Eulerian Lagrangian Spray Atomization Research Articles

Numerical modeling of the impact of a large scale waterfall on a solid plate

Recent hydroelectric power plant safety developments have necessitated detailed studies on dam spillway operations, especially during emergency water discharge scenarios such as overtopping. This paper presents a numerical investigation of a 10-meter high waterfall impinging on a solid plate using two-phase flow models. Our approach integrates a coupled Eulerian–Lagrangian Spray Atomization (ELSA) model with an Interface Capturing Method (ICM) to simulate the complex multiphase flow and atomization processes. Our model proficiently mapped the velocity and turbulence within the pre-impact region. To refine the accuracy of the impact pressures, we isolated this zone and implemented the Injection–Reinjection strategy, a novel numerical procedure for this type of configuration. The study reveals significant insights into the dynamic interactions of water packets with the dam structure, highlighting critical impact pressures that can influence dam stability and integrity. Our results, compared against experimental data, demonstrate the effectiveness of the modeling strategies in predicting the fluid behaviors and the subsequent pressures exerted on structural components.

Three-component volume of fluid method coupling with interface compression method and Eulerian–Lagrangian spray atomization surface density model for prediction of cavitating sprays

In this work, a new three phase cavitation model with Eulerian–Lagrangian Spray Atomization (ELSA) and Interface Capturing Method (ICM) coupling is presented to allow for, in a unified approach, physical insight of the surface evolution of cavitating sprays at the Sub-Grid Scale (SGS). Phase change is accounted for in the framework via mass transfer across a liquid and corresponding vapor phase. The surface density model was validated against direct numerical simulation data of an atomizing jet with a systematic variation of mesh resolutions. The sensitivity of the adjustable parameters such as the critical Weber number was also demonstrated. Then, experimental comparisons were made with a more realistic orthogonal spray geometry within a cavitating and turbulent non-cavitating system. These comparisons include both large scale visualizations and small scale SGS quantities such as the Sauter mean diameter. To our knowledge, this is the first study that presents the performance of a three phase cavitating framework with SGS ELSA-ICM coupling.

A physics-driven Σ-Y atomization model for heavy-duty engine simulations

The atomization of a liquid jet is a multi-scale and multi-physics problem of interest for many engineering applications. Particularly, it drives the fuel-oxidizer mixing and dictates the efficiency of combustion engines. High-fidelity multi-phase simulations remain challenging due to the excessive computational cost required to capture all the atomization scales. Thus, atomization models are necessary to represent sub-grid liquid structures. In this work, a modified Σ-Y model in the context of Eulerian-Lagrangian Spray Atomization (ELSA) is used to transport the surface area density of the spray. The model's predictive performance is assessed under various operating conditions relevant to heavy-duty engines using the Engine Combustion Network (ECN) Spray C and Spray D research-grade injectors. The classic droplet collision formulation of the Σ-Y model alone does not replicate the response of the measured spray surface area to changes in injector, ambient pressure, and injection pressure, requiring individual tuning of the model's parameters. Instead, a transition between dense and dilute spray breakup mechanisms is proposed in terms of the average droplet spacing. The collision breakup mechanism represents the dilute spray, whereas the droplet size in the dense spray is driven by a competition between the integral scale of turbulence and the balance between the turbulent kinetic energy and the surface energy of the droplets. Such an approach minimizes the requirements for model tuning. Moreover, the role of the constants of a compressible standard k-ε RANS model is assessed in the injector's internal flow and external spray simulation framework, and an updated set is proposed. The results are validated against x-ray radiography and Ultra-Small Angle X-ray Scattering (USAXS) data and highlight the predictive capabilities of the proposed physics-driven Σ-Y model, which is compatible with engine simulation turnaround times.

Effect of Particle Diameter on Primary Breakup of High-Pressure Diesel Spray Atomization: A Study Based on Numerical Simulations Using the Eulerian–Lagrangian Model

The coupling of Eulerian and Lagrangian methods in the Eulerian–Lagrangian Spray Atomization (ELSA) approach is critical. This study proposes an equation for the primary breakup particle diameter D of a diesel fuel spray and adopts it as a key transition criterion for coupling. A three-dimensional diesel spray is modeled by the large-eddy simulation (LES) approach. This improved ELSA simulation was conducted using various transition criteria for particle diameter Dcr. The results show that fuel spray experiences two stages: stage I, when a liquid column appears without a dispersed phase, and stage II, when primary breakup occurs with many discrete particles. Although Dcr has little influence on the macro-spray characteristics, such as top penetration distance S and spray cone angle θ, it has significant effects on discrete particles, such as their number, average diameter, distribution and location, and spray cone area. Dcr should be determined on the basis of actual operating conditions.

