On the local acceleration and flow trajectory of jet flows from circular and semi-circular pipes via 3D particle tracking velocimetry

The distinctive differences between two jet flows that share the same hydraulic diameter $d_{h}=$ 0.01 m and \textit{Re }$\approx $ 6000, but different (nozzle) shape are explored via 3D Particle Tracking Velocimetry using OpenPTV (\underline {http://www.openptv.net}). The two jets are formed from circular and semicircular pipes and released in a quiescent water tank of 40 $d_{h}$ height, 40 $d_{h}$ wide, and 200 $d_{h}$ long. The recirculating system is seeded with 100 $\mu $m particles, where flow measurements are performed in the intermediate flow field (14.5 \textless $x/d_{h\thinspace }$\textless 18.5) at 550Hz for a total of $\approx $ 30,000 frames. Analysis is focused on the spatial distribution of the local flow acceleration and curvature of the Lagrangian trajectories. The velocity and acceleration of particles are estimated by low-pass filtering their position with a moving cubic spline fitting, while the curvature is obtained from the Frenet-Serret equations. Probability density functions (p.d.f.) of these quantities are obtained at various sub-volumes containing a given streamwise velocity range, and compared between the two cases to evaluate the memory effects in the intermediate flow field.