3D拉格朗日粒子追踪测速

智能文字提取功能测试中

拉格朗日粒子跟踪（LPT）是一种体积流量测量技术，能够在长时间内跟踪大量示踪粒子，即使在高度湍流的情况下也能做到。在本介绍中，我们从物理上说明这些技术及其相关性的重要性，介绍其一般原理，概述其历史发展，并描述了后处理方面的最新进展。这些主题的深入讨论在第2至4节中提供。我们在日常生活中遇到的大多数流动都是非定常、湍流和三维的。在自然界、空气动力学和许多相关的技术应用中达到的雷诺数通常远高于湍流发生的临界值。人类从字面上说是沉浸在非定常的流体流动现象中，从我们的血管和呼吸道中到各种交通工具内部和周围的流动、海洋中的洋流、大气湍流边界层（TBLs）以及封闭房间内的混合热对流。为了在各种应用和情况下充分利用流体流动，需要详细了解它们的拉格朗日和欧拉特性。湍流流动的主要特征是其动态能量转移机制，从大流动尺度向越来越小的（旋涡）流动尺度级联到耗散（Richardson 1922），并且随着雷诺数的增加而增加空间和时间尺度的分离，例如L/η ∼ Re3/4λ和TL/τη ∼ Re1/2λ（Toschi和Bodenschatz 2009；另请参见名为“湍流流动尺度”的侧栏）。根据局部速度梯度张量（VGT）（Chong等，1990），湍流流动结构可以定义为3D拓扑，即稳定或不稳定的鞍点或稳定或不稳定的节点，其在时间上改变形状和方向，同时随着整个流体流动（向下游）传导。另一方面，流动及其相干结构本身可以被理解和描述为几乎无限数量的流体元素的动态组成，这些元素沿着拉格朗日轨迹与局部流一起移动，并通过压力梯度和黏度与相邻元素耦合。在拉格朗日参考系中，这些流体元素正在进入和退出更持久的欧拉相干流结构，从而使它们保持活跃或导致它们的最终衰减。因此，流动拓扑可以在欧拉参考系（例如，通过VGT的Q和R不变量描述不可压缩流动），或者从拉格朗日视角作为与流体元素一起移动的拉格朗日相干结构（LCS）（Haller 2015）来定义。尽管如此，两个参考系都允许描述相同的流动，因为每个时间步长的拉格朗日和欧拉速度向量是相同的。Figure 2 (Figure appears on preceding page) Time-resolved multicamera recordings Annu. Rev. Fluid Mech. 2023.55：511-40 First published as a Review i n Advance on October 13，2022 The Annual Review of Fluid Mecbanics is online at fluid.annualreviews.org https：//doi.org/10.1146/annurev-fluid-031822-041721 Copyright O 2023 by the author(s). This work is licensed under a Creative Commons Attribution 4.0International License， which permits unrestricted use， distribution， and reproduction in any medium，provided the original author and source are credited.See credit l ines of images or other third-party material in this article for license information. ANNUAL REVIEWS CONNECT www.annualreviews.org ·Down l oad figures ·Navigate c ited references · Keyword search · Explore related ar t icles · Share via email or social media Annual Review of Fluid Mechbanics 3D Lagrangian Particle Tracking in Fluid Mechan i cs Andreas Schroder1，2 and Daniel Schanz lInstitute of Aerodynamics and Flow Technology， Deutsches Zentrum f ur Luft- u nd Raumfahrt (DLR)， Gottingen， Germany； email： andreas.schroeder@dlr.de 2Institute for Traffic Engineering ， Brandenburgisch Technische Universitat (BTU) Cottbus-Senftenberg， Cottbus， Germany Keywords 3D particle tracking velocimetry， iterative particle reconstruction，Shake-The-Box， one- and multipoint s tatistics， velocity gradient t ensor，3D pressure fields， data assimilation Abstract In the past few decades various particle i mage-based volumetric flow mea-surement techniques have been developed that have demonstrated their potential in accessing unsteady flow properties quantitatively in various POt experimental applications i n fluid mechanics. In this review， we f ocus on physical properties and circumstances of 3D part i cle-based measurements and what knowledge can be used for advancing reconstruction accuracy and spatial and temporal resolution， as well as completeness. The natural candi-date for our focus i s 3D Lagrangian particle tracking (LPT )， which allows for position， velocity， and acceleration to be determined alongside a l arge number of individual particle tracks in the i nvestigated volume. The ad-vent of the dense 3D LPT technique Shake-The-Box in the past decade has opened further possibilities for characterizing unsteady flows by delivering input data for powerful data assimilation techniques that use Navier-Stokes constraints . As a result， high-resolut i on Lagrangian and Eulerian data can be obtained， including long particle t rajectories embedded i n time-resolved 3D velocity and pressure fields. 1. INTRODUCTION Lagrangian particle tracking (LPT) is a volumetric f low measurement technique capable of fol-lowing high numbers of tracer particles over extended periods of time， even in highly t urbulent scenarios. In this introduction we physically motivate the importance of these and related tech-niques， introduce the general principle， provide an overv i ew of the historical development， and describe recent advances in postprocessing. In-depth discussions of these t opics are provided in Sections 2-4. Most f lows we encounter in everyday l i fe are unsteady， turbulent ， and three dimensional (3D).The Reynolds numbers reached in nature， aerodynamics， and i n many relevant t echnical appli-cations are typically f ar above the onset of turbulence. Human beings are literally i mmersed in unsteady fluid flow phenomena， from