Lagrangian Particle Trajectories Research Articles

Riverine substance transport dynamics in a semi-enclosed inland sea

Given the considerable hydrodynamic and ecological implications associated with riverine substances in estuaries, a comprehensive investigation on their fates, pathways, and driving mechanisms is imperative. Consequently, observed drifters were deployed in the Bohai Sea in November 2019, revealing a primary hydrodynamic pattern. To complement the observed trajectories, an unstructured-grid-based particle-tracking model was implemented for the Bohai Sea to delineate the riverine particle transport dynamics during ice-free months (April to November) in 2019. The Lagrangian particle trajectories from riverine substances showed distinct spatial and temporal characteristics. Particles from the Yellow River reached the Central Basin in July, while those from the Hai and Liao Rivers remained localized. Particles from the Luan River travelled to the Central Basin and Bohai Bay regions. Winds significantly alter the spatial scales of particle-influenced area: southerly winds transport particles offshore from the Yellow River, northerly winds move particles from the Hai and Liao Rivers, and both southerly and westerly winds aid in moving particles offshore from the Luan River. While river discharge influences the size of these area, their overall spatial distribution patterns remained mostly consistent regardless of the presence or absence of river discharge. Moreover, momentum analysis confirmed that wind-induced Ekman transport strengthens the coastal-shelf connection, dispersing riverine substances from the Yellow and Luan Rivers away from the coast. In contrast, horizontal advection and the dominance of viscous force override Ekman transport, reducing the coastal-shelf connection in the Bohai and Liaodong Bays.

Near-Wall Flow Features In ZPG-TBL At Various Reynolds Numbers Using Dense 3D Lagrangian Particle Tracking

The 3D Lagrangian particle tracking method Shake-The-Box (STB) and, subsequently, the data assimilation method FlowFit3 have been applied to measure the flow field in a narrow wall-parallel volume inside the nearwall region of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) flow at various Reynolds numbers. The STB experiments have been conducted in the 1m- wind tunnel facility of DLR in Göttingen at relatively high particle image densities (~0.07 ppp) using µm-sized DEHS particles and high-repetition pulse laser at up to 38.1 kHz. The results show that the chosen methodology is able to volumetrically resolve almost all features of the flow inside the viscous sub-, buffer- and lower logarithmic- layer in space and time at Reynolds numbers up to Re θ = 5,455. The gained data consists of time-series of spatially well resolved 3D velocity, acceleration and pressure fields, as well as a huge amount of long Lagrangian particle trajectories. Selecting the viscous sublayer part of the measurement volume provides time-series of the 2D distribution of both components of the instantaneous wall-shear stresses w,x/z . The resulting data are used for conditional and time-resolved 3D analyses of coherent structures, rare (e.g. back flow) events and two-point space-timecorrelations.

Confinement-induced drift in Marangoni-driven transport of surfactant: a Lagrangian perspective

Successive drops of coloured ink mixed with surfactant are deposited onto a thin film of water to create marbling patterns in the Japanese art technique of Suminagashi. To understand the physics behind this and other applications where surfactant transports adsorbed passive matter at gas–liquid interfaces, we investigate the Lagrangian trajectories of material particles on the surface of a thin film of a confined viscous liquid under Marangoni-driven spreading by an insoluble surfactant. We study a model problem in which several deposits of exogenous surfactant simultaneously spread on a bounded rectangular surface containing a pre-existing endogenous surfactant. We derive Eulerian and Lagrangian formulations of the equations governing the Marangoni-driven surface flow. Both descriptions show how confinement can induce drift and flow reversal during spreading. The Lagrangian formulation captures trajectories without the need to calculate surfactant concentrations; however, concentrations can still be inferred from the Jacobian of the map from initial to current particle position. We explore a link between thin-film surfactant dynamics and optimal transport theory to find the approximate equilibrium locations of material particles for any given initial condition by solving a Monge–Ampère equation. We find that as the endogenous surfactant concentration $\delta$ vanishes, the equilibrium shapes of deposits using the Monge–Ampère approximation approach polygons with corners curving in a self-similar manner over lengths scaling as $\delta ^{1/2}$ . We explore how Suminagashi patterns may be produced by using computationally efficient successive solutions of the Monge–Ampère equation.

