Application of a flamelet-based CFD combustion model to the LES simulation of a diesel-like reacting spray

Highlights

• Spray A from ECN is analysed with LES simulations and a flamelet model.

• Results in very good agreement with experimental measurements.

• Low fluctuations for the lift-off length due to the intense chemistry.

• Ignition kernels appear spontaneously and detached from the main flame.

Abstract

Spray A from ECN, representative of diesel-like sprays, is modelled in the frame of Large-Eddy Simulations (LES) with a Dynamic Structure (DS) turbulence model in conjunction with an Unsteady Flamelet Progress Variable (UFPV) combustion model. In this work, the spray flow field is first calibrated under inert conditions against experimental data. In a second step, the reactive spray is simulated in order to describe the flame internal structure when varying ambient temperature. The model shows a good agreement with experimental results and describes the trends observed in flame global parameters, such as ignition delay (ID) and lift-off length (LOL). Low fluctuations are observed in LOL positioning revealing an intense chemical activity at the height of the base of the flame, which stabilizes the reaction in spite of the turbulent fluctuations. The analysis of the LES instantaneous fields shows how ignition kernels appear upstream of the base of the flame, clearly detached from the reaction zone, and grow and merge with the main flame in agreement with previous reported experimental and modelling results. The ambient temperature has a clear impact on the flame structure described by the model and the whole set of results reveal that in the frame of LES simulations the UFPV model is suitable for the calculation of diesel flames.

Introduction

The ever-increasing relevance of the transport and energy sectors in our society has lead to the optimization of combustion devices in order to increase their efficiency and reduce pollutant emissions. In particular, understanding the complex phenomena involved in diesel-like reacting sprays and their interaction is a challenging field in the research of partially premixed and non-premixed combustion. These phenomena could be summarized in atomization and break-up, evaporation, mixing, chemical oxidation and spray-wall interaction occurring in a high Reynolds turbulent flow [1].

The complete resolution of the whole physical and chemical processes developing in so different spatial and temporal length scales leads to an unaffordable computational cost and, consequently, different hypothesis have to be introduced in order to derive simplified models. However, these assumptions entail new uncertainties that have to be verified. Unfortunately, measuring in an engine is a difficult task that, in general speaking, only provides global or integral variables, insufficient to give an exact picture of the whole combustion process and validate the models.

In this context, the Engine Combustion Network (ECN) [2] has suggested a set of representative experiments to be carried out in special combustion chambers, constant-volume pre-burn (CVP) combustion vessels and constant-pressure flow (CPF) rigs [3], [4], that discard many uncertainties and allow to measure with the most advanced experimental techniques. The empirical observations are complemented with Computational Fluid Dynamics (CFD) simulations. The participation of a wide sector of the researcher community allows to diffuse and improve the state of the art.

In line with this goal, this work deals with simulating the well-known spray A from ECN, a single nozzle spray with boundary conditions corresponding to modern diesel-like sprays. Liquid length, vapour penetration and some relevant spatial fields together with ignition delay (ID), lift-off length (LOL) are measured in these combustion chambers. A CPF rig is available at CMT-Motores Térmicos whose experimental results are used along this paper [5], [6] unless otherwise stated.

Regarding diesel spray modelling an extensive literature may be found for inert and reactive conditions. As mentioned previously, the great variety of physical and chemical phenomena occurring at different scales in the flow has given rise to the formulation of many different models aiming to describe these phenomena with different levels of accuracy and computational cost.

For years, the Reynolds Averaged Navier-Stokes (RANS) equations have been widely used due to their relative reduced computational cost compared to other approaches. Excellent results have been reported in the frame of combustion modelling by means of RANS simulations [7], [8], [9], [10]. Notwithstanding, and despite the positive capabilities of the RANS approach, as the whole range of scales are modelled their hypothesis may not be completely fulfilled.

In order to solve more accurately the flow, Large-Eddy Simulations (LES) have gained attention during the last years since, in spite of their higher computational cost, the large eddies are solved and only the smallest scales, that tend to show statistical isotropy and universality [11], have to be modelled leading to the development of more accurate models [12].

Notwithstanding, chemical reactions occur when the species are mixed at molecular level implying that combustion takes place at or even below the smallest scales of the flow. Hence, the LES simulation does not solve the chemical source term, which is completely modelled [13], [14], and this leads to directly extend the RANS combustion models to the LES approach. However, it is expected to obtain more accurate results for LES since the shape of the filtered probability density function (FPDF) has less impact [14] and the integral scales are better predicted. These advantages are conjugated with the capability to reproduce intermittency [15], [16]. LES calculations have been successfully applied to combustion simulation [17], [18], [19], [20].

Regarding the LES turbulence models, some of them are based on the Boussinesq hypothesis as the Smagorinsky model, which requires adjusting ad hoc the value of its constant C_S. This shortcoming can be palliated with the dynamic model [21]. More refined approaches can be obtained when transporting the sub-grid kinetic energy k_sgs as in the One Equation Eddy model (OEE) [22], which allows to use coarser meshes which are more compatible with Lagrangian droplet models, conventionally used to model the liquid phase in spray simulations. In addition, the presence of two phases in diesel sprays adds new terms to the sub-grid scale modelling and complicates the turbulence models [23].

