Turbulent flow in a sharp $90°$ elbow in a square duct was numerically investigated by performing a direct numerical simulation (DNS) and the results were compared to experimental and Reynolds Averaged Navier–Stokes (RANS) data. This is the first part of an effort to expand the understanding of particle transport in complex geometries. The paper is divided into two parts: a validation of the flow, and then a discussion of additional flow quantities that are important for modeling particles but were not measured experimentally. In the validation section the DNS results were compared to experimental and RANS data at a Reynolds number of $11,500$. Profiles of the mean and root-mean-square (RMS) fluctuating velocities were compared at various points along the elbow’s midplane. Upstream of the bend, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing only slightly near the walls. Downstream of the bend the DNS and the experimental results were virtually identical, varying by no more than $2\%$. However, the RANS results deviated, showing a more extended region of flow re-circulation, causing the mean and RMS velocities to differ by as much as $40\%$. After the validation, one of the additional quantities was the secondary flow structures in the plane perpendicular to the mean flow direction. The RANS and DNS showed similar results upstream of the bend, exhibiting in-plane vortices of the second-kind. Downstream, the vortical flows of the first-kind were observed with a magnitude of about $40\%$ of the mean flow and differed by about $5\%$ between the DNS and the RANS. Eulerian time scales at different locations upstream and downstream of the elbow were also evaluated. The upstream Eulerian time scales showed trends similar to channel flow data, with maximum time scales near the wall. The downstream time scales were qualitatively different showing non monotonic behavior across the channel and values that were significantly different than a channel flow.

湍急的流动 $90°$通过执行直接数值模拟 (DNS) 对方形管道中的弯头进行数值研究，并将结果与​​实验和雷诺平均纳维 - 斯托克斯 (RANS) 数据进行比较。这是扩大对复杂几何中粒子传输理解的努力的第一部分。该论文分为两部分：流动的验证，然后讨论对粒子建模很重要但未通过实验测量的附加流量。在验证部分，将 DNS 结果与雷诺数为 的实验和 RANS 数据进行比较$11,500$. 沿肘部中平面的各个点比较了平均和均方根 (RMS) 波动速度的轮廓。在弯道上游，来自 RANS 和 DNS 模拟的预测平均速度和 RMS 速度与实验相比很好，仅在壁附近略有不同。DNS 的下游和实验结果几乎相同，变化不超过$2\%$. 然而，RANS 结果出现偏差，显示出更广泛的流动再循环区域，导致平均速度和 RMS 速度相差$40\%$. 验证后，附加量之一是垂直于平均流动方向的平面中的二次流结构。RANS 和 DNS 在弯道上游显示类似的结果，表现出第二类平面内涡流。在下游，观测到第一类涡流，其震级约为$40\%$ 的平均流量和相差约 $5\%$在 DNS 和 RANS 之间。还评估了肘部上游和下游不同位置的欧拉时间尺度。上游欧拉时间尺度显示出与通道流量数据相似的趋势，最大时间尺度靠近壁。下游时间尺度在性质上不同，显示跨通道的非单调行为和与通道流显着不同的值。