those in our blood vessels and respiratory t racts to flows around and inside various transport vehicles， currents in oceans， atmospheric turbulent boundary layers (TBLs)， and mixed therma l convection i nside closed rooms. In order to make any technical use of fluid flows， one needs to understand their Lagrangian and Eulerian propert i es in detail in various applications and situations. The main f eatures of turbulent f l ows are their dynamic energy transfer mechanism in a cascade from l arge to i ncreasingly smaller (vortical) flow scales down to dissipation (Richardson 1922) and their increase of spatial and temporal scale separation with Reynolds number as L/n~ Re’4 and T/t~ Re (Toschi & Bodenschatz 2009； see also the sidebar titled Scales of Turbulent Flows). Turbulent flow structures can be defined as 3D topologies， either s table or unstable saddle-points or stable or unstable nodes， according to the local velocity gradient tensor (VGT) (Chong et al . 1990)， that change their shape and orientation in t i me while convecting (downstream) with the bulk flow. On the other hand， the flow and its coherent structures t hemselves can be under-stood and described as a dynamic composition of an almost i nfinite number of fluid elements that are moving with the local flow as Lagrangian trajectories and are coupled with neighboring ele-ments by pressure gradients and viscosity. In a Lagrangian frame of reference， these fluid elements are entering and exiting more persistent Eulerian coherent f low s tructures， thereby keeping them alive or leading to t heir final decay. Therefore， flow topologies can be defined either i n a Eulerian (laboratory) reference system， for example， by the invariants Q and R of the VGT (for incompress-ible flows)， or from a Lagrangian perspective as Lagrangian coherent structures (LCS) (Haller 2015) moving with the fluid elements. Nevertheless， both reference systems allow the same flow to be described， as the Lagrangian and Eulerian velocity vectors are i dentical for each time step. Fluid f low dynamics follow physical l aws describing their momentum exchange and mass conservation by a set of equations， which were first discovered by Navier and Stokes. These gov-erning laws are nonlinear partial differential equations and， nowadays， allow numerical methods to predict flows and their features by computer simulations， such as for aerodynamical design purposes. At high Reynolds numbers， the resolution requirements in space and time and the non-linearity of the flow physics involved pose many problems for numerical codes， regarding either the available computer resources or the validity and applicability of established turbulence mod-els or scaling laws (Mani & Dorgan 2023). A very high degree of computational effort i s already needed for predicting turbulent flows at moderate Reynolds numbers by direct numerical sim-ulations (DNS). Today， even with modern high-performance computing resources， converged DNS results (e.g.， for the flow around a small passenger aircraft) cannot be provided at all and will most probably not be reachable within the next couple of decades. Therefore， (advanced)computational fluid dynamics code developments that use turbulence or subgrid-scale models to solve their c l osure problem [large eddy simulations， (unsteady) Reynolds averaged Navier-Stokes (NS) equations， etc.] require spatially (and temporally) well-resolved experimental validation data at high Reynolds numbers， preferably in f ull volumes around various model geometries. High-quality velocity vector f ields (instantaneous and mean with Reynolds stresses) enable the tuning of numerical parameters and the adaptation or further development of various t urbulence mod-els. Promising fields that will be closely l inked to velocity， acceleration， and pressure data from 3D LPT measurements in the near future include data-driven turbulence models (Duraisamy et al.2019) and the exploration of universal constants (Viggiano et al. 2021) or turbulent t ransport properties in inhomogeneous turbulence from Lagrangian s tatistics. 