Case Study of Contaminant Transport Using Lagrangian Particle Tracking Model in a Macro-Tidal Estuary

This study presents a comprehensive analysis of contaminant transport in estuarine environments, focusing on the impact of tidal creeks and flats. The research employs advanced hydrodynamic models with irregular grid systems and conducts a detailed residual current analysis to explore how these physical features influence the movement and dispersion of contaminants. The methodology involves simulating residual currents and Lagrangian particle trajectories in both ‘Creek’ and ‘No Creek’ cases, under varying tidal conditions. The results indicate that tidal creeks significantly affect particle retention and transport, with notable differences observed in the dispersion patterns between the two scenarios. The ‘Creek’ case demonstrates enhanced material retention along the creek pathways, while the ‘No Creek’ case shows broader dispersion, potentially leading to increased sedimentation in open sea areas. The discussion highlights the implications of these findings for sediment dynamics, contaminant transport, and estuarine ecology, emphasizing the role of tidal creeks in modulating flow and material transport. The research underlines the necessity of incorporating detailed environmental features in estuarine models for accurate contaminant transport prediction and effective estuarine management. This study contributes to a deeper understanding of estuarine hydrodynamics and offers valuable insights for environmental policy and management in coastal regions.

A Direct Infection Risk Model for CFD Predictions and Its Application to SARS-CoV-2 Aircraft Cabin Transmission

Current models to determine the risk of airborne disease infection are typically based on a backward quantification of observed infections, leading to uncertainties, e.g., due to the lack of knowledge whether the index person was a superspreader. In contrast, the present work presents a forward infection risk model that calculates the inhaled dose of infectious virus based on the virus emission rate of an emitter and a prediction of Lagrangian particle trajectories using CFD, taking both the residence time of individual particles and the biodegradation rate into account. The estimation of the dose-response is then based on data from human challenge studies. Considering the available data for SARS-CoV-2 from the literature, it is shown that the model can be used to estimate the risk of infection with SARS-CoV-2 in the cabin of a Do728 single-aisle aircraft. However, the virus emission rate during normal breathing varies between different studies and also by about two orders of magnitude within one and the same study. A sensitivity analysis shows that the uncertainty in the input parameters leads to uncertainty in the prediction of the infection risk, which is between 0 and 12 infections among 70 passengers. This highlights the importance and challenges in terms of superspreaders for risk prediction, which are difficult to capture using standard backward calculations. Further, biological inactivation was found to have no significant impact on the risk of infection for SARS-CoV-2 in the considered aircraft cabin.

Characteristics and mechanism of spray deviation of ethanol and its blended fuel in multi-hole spray

Research on renewable fuels is crucial to render engines compliant with energy and environmental efficiency, and alcohol fuels have become hotspots in the field of modern gasoline direct injection engines. This study aims to elucidate the effects of ethanol addition on spray deviation under non-flash and flashing conditions. Macroscopic characteristics and microscopic characteristics can be obtained from Diffused Back Illumination and Phase Doppler Anemometry. The influential factors accounting for the spray deviation were examined, and internal flow simulations were also performed to obtain in-nozzle flow information. The angled momentum induced by the short L/D ratio leaves space for ambient gas ingestion into the counterbore under non-flash conditions. The entrained gas was affected by cavitation intensities, leading to the spray deviation, which was tracked by the Lagrangian particle trajectory method. The spray deviation is also affected by the formation of the low-pressure zone and droplets' migration. The higher surface tension and lower molecular weight of ethanol facilitate the spray expansion, forming the liquid barrier to draw the spray moving toward the injector center. Ethanol's high latent heat of evaporation inhibits the further reduction in droplets' radius, resulting in a persistent decrease in the relative span factor. On the other hand, the high latent heat of evaporation leads to a larger pressure drop induced by the vapor condensation, accounting for the “more powerful” abilities in drawing droplets into the jet center. The trade-off between the droplets' size and migration ability should be achieved to efficiently modulate spray deviation.

