Lagrangian Simulations Research Articles

On the interplay between pressure and gravitational forces in coalescing filters

This paper provides insights into processes governing oil–mist filtration in coalescing filters. In particular, it resolves an apparent inconsistency between different published studies regarding the occurrence (or not) of internal gravity-induced flows. As a result of this, it also clarifies whether in industrially-relevant scenarios such as those pertaining to vertical filter cartridges, non-homogeneous vertical saturation patterns are triggered by these internal flows or are just a result of different oil loading rates. To address these issues, we use Eulerian–Lagrangian CFD simulations, which properly account for the effects of turbulent diffusion of liquid aerosol particles, to replicate an experimental setup available in the literature. In order to interpret results data, we introduce a new dimensionless number, termed SM, defined as the ratio between pressure gradient and gravitational forces, which provides a bulk characterization of the flow and allows to assess whether internal gravity-induced flows, in a given cartridge–oil system, should be expected or not. We show that SM explains well the few experimental data available in the literature and identifies specific behaviors associated with limiting SM values being either very large or close to 1.

Simulating Lagrangian Subgrid-Scale Dispersion on Neutral Surfaces in the Ocean.

To capture the effects of mesoscale turbulent eddies, coarse‐resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper‐accelerations. These parameterizations are referred to as the first, second and third order “Markov models” (Markov‐N), respectively. Most previous studies investigate these parameterizations in two‐dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov‐0) dispersion. Here, we present a three‐dimensional isoneutral formulation of the Markov‐1 model. We also implement an anisotropic, shear‐dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov‐1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov‐1 produce similar particle distributions over time when using our ocean model output, Markov‐1 yields Lagrangian trajectories that better resemble trajectories from eddy‐resolving simulations. Markov‐1 also yields a smaller spurious dianeutral flux.

Total Lagrangian Material Point Method simulation of the scratching of high purity coppers

In many industries, e.g., mining and agricultural industry, minerals handling, wear in machine elements causes functional surfaces to degrade, eventually leading to material failure or loss of functionality. To understand the abrasive wear resistance of materials scratch tests are sometimes conducted. However, the amount of information that can be obtained from well-defined scratch tests is limited due to the coupling of different physical processes, with a complex stress state. This paper presents a study of the Total Lagrangian Material Point Method (TLMPM) for the simulation of scratch tests. To this end we simulate the scratch of high purity coppers and compare with existing smooth particle hydrodynamics results and experiments. The results show that the TLMPM is stable for any indentation loads considered in the experiments and the results are in excellent agreement with experiments when friction is considered. Moreover, the results show the presence of oscillations in the groove profile at high loads, with and without friction. We show that the origin of these oscillations is linked to both the plastic strain and work hardening rates.

Optimal Time Step Length for Lagrangian Interacting-Particle Simulations of Diffusive Mixing

Optimal Time Step Length for Lagrangian Interacting-Particle Simulations of Diffusive Mixing

Arctic cod (Boreogadus saida) hatching in the Hudson Bay system

Buoyant Arctic cod (Boreogadus saida) eggs are found at the surface or at the ice-water interface in winter. While winter temperatures in saline waters fall below 0°C, the temperature in areas affected by under-ice river plumes is slightly higher. Under-ice river plumes may therefore provide thermal refuges favoring the survival of the vulnerable early life stages of Arctic cod. Thermal refuges would allow early hatchers to survive, benefit from a long growing period, and add to the number of individuals recruiting to the adult population: These expectations define the freshwater winter refuge hypothesis. More than 42 rivers drain into Hudson Bay making it particularly well suited to test this hypothesis. Whereas the bulk of Arctic cod observed in Hudson Bay hatch between mid-April and June, some larvae hatch as early as January. We used two independent but complementary methods to test the hypothesis: (1) Lagrangian model simulations that traced back the planktonic trajectories of the sampled larvae and (2) measurements of the concentration of strontium-88 in the otolith cores. Throughout the Hudson Bay system, Lagrangian simulations revealed that early hatchers were more likely to hatch in lower surface salinities and that larvae reaching larger prewinter lengths were likely to have hatched near or within estuaries. Analysis of otolith microchemistry showed that larvae with low strontium-88 concentration in the otolith core, indicating a low salinity hatch location, had hatched earlier and thus had a longer growth period before freeze-up. These results show the potential for Arctic cod persistence in the Arctic where freshwater input is projected to increase and the ice regime is predicted to become more seasonal, provided that the surface temperatures remain below embryonic and larval lethal limits.