1.1. Particle Image-Based Velocimetry During the past decades a tremendous increase of flow field information has been gained from ex-perimental investigations applying image-based measurement techniques. Particle image-based methods visualize the flow using clouds of small tracer particles that are illuminated and observed by one or more cameras (complementary or alternative to existing probe techniques). For exper-iments in unsteady and turbulent f lows， nonintrusive volumetric and t i me-resolved measurement techniques， determining al l three components of the velocity (and acceleration) vectors at many points instantaneously， are highly desired. Consequently， i n recent years particle image velocime-try (PIV) techniques have been extended from 2D to 3D and from two-pulse snapshot modes to temporal resolution (Adrian & Westerweel 2011， Raffel et al. 2018， Beresh 2021). Various vol-umetric (and time-resolved) PIV and particle tracking velocimetry (PTV) techniques and their capabilities have already been presented in dedicated papers. For single (or stereo) camera views，scanning PIV has been proposed by， for example， Gray et al . (1991) and Brucker (1997)； holo-graphic PIV techniques have been presented by Hinsch (2002)， Katz & Sheng (2010)， and others；coded aperture PIV was first introduced by Willert & Gharib (1992)； defocusing PIV was de-scribed by Pereira et al . (2000)； structured-light PIV was described by， e.g.， Aguirre-Pablo et al.(2019)； and light field or plenoptic PIV was described by Fahringer et al. (2015) and others. Appli-cations of single-camera 3D PTV for microfluidics include astigmatism (Cierpka et al. 2010) and holographic PTV (Choi et al. 2012). Single-view 3D PIV and PTV techniques can operate with less optical access， but due to the l imited aperture， the reconstructed particle position uncertainty in depth direction (the direction parallel to the main viewing direction of the camera) is much larger (typically by a factor greater than 3) compared to the in-plane uncertainties. Multicamera methods rely on several camera projections， allowing similar position and velocity uncertainties in al l three directions in space when appropriate projection angles are applied (ideally an angle of 90° is used between the two outermost cameras-the “aperture”of the camera system). Tomographic PIV (Tomo-PIV)， which was introduced by Elsinga et al. (2006) and further developed by Wieneke (2008)， Atkinson & Soria (2009)， and Novara et al. (2010)， significantly Particle i mage velocimetry (PIV)： flow measurement method for obtaining 2D fields of veloc i ty vectors by cross-correlat i ng subsequent images of tracer particles Particle image density， Nr： measure to describe the density of particle image peaks on a camera i mage；expressed in part i cles per pixel (ppp) Ghost particle： falsely reconstructed 3D particle (position) that does not exist in the originally imaged part i cle cloud Peak： image of a single particle on a camera，typically a (distorted)Gaussian with a diameter of 2-3 pixels Line-of-sight (LOS)：the viewing path through the measurement region of a given camera image coordinate， as given by the calibration enhanced the spatial resolution of volumetric velocimetry. Therefore， Tomo-PIV rapidly evolved to become the most commonly used and robust 3D flow measurement technique in the decade following its first publication. It enables flow field estimates to be delivered on regular 3D velocity vector grids via iterative local cross-correlation schemes with relatively high spatial resolution based on， typically， four to six camera projections and at particle image densities around Nr=0.05particles per pixel (ppp). Furthermore， by using many camera projections one can i ncrease the number of truly reconstructed particles per t ime step while reducing t he so-called ghost particle fraction (Elsinga et al . 2006)， which holds true as well for particle-based reconstruction schemes for 3D LPT. For all 3D reconstruction techniques， Nr determines the possible spatial resolution i nside the investigated flow for a given depth of t he measurement volume； however， the reconstruction dif f iculty increases with N. The maximum value of Nr at which a method can reliably reconstruct true part i cles while not creating too many ghost particles typically determines i ts performance.Novel machine l earning (ML) approaches are promising methods for increasing t he range of N-values for Tomo-PIV techniques (Gao et al . 