Eulerian-Lagrangian Simulation Research Articles

Interpolation of probability‐driven model to predict hydrodynamic forces and torques in particle‐laden flows

AbstractThe development of hydrodynamic force/torque closure models with physical fidelity is crucial for ensuring reliable Euler–Lagrange simulations in particle‐laden flows. Our previous work (Seyed‐Ahmadi and Wachs. J Fluid Mech. 2020;900:A21) proposed a microstructure‐informed probability‐driven point‐particle (MPP) method to construct a data‐driven particle‐position‐dependent closure model, incorporating the effect of surrounding particle positions on forces/torques. However, the MPP model is not pluggable in Euler–Lagrange simulations due to the computation of constant coefficients through linear regression and reliance on statistical arguments to obtain the probability map for a pair of values of solid volume fraction (Φ) and Reynolds number (Re). To overcome this limitation, we propose an interpolated MPP (iMPP) method, involving interpolation in the Φ and Re spaces. Our results demonstrate that the iMPP method can capture over 70% of the total fluctuations in hydrodynamic forces/torques in approximately 97.8% of the tested cases. This advancement contributes to a more versatile closure model suitable for integration into E‐L simulations.

Simulation on coal combustion and calcium carbonate decomposition in a 5500 t/d full scale cement calciner

With the continuous growth of global cement production, the increasing coal consumption in the cement industry has been drawing great attention, thus adopting advanced technologies to reduce energy consumption has become an important issue. To address this problem, this study carried out 3D Eulerian-Lagrangian simulations of the coupling process of pulverized coal combustion and CaCO3 decomposition in a 5500 t/d full-scale cement calciner. On the basis of the multiphase particle-in-cell (MP-PIC) approach, reaction models including devolatilization, combustion of char and volatiles, and CaCO3 decomposition are incorporated into the scheme. Detailed combustion characteristics including temperature distribution, carbon exhaust rate, and gas emission characteristics, as well as decomposition characteristics are comprehensively analyzed. Besides, effects of different operating performances including O2 content in bottom flue gas on carbon exhaust rate, CaCO3 decomposition rate, and NOx emission are also investigated. Results show that under the typical working condition with O2 concentration in the flue gas of 1.7 %, the CaCO3 decomposition rate can reach around 96.42 %, the carbon conversion rate is up to 98.65 %, and the NOx can be controlled at around 105 ppm. The increase of O2 content promotes higher carbon conversion rates with excessive O2 leading to higher NOx emission. Appropriately increasing the proportion of raw material flow rate in upper tubes can facilitate a more complete CaCO3 decomposition.

Numerical study of the momentum and heat transfer between an oblate ellipsoid and a gas in uniform flow

In this study, drag coefficient (cd ) and Nusselt number (Nu) for oblate ellipsoids with different incident angles (θ) and particle aspect ratios (Ar) in uniform flow have been computed over a wide range of Re ∈[10,500]. Finally, a new drag coefficient correlation is proposed, which covers a wider range of oblate ellipsoids. Surprisingly, we observe that the incident angle has a negligible effect on the Nusselt number for the oblate ellipsoids in the Reynolds number range studied. The Nusselt number for oblate ellipsoids with incident angle (θ) can be approximated accurately by the averaged Nusselt number for different incident angles. Thus, a new Nusselt number correlation for oblate ellipsoids for Re ∈[10,500] and Ar ∈[0.1,0.8] is proposed. The new correlations developed are expected to improve the accuracy of Euler-Lagrange simulations of gas-solid heat transfer comprising oblate ellipsoids.

