Fuel injection model for Euler–Euler and Euler–Lagrange large-eddy simulations of an evaporating spray inside an aeronautical combustor

Large-Eddy Simulations (LES) of an evaporating two-phase flow in an experimental burner are investigated. Two different numerical approaches for the simulation of the dispersed phase are coupled to the same gaseous solver: a mesoscopic Eulerian method and a Lagrangian particle tracking technique. The spray is represented by a single droplet size owing to the locally monodisperse formulation of the employed mesoscopic Eulerian approach. Both approaches use the same drag and evaporation models. They do not take into account the atomization process and a simplified injection model is applied instead. The presented methodology, referred as FIM-UR (Fuel Injection Method by Upstream Reconstruction) defines injection profiles for the monodisperse spray produced by a pressure-swirl atomizer. It is designed so as to ensure similar spray characteristics for both approaches and allows for a direct comparison between them. After a validation of the purely gaseous flow in the burner, liquid-phase dynamics and droplet dispersion are qualitatively and quantitatively evaluated for the Eulerian and Lagrangian simulations. Results obtained for both approaches are in very good agreement and compare reasonably with experiments, indicating that simplified injection methods are appropriate for the simulation of realistic combustor geometries.     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.     

Systematic tuning of dispersion models for simulation of evaporating sprays

In this study, via an Eulerian–Lagrangian framework, the performance of two recent dispersion models, i.e. a first-order autoregressive process and the PDF model, is compared. The appropriate relations for the turbulence scales and the drift correction term are suggested and the tuned values for the constants of the models are proposed in a systematic approach by starting with the simplest case, i.e. particle-laden stationary isotropic turbulence and adding more complexities in the subsequent cases, including the homogeneous anisotropic shear flow, decaying grid turbulence, and inhomogeneous gas–solid spray. Also, the isotropic relation for the effect of inertia in the Lagrangian turbulence time scale seen by particles is extended to the anisotropic case while it remains consistent in the isotropic limit. Finally, the performance of the tuned models is evaluated for the simulation of an evaporating spray. It is observed that, the tuned constants for the evaporating spray are close to the ones obtained for the homogeneous shear flow.     

Large Eddy Simulation of Reactive Two-Phase Flow in an Aeronautical Multipoint Burner

Because of compressibility criteria, fuel used in aeronautical combustors is liquid. Their numerical simulation therefore requires the modeling of two-phase flames, involving key phenomena such as injection, atomization, polydispersion, drag, evaporation and turbulent combustion. In the present work, particular modeling efforts have been made on spray injection and evaporation, and their coupling to turbulent combustion models in the Large Eddy Simulation (LES) approach. The model developed for fuel injection is validated against measurements in a non-evaporating spray in a quiescent atmosphere, while the evaporation model accuracy is discussed from results obtained in the case of evaporating isolated droplets. These models are finally used in reacting LES of a multipoint burner in take-off conditions, showing the complex two-phase flame structure.     

Numerical and experimental study on effect of wall geometry on wall impingement process of hollow-cone fuel spray under various ambient conditions

The spray–wall impingement process in gasoline direct injection (GDI) engines, which is caused by the interaction among spray, wall and air to move the air–fuel mixture near the spark plug, directly influences the engine performance and emissions. Therefore, a detailed understanding of this process is very important in designing an injection system and controlling a strategy of GDI engines. The purpose of this study is to understand the spray–wall impingement characteristics for more efficient designing of the injection system in GDI engines and to supply the fundamental data under engine operation conditions. The wall impingement processes of hollow-cone fuel spray according to ambient gas conditions and wall geometry are calculated by validated spray models. The calculated results were compared with the experimental results obtained by the laser-induced exciplex fluorescence (LIEF) technique. It was found that the spray and vortex cloud at the high ambient pressure were distributed at inner area of cavity and the more fuel film mass observed at this condition. The fuel film mass decreased with the increase of ambient temperature, while the fuel film mass increased at high cavity angles.     