2021). A further i ncrease of spatial resolution or particles per volume (ppv) has been achieved by a scanning Tomo-PIV setup in a turbulent l ow-speed flow (Lawson & Dawson 2014). However， for all cross-correlation-based PIV techniques，a spatial low-pass filter modulation of the velocity gradients inside the measured f low has to be accepted because only a group of particle images (typically four to ten) located i nside a 2D or 3D correlation window [e.g.， 322px (pixels) or 323 voxels] enables a robust estimation of the position of t he local displacement vector peak. Furthermore， acceleration vector fields are not di r ectly accessible by this method. Consequently， a measurement technique that enables i ndividual t racer particles to be followed volumetrically and at high densities i n t ime i s more suited to bridge the scattered measurement data， i ncluding position， velocity， and acceleration， along reconstructed particle t rajectories to the governing NS equations. px： normalized l ength of a camera pixel，scaled by the average magnification； it is thereby a universal measure for comparing 3D i maging systems 1.2. Particle Trackin g M ethods In contrast to PIV methods， particle tracking methods have been developed with 3D PTV schemes that enable relatively sparse particle track reconstructions (e.g.， Nishino et al. 1989， Maas et al.1993， Malik et a l . 1993， Guezennec et al. 1994， Virant & Dracos 1997， Ouellette et al. 2006，Machicoane et al . 2019， Dabiri & Pecora 2020) at particle image densities between ~0.005 and 0.02 ppp. Increased particle track densities in the measurement volume can be achieved with scan-ning 3D PTV techniques (Hoyer et al. 2005， Kozul et al. 2019)， reaching higher ppv values for relatively low flow velocities. Nowadays， state-of-the-art 3D LPT techniques can reach high par-ticle image densities of ~0.05-0.2 ppp using the Shake-The-Box (STB) method (Schanz et al.2016，Jahn et al. 2021， Leclaire et al . 2021， Sciacchitano et al.2021b). Figure 1 depicts the general working principle of 3D particle tracking experiments： First， par-ticle images of (illuminated) passive tracers inside the flow are taken simultaneously f rom several camera projections (typically three to six) for each time step. Then， particle image peaks are de-tected on each camera and the l ines-of-sight (LOS) of each peak are virtually elongated into t he measurement volume according to the 3D camera calibration. When LOS of detected particle image peaks on several cameras i ntersect below an allowed t r iangulation error (~1 px)， a t rue 3D particle position can be assumed. Using all detected peaks on the different cameras， one can recon-struct clouds of 3D particle positions for each time step. A tracking approach is then applied in a second step that aims at always f inding the identical imaged particle along the corresponding time-line of 3D particle reconstructions in order to build up long 3D particle trajectories. The actual implementations of the different LPT steps can be performed with varying levels of sophistication and are discussed in Sections 2 and 4. Reconstruction： 3D positions from 2D peaks using calibrated l ines-of-sig ht Figure 1 The basic steps of a Lagrangian particle t racking experiment. 2D particle i mages (peaks) are identified on all camera images for a certain t ime step (green dots) and then used to determine 3D positions (blue dots) using (iterative) triangulation procedures (red lines). The particle clouds from several t ime steps can be connected to tracks under certain constraints. Velocity and acceleration of the trajectories yield several properties via postprocessing (e.g.， flow structures) by applying regularized interpolation (data assimilation) to all particles tracked at a certain time step. Figure 2 shows a specific application of LPT i n a large and densely seeded Rayleigh-Benard convection cell. The key aspects of the setup are a pulsed volumetric illumination and a multicam-era setup consisting of at least three cameras and capable of temporally resolving the flow. Here，the STB algorithm (see Section 3.1) was used to i nstantaneously track up to 560，000 tracers over long periods of time from the images obtained from six cameras (Bosbach et al. 2021， Godbersen et al. 2021). Here we would like to sugges t using the name “3D LPT”for volumetric measurements ofindi-vidual particle trajectories (following， e.g.