An ocean–wave–trajectory forecasting system for the eastern Baltic Sea: Validation against drifting buoys and implementation for oil spill modeling

We present the implementation and validation of OpenDrift, an open-source Lagrangian particle trajectory modeling framework for oil spill modeling in the coastal waters of Estonia in the Baltic Sea. The framework was coupled with ECMWF winds, NEMO-EST05 hydrodynamical model, and SWAN-EST wave model, and validated using six drift experiments from 2022. The sensitivity analysis revealed the importance of incorporating additional forcing factors, such as Stokes drift and currents, which generally improved the accuracy of the trajectory model compared to using wind alone. Nevertheless, the benefits of providing OpenDrift with, for example, the Stokes drift seemed to depend on whether currents are also included or not. The wind drift factors of the utilized drifters align closely with those commonly employed in oil spill modeling. Furthermore, the modeling results for hypothetical oil spills in severe weather conditions and high-risk regions emphasize the critical need for preparedness and rapid response strategies.

Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh–Bénard convection

We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh–Bénard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Second, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.

A kind of Lagrangian chaotic property of the Arnold–Beltrami–Childress flow

Three-dimensional steady-state Arnold–Beltrami–Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier–Stokes (NS) equations with an external force per unit mass. It is well known that, although trajectories of a chaotic system have sensitive dependence on initial conditions, i.e. the famous ‘butterfly effect’, their statistical properties are often insensitive to small disturbances. This kind of chaos (such as governed by the Lorenz equations) is called normal-chaos. However, a new concept, i.e. ultra-chaos, has been reported recently, whose statistics are unstable to tiny disturbances. Thus, ultra-chaos represents higher disorder than normal chaos. In this paper, we illustrate that ultra-chaos widely exists in Lagrangian trajectories of fluid particles in steady-state ABC flow. Moreover, solving the NS equation when $Re=50$ with the ABC flow plus a very small disturbance as the initial condition, it is found that trajectories of nearly all fluid particles become ultra-chaotic when the transition from laminar to turbulence occurs. These numerical experiments and facts highly suggest that ultra-chaos should have a relationship with turbulence. This paper identifies differences between ultra-chaos and sensitivity of statistics to parameters. Possible relationships between ultra-chaos and the Poincaré section, ultra-chaos and ergodicity/non-ergodicity, etc., are discussed. The concept of ultra-chaos opens a new perspective of chaos, the Poincaré section, ergodicity/non-ergodicity, turbulence and their inter-relationships.

Evaluation of the distribution of COVID-19 particles in an Isolation room to reduce the possibility of transmission via CFD simulation

The outbreak and prolonged COVID-19 pandemic has caused a population decline as well as a profound impact on the global economy, the COVID virus spreads highly in the air through the process of sneezing, contact leads to many dangers to the health and safety of people around the world. Many simulation studies have been carried out to predict the risk of spread, as well as to find solutions to limit the infection when spreading sneeze droplets in the air. In this study, the motion and distribution of droplets containing coronaviruses emitted by coughing or sneezing in the isolation room at Ho Chi Minh City, Vietnam National University were investigated using ANSYS Fluent software. The airflow in the isolation room was simulated by a 3D turbulence model and energy equation using the finite volume method (FVM) with a domain of isolation room solved for appropriate boundary conditions. The effect of ventilation airflow speed and the size of droplets on the distribution of particles in the air were investigated by the Lagrangian particle trajectory analysis method. The CFD analysis result showed that the velocity distribution, turbulent kinetic energy, and flow dynamics had strongly affected the reducing rate of average droplet concentration in the isolation room. Specifically, the study focused on the dispersion of liquid droplets containing the virus under fixed operating conditions of ventilation systems and exhaust fans, with a flow rate of 840 m3/h. Under these conditions, the retention time of liquid droplets was determined to be 37.5 seconds, corresponding to droplet diameters ranging from 5 to 100 micrometres. The results indicate that the presence of particles in the room gradually becomes diluted over time due to the continuous circulation of air. The ability of air to diffuse within the vicinity of the occupant's position and the limited spread of small particles within the room demonstrate that the operating conditions are suitable.