Lagrangian Numerical Simulation of Proppant Transport in Channel Fracturing

Lagrangian Numerical Simulation of Proppant Transport in Channel Fracturing

Graupel Precipitating From Thin Arctic Clouds With Liquid Water Paths Less Than 50 g m−2

AbstractRimed precipitation growth can efficiently remove moisture and aerosols from the boundary layer, yet thin low‐level Arctic mixed‐phase clouds are generally thought to precipitate pristine and aggregated ice crystals. Here we present automated surface photographic measurements showing that only 34% of precipitation particles exhibit negligible riming and that graupel particles in diameter commonly fall from clouds with liquid water paths less than 50 g m−2. Analyses indicate that significant riming enhancement can occur provided sustained updrafts of 0.4 m s−1, consistent with those measured in Arctic clouds. A Lagrangian numerical simulation that tracks falling particles suggests that similar updraft speeds can account for about one half of the observed riming enhancement. Riming enhancement appears particularly likely when weak temperature inversions are observed at cloud top, but a full explanation remains to be determined.

The Corrected Distortion model for Lagrangian spray simulation of transcritical fuel injection

In this work, we present a detailed implementation and validation of the droplet modeling framework proposed by Dahms and Oefelein (2016) into the engine commercial CFD software CONVERGE using the User Defined Function (UDF) interface. The model accounts for the nonlinear deformation and oscillation experienced by liquid spray droplet injected into high pressure and temperature. Lagrangian spray simulations of Engine Combustion Network (ECN) Spray A are performed. Model validation against standard experimental measurements of liquid velocity, vapor mixture fraction is conducted. To perform more rigorous model validation, new experimental measurements based on Diffused Back Illumination (DBI) are introduced. The new measurements are processed for Projected Liquid Volume (PLV), which offers as close as possible one-to-one model validation for liquid penetration while offering new insights into the spray physics. Comparison with a One-D model based on adiabatic mixing theory by Siebers (1999) and Desantes et al. (2007) are also conducted. Through these model validation exercises, it is shown that the new framework improves liquid-phase penetration predictions, following a tendency for enhanced evaporation, compared to the standard approach for both Reynolds Average Navier Stokes (RANS) and Large Eddy Simulation (LES). At the liquid length, maximum mixture fraction values predicted by the new approach are in good agreement those of an adiabatic mixing model. Qualitative analysis of the spray behaviors during the early stage of the injection process reveals that the proposed framework predicts significant increase in droplet evaporation rate with lower drop drag compared to the current standard approach.

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

The accuracy of coarse-grained Euler–Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved subgrid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macroscale markers using fine-grid Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) simulations. The traditional nonlinear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen–Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R2 values. The utilization of the gas inlet velocity as an additional macroscale marker reduced the errors by up to 55.3% in the tested cases.

Realism of Lagrangian Large Eddy Simulations Driven by Reanalysis Meteorology: Tracking a Pocket of Open Cells Under a Biomass Burning Aerosol Layer.