， Ouellette et al. 2006) because t he achievable measures along individual particle paths are manifold， including position， velocity， acceleration (material derivative)， and (sometimes even) j erk， as well as t heir Lagrangian properties. All of these are important for the f luid mechanical characterization of the investigated flow and are valuable i n-puts for high-resolution postprocessing approaches using bin-averaging for one- and multipoint statistics， data assimilation (DA)， ML， and integration [e.g.， pressure from LPT (Rival & van Oudheusden 2017， van Gent et al. 2017)]. The velocity ， as might be suggested by t he t erm“PTV，”is not the only i mportant outcome. Tomo-PIV and 3D LPT/PTV techniques， as well as various similar volumetric velocimetry techniques for f luid flows， have been extensively presented and discussed i n recent reviews (e.g.，Scarano 2013， Westerweel et al . 2013， Discetti & Coletti 2018， Machicoane et al. 2019) and text-books (Schroder & Willert 2008， Adrian & Westerweel 2011， Raffel et al. 2018， Dabiri & Pecora 2020). Furthermore， with the recent development of high-speed l asers and cameras， the range of flow velocities i n which time-resolved velocity field information can be gained via PIV and LPT has been widened significantly in spatial and temporal resolution (Beresh 2021). In all various volumetric flow measurement techniques， the achievable dynamic spatial range (DSR) (see Adrian 1997) for sampling any (turbulent) f low f ield is mainly rest r icted by the res-olution of the used camera sensor and the reachable volumetric particle density， which l imit the Data assimilation (DA)： the process of combining measurement data (e.g.， particle position， Tracking of ≈560，000 tracers Q-criterion from FlowFit in the ful l RBC volume int e rpolation of tracks (a) Exemplary setup of a Lagrangian particle tracking (LPT) experiment， consisting of a Rayleigh-Benard convection (RBC) cell 1.1 m in height with tracer particles (here， helium-filled soap bubbles) illuminated by a pulsed light source (here， f rom above by arrays of high-power LEDs (light-emitting diodes) shining through a transparent water-cooled top plate). The i lluminated tracers are r ecorded in a time-resolved f ashion by a system of cameras， all i maging the same (illuminated) volume. (b) Actual i mage f rom one camera of t he experiment ， showing bubbles i nside the cell and the illuminated heated floor. The i nsets show examples at several particles per pixel (ppp) concentrations. (c) LPT was performed on the high-density i mages using the Shake-The-Box method. (d) Flow structures can be visualized by applying FlowFit data assimilation to the tracked part i cle field in panel c. Panels adapted from Godbersen et al. (2020)(CC BY-NC 4.0； https：//doi.org/10.1103/APS.DFD.2020.GFM.V0074). instantaneous sampling of the l argest and smallest achievable f low structures， respectively. The latter is directly related to Ni and the depth of the investigated volume. Therefore， if flow dy-namics and repetition rates of cameras and illumination allow， 3D scanning methods can achieve relatively high volumetric particle densities (and DSR values) and do not suffer (like many other techniques) from both the reduction of scattered particle l ight due to smal l camera l ens apertures and the expansion of the available (laser) light for full volumetric i llumination. On the other hand， the dynamic velocity range (DVR) (Adrian 1997) and dynamic accelera-tion range (DAR) (Schanz et al. 2016) are strongly linked to the reconstructed particle position accuracy and the temporal sampling along the (exploitable) particle trajectories. To enhance DSR and DVR of particle-based measurements ， the need for a “completely new approach”has already been proclaimed (Westerweel et al . 