Modelling of Spray Flames with Doubly Conditional Moment Closure

Simulations of a pilot-stabilised flame in a uniformly dispersed ethanol spray are performed using a Doubly Conditional Moment Closure (DCMC) model. The DCMC equation for spray combustion is derived, using the mixture fraction and the reaction progress variable as conditioning variables, including droplet evaporation and differential diffusion terms. A set of closure sub-models is suggested to allow for a first, preliminary application of the DCMC model to the test case presented here. In particular, the DCMC model is used to provide complete closure for the Favre-averaged spray terms in the mean and variance equations of the conditioning variables and the present test case is used to assess the importance of each term. Comparison with experimental data shows a promising overall agreement, whilst differences are related to modelling choices.     

Large eddy simulation of high pressure spray with the focus on injection pressure

This paper presents a detailed numerical analysis of diesel engine spray structure induced by the Engine Combustion Network (ECN) Spray A at different injection pressures. The non-reacting simulations are performed using OpenFOAM where an Eulerian–Lagrangian model is adopted in the large eddy simulation (LES) framework. Effects of the LES mesh resolution as well as the spray model parameters are investigated with the focus on their impact on spray structure as the injection pressure varies. The predicted liquid and vapour penetration lengths agree well with the measurements at different injection pressures. The mixture fraction is well captured for the injection pressure of 100 and 150 MPa while a slight deviation from the measurements is observed for the injection pressure of 50 MPa near the nozzle. The parametric analysis confirms that the LES mesh resolution has significant effects on the results. A coarser mesh leads to higher liquid and vapour penetration lengths where the deviation from the measurements is larger, resulting in the highest error at the lowest injection pressure. As the mesh size increases, the droplet size distribution becomes narrower, its pick moves to the smaller droplet size and the probability of droplets with higher temperature increases. On the other hand, with increasing the mesh size, the carrier gas velocity decays slower and its radial dispersion decreases. It is found that the droplet characteristics are more affected by the mesh resolution when the injection pressure is the lowest while the opposite is true for the carrier phase. The number of Lagrangian particles also affects the droplet characteristics and the fuel-air mixing but their effects are not as significant as the mesh size. The results become less sensitive to the number of Lagrangian particles as the pressure injection decreases. Finally, the importance of the initial droplet size distribution is investigated, confirming its impact is marginal, particularly on the liquid length. It is observed that the initial droplet size is only important at very close to the nozzle and its impact on the spray structure becomes quickly insignificant due to the high rates of breakup and evaporation. This trend is consistent at different injection pressures.     

Improved atomization,collision and sub-grid scale momentum coupling models for transient vaporizing engine sprays

A computationally efficient spray model is presented for the simulation of transient vaporizing engine sprays. It is applied to simulate high-pressure fuel injections in a constant volume chamber and in mixture preparation experiments in a light-duty internal combustion engine. The model is based on the Lagrangian-Particle/Eulerian-Fluid approach, and an improved blob injection model is used that removes numerical dependency on the injected number of computational parcels. Atomization is modeled with the hybrid Kelvin–Helmholtz/Rayleigh–Taylor scheme, in combination with a drop drag model that includes Mach number and Knudsen number effects. A computationally efficient drop collision scheme is presented, tailored for large numbers of parcels, using a deterministic collision impact definition and kd-tree data search structure to perform radius-of-influence based, grid-independent collision probability estimations. A near-nozzle sub-grid scale flow-field representation is introduced to reduce numerical grid dependency, which uses a turbulent transient gas-jet model with a Stokes–Strouhal analogy assumption. An implicit coupling method was developed for the Arbitrary Lagrangian–Eulerian (ALE) turbulent flow solver. A multi-objective genetic algorithm was used to study the interactions of the various model constants, and to provide an optimal calibration. The optimal set showed similar values of the primary breakup constants as values used in the literature. However, different values were seen for the gas-jet model constants for accurate simulations of the initial spray transient. The results show that there is a direct correlation between the predicted initial liquid-phase transient and the global gas-phase jet penetration. Model validation was also performed in engine simulations with the same set of constants. The model captured mixture preparation well in all cases, proving its suitability for simulations of transient spray injection in engines.     