An approach to drive Lagrangian large eddy simulation (LES) of boundary layer clouds with reanalysis data is presented and evaluated using satellite (Spinning Enhanced Visible and Infrared Imager, SEVIRI) and aircraft (Cloud‐Aerosol‐Radiation Interactions and Forcing, CLARIFY) measurements. The simulations follow trajectories of the boundary layer flow. They track the formation and evolution of a pocket of open cells (POC) underneath a biomass burning aerosol layer in the free troposphere. The simulations reproduce the evolution of observed stratocumulus cloud morphology, cloud optical depth, and cloud drop effective radius, and capture the timing of the cloud state transition from closed to open cells seen in the satellite imagery on the three considered trajectories. They reproduce a biomass burning aerosol layer identified by the in‐situ aircraft measurements above the inversion of the POC. Entrainment of aerosol from the biomass burning layer into the POC is limited to the extent of having no impact on cloud‐ or boundary layer properties, in agreement with the CLARIFY observations. The two‐moment bin microphysics scheme used in the simulations reproduces the in‐situ cloud microphysical properties reasonably well. A two‐moment bulk microphysics scheme reproduces the satellite observations in the non‐precipitating closed‐cell state, but overestimates liquid water path and cloud optical depth in the precipitating open‐cell state due to insufficient surface precipitation. A boundary layer cold and dry bias occurring in LES can be counteracted by reducing the grid aspect ratio and by tightening the large scale wind speed nudging towards the surface.

POD-based identification approach for powder mixing mechanism in Eulerian–Lagrangian simulations

Numerous products are manufactured through powder mixing. Understanding the mixing mechanism is essential to improve product quality. Convection, diffusion, and shear are well-known classifications in the powder mixing mechanism. During powder mixing, plural mixing mechanisms may occur simultaneously. In this study, to identify the main mixing mechanisms and investigate the transition of the main mixing mechanisms, an advanced identification technique is developed by incorporating the proper orthogonal decomposition (POD) method into numerical modeling for powder mixing. The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is employed to simulate powder mixing. Several investigations are performed to show the adequacy of the developed technique. First, numerous CFD–DEM simulations for solid–liquid flows are performed in a rotating paddle mixer. Next, an efficient Lanczos-based POD (LPOD) method is proposed to characterize the main features of powder mixing via the POD analysis. The results show that the mixing mechanism is dominated by convection in the early stage and by diffusion in the late stage. Besides, a novel mixing identification technique is established by giving the relation between POD modes and mixing mechanisms, namely, clumped and random spatial distributions of the POD modes appear in convective and diffusive mixing, respectively. Consequently, it is shown that combining the CFD–DEM simulation with the LPOD method is effective to identify the main mixing mechanism and to explain the time transition of mixing mechanisms between convective and diffusive mixing.

Mixing in the NETmix Reactor

NETmix is a static mixing reactor composed of a network of mixing chambers interconnected by channels. The repetitive mixing pattern inside the reactor enables the use of reduced geometries to represent the NETmix network, such as the ExtendedNUB model, used in this work. Mixing in NETmix is based on the impingement of jets, issuing from channels. Inside the chambers, the jets are engulfed by dynamic vortices which can be quantified using Lagrangian techniques. Batch Lagrangian Mixing Simulation (BLMS) is based on successive injections of particles to measure the fraction of the fluids at the outlet of the mixing chambers. The distribution of the outlet fraction of particles indicates that it is possible to have nearly perfect mixing inside the NETmix chambers, depending on the dimensions of the channels and chambers. The NETmix design is here optimized in relation to the chamber diameter to channel width ratio, D/d. Results from BLMS show that best performance in NETmix occurs for 6.65≤D/d≤6.85.

An GPU-accelerated particle tracking method for Eulerian–Lagrangian simulations using hardware ray tracing cores

To address the high computational cost of particle tracking for realistic Eulerian–Lagrangian simulations, a novel efficient and robust particle tracking method (RT method) for unstructured meshes is presented. The method, for the first time, leverages both hardware ray tracing (RT) cores and GPU parallel computing technology to accelerate Eulerian–Lagrangian simulations. The method includes a hardware-accelerated hosting cell locator using bounding volume hierarchy tree (BVH) and a robust treatment of particle-wall interaction (multiple specular reflection) using an improved neighbor searching approach. The method is implemented in a GPU-accelerated open-source code, which is verified against a reference neighbor-searching particle-tracking method (NS method) and experimental observations. To evaluate the performance of our method, several numerical simulations of fluid-driven scalar transport problem are solved. Using a verification case, we show that the particle distribution simulated by our code is in a good agreement with an experimental observation. Tracking failures and stuck particles are not observed in any simulations. Benchmark results indicate that our RT method leads to a roughly 1.8−2.0× performance improvement compared to the reference NS method for large-scale simulations (millions of mesh cells and particles).