2013，p. 409). In general， multi-illumination or t ime-resolved imaging strategies of tracer particles inside f lows enable higher accuracies t han can be achieved with two-pulse strategies when determining temporal derivatives of the particle trajectory. All three characteristic values， DSR， DVR， and DAR， can be maximized in a 3D LPT experiment by exploiting the knowledge of the physical (fluid mechanical and optical) properties of the i ndi-vidual tracer particles and their imaging. Applying this physical knowledge for an enhanced 3D particle reconstruction and tracking scheme was the path followed by the STB development i n the past decade. High position accuracies of reconstructed particles require well-sampled particle images (~2 px i n diameter， no pixel-locking) at high signal-to-noise ratio (SNR)， as the discret i zed gray values of particle i mages contain the particles’ posit i on i nformation. Then， the applied 3D reconstruction scheme should aim at a strong reduction of ghost part i cles i n order to keep the distributed i mage intensity at the true particles’ positions for enhancing their position accuracy.Finally， having obtained such high positional accuracies， accurate temporal derivatives along f itted tracks， like velocity and acceleration， are only available at sufficiently high sampling frequencies.With respect to extreme but rare acceleration events inside turbulent flows， it has been proposed that one samples at l east 40 times faster than the Kolmogorov t imescales， t ，， in order to avoid respective t racking and truncation errors (Lawson et al. 2018). However， hardware restrictions do not always allow for such high illumination and i maging frequencies. In Section 3.2 below the temporal sampling problem for high-acceleration (and -jerk) events i s addressed again in the context of an advanced prediction and correction STB scheme. 1.3. Advanced 3D Particle Tracki ng a nd Data Assimilation Techniques The STB technique is an advanced 3D LPT method t hat combines the triangulation-based ad-vanced iterative part i cle reconstruction (IPR) technique (Wieneke 2012，J ahn et al. 2021) with t he exploitation of the temporal and spatial coherence of Lagrangian part i cle tracks i n the i nvestigated flow. STB enables the processing of particle i mage densities up to Nr=0.2 ppp under good ex-perimental conditions with an almost complete suppression of ghost particles. Subsequently， the dense scattered particle tracks are temporal l y filtered (Gesemann et al. 2016， Gesemann 2021) for estimating position， velocity， and acceleration (material derivative)， which can be used in a second step as input for DA approaches using NS constraints， delivering the f ul l time-resolved 3D veloc-ity gradient tensor and pressure fields (e.g.， Gesemann et al . 2016， Schneiders & Scarano 2016，Jeon 2021). Using only solenoidal constraints applied to dense LPT data， in case D of the Fourth International PIV Challenge in 2014， the first DA schemes hav e already shown better spatial and temporal resolution of the reconstructed volumetric flow f ield than advanced Tomo-PIV tech-niques (see Kahler et al. 2016). A f urther benchmark test of the 3D pressure f ield reconstruct i on capabilities of various pressure from PIV and LPT approaches also showed strong benefits in us-ing dense LPT data， delivering velocity and acceleration vector f ields as i nput f or DA schemes that apply fully nonlinear NS constraints (see van Gent et al. 2017). Current developments aim at maximizing the achievable flow information from s ingle flow experiments at high particle im-age densities by applying (combined) 3D LPT， DA， and ML (Brunton et al. 2020) approaches.However， in many high-speed flow experiments， ful l temporal resolution for particle i mage-based volumetric velocimetry is still not possible. Here， multipulse and multi-illumination techniques for Tomo-PIV (Lynch & Scarano 2014， Schroder et al. 2013) and LPT (Novara et al. 2016b，2019)have been developed that can capture volumetric velocity f ields at high spatial resolution， as well as DVR (see Figure 5) (e.g.， van Gent et al. 2017). The scattered nature of the individually tracked partic l es provides a great advantage over other related measurement techniques such as PIV. Instead of a fixed regular grid of convolution win-dows whose size imposes a low-pass filtering effect on resolvable flow structures and gradients，the particle track positions are distributed homogeneously and provide l ocal point measurements of f luid elements when using particles with diameters below the smallest scales of the investi-gated flows， such as the Kolmogorov length scale dp