Lagrangian Large-eddy Simulation Research Articles

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Backward-Eulerian Footprint Modelling Based on the Adjoint Equation for Atmospheric and Urban-Terrain Dispersion

This study developed a backward-Eulerian footprint modelling method based on an adjoint equation for atmospheric boundary-layer flows. In the proposed method, the concentration footprint can be obtained directly by numerical simulation with the adjoint equation, and the flux footprints can be estimated using the adjoint concentration based on the gradient diffusion hypothesis. We first tested the proposed method by estimating the footprints for an ideal three-dimensional boundary layer with different atmospheric stability conditions based on the Monin–Obukhov profiles. It was indicated that the results were similar to the FFP method (Kljun et al. in Boundary-Layer Meteorol 112:503–523, 2004, https://doi.org/10.1023/B:BOUN.0000030653.71031.96; Geosci Model Dev 8:3695–3713, 2015, https://doi.org/10.5194/gmd-8-3695-2015) for convective conditions and the K–M method (Kormann and Meixner in Boundary-Layer Meteorol 99:207–224, 2001, https://doi.org/10.1023/A:1018991015119) for stable conditions. The proposed method was then coupled with the Reynolds averaged Navier–Stokes model to calculate the footprints for a block-arrayed urban canopy. The results were qualitatively compared to the results from the Lagrangian-Large-Eddy-Simulation (LL) method (Hellsten et al. in Boundary-Layer Meteorol 157:191–217, 2015, https://doi.org/10.1007/s10546-015-0062-4). It was shown that the proposed method reproduced the main features of footprints for different sensor positions and measurement heights. However, it is necessary to simulate the adjoint equation with a more sophisticated turbulence model in the future to better capture turbulent effects in the footprint modelling.

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.

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.

Multiphase Eulerian–Lagrangian LES of particulate fouling on structured heat transfer surfaces

In this study, multiphase Eulerian–Lagrangian large-eddy simulation (LES) is used to analyze the interaction between local flow structures, convective heat transfer and particle depositions (fouling) for a turbulent channel flow with a dimpled surface. Thus, eddy-resolving LES is applied for calculation of the turbulent working fluid (carrier flow), combined with an efficient Lagrangian particle tracking (LPT) algorithm, suitable to predict the trajectories of the suspended foulant particles precisely in time and space. In order to decrease the computational effort and to enhance the applicability of the proposed approach, deposited particles are deactivated and converted into a second continuous phase (fouling layer), which is modeled as a porous medium and accounts for the hydraulic losses as well as for the additional thermal resistance due to the fouling deposits. Prior to the fouling simulations, the envisaged method is validated for a turbulent particle-laden channel flow at Reτ=150, based on DNS results available in the literature, which shows the capability of the Eulerian–Lagriangian LES of capturing the flow physics within turbulent particle-laden, wall-bounded flows. Based on this observations, fouling simulations were carried out for a turbulent particle-laden channel flow over a staggered arrangement of sharp-edged spherical dimples, whereby two different dimple depth-to-diameter ratios are considered (d/D=0.26 and 0.35). The thermo-hydraulic performance is analyzed for the clean and contaminated dimpled surfaces.

Broadening of Cloud Droplet Spectra through Eddy Hopping: Turbulent Adiabatic Parcel Simulations

Abstract This paper investigates spectral broadening of droplet size distributions through a mechanism referred to as the eddy hopping. The key idea, suggested a quarter century ago, is that droplets arriving at a given location within a turbulent cloud follow different trajectories and thus experience different growth histories and that this leads to a significant spectral broadening. In this study, the adiabatic parcel model with superdroplets is used to contrast droplet growth with and without turbulence. Turbulence inside the parcel is described by two parameters: (i) the dissipation rate of the turbulent kinetic energy ε and (ii) the linear extent of the parcel L. As expected, an adiabatic parcel without turbulence produces extremely narrow droplet spectra. In the turbulent parcel, a stochastic scheme is used to account for vertical velocity fluctuations that lead to local supersaturation fluctuations for each superdroplet. These fluctuations mimic the impact of droplets hopping turbulent eddies in a natural cloud. For L smaller than a few meters, noticeable spectral broadening is possible only for strong turbulence—say, ε > 100 cm2 s−3. For L typical for grid lengths of large-eddy simulation (LES) models (say, L between 10 and 100 m), the impact is significant even with relatively modest turbulence intensities. The impact increases with both L and ε. The representation of eddy hopping developed in this paper can be included in a straightforward way in the subgrid-scale scheme of a Lagrangian LES cloud model and may lead to a significant acceleration of simulated rain development through collision–coalescence.

Investigation of Bubble-Slag Layer Behaviors with Hybrid Eulerian–Lagrangian Modeling and Large Eddy Simulation

In ladle metallurgy, bubble–liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The Eulerian volume of fluid model is adopted to track the liquid steel–slag–air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O’Rourke’s algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air–liquid interface. The turbulent liquid flow that is induced by bubble–liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open–close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid Eulerian–Lagrangian–LES model provides a valid modeling framework to predict the unsteady gas bubble–slag layer coupled behaviors.

Measurement and simulation of swirling coal combustion

Particle image velocimetry (PIV), thermocouples and flue gas analyzer are used to study swirling coal combustion and NO formation under different secondary-air ratios. Eulerian–Lagrangian large-eddy simulation (LES) using the Smagorinsky–Lilly sub-grid scale stress model, presumed-PDF fast chemistry and eddy-break-up (EBU) gas combustion models, particle devolatilization and particle combustion models, are simultaneously used to simulate swirling coal combustion. Statistical LES results are validated by measurement results. Instantaneous LES results show that the coherent structures for swirling coal combustion are stronger than those for swirling gas combustion. Particles are shown to concentrate along the periphery of the coherent structures. Combustion flame is located in the high vorticity and high particle concentration zones. Measurement shows that secondary-air ratios have little effect on final NO formation at the exit of the combustor.

A Dynamic LES Scheme for the Vorticity Transport Equation: Formulation anda PrioriTests

This work aims at the development of a Lagrangian large eddy simulation (LES) scheme. The scheme is based on the filtered vorticity transport equation and on modeling the effects of subfilter scale (SFS) velocity and vorticity fluctuations using a dynamic eddy diffusivity model. The dynamic implementation of the model relies on multiple filtering in order to determine model coefficients from the resolved data. The performance of the dynamic SFS model is examined usinga prioritests that are based on direct numerical simulations of forced, homogeneous, isotropic turbulence. The tests show a fair correlation of the model with SFS convection of vorticity. In addition, the computed value of the dynamic model coefficient is in good agreement with predictions based on enstrophy balances. Finally, the direct numerical simulation data is used to compare a three-dimensional particle representation of the model with spectral evaluations. The tests show that when the particle representation is sufficiently resolved, the Lagrangian model predictions are in good agreement with spectral results.