Interaction of a polydisperse spray with vortices

The objective of the present work is to provide, through the association of optical diagnostics on a well-chosen experimental configuration, new insights into the coupling of a vortical gaseous flow with a polydisperse evaporating spray representative of practical injections. A cloud of droplets is injected in an inert laminar round jet, axisymmetric and pulsated, enabling the study of the interaction of strong-vorticity structures with a polydisperse spray. The experiment is a laboratory-scale representation of realistic injection configurations such as in engine combustion chambers or industrial burners. The chosen set-up leads to a well-controlled configuration and allows the coupling of two optical diagnostics, particle imaging velocimetry (PIV) and interferometric particle imaging (IPI), which leads to the study of both the flow dynamic and the droplet size distribution. The behaviour of droplets is analysed regarding their relaxing and evaporating properties. Size-conditioned preferential concentration of both weakly evaporating and strongly evaporating sprays is investigated. Droplet trajectories are also analysed by means of high-rate tomographic visualizations. The time history between their ejection from the nozzle and their interaction with the vortex is strongly related to the droplet preferential concentration and the observed heterogeneous repartition in the gas flow.     

The Numerical Simulation of Diesel Spray Combustion with LES-CMC

A Large Eddy Simulation (LES) approach together with the Conditional Moment Closure (CMC) method have been used for the simulation of spray combustion in engine-like conditions. The strategy consists of coupling an academic CMC code with the commercial CFD software Star-CD?(CD-adapco). Two issues have been investigated: firstly, the applicability of conventional spray models to LES and secondly, LES-CMC for spray combustion. Conventional spray models that were originally developed for use in Reynolds-averaged equations have been assessed for their applicability within the LES framework by conducting non-reacting spray computations. Liquid core penetration, spray spreading angle and vapour phase penetration have been compared to the available experimental data and the agreement between LES and experiments is satisfactory. Several reacting spray calculations have been performed with a range of initial mixture and temperature conditions, which mimic Diesel engine configurations. The computed auto-ignition time and flame lift-off length are in good agreement with the experimental data. Despite the uncertainties associated with the spray models and the chemistry, the results illustrate that the LES-CMC methodology can reproduce well the experimental results.     

Effects of turbulence enhancement on combustion process using a double injection strategy in direct-injection spark-ignition (DISI) gasoline engines

Direct-injection spark-ignition (DISI) gasoline engines have been spotlighted due to their high thermal efficiency. Increase in the compression ratio that result from the heat absorption effect of fuel vaporization induces higher thermal efficiency than found in port fuel injection (PFI) engines. Since fuel is injected at the cylinder directly, various fuel injection strategies can be used. In this study, turbulent intensity was improved by a double injection strategy while maintaining mixture homogeneity. To analyze the turbulence enhancement effects using the double injection strategy, a side fuel injected, homogeneous-charge-type DISI gasoline engine with a multi-hole-type injector was utilized. The spray model was evaluated using experimental data for various injection pressures and the combustion model was evaluated for varied ignition timing. First and second injection timing was swept by 20 degree interval. The turbulent kinetic energy and mixture inhomogeneity index were mapped. First injection at the middle of the intake stroke and second injection early in the compression stroke showed improved turbulent characteristics that did not significantly decrease with mixture homogeneity. A double injection case that showed improved turbulent intensity while maintaining an adequate level of mixture homogeneity and another double injection case that showed significantly improved turbulent intensity with a remarkable decrease in mixture homogeneity were considered for combustion simulation. We found that the improved turbulent intensity increased the flame propagation speed. Also, the mixture homogeneity affected the pressure rise rate.     

