A hypothesis is tested and validated for predicting the vortex strength induced by a vortex generator in wall-bounded flow by combining the knowledge of the Vortex Generator (VG) geometry and the approaching boundary layer velocity distribution. In this paper, the spanwise distribution of bound circulation on the vortex generator is computed from integrating the pressure force along the VG height calculated using CFD. It is then assumed that all this bound circulation is shed into the wake to fulfill Helmholtz's theorem and then curl up into one primary tip vortex. To validate this, the trailed circulation estimated from the distribution of the bound circulation is compared to the one in the wake behind the vortex generator determined directly from the wake velocities at some downstream distance. In practical situations, the pressure distribution on the vane is unknown and consequently other estimates of the spanwise force distribution on the VG must instead be applied, such as using 2D airfoil data corresponding to the VG geometry at each wall-normal distance. Such models have previously been proposed and used as an engineering tool to aid preliminary VG design and it is not the purpose of this paper to refine such engineering models, but to validate their assumptions such as applying a lifting line model on a VG that has a very low aspect ratio and placed in wall boundary layer. Herein, high Reynolds number boundary layer measurements of VG induced flow were used to validate the Reynolds Averaged Navier-Stokes (RANS) modeled circulation results and are used for further illustration and validation of the hypothesis.
Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization
本文研究了在圆柱形区域$V = D \times [0,L]$中演化的零厚度涡环的量子振荡。符号$D$表示由某个闭连通曲线$S$界定的平面域。这个动力系统的量子化方案是基于作者早先提出的方法。结果，我们找到了循环$Γ$的离散值$Γ_n$。在传统的方法，这些数量通常是假设，值$Γ_n$推导严格的传统计划的量子理论的结果。该模型还展示了水平的分裂。特别地，水平校正值取决于域$V$：圆柱体高度$L$和曲线$S$的形式都影响量$Γ_n$的最终公式。此外，我们证明了基本循环水平表现出“精细结构”。本文还计算了这些与$\hbar^2$值成比例的反常项。所得结论与其他作者的数值模拟结果进行了比较。
Unified Hydrodynamic Analogue of Aharonov-Bohm and Lense-Thirring Effects
OIST Graduate University（冲绳科学技术大学院大学）；International Centre for Theoretical Sciences（国际理论科学中心）；Raman Research Institute（拉曼研究所）；University of Oslo（奥斯陆大学）；Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学）；Condensed Matter i-Lab, Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学凝聚态i实验室）；CIIBEC, Research Center（CIIBEC研究中心）