Effects of spalled particles thermal degradation on a hypersonic flow field environment

The presence of spalled particles might affect the flow field and the material, thereby influencing the aerodynamic heating rates of the thermal protection system. In order to study the impact of particles on the flowfield, a two-way coupling is performed between a Lagrangian particle trajectory model and a hypersonic aerothermodynamics flow solver. Time-accurate solutions are computed for argon and air flowfields. Single-particle and multiple-particle simulations are performed and results are studied. The studies in the argon environment indicated that the particles start sublimating soon after they cross the shock and keep sublimating during the remainder of their time in the flow. In the air environment, the particles start releasing carbon vapor soon after their ejection, and the magnitudes of different carbon products vary based on the particle’s location relative to the shock. Similar behavior is observed for multiple-particle simulations but with an increase in the amount of released carbon vapor that diffuses and convects over a larger area. A single-particle simulation is also run by adding additional gas phase reactions, and it is found that the production rate of certain carbon products (C1 and CN) increases. A parametric study is conducted based on parameters that affect the motion of the particles. The results of the comprehensive study show that the carbon vapor released by spalled particles tends to change the composition of the flow field, particularly the upstream region of the shock, which affects the heat flux incident on the test sample.

Modelling the transport of sloughed cladophora in the nearshore zone of Lake Michigan

The invasion of dreissenid mussels has profoundly altered benthic physical environments and whole-lake nutrient cycling in the Great Lakes over the past several decades. The resurgence of the filamentous green alga Cladophora appears to be one of the consequences of this invasion. Sloughed Cladophora deteriorates water quality, fouls recreational beaches, and may contribute to outbreaks of avian botulism, which have been especially severe in the Sleeping Bear Dunes National Lakeshore (SLBE) region of Lake Michigan. To help determine the fate of sloughed Cladophora, a Lagrangian particle trajectory model was developed to track the transport of Cladophora fragments in the nearshore zone based upon a physical transport-mixing model. The model results demonstrate that the primary deposition sites of sloughed Cladophora within the SLBE region are mid-depth sites not far away from their initial growth area. Because of high algae production in the nearshore waters and limited exchange between the inner and outer bay, the shoreline beach of Platte Bay appears to be particularly vulnerable to fouling, with overall three times as many accumulated particles as those along the Sleeping Bear Bay and Good Harbor Bay. The results of this model may be used to guide regional environmental management initiatives and provide insights into the mechanisms responsible for avian botulism outbreaks. This model may also inform the development of whole-lake ecosystem models that account for nearshore-offshore interactions.

Eulerian-Lagrangian Modelling of Turbulent Two-Phase Particle-Liquid Flow in a Stirred Vessel: CFD and Experiments Compared

A 3D Eulerian-Lagrangian CFD model is set up to simulate the turbulent flow and mixing of coarse dense particles in a standard batch vessel, mechanically agitated by a down-pumping pitched-blade turbine. Flow is investigated in the just-suspended regime and regimes much above. All simulations are fully and successfully validated by experimental Lagrangian measurements provided by positron emission particle tracking. Predicted distributions of the local 3D phase-velocity components, local particle slip velocities and local particle concentration show very good agreement with experiment. Lagrangian particle trajectories are exploited to infer detailed accurate information on particle circulation time and local residence time. The predicted two-phase flow number is in excellent agreement with experimental values under all flow regimes. Being accurate and robust, the numerical model can be extended to study even more complex particle-liquid suspensions of industrial relevance, and to provide much needed Lagrangian data to other data-driven modelling techniques.