Application of various ice accretion simulation approaches in the LOGOS software package

This paper presents results of the ice accretion simulations by the techniques implemented in the LOGOS-Aero module of the LOGOS software package. The results of the Eulerian and the Lagrangian ice accretion simulations are reported for NACA verification problems, which are used to test the software package Lewice. The approaches implemented in the LOGOS-Aero enable simulations of the aircraft icing conditions and the predictions of the shapes and locations of ice deposits on computational models.

Propagation of Mouth-Generated Aerosols in a Modularly Constructed Hospital Room

Modular construction methods have been widely used in the civil engineering industry due to ease of assembly, the convenience of design, and allowing for flexibility in placement while making the construction more sustainable. With the increasing number of COVID-19 cases, the capacity of the hospital is decreasing as more intensive care units (ICU) are allocated to COVID-19 cases. This limited capacity can be addressed by using modular construction to provide field hospitals. This paper adopts transient Lagrangian computational fluid dynamics simulations to investigate the importance of having an appropriate ventilation system in place to ensure sustainable infection control against airborne viruses and pathogens within a modular room. The performance of having a ventilation system using 10, 20, and 40 air changes per hour (ACH) was examined. In addition, different room configurations were also compared to provide useful guidelines for air conditioning units placement. It was determined that as the ACH rate increases while maintaining a direct flow field between the inlet and outlet, the rate of aerosol removal increases. Furthermore, the flowfield in which can be controlled by the placement of the inlet and outlet can impact the removal of aerosols, as it dictates how far the droplets travel before being removed from the enclosure.

Advective pathways and transit times of the Red Sea Overflow Water in the Arabian Sea from Lagrangian simulations

The present study investigates the advective pathways and transit times of virtual particles released in the Red Sea outflow area as a proxy for the poorly understood spreading of the Red Sea Overflow Water (RSOW) in the Arabian Sea. This work uses the Parcels toolbox, a Lagrangian framework, to simulate tens of thousands of trajectories under different initial conditions. Six different Lagrangian simulations are performed at isobaric and isopycnal surfaces within the RSOW layer. All simulations are based on the eddy-rich GLORYS12 reanalysis that merges almost all in-situ (temperature–salinity) and satellite observations collected over the last two decades into a dynamical framework. This study shows that GLORYS12 reproduces relatively well the climatological seasonal cycle of the RSOW to the Gulf of Aden and essential characteristics of the exchange at the Strait of Bab al-Mandab. Statistical comparisons between synthetic trajectories and RAFOS floats in the Gulf of Aden corroborate the quality of GLORYS12 velocity fields used for the Lagrangian simulations. Six main advective pathways are uncovered (by order of preference): Southwest, Northwest, Socotra Passage, Central, Eastern, and Southern. Trajectories from Argo floats give observational support for some of these paths. Although most particles are exported out of the Arabian Sea off Somalia, the simulations reveal robust connectivity of the RSOW to the Arabian Sea interior and its eastern boundary. The fact that particles have long trajectories in the interior increases the potential of RSOW mixing with the fresher and oxygen-poor ambient waters. Thus, these pathways may have profound implications for the salt and oxygen budgets in the Arabian Sea and beyond since the RSOW is also part of the global overturning circulation and exported out of the Indian Ocean via the Agulhas Current. Transit time distributions indicate that it takes about six months for outflow-originated particles to spread over the entire Gulf of Aden and one to three years to be exported along the western boundary, toward Somalia (Socotra Passage and Southwest pathways) and off the Yemeni–Omani coast (Northwest Pathway). In contrast, reaching the eastern boundary takes much longer. North of 14°N, the most frequent time is around 10–15 years, and about 20–25 years at the southeastern Arabian Sea. Hence, the RSOW can often carry oxygen to the western boundary but not to the eastern basin. This may contribute to the eastern shift of the Arabian Sea Oxygen Minimum Zone, a subject that deserves investigation.