Effects of MWCNT nanoparticles injection points on incompressible laminar hydrogen flow through discrete phase modeling by CFD approach

Discrete phase model used in the aerospace industry to stimulate the behavior of particles inside the aircraft engines. The application of the discrete phase modeling (DPM) is extensive in solving the real-time engineering problems in optimization of numerous systems. In the current study, the DPM model has been simulated to examine the effect of injection point on the hydrogen flow field. A domain has been proposed and the injection point has been positioned in the four different places at the regular intervals. The location of the injection points was 0.2 m, 0.3 m, 0.4 m and 0.6 m. Dense discrete Eulerian lagrangian numerical simulation has been employed to analyze the effect of the multi-walled carbon nanotubes (MWCNT) nanoparticles. The hydrogen has been supplied at the injection velocity of 2 m/s. ANSYS implicit simulation setup has been tested across various injection points. The research found that the location of injection points plays a significant role in DPM concentration, with the highest concentration at 0.2 m and the lowest at 0.6 m, but has no significant impact on dynamic pressure. MWCNT nanoparticles had a negligible effect on skin friction coefficient, but shifting the injection point could reduce skin friction rates. The inclusion of MWCNT nanoparticles increased hydrogen flow velocity through downstream effects, vortices, and the nano-enhancement effect. The study suggests that MWCNT can significantly enhance hydrogen flow velocity in various applications, and DPM concentration data can provide valuable insights for optimizing injection locations to prevent unwanted nanoparticle effects.

Determining the mechanism of defect formation and material flow characteristics in underwater stationary shoulder friction stir welding using coupled Eulerian-Lagrangian simulation

Determining the mechanism of defect formation and material flow characteristics in underwater stationary shoulder friction stir welding using coupled Eulerian-Lagrangian simulation

Compressible pairwise interaction extended point-particle model for force prediction of shock-particle bed interaction

Euler-Lagrange simulations are often required to study complex compressible multiphase problems. Such systems include volcanic explosions and supernovas. We developed an unsteady neighboring particle interaction framework with the help of the compressible Maxey-Riley-Gatignol equation and the scattering theory, which further improves force predictions used in Euler-Lagrange simulations.

A Model for the Fate of a Gas Bubble Interacting with a Wire Mesh.

In the concept of a microstructured bubble column reactor, microstructuring of the catalyst carrier is realized by introducing a static mesh of thin wires coated with catalyst inside the column. Meanwhile, the wires also serve the purpose of cutting the bubbles, which in turn results in high interfacial area and enhanced interface hydrodynamics. However, there are no models that can predict the fate of bubbles (cut/stuck) passing through these wires, thus making the reactor optimization difficult. In this work, based on several typical bubble-wire interacting configurations, we analyze the outcomes by applying the energy balance of the bubble focusing on buoyancy and surface tension. Two limiting cases of viscosity, corresponding to the ability of the bubble to reconfigure into the lowest energy state, are investigated. Upon analysis, it is observed that a narrow mesh spacing and a smaller bubble Eötvös number generally result in bubbles getting stuck underneath the wire. We have obtained the threshold grid spacing and the critical Eötvös number for bubble passage and bubble cutting, which are verified by the direct numerical simulation results of bubble passing through a single mesh opening. The derived energy balance is generalized to large meshes with multiple openings and different configurations. Finally, a closure model based on the outcomes of energy-balance analysis is proposed for Euler-Lagrange simulations of microstructured bubble columns.

Estimating initiation conditions for extrusion buckling of driven open-ended piles

The potential for pile tip damage and extrusion buckling has become an increasing concern for the offshore wind industry following the trend toward the use of large-diameter thin-walled pile foundations, either as monopiles or as part of a jacket structure. Extrusion buckling may be triggered by an initial pile tip fabrication imperfection or pile damage during transport and handling. It may also be triggered during driving through strong heterogeneous sediments. Numerical analysis of the problem requires advanced and computationally expensive techniques because of the three-dimensional, dynamic and large-deformation nature of the pile and soil deformations. The problem is addressed here by combining coupled Eulerian–Lagrangian simulations with geotechnical centrifuge model test data in dry dense sand. Both approaches consider pre-dented piles with the objective of estimating the soil strength, characterised by the cone resistance, at which minor initial damage will start to propagate. Simplified analysis of structural dent propagation and radial stresses generated in the soil during advance of a deformed pile led to a simple calculation procedure to assess the potential for extrusion buckling. Reasonably good agreement was achieved between the proposed calculation method, numerical simulations and centrifuge tests data, rendering the approach a valuable screening tool for practical application.

