Swirling pipe flows are studied here with an aim towards understanding the onset of the inertial region — where the turbulent-inertia term in the mean momentum equation is balanced by pressure gradient and viscous term is sub-dominant — as well as the clarifying the velocity–vorticity correlations that make up the turbulent inertia. To this end, we first manipulate the mean momentum equation in both axial and azimuthal directions and find some exact results in the inertial region, and carry out direct numerical simulations of swirling pipe flows at axial friction Reynolds numbers of 170 and 500. The swirl number considered in our simulations is $S\approx 0.3$, and we compare our results to non-swirling pipe flows at similar Reynolds numbers. We find that swirling produces a drag increase and an influence on the turbulence statistics similar to increasing the Reynolds number except for the streamwise turbulence intensity. An analysis on the axial and azimuthal mean momentum equations shows that swirling shifts the beginning of the inertial region wall-normal location closer to the wall. The turbulent inertia decomposition reveals that the near-wall region the velocity–vorticity correlations of the axial direction are similar to a 2D channel flow and interpreted as vorticity stretching/reorientation and dispersion, whereas in the new correlations in the azimuthal direction can also be given a similar physical meaning in the near-wall region. In the outer-region, however, the pipe axial correlations are different to the 2D-channel, and so are the azimuthal correlations. We find that the pipe has new a ‘geometric’ contribution in both axial and azimuthal directions that play an important role in contributing towards vorticity dispersion in the outer core region of a swirling pipe flow.

此处对旋流流动进行了研究，旨在了解惯性区域的开始-在平均动量方程中，湍流惯性项受压力梯度平衡，粘性项次于主导-并阐明了速度-构成湍流惯性的涡度相关性。为此，我们首先在轴向和方位角方向上操纵平均动量方程，并在惯性区域中找到一些精确的结果，然后在轴向摩擦雷诺数为170和500的情况下对旋流管流动进行直接数值模拟。旋流数在我们的模拟中考虑的是$\mathrm{小号}\approx 0.3$，并将我们的结果与雷诺数相似的非旋流管流量进行比较。我们发现，涡流产生阻力增加，并且对湍流统计的影响与增加雷诺数相似，除了沿流湍流强度不同。对轴向和方位角平均动量方程的分析表明，涡旋使惯性区域壁法线位置的开始位置更靠近壁。湍流惯性分解表明，近壁区域的轴向速度-涡度相关性类似于二维通道流，并解释为涡度拉伸/重新定向和弥散，而在新方向上还可以给出方位角相关性在近壁区域具有相似的物理意义。但是在外围地区，管道轴向相关性不同于2D通道，方位相关性也不同。我们发现，管道在轴向和方位角方向都具有新的“几何”贡献，在促进旋流管道外芯区域的涡度扩散中起着重要作用。