Measurements of multicomponent microdroplet evaporation by using Rainbow Refractometer and PDA

The evaporation process of a multi-component droplet has been studied utilizing optical diagnostic techniques. Investigation focused on the measurements of the different volatility mixtures and the variation of the mass fraction within a droplet of different components. The method for determining the temperature of a multicomponent droplet containing nonvolatile and volatile compositions has been proposed. For a droplet with two volatile compositions, such as water and ethanol mixture, the model of evaporation for droplet temperature measurements was also suggested based on the experimental data. Droplets with different mass fractions of each component under different temperature conditions were measured utilizing a primary rainbow refractometer and a recently improved phase-Doppler analyzer. It was also found that the droplet temperature could hardly reach its saturation temperature within the droplet unlike explained by previous researchers. The effects of temperature gradient within an evaporating microdroplet and the temperature discontinuity on the evaporating surface have been discussed.     

High order moment method for polydisperse evaporating sprays with mesh movement: Application to internal combustion engines

Relying on two recent contributions by Massot et al. [SIAM J. Appl. Math. 70 (2010), 3203–3234] and Kah et al. [J. Comput. Phys. 231(2012)], where a Eulerian Multi-Size Moment (EMSM) model for the simulation of polydisperse evaporating sprays has been introduced, we investigate the potential of such an approach for the robust and accurate simulation of the injection of a liquid disperse phase into a gas for automotive engine applications. The original model used a high order moment method in droplet size to resolve polydispersity, with built-in realizability preserving numerical algorithm of high order in space and time, but only dealt with one-way coupling and was restricted to fixed meshes. Extending the approach to internal combustion engine and fuel injection requires solving two major steps forward, while preserving the properties of robustness, accuracy and realizability: 1 – the extension of the method and numerical strategy to two-way coupling with stable integration of potential stiff source terms, 2 – the introduction of a moving geometry and meshes. We therefore present a detailed account on how we have solved these two issues, provide a series of verification of the proposed algorithm, showing its potential in simplified configurations. The method is then implemented in the IFP-C3D unstructured solver for reactive compressible flows in engines and validated through comparisons with a structured fixed mesh solver. It finally proves its potential on a free spray jet injection where it is compared to a Lagrangian approach and its reliability and robustness are assessed, thus making it a good candidate for realistic injection applications.     

Similarity solutions for the evolution of polydisperse droplets in vortex flows

A new mathematical analysis of the dynamics of evaporating sprays in the vicinity of a vortex flow field is presented. The governing equations for a polydisperse spray evaporating in an unsteady viscous vortex flow are formulated using the sectional approach. First, new similarity solutions are found for the dynamics of the spray in a mono-sectional framework. It is shown that similarity for the droplets’ drag term exists, and an explicit model for the drag is found using perturbation theory. Numerical simulations are conducted to validate the main assumptions of the analytic approach adopted in this study. An extension of the mono-sectional solution of the spray equations to a polydisperse spray solution is then derived and the dynamics of polydisperse spray in an Oseen type vortex are presented. It is shown that for a given radial location, the droplets in each section reach a maximal radial velocity due to the effect of vorticity. A simple model is derived for the prediction of this maximal radial velocity of the droplets using perturbation theory, which agrees very well with the full similarity solution. The present study shows that spray dynamics is highly affected by the droplets’ size, but also by the spray initial size distribution, even when the same Sauter mean diameter is considered. This may have far reaching implications, especially in spray combustion applications.     

A unified spray model for engine spray simulation using dynamic mesh refinement

This study is based on dynamic mesh refinement and uses spray breakup models to simulate engine spray dynamics. It is known that the Lagrangian discrete particle technique for spray modeling is sensitive to gird resolution. An adequate spatial resolution in the spray region is necessary to account for the momentum and energy coupling between the gas and liquid phases. This study uses a dynamic mesh refinement algorithm that is adaptive to spray particles to increase the accuracy of spray modeling. On the other hand, the accurate prediction of the spray structure and drop vaporization requires accurate physical models to simulate fuel injection and spray breakup. The present primary jet breakup model predicts the initial breakup of the liquid jet due to the surface instability to generate droplets. A secondary breakup model is then responsible for further breakup of these droplets. The secondary breakup model considers the growth of the unstable waves that are formed on the droplet surface due to the aerodynamic force. The simulation results are compared with experimental data in gasoline spray structure and liquid penetration length. Validations are also performed by comparing the liquid length of a vaporizing diesel spray and its variations with different parameters including the orifice diameter, injection pressure, and ambient gas temperature and density. The model is also applied to simulate a direct-injection gasoline engine with a realistic geometry. The present spray model with dynamic mesh refinement algorithm is shown to predict the spray structure and liquid penetration accurately with reasonable computational cost.     