Secondary Motion of Non-Spherical Particles in Gas Solid Flows

Objective of this study is to investigate the effect of secondary motion of particles in multiphase gas-solid flows parametrically and test the relative impacts of particle shape and orientation information on particle distribution. For that purpose, predictive accuracies of simplified drag coefficient models are assessed for the conditions relevant to a wood recovery plant operating at dilute flow regime. After demonstrating the strong impact of the shape and orientation information on the force balance for single particles, we compared the steady state Eulerian-Lagrangian simulation results for particle volume fractions, residence times and particle diameter distributions within the chamber for different (i) superficial gas velocities (5 m/s, 7.5 m/s), (ii) orientation tendencies and (iii) particle shapes. Transient simulations are performed until the system reaches steady state conditions by monitoring the mass flow rates of the particulate phases leaving the chamber. The secondary motion of non-spherical particles is represented by stochastic sampling from the available experimental data. Analysis of the force balance on single particles revealed log-scale variations if the orientation of the particles with respect to flow fluctuates. Variations in the single particle force balances are found to be still visible in the CFD analysis, where the secondary motion of particles drastically changed the particle distribution in the chamber. The native non-spherical model which only accounts for the shape correction was found to over-predict the entrainment, leading to a significantly different particle volume fraction and diameter distributions. Spherical particle assumption also caused significant errors in the particle distribution, which increases as aspect ratio of the cylindrical particle diverges from one. Results show that particle orientation statistics are extremely important to capture the particle mixing and segregation patterns at dilute regime, which cannot be captured with such simplifying assumptions.

Hybrid MPI-Openmp Accelerated Euler-Lagrange Simulations of Microbubble Enhanced Hifu for Tumor Ablation.

Microbubble enhanced HIFU is of great interest to tissue ablation for solid tumor treatments, where contrast agents/microbubbles are injected into the targeted region to promote heating and reduce pre-focal tissue damage. A compressible Euler-Lagrange model has been developed to accurately characterize the acoustic and thermal fields during this process. This employs a compressible Navier-Stokes solver for the ultrasound acoustic field and a discrete singularities model for bubble dynamics. To address the demanding computational cost in practical medical applications, a hybrid MPI-OpenMP parallelization scheme is developed to take advantage of both scalability of MPI and load balancing of OpenMP. Firstly the Eulerian computational domain is divided into multiple subdomains and the bubbles are subdivided in groups based on which subdomain they fall into. Then, in each subdomain containing bubbles, multiple OpenMP threads are activated to speed up the computations of the bubble dynamics. OpenMP threads are more heavily distributed to subdomains where the bubbles are clustered. Thus MPI load imbalance due to uneven bubble distribution is mitigated by OpenMP speedup locally for those subdomains hosting more bubbles. The is used to conduct simulations and physical studies of bubble-enhanced HIFU containing a large number of microbubbles. The phenomenon of acoustic shadowing caused by the bubble cloud is then analyzed and discussed. Efficiency tests on two different machines with 48 processors are conducted and indicate 2 to 3 times of speedup with the same hardware by introducing an OpenMP parallelization in combination to the MPI parallelization.

Point-particle drag, lift, and torque closure models using machine learning: Hierarchical approach and interpretability

Point-particle closure models that are utilized in Euler-Lagrange simulations play an important role in replicating true dynamics of particle-laden flows. The accuracy of these point-particle models depends on how well they incorporate the local microstructural information of neighboring particles. The current work presents a physics-based hierarchical machine learning approach for developing robust N-body closures. The inclusion of ternary interactions, in addition to binary interactions, enabled by the hierarchical approach leads to improved predictions.