Statistical Properties of Lagrangian Trajectories of Small Particles in Superfluid $$^4$$He

Statistical Properties of Lagrangian Trajectories of Small Particles in Superfluid $$^4$$He

Tomographic X-ray particle tracking velocimetry

We investigate the feasibility of in-laboratory tomographic X-ray particle tracking velocimetry (TXPTV) and consider creeping flows with nearly density matched flow tracers. Specifically, in these proof-of-concept experiments we examined a Poiseuille flow, flow through porous media and a multiphase flow with a Taylor bubble. For a full 360^circ computed tomography (CT) scan we show that the specially selected 60 micron tracer particles could be imaged in less than 3 seconds with a signal-to-noise ratio between the tracers and the fluid of 2.5, sufficient to achieve proper volumetric segmentation at each time step. In the pipe flow, continuous Lagrangian particle trajectories were obtained, after which all the standard techniques used for PTV or PIV (taken at visible wave lengths) could also be employed for TXPTV data. And, with TXPTV we can examine flows inaccessible with visible wave lengths due to opaque media or numerous refractive interfaces. In the case of opaque porous media we were able to observe material accumulation and pore clogging, and for flow with Taylor bubble we can trace the particles and hence obtain velocities in the liquid film between the wall and bubble, with thickness of liquid film itself also simultaneously obtained from the volumetric reconstruction after segmentation. While improvements in scan speed are anticipated due to continuing improvements in CT system components, we show that for the flows examined even the presently available CT systems could yield quantitative flow data with the primary limitation being the quality of available flow tracers.Graphic abstract

Dense Water Formation on the Icelandic Shelf and Its Contribution to the North Icelandic Jet

AbstractThe North Icelandic Jet (NIJ) is the densest component of the Denmark Strait Overflow Water, feeding the abyssal limb of the Atlantic Meridional Overturning Circulation. Here, by using observational and numerical model data, we explore the formation of overflow water on the Icelandic shelf, the mechanisms involved, and its potential contribution to the NIJ. The sparse observational data on the western Icelandic shelf for the month of February shows top‐to‐bottom mixing on the shelf, distinct and well separated from the dense water offshore, with densities larger than 27.8 kg/m3 in some years. Using a 1‐D mixing model and winter heat flux reanalysis, we suggest that waters with densities exceeding 27.8 kg/m3 are likely to be formed on the shelf in most years by the end of winter. High‐resolution numerical model data shows that the transformation of the Atlantic inflow along the northwest Icelandic shelf generates a dense plume whose waters feed into the NIJ. The bulk of the plume cascades down‐slope north of Iceland, funneled through deep cross‐shelf troughs, with some cascading occurring west of Iceland as well. During years of strong cascading events (2008, 2013, and 2016), the modeled dense plume potentially feeds up to 21% of the NIJ transport at the Siglunes and Kögur sections. Back‐tracked Lagrangian particle trajectories confirm that the western Icelandic shelf is a source of the NIJ. The dense plume transport and variability are found to be dependent on the total oceanic heat loss west of Iceland and along Denmark Strait.

COVID-19 spread in a classroom equipped with partition – A CFD approach

In this study, the motion and distribution of droplets containing coronaviruses emitted by coughing of an infected person in front of a classroom (e.g., a teacher) were investigated using CFD. A 3D turbulence model was used to simulate the airflow in the classroom, and a Lagrangian particle trajectory analysis method was used to track the droplets. The numerical model was validated and was used to study the effects of ventilation airflow speeds of 3, 5, and 7 m/s on the dispersion of droplets of different sizes. In particular, the effect of installing transparent barriers in front of the seats on reducing the average droplet concentration was examined. The results showed that using the seat partitions for individuals can prevent the infection to a certain extent. An increase in the ventilation air velocity increased the droplets’ velocities in the airflow direction, simultaneously reducing the trapping time of the droplets by solid barriers. As expected, in the absence of partitions, the closest seats to the infected person had the highest average droplet concentration (3.80 × 10−8 kg/m3 for the case of 3 m/s).

