Direct Lagrangian method to characterize entrainment dynamics using particle residence time: a case study on a laminar s
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RESEARCH ARTICLE
Direct Lagrangian method to characterize entrainment dynamics using particle residence time: a case study on a laminar separation bubble Kai Zhang1 · David E. Rival1 Received: 10 April 2020 / Revised: 26 August 2020 / Accepted: 16 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study demonstrates the feasibility of characterizing small-scale flow dynamics using path-specific Particle Residence Time (PRT). PRT, defined as the time a parcel of fluid spends in a region of interest, is a clear indicator of stagnation and recirculation. To test the concept, two-dimensional particle tracking velocimetry is used to measure a laminar separation bubble (LSB) on the suction side of an SD7003 airfoil at Re = 60, 000 . Extended pathlines are calculated from the Lagrangian data such that fluid parcels entering the region of interest are tracked continuously. PRT is then directly calculated and used to quantify the entrainment process across the LSB. Using convential Eulerian quantities, the flow field around the LSB is divided into outer (free stream) and inner layers—separated by the local minimum velocity magnitude line. Entrainment, initiated by the formation of vortices near the reattachment point, is quantified according to the trajectories of fluid parcels crossing into the inner flow layer. The PRT values of entrained fluid parcels are significantly increased compared to the bulk flow. Variations of the mean PRT of entrained fluid reveal unsteady features, including the transition and reattachment of the LSB. The path-dependent indicators of separation, transition and reattachment are shown to closely agree with Eulerianbased benchmark measurements. Graphic abstract
Keywords Lagrangian tracking · Particle residence time · Laminar separation bubble Extended author information available on the last page of the article
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Experiments in Fluids
(2020) 61:243
1 Introduction A fluid parcel’s motion is inherently unstable owing to its sensitivity to local perturbations. As a result, directly mapping the trajectory of individual fluid parcels generates poor results (Haller 2015). The majority of current Lagrangian measurements feature fluid motion using Lagrangian coherent structures (LCSs); see Shadden et al. (2006); Green et al. (2007); Mundel et al. (2014); Haller (2015). LCSs are usually defined as ridges in a finite time Lyapunov exponent (FTLE) field, which represent the regions of greatest attraction, repulsion, or shearing. However, FTLE fields do not contain information describing the time history of individual fluid trajectories. Inspired by flow-map compilation techniques (Brunton and Rowley 2010; Raben et al. 2014), Rosi and Rival (2018) developed an algorithm to extend short Lagrangian pathlines beyond their original measured length. The history of path-dependent flow quantities can be tracked along the extended pathlines, which is particularly useful when investigating problems where the source of a fluid t
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