Plasma Actuation for the Turbulent Mixing of Fuel Droplets and Oxidant Air in an Aerospace Combustor

In order to explore plasma-assisted turbulent mixing in aerospace engines, the dielectric barrier discharge plasma actuation for the turbulent mixing of fuel droplets and oxidant air in a ramjet combustor was studied using computational fluid dynamics. A two-way coupling of turbulent air and discrete droplets was realized by Eulerian–Lagrangian simulation, and the dielectric barrier discharge plasma action on flow was modeled by body force. The results show that the plasma actuation can rearrange the recirculation zone behind the evaporative V-groove flameholder, and the main mechanism of actuation is to increase the local momentum of the fluid; the actuation dimension, actuation intensity, and actuation position of the dielectric barrier discharge plasma have strong effects on the turbulent mixing of fuel droplets and oxidant air; and a relatively optimal turbulent mixing can be achieved by adjusting the actuation parameters.

Euler–Lagrange stochastic modeling of droplet breakup and impact in supersonic flight

Blunt bodied aircraft traveling supersonically in weather environments may be damaged by impacts with water droplets and other airborne particles, such as snow and ice. Prior to an impact, these particles will encounter a bow shock that causes a discontinuity in their relative velocity with the gas phase, which can lead droplets to breakup into smaller droplets. These smaller droplets are more easily diverted from colliding with the blunt body due to their significantly reduced inertia relative to the initial rain droplets. One-way coupled Euler–Lagrange simulations are used to study the dynamics of droplets approaching a blunt body in steady two dimensional and axi-symmetric flow fields using a stochastic version of the Taylor analogy breakup model for the breakup dynamics. Ultimately, the dominant mechanism determining engineering quantities of interest was observed to be a competition between breakup time and the time available for a droplet to reach the body after encountering the bow shock. At Mach numbers 2, 3, and 6, the competition between these mechanisms was the dominant factor determining the momentum transfer to the blunt body via droplet collisions, which can be well characterized by a scaling relation.

Development of Eulerian–Lagrangian simulation for snow transport in the presence of obstacles

The aim of this study is to develop a wind-induced snow transport model in a turbulent atmospheric boundary layer with the multiphase particle-in-cell (MP-PIC) approach. The airflow is treated as a continuum (Eulerian phase), and the snow is treated as discrete particles (Lagrangian phase). The momentum exchange between airflow and snow particles is considered, as well as the drag force of fluctuation velocity on particles, the turbulence damping near the snow-airflow interface, and the inter-particle collisions. The validation comprised wind-induced snow transport on flat terrain and around the roadbed, with the typical Eulerian–Eulerian approach serving as a control. The Eulerian–Lagrangian approach yields a better agreement with the experimental observations, especially in the presence of obstacles. On the contrary, considerable discrepancies with the experimental data are detected when utilizing the Eulerian–Eulerian approach. The Eulerian–Lagrangian approach is thought to have the advantages of independent snow momentum-governing equations and a precise snow-airflow momentum exchange model, which could be beneficial for snow transport prediction in urban environments.

A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations

The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. A simple empirical approach is also presented to account for unsteady effects in the correction procedure.

Analysis of particle dispersion in a turbulent flow considering particle rotation

Non-spherical particles exist widely in natural and industrial fluid systems and the motions of non-spherical particles are significantly different from that of spherical particles. In this paper, a simplified model of non-spherical particles considering particle drag correction, lift, and rotation was established. Based on the Eulerian–Lagrangian simulation, the dispersion characteristics of spherical and non-spherical particles with different Stokes numbers in a high-speed turbulent jet were analyzed and compared considering the effect of particle rotation. The results show that, the differences in particle dispersion and radial velocity fluctuation between non-spherical particles and spherical particles in the jet are significant, especially when Stokes number is large. Moreover, the effects of different type of forces on the dispersion of non-spherical particles and spherical particles were compared in detail, which revealed that the change of the Magnus force caused by the increase in the angular velocity of non-spherical particles plays a dominant role in the differences of particle dispersion.