Investigation on Primary Breakup of High-Pressure Diesel Spray Atomization by Method of Automatic Identifying Droplet Feature Based on Eulerian–Lagrangian Model

To investigate primary breakup close to an injector, this paper presents both experimental and numerical research on high-pressure common-rail diesel injection. We propose a new method named SD-ELSA model to realize automatically identifying droplet features for high-pressure diesel spray based on the classic ELSA (Eulerian Lagrangian Spray Atomization) model; this method is suitable for varied injection operation conditions. The SD-ELSA first identifies the liquid bulk due to breakup of the continuous phase in near field, and then converts the Eulerian liquid bulk into Lagrangian particles to complete the calculation of the total spray atomization. The SD-ELSA model adopts two key criteria, i.e., the sphericity (S) and the particle diameter (D); the qualified liquid mass is transformed into Lagrangian particle, realizing the coupling of the Eulerian–Lagrangian model. The SD-ELSA model illustrates the total diesel spray atomization process from the breakup liquid column to the droplets.

Eulerian–Lagrangian spray atomization model coupled with interface capturing method for diesel injectors

Traditional Discrete Particle Methods (DPM) such as the Euler–Lagrange approaches for modeling atomization, even if widely used in technical literature, are not suitable in the near injector region. Indeed, the first step of atomization process is to separate the continuous liquid phase in a set of individual liquid parcels, the so-called primary break-up. Describing two-phase flow by DPM is to define a carrier phase and a discrete phase, hence they cannot be used for primary breakup. On the other hand, full scale simulations (direct simulation of the dynamic DNS, and interface capturing method ICM) are powerful numerical tools to study atomization, however, computational costs limit their application to academic cases for understanding and complementing partial experimental data. In an industrial environment, models that are computationally less demanding and still accurate enough are required to meet new challenges of fuel consumption and pollutant reduction. Application of DNS-ICM methods without fairly enough resolution to solve all length scales are currently used for industrial purposes. Nevertheless, effects of unresolved scales are generally cast aside. The Euler-Lagrange Spray Atomization model family (namely, ELSA, also called, Σ−Y or Ω−Y) developed by Vallet and Borghi pioneering work (Vallet and Borghi, 1999a), and (Vallet et al., 2001), at the contrary aims to model those unresolved scales. This approach is actually complementary to DNS-ICM method since the importance of the unresolved term depends directly on mesh resolution. For full interface resolution, the unclosed terms are negligible, except in the far-field spray when the unresolved terms become dominant. Depending on the complexity of the flow and the available computational resources, a Large Eddy Simulation (LES) formalism could be employed as modeling approach. This work focus on the two main terms that drive these different modeling approaches namely the sub-grid turbulent liquid flux and the unresolved interface. Thanks to the open source library OpenFoam® (Weller et al., 1998) this work is an attempt to review and to release an adapted modeling strategy depending on the available mesh resolution. For validation, these solvers are tested against realistic experimental data to see the overall effect of each model proposal. It was found that both showed good agreement with experiments, and particularly under Diesel Spray injection conditions, the sub-grid scales represent the major driving force, thus diffusing the interface rapidly at the exit of the injector.

Where does the droplet size distribution come from?

This study employs DNS of two-phase flows to enhance primary atomization understanding and modeling to be used in numerical simulation in RANS or LES framework. In particular, the work has been aimed at improving the information on the liquid-gas interface evolution for modeling approaches, such as the Eulerian–Lagrangian Spray Atomization (ELSA) framework. Even though this approach has been already successfully employed to describe the complete liquid atomization process from the primary region to the dilute spray, improvements are still expected on the derivation of the drop size distribution (DSD). The main aim of the present work is the introduction of a new framework to achieve a continuous description of the DSD formation during the atomization process. The attention is here focused on the extraction from DNS data of the behavior of geometrical variable of the liquid-gas interface, such as the mean (H) and Gauss (G) surface curvatures. The use of a Surface Curvature Distribution is also proposed and studied.A Rayleigh–Plateau instability along a column of liquid and a droplet collision case are first of all considered to analyze and to verify the capabilities of the code to correctly predicting the curvature distributions. A statistical analysis based on the curvatures data, in terms of probability density function, is presented in order to determine the physical parameters that control the curvatures on this test case. Then, the same formulation is applied in the analysis of the two phase Homogeneous Isotropic Turbulence (HIT) configuration to study how the curvatures evolve all along the atomization process. Joint PDFs are used to illustrate the topological changes of the interface when increasing the liquid volume fraction.