A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions

Kernel smoothers are often used in Lagrangian particle dispersion simulations to estimate the concentration distribution of tracer gasses, pollutants etc. Their main disadvantage is that they suffer from the curse of dimensionality, i.e., they converge at a rate of 4/(d+4) with d the number of dimensions. Under the assumption of horizontally homogeneous meteorological conditions, we present a kernel density estimator that estimates a 3D concentration field with the faster convergence rate of a 1D kernel smoother, i.e., 4/5. This density estimator has been derived from the Langevin equation using path integral theory and simply consists of the product between a Gaussian kernel and a 1D kernel smoother. Its numerical convergence rate and efficiency are compared with that of a 3D kernel smoother. The convergence study shows that the path integral-based estimator has a superior convergence rate with efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Horizontally homogeneous meteorological conditions are often assumed in near-field range dispersion studies. Therefore, we illustrate the performance of our method by simulating experiments from the Project Prairie Grass data set.

Considerations for the modeling of the laser ablation region of ICF targets with Lagrangian simulations

Recently, much effort has been dedicated to the improvement of models and modeling choices utilized in radiation hydrodynamic simulations of direct drive inertial confinement fusion experiments in an effort to improve their predictive capability. In this paper, we consider the choice in mesh for the simulation of the laser ablation of a direct-drive-like target and compare Lagrangian simulations with various mesh zoning choices with Eulerian simulations with fixed resolution in the laser energy deposition region. Using these simulations, we demonstrate how errors in ablation pressure, laser deposition rate, shock speed, and density profile arise from insufficient zoning following from the conservation of mass of Lagrangian zones. These considerations place stringent requirements on the initial t = 0 zoning in the solid density shell for simulations aiming at resolving the ablation and laser absorption region. However, with sufficiently fine zoning in the t = 0 shell, agreement with Eulerian simulations and analytic scaling laws can be recovered.

From Sugar to Flowers: A Transition of Shallow Cumulus Organization During ATOMIC

AbstractThe Atlantic Tradewind Ocean‐Atmosphere Mesoscale Interaction Campaign (ATOMIC) took place in January–February, 2020. It was designed to understand the relationship between shallow convection and the large‐scale environment in the trade‐wind regime. A Lagrangian large eddy simulation, following the trajectory of a boundary‐layer airmass, can reproduce a transition of trade cumulus organization from “sugar” to “flower” clouds with cold pools, observed on February 2–3. The simulation is driven with reanalysis large‐scale meteorology, and in‐situ aerosol data from ATOMIC and its joint field study EUREC4A. During the transition, large‐scale upward motion deepens the cloud layer. The total water path and optical depth increase, especially in the moist regions where flowers aggregate. This is due to mesoscale circulation that renders a net convergence of total water in the already moist and cloudy regions, strengthening the organization. An additional simulation shows that stronger large scale upward motion reinforces the mesoscale circulation and accelerates the organization process by strengthening the cloud‐layer mesoscale buoyant turbulence kinetic energy production.

On the thermal entrance length of moderately dense gas-particle flows

The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature – the thermal entrance length – is a consequence of diffusion and mixing by convection. The presence of particles can modify the thermal entrance length due to interphase heat transfer and turbulence modulation by momentum coupling. In this work, Eulerian–Lagrangian simulations are utilized to probe the effect of solids heterogeneity (e.g., clustering) on the thermal entrance length. For the moderately dense systems considered here, clustering leads to a factor of 2–3 increase in the thermal entrance length, as compared to an uncorrelated (perfectly mixed) distribution of particles. The observed increase is found to be primarily due to the covariance between volume fraction and temperature fluctuations, referred to as the fluid drift temperature. Using scaling arguments and Gene Expression Programming, closure is obtained for this term in a one-dimensional averaged two-fluid equation and is shown to be accurate under a wide range of flow conditions.