An improved lift model for Euler-Lagrange simulations of bubble columns

The objective of this work is to establish a lift model which can account for the variation in the bubble spreading mechanism with different column aspect ratios. To this end, a strategic approach has been developed and applied to explore the dependency of the lift variation with local flow variables. Numerical simulations are performed by using Computational Fluid Dynamics - Discrete Particle Method (CFD-DPM) coupled with Volume of Fluid (VOF) method in the open-source framework OpenFOAM. Both homogeneous and heterogeneous bubbly flows are considered with the results from reported experiments in literature. It has been found that the local gas fraction and the vorticity are strongly correlated with the lift coefficient. However, using one of these two variables alone cannot describe the lift variation within the bubble columns. Finally, a unified lift model is established that depends on both local gas fraction and vorticity. Euler–Lagrange simulations using this lift model are demonstrated to provide excellent agreement on the bubbly dynamics with experiments of homogeneous bubbly flows and bubble swarms.

Detailed chemistry modeling of rotating detonations with dilute n-heptane sprays and preheated air

Utilization of liquid fuels is crucial to enabling commercialization of rotating detonation engines (RDE) in the near future. In this study, Eulerian-Lagrangian simulations are conducted for rotating detonative combustion with dilute n-heptane sprays and preheated air. Two-dimensional flattened configuration is used and a skeletal chemical mechanism with 44 species and 112 elementary reactions for n-heptane combustion is adopted. The flow structure, droplet distribution, and thermochemical parameters in the refill zone are first analyzed. It is shown that the mixture in the refill zone is heterogeneous, including evaporating droplets, vapor, and air. When the total temperature is below 950 K, the average equivalence ratio increases with the total temperature. When it is higher than 950 K, the average equivalence ratio is almost constant. Subsequently, the chemical explosive mode analysis is applied to identify the controlling reactions and dominant combustion modes in the fuel refill zone and reaction fronts. Results demonstrate that the initiation reaction (R104: n-C7H16 + O2→ 2-C7H15 + HO2) and low-temperature reaction (R107: RO2→ R'O2H) are dominant in the upstream and downstream of the refill zone, respectively. The intermediate species from low-temperature chemistry, R'O2H, is found to be important for the chemical explosive mode in the undetonated mixture. The influence of species diffusion and dispersed droplets is further analyzed. Results show that vapor autoignition facilitated by droplet evaporation occurs in the refill zone. Finally, the effects of the air total temperature on the detonation propagation speed and RDE propulsion performance are investigated. It is found that the detonation propagation speed and specific impulse increase with air total temperature. The total pressure ratio first increases and then decreases as the air total temperature increases. Moreover, when the total temperature of the preheated air is above 1,300 K, the effects of low-temperature chemistry are negligible.

Simulation of liquid droplets combustion in a rotating detonation engine

Recent research towards using liquid fuel in rotating detonation engines (RDE) has been assessed here using numerical simulations of a representative three-dimensional (3D) configuration. Eulerian-Lagrangian simulations of a 3D non-premixed RDE configuration are conducted and it is demonstrated that kerosene injection through the air plenum helps stabilize the RDE operation at the conditions where a pure gaseous H2 RDE is unable to sustain the propagation of a detonation. The H2-fueled RDE is first simulated at a global equivalence ratio of 0.5, which shows unstable burning with localized extinction and re-ignition followed by system failure, and then compared against another simulation where kerosene droplets are injected in the air plenum keeping the same H2 fueling condition. The results show that the existence of the detonation aids in the evaporation of the injected droplets behind it, allowing the vaporized mixture to properly mix before the next detonation cycle such that continuous (cyclic and stable) propagation can be achieved. It is further shown that whereas hydrogen mainly reacts near the bottom of the chamber, the injected droplets vaporize slow and react at larger heights. As a result, for the latter case the heat release is more distributed and provides an additional mechanism to stabilize the detonation cycle.

An Arbitrary Lagrangian Eulerian Approach for Estimating Energy Dissipation in Micromirrors

Quantification and minimisation of energy consumption in resonant MEMS micromirrors is a key aspect for a proper structural design. In this setting, the quality factor Q of the drive mode of the device needs to be estimated and, eventually, improved. In this work, we propose a simulation strategy for the numerical computation of MEMS micromirrors quality factors. Full order Arbitrary Lagrangian Eulerian Navier-Stokes simulations have been performed using a SUPG stabilised Chorin-Themam scheme. Finally, the numerical results are compared with experimental data, highlighting the accuracy and efficiency of the proposed method.