Large Eddy Simulation of a Polydisperse Ethanol Spray Flame

Ethanol is identified as an interesting alternative fuel. In this regards, the predictive capability of combustion Large Eddy Simulation approach coupled to Lagrangian droplet dynamic model to retrieve the turbulent droplet dispersion, droplet size distribution, spray evolution and combustion properties is investigated in this paper for an ethanol spray flame. Following the Eulerian-Lagrangian approach with a fully two way coupling, the Favre-filtered low Mach number Navier-Stokes equations are solved on structured grids with dynamic sub-grid scale models to describe the turbulent carrier gas phase. Droplets are injected in polydisperse manner and generated in time dependent boundary conditions. They evaporate to form an air-fuel mixture that yields spray flame. Part of the ethanol droplets evaporates within the prevaporization area before reaching the combustion zone, making the flame to burn in a partially premixed regime. The chemistry is described by a tabulated detailed chemistry based on the flamelet generated manifold approach. The fuel, ethanol, is modeled by a detailed reaction mechanism consisting of 56 species and 351 reversible reactions. The simulation results including excess gas temperature, droplet velocities and corresponding fluctuations, droplet mean diameters and spray volume flux at different distances from the exit plane show good agreement with experimental data. Analysis of combustion spray features allows gaining a deep insight into the two-phase flow process ongoing.     

Assessment of a 3D CFD model for GDI spray impact against wall through experiments based on different optical techniques

Performance of internal combustion engines is well known being greatly affected by the air-fuel mixture formation process. In spark ignition engines, in particular, the gasoline direct injection (GDI) technology is currently preferred, as it allows obtaining the desired air-to-fuel ratio distribution at each regime of operation, either by creating stoichiometric mixtures under high power demands, or through charge stratification around the spark plug at intermediate or lower loads. The impact of the gasoline spray on the piston or cylinder walls is a key factor, especially under the so-called wall-guided mixture formation mode. The impact causes droplets rebound and/or the deposition of a liquid film (wallfilm). After being rebounded, droplets undergo what is called secondary atomization. The wallfilm, on the other hand, may remain of no negligible size and evaporate slowly, leading to increased unburned hydrocarbons and particulate matter emissions.Optimization of the heterogeneous mixture behavior in GDI engines is fundamental for guaranteeing high energetic and environmental performance over the whole working map. Computational fluid dynamics (CFD) can be useful in this perspective to effect proper choices of control strategies. Assessment of predictive engine models, able to describe the complex phenomena underlying energy conversion in modern engines, is therefore mandatory to the scope.In the present paper, a basic study is performed on gasoline sprays issuing from high pressure injectors under controlled conditions: the experimental characterization of multi-hole and single-hole GDI sprays in their impact over a plate is carried out with the aim of creating a set of data to be used for the validation of a properly developed simulation model. The multi-hole spray allows accounting for the jet-to-jet interaction and represents a condition closer to the actual gasoline supply mode in present GDI engines. The single-hole injector configuration is instead preferred for a more detailed study, as it allows capturing effects related to the role that diverse parameters characterizing the liquid droplet dynamics play during and after their impingement on heated solid surfaces. The CFD model is conceived with the scope of its future application within numerical calculations of entire engine working cycles. A highly portable free spray sub-model allows correctly reproducing the injection dynamics under different conditions in a confined vessel, while the spray-wall impingement sub-model is shown being able to highlight to an acceptable extent the gasoline splashing and deposition phenomena.