Development of a turbulent liquid flux model for Eulerian–Eulerian multiphase flow simulations

The present work introduces a multiphase Eulerian solver, developed in the framework of the CFD suite OpenFOAM, aimed at including all the major physical phenomena that characterize liquid fuel atomization. The study begins with the Eulerian solver derived from the Eulerian Lagrangian Spray Atomization (ELSA) model [Borghi, R., Vallet, A., Sep. 1999. Modelisation eulerienne de l'atomisation d'un jet liquide. Comptes Rendus de l'Academie des Sciences - Series IIB - Mechanics-Physics-Astronomy 327 (10), 1015–1020, Vallet, A., Burluka, A. A., Borghi, R., 2001. Development of a eulerian model for the atomization of a liquid jet. Atomization and Sprays 11 (6), 619–642.]. This approach is suitable to describe the liquid-gas flow for all liquid volume fraction from bubbly, dense to spray flows without any assumption on the topology of the phase (droplets, bubbles, ligaments or any continuous structures). However, due to its single phase flow formalism, the slip velocity between phases is hidden in the turbulent liquid flux term inside the liquid volume fraction equation. An innovative second order closure for this variable is here proposed and implemented. A detailed analysis of the resulting Quasi-Multiphase Eulerian (QME) solver capabilities is performed in RANS context exploiting a jet in crossflow test case with available experimental and computational data. The test is extremely challenging as it involves a high density ratio (R) (i.e. two cases at R = 10 and R = 1000 were simulated) and it explores the entire range of liquid phase concentration from purely liquid to dispersed phase. The comparison with the experimental results shows that the proposed approach leads to a comprehensive and physically consistent description of the phenomena related to liquid injection.

A RECENT EULERIAN–LAGRANGIAN CFD METHODOLOGY FOR MODELING DIRECT INJECTION DIESEL SPRAYS

The global objective of this work is to show the capabilities of the Eulerian–Lagrangian spray atomization (ELSA) model for the simulation of Diesel sprays in cold starting conditions. Our main topic is to focus in the analysis of spray formation and its evolution at low temperature 255 K (-18°C) and nonevaporative conditions. Spray behavior and several macroscopic properties, included the liquid spray penetration, and cone angle are also characterized. This study has been carried out using different ambient temperature and chamber pressure conditions. Additionally, the variations of several technical quantities, as the area coefficient and effective diameter are also studied. The results are compared with the latest experimental results in this field obtained in our institute. In the meantime, we also compare with the normal ambient temperature at 298 K (25°C) where the numerical validation of the model has shown a good agreement.

MS2-2 A combined Eulerian Lagrangian spray atomization (ELSA) coupled with ECFM-CLEH Combustion model for DI-Diesel combustion modelling with a special emphasis on low temperature NO formation(MS: Modeling and Simulation,General Session Papers)

The spray atomization mechanisms under the common conditions for Diesel engines are very complex and not completely understood. At the same time the detailed spray information is necessary to provide a better control of the combustion process. The main difficulty of numerical spray simulation is the correct representation of the two characteristic zones of the spray: dense near the nozzle and dilute downstream. Combining the advantages of Eulerian and Lagrangian approaches, ELSA model is able to continuously predict the whole spray evolution. In the dense zone the spray and its gaseous environment are presented as an effective single-phase fluid with a highly variable density. To describe the liquid dispersion, transport equations for the liquid mass fraction and for the liquid/gas interface density are solved. The transition to the Lagrangian calculation is applied when the spray is considered to be enough diluted. This complete Eulerian-Lagrangian spray atomization model has been implemented into the computational fluid dynamics code STAR-CD. The model implementation was validated by comparing predicted liquid and vapor penetrations with experimental data reported in literature. Once validated, the ELSA model was coupled with an inside nozzle simulation to study the impact of internal nozzle flow (geometry, cavitation formation) on the spray and its characteristics. Finally, the coupling with the ECFM-CLEH combustion model has been completed in this work. ECFM-CLEH stands for Extended Coherent Flame Model with Combustion Limited by Equilibrium Enthalpy. It simulates the different phases of Diesel combustion i.e. the auto-ignition, the premixed and the diffusion flame. In the premixed phase, combustion is mainly controlled by flame propagation while fuel and air mixing play an important role in the diffusion phase. The auto-ignition is modeled from tabulated fully detailed chemistry. The tabulated TKI (Tabulated Kinetics for Ignition) strategy proposed by IFP in combination with a presumed PDF using the temperature fluctuations for integration is used. Also a special attention has been made to improve the NOx formation considering the extended Zeldovich thermal NO. The set of sub-models presented above has been implemented in STAR-CD. Applications and validations for a full DI Diesel combustion process have been performed for typical automotive DI Diesel engines with variation of EGR level, Injection Timing and injector's nozzle diameter.

