Towards the Use of Eulerian Field PDF Methods for Combustion Modeling in IC Engines

Abstract

Dear session organizers, authors thanks the reviewers for the very useful suggestion and comments to include the quality of the paper. The text was modified accordingly and changed parts were highlighted with the red color. A detailed response to reviewer comments follows. Response to Reviewer 1 Stochastic Eulerian field PDF methods are combined with a combination of acceleration strategies to reduce the computational cost associated with the use of large chemical mechanisms in CFD.The resulting model is used to simulate autoignition in a high-pressure turbulent spray combustion vessel under diesel-engine-like conditions. While the individual methods are not new, the combination of methods and their application to autoignition for enginerelevant conditions is novel, and would be of interest to the SAE audience. This is an approach that has significant potential for accurately capturing effects of turbulence-chemistry interaction over a wide range of engine operating conditions.Authors thanks the reviewer for the comments. The proposed combustion model based on Eulerian Stochastic fields will be continuosly developed and applied soon to more realistic engine studies. The title of the paper "Towards the Use of Eulerian Field PDF Methods for Combustion Modeling in IC Engines" should clearly indicate that this is a first attempt to apply what is considered by the combustion community to be one of the most complex and realistic models currently available to predict flame propagation. Presentation of preliminary results and discussion about them within the SAE world congress toghether with the major experts of the engine combustion community represents, to the authors' opinion, one of the best ways to understand the main advantages and drawbacks of such model and to find proper ways to improve it. For this reason, authors do not think this work is incomplete but it represents an important step towards the adoption of advanced models to predict combustion in IC engines. This reviewer's comment is not completely clear to the authors. The first sentence is just a general consideration, while the last one clearly states that this is just a preliminary work and for this reason further validation is required. For what concerns the model description, in this work it was not possible to include all the complete details about 1 how stochastic combustion models and related processes work. We recommend the reviewer to look at references [21][22][23][24][25][26][27][28] for further information. Eq. 1 illustrate the generic formulation of a transport equation for the joint pdf function inside the computational domain. Such equation is too complex to be solved directly (it is a transport equation for a function and not a scalar or vector field) and for this reason it is solved either with the help of Lagrangian particles (Lagrangian PDF methods) or by using Stochastic fields. The statement "summation is implied ..." is referred to divergence terms appearing in Eq. 1 and other transport equations included in this work as well. The W...

Heavy-Duty Diesel Engine Spray Combustion Processes: Experiments and Numerical Simulations

“…perfectly stirred reactor or laminar diffusion flame) the cell size restriction can be lifted at the expense of extra overhead to describe the sub-grid mixing and turbulence chemistry interaction. This is related to the integration of the presumed probability function, or the transport of many species and energy equations such as the number of simulated flow realizations or stochastic fields [43]. Therefore, tabulated kinetics can offer a possible solution to reduce the CPU time and to keep an acceptable accuracy.…”

Modeling Non-Premixed Combustion Using Tabulated Kinetics and Different Fame Structure Assumptions

“…The same figure reports also iso-contours of stoichiometric mixture fraction with the greeen line and a dashed white line located where experimental lift-off length was found. As already discussed in past works [5,15], the well-mixed model with direct chemistry integration overestimates the lift-off since it does not consider turbulence-chemistry interaction and, because of this assumption, there is a larger region where the scalar dissipation rate is higher than the value at which diffusion flame extinguishes. In the TWM model, the flame has a shorter lift-off length because of the higher mixture reactivity where the mixture is rich, as already discussed in Figs.…”

“…To reduce the computational time, different techniques were developed in the past: among them we can mention on-line tabulation or cell clustering: when applied in combination with the well-mixed model they offer acceptable speed-up factors in case relatively small mechanisms (up to 50 species) are employed [11,12,13,14]. Inclusion of turbulence-chemistry interaction adds significant overheads related to the need to consider the effects of sub-grid mixing either by integrating a presumed PDF or solving additional equations for the different expected flow realizations [5,15]. This explains the reason why the most widely used approaches are the wellmixed and the Representative Interactive Flamelet (RIF) ones.…”

Modelling of diesel spray flames under engine-like conditions using an accelerated Eulerian Stochastic Field method

“…Framework Type of fuel combustion TCI closure Soot model Jangi et al [1] URANS n-Heptane ESF -Pei et al [10,21] URANS n-Dodecane L-tPDF -Pang et al [12,29,43] URANS Diesel, n-Heptane WSR Four-step D'Errico et al [13] URANS n-Dodecane WSR+PDF -Pei et al [19,20] URANS n-Heptane L-tPDF -Bhattacharjee and Haworth [22] URANS n-Heptane, n-Dodecane L-tPDF -Bolla et al [23][24][25] URANS n-Heptane, Diesel CMC Four-step Irannejad et al [27] LES n-Heptane FMDF -Lucchini et al [28] URANS n-Dodecane ESF -Wang et al [30] URANS n-Dodecane WSR Five-step Gong et al [31] LES n-Dodecane WSR Two-step Chishty et al [32] URANS n-Dodecane L-tPDF Four-step Frassoldati et al [33] URANS n-Dodecane mRIF -Cheng et al [34] URANS Biodiesel WSR Four-step Poon et al [35] URANS Diesel WSR Four-step Vishwanathan and Reitz [36] URANS Diesel WSR Five-step D'Errico et al [37] URANS n-Dodecane WSR, mRIF -Gong et al [38] URANS n-Heptane ESF -Gallot-Lavallée and Jones [39] LES n-Heptane ESF -Pandurangi et al [40] URANS n-Dodecane CMC Four-step Wehrfritz et al [41] LES n-Dodecane FGM -Jangi et al [42] URANS n-Heptane WSR Two-step Bolla et al [44,45] URANS n-Dodecane L-tPDF Four-step Note: L-tPDF denotes the Lagrangian particle transported PDF model. The two-step soot model represents the Hiroyasu-Nagle and Strickland-Constable (NSC) model which describes soot formation and oxidation [48].…”