Finally, in other approaches like the Dynamic Structure model (DS) [24], which is not based on the Boussinesq hypothesis, the residual stress fluxes are considered proportional to the sub-grid turbulent kinetic energy k_sgs by means of a coefficient tensor and k_sgs is transported. This model fulfils some important properties that are desirable for any turbulence model, namely, solvability, scaling, frame invariance and realizability [24]. Due to its capabilities to perform accurate simulations and its formulation for multiphase simulations [25], [26], it has been adopted in the current work.

Solving a diesel spray simulation requires a combustion model with the ability to manage complex chemical schemes while retaining turbulence-chemistry interaction (TCI). In some works the diesel spray has been modelled with Perfect Stirred Reactors (PSR) [27], [28] but, as Bhattacharjee et al. [29] point out, the lack of TCI makes this model not suitable for this problem especially for conditions of low reactivity. It is worth mentioning the previous mentioned works were carried out in the frame of RANS simulations, however, it is expected that when calculating with LES simulations the impact of not considering TCI, even not being a correct modelling approach since chemistry occurs at the smallest scales of the flow which are not solved in LES, may lead to more accurate results [17]. Other models like the Representative Interactive Flamelet (RIF) model can provide good results [30], [31], [32] but lead to a non-local description of the flame and the need of injecting a high number of flamelets, that increase the computational cost in order to obtain accurate results. Using similar concepts the Flamelet Generated Manifold (FGM) has been demonstrated to be a powerful model that captures many phenomena of the diesel flame [20], [33]. Finally, transporting probability density functions (PDFs) has been shown to be a fruitful approach to describe combustion, for which very accurate results for ID and LOL as well as flame structure have been provided [9], [29], [34]. However, its very high computational cost makes this model difficultly affordable for practical engine simulations.

Regarding the physical phenomena observed in the diesel flame a great effort has been devoted to study combustion development at the LOL. This distance delimits the height at which important amounts of heat are released and provides an indirect measure of the soot being formed, since it determines the maximum mixture fraction that reacts in the spray [35]. In this region the flame stabilizes and the mechanism of how this occurs is still a matter of intense study. Experimentally it has been observed how hot pockets of partially premixed fuel-air mixtures ignite spontaneously upstream and detached from the flame [36], [37] and this observation has been confirmed by means of LES simulations [17], [20]. This is an important result since it is an indirect evidence that one of the flame stabilization mechanisms is auto-ignition although some authors specify that the predominance of auto-ignition or other stabilization mechanisms, such as flame propagation, depends on the boundary conditions too, being more important flame propagation for high ambient temperatures [38]. Due to its interest this aspect will be covered in this paper too.

Considering previous picture for the different models available in the literature and their capabilities, the flamelet-based model appears as one of the most promising alternatives [8], [39], [40], [41], [42], [43] with a remarkable balance between accuracy and computational cost. This model describes the turbulent flame as an ensemble of strained laminar flames called flamelets [44]. The flamelet equations may be rewritten in the mixture fraction space yielding a system of one-dimensional transport equations [45], [46]. In LES framework, the solutions provided by this system are integrated by means of FPDFs in order to account for the TCI.

Depending on the approach, the flamelet equations may be solved during the CFD calculation, as in the Representative Interactive Flamelet model (RIF) [30], or, on the contrary, the flamelet solutions may be pre-tabulated, as in the Flamelet Generated Manifold (FGM) [39] or the Flame Prolongation of ILDM (FPI) [47], which are based on the Intrinsic Low Dimensional Manifold (ILDM) [48]. The FPI approach is adopted in this work.

However, despite the advantages provided by these models the computational cost may increase exponentially when dealing with diesel engine simulations where the boundary conditions may span over wide ranges, complex mechanisms are required and a local description of the flame is necessary [49], [50]. In this context, a simplified approach called Approximated Diffusion Flamelets (ADF) was suggested in order to reduce drastically the computational cost while retaining the ability to manage complex chemistry [49]. This approach is adopted for the current work given the excellent reported results provided in the literature [10], [43], [50], [51].

With this work many results found by means of experiments and modelling techniques [33], [36], [37], [52], [53] are intended to be corroborated with the application of the Dynamic Structure model used in conjunction with the ADF flamelet model which is used in the context of LES simulations. To demonstrate the suitability of such combination of modelling approaches applied to diesel sprays simulations is another target which is intended to be covered with the perspective of giving validity to future numerical experiments where more complex phenomena will be incorporated. Hence, the objective of this work is the analysis of the diesel flame structure, with special attention to the behaviour at the base of the flame where the LOL is positioned, and how such structure is influenced by the change of the boundary conditions, in particular the air temperature. For this purpose, spray A from ECN [2] has been simulated since there exists a vast set of experimental results that allows to contrast many of the conclusions extracted along the work.

The paper is structured with the description of the problem, followed by a section where the numerical algorithms and mesh are explained. This information is complemented with the description of the DDM (Discrete Droplet Method) and combustion models. Subsequently, a first validation in inert conditions is carried out which is closed with an initial assessing of the reacting flame. The capability of the model is evaluated with the analysis of the global parameters, ID and LOL, with special attention to the last one. The instantaneous fields are described by means of spatial and Z-T maps, first for the nominal case, and then for the rest of boundary conditions. This is followed by an analysis of the flame at the LOL in order to shed light in the flame stabilization mechanism. Previous analysis is complemented with the description of the averaged fields before giving the conclusions of the work which close the paper.