Primary Break-up: DNS Of Liquid JetTo Improve Atomization Modelling

Two different approaches for numerical simulations of primary break-up of liquid jet are described. In the ELSA model (Eulerian Lagrangian Spray Atomization) the liquid and the gas are considered as two species of a same mixture, but without necessarily the same velocity. The drift velocity and the liquid mass dispersion are exactly related to the turbulent liquid mass flux. To describe the topology of the spray the liquid/gas interface density per unit of volume is used instead of the droplet diameter that has no meaning in the dense part of the spray. To establish definitely the model for the turbulent liquid mass flux and for the liquid/gas interface density equation, DNS simulations are carried out to obtain information in the dense zone of the spray where nearly no experimental data are available. Interface tracking is ensured by the Level Set Method and the Ghost Fluid Method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. Coupling between the Level Set and VOF method is used for mass conservation. Fluid motion is predicted with a projection method for incompressible flows.

Evaluation of the Eulerian–Lagrangian Spray Atomization (ELSA) model in spray simulations: 2D cases

The aim of this paper is the evaluation and validation of the Eulerian–Lagrangian Spray Atomization (ELSA) model implemented in a CFD code by Renault. ELSA is an integrated model for capturing the whole spray evolution, in particular including primary break-up and secondary atomization. Two-dimensional simulations have been performed during the study, which is in fact enough to capture some of the main features of the spray, such as the spray penetration and the axial velocity. A mesh independence study has also been carried out in order to characterize the lowest mesh size that can be used to correctly characterize the spray. Furthermore, the two-equation k–ε turbulence model has been adjusted by changing some of the parameters of the dissipation rate transport equation in order to accurately characterize the spray. Finally some analyses of the results obtained, in terms of penetration, liquid mass fraction and droplet number and size, are presented in the last section of the paper.

MODELING COLLISION OUTCOME IN MODERATELY DENSE SPRAYS

To simulate primary atomization, the dense zone of sprays has to be addressed and new atomization models have been developed as the Eulerian-Lagrangian spray atomization (ELSA) model [Blaisot, J. B., and Yon, J., (2005) Exp. Fluids, 39(6), pp. 977−994]. A transport equation for the liquid/gas interface density is stated and extends the concept of droplet diameter. Several related source terms require modeling attention. This work describes the contribution of collision and coalescence processes. Several questions arise: Is it possible to represent collision/coalescence from an Eulerian description of the flow? What are the key parameters? What are the particular features of collision in dense spray? To answer these questions, a Lagrangian test case, carefully resolved statistically, is used as a basis to evaluate Eulerian models. It is shown that a significant parameter is the equilibrium Weber number. If it is known, Eulerian models are able to reproduce the main features of Lagrangian simulations. To overcome the Lagrangian collision model simplification that mostly considers collisions between spherical droplets, a new test case was designed to focus on the collision process in dense spray. The numerical code, Archer, which is developed to handle interface behaviors in two-phase flow by way of direct numerical simulation (DNS) [Iyer, V., and Abraham, J., (2005), Atomization Sprays, 15(3), pp. 249−269], was used. Thanks to DNS simulations and experimental observations, the importance of nonspherical collisions is demonstrated. Despite some classical drawbacks of DNS, we observed that an equilibrium Weber number can be determined in the considered test case. This work emphasizes the ability of interface DNS simulations to describe complex turbulent two-phase flows with interfaces and to stand as a complement to new experiments.

Numerical simulation of primary break-up and atomization: DNS and modelling study

This work deals with numerical simulations of atomization with high Weber and Reynolds values. A special attention has been devoted to the modelling of primary break-up. Due to progress of direct numerical simulations (DNS) of two phase flows it is now possible to simulate the primary break-up of a Diesel spray [Menard, T., Tanguy, S., Berlemont, A., 2007. Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet. Int. J. Multiphase Flow 33 (5), 510–524]. The present formulation of the so-called ELSA (Eulerian–Lagrangian Spray Atomization model) [Vallet, A., Borghi, R., 1999. Modélisation Eulerienne de L’atomisation d’un Jet Liquide. C. R. Acad. Sci. Paris Sér. II b 327, 1015–1020] for atomization is presented and evaluated in the dense zone of the spray by comparison to a DNS based on a coupled level set/VOF/ghost fluid method. Once constants and parameters of the model are fixed thanks to comparisons with DNS, the model is tested with experimental data. The liquid and vapour penetrations show a good agreement when they are compared to experiments of Diesel atomization. In particular the influence of the gas temperature is well recovered. For different temperatures, similarly to the experiments, vapour penetrations are unchanged, but the corresponding equivalent ratio fields are strongly modified. Finally, the combustion model ECFM-3Z [Colin, O., Benkenida, A., 2004. The 3-zones extended coherent flame model (ecfm-3z) for computing premixed/diffusion combustion. Oil Gas Sci. Technol. 59 (6) 593–609] is joined to the ELSA model and the effect of gas temperature changes on a Diesel spray flame is reproduced.