Validation of Novel Lattice Boltzmann Large Eddy Simulations (LB LES) for Equipment Characterization in Biopharma

Detailed process and equipment knowledge is crucial for the successful production of biopharmaceuticals. An essential part is the characterization of equipment for which Computational Fluid Dynamics (CFD) is an important tool. While the steady, Reynolds-averaged Navier–Stokes (RANS) k − ε approach has been extensively reviewed in the literature and may be used for fast equipment characterization in terms of power number determination, transient schemes have to be further investigated and validated to gain more detailed insights into flow patterns because they are the method of choice for mixing time simulations. Due to the availability of commercial solvers, such as M-Star CFD, Lattice Boltzmann simulations have recently become popular in the industry, as they are easy to set up and require relatively low computing power. However, extensive validation studies for transient Lattice Boltzmann Large Eddy Simulations (LB LES) are still missing. In this study, transient LB LES were applied to simulate a 3 L bioreactor system. The results were compared to novel 4D particle tracking (4D PTV) experiments, which resolve the motion of thousands of passive tracer particles on their journey through the bioreactor. Steady simulations for the determination of the power number followed a structured workflow, including grid studies and rotating reference frame volume studies, resulting in high prediction accuracy with less than 11% deviation, compared to experimental data. Likewise, deviations for the transient simulations were less than 10% after computational demand was reduced as a result of prior grid studies. The time averaged flow fields from LB LES were in good accordance with the novel 4D PTV data. Moreover, 4D PTV data enabled the validation of transient flow structures by analyzing Lagrangian particle trajectories. This enables a more detailed determination of mixing times and mass transfer as well as local exposure times of local velocity and shear stress peaks. For the purpose of standardization of common industry CFD models, steady RANS simulations for the 3 L vessel were included in this study as well.

Oceanic Pathways of an Active Pacific Meridional Overturning Circulation (PMOC)

AbstractIn contrast to the modern‐day climate, North Pacific deep water formation and a Pacific meridional overturning circulation (PMOC) may have been active during past climate conditions, in particular during the Pliocene epoch (some 3–5 million years ago). Here, we use a climate model simulation with a robust PMOC cell to investigate the pathways of the North Pacific deep water from subduction to upwelling, as revealed by Lagrangian particle trajectories. We find that similar to the present‐day Atlantic Meridional Overturning Circulation (AMOC), most subducted North Pacific deep water upwells in the Southern Ocean. However, roughly 15% upwells in the tropical Indo‐Pacific Oceans instead—a key feature distinguishing the PMOC from the AMOC. The connection to the Indian Ocean is relatively fast, at about 250 years. The connection to the tropical Pacific is slower (∼800 years) as water first travels to the subtropical South Pacific then gradually upwells through the thermocline.

Submesoscale Mixing Across the Mixed Layer in the Gulf of Mexico

Submesoscale circulations influence momentum, buoyancy and transport of biological tracers and pollutants within the upper turbulent layer. How much and how far into the water column this influence extends remain open questions in most of the global ocean. This work evaluates the behavior of neutrally buoyant particles advected in simulations of the northern Gulf of Mexico by analyzing the trajectories of Lagrangian particles released multiple times at the ocean surface and below the mixed layer. The relative role of meso- and submesoscale dynamics is quantified by comparing results in submesoscale permitting and mesoscale resolving simulations. Submesoscale circulations are responsible for greater vertical transport across fixed depth ranges and also across the mixed layer, both into it and away from it, in all seasons. The significance of the submesoscale-induced transport, however, is far greater in winter. In this season, a kernel density estimation and a detailed vertical mixing analysis are performed. It is found that in the large mesoscale Loop Current eddy, upwelling into the mixed layer is the major contributor to the vertical fluxes, despite its clockwise circulation. This is opposite to the behavior simulated in the mesoscale resolving case. In the “submesoscale soup,” away from the large mesoscale structures such as the Loop Current and its detached eddies, upwelling into the mixed layer is distributed more uniformly than downwelling motions from the surface across the base of the mixed layer. Maps of vertical diffusivity indicate that there is an order of magnitude difference among simulations. In the submesoscale permitting case values are distributed around 10–3 m2 s–1 in the upper water column in winter, in agreement with recent indirect estimates off the Chilean coast. Diffusivities are greater in the eastern portion of the Gulf, where the submesoscale circulations are more intense due to sustained density gradients supplied by the warmer and saltier Loop Current.