位于Derivative分类下。²

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1. Kolář V. Brief notes on vortex identification[C]//Proceedings of the 8th WSEAS International Conference on Fluid Mechanics and 8th WSEAS International Conf. on Heat and Mass Transfer. Stevens Port, WI: World Scientific and Engineering Academy and Society (WSEAS), 2011: 23-28.↩︎

2. 涡量与应变率的定义式见Vorticity_and_StrainRate.pdf↩︎