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Conditional Source-term Estimation (CSE) is a combustion model based on the conditional moment hypothesis where transport equations for reactive species are conditionally averaged on conserved scalars. Major advantages of this strategy are the reduced spatial dependence of the conditional averages and negligible fluctuations around the conditional averages, which considerably simplify the reaction rate closure. Historically, simulations using CSE are limited to low carbon fuels (i.e. methane and hydrogen) where the reduced chemistry manifold can be constructed through techniques including intrinsic low dimensional manifolds and trajectory generated manifolds. However, the use of such strategies to create manifolds for diesel surrogates has proven problematic. In this study, the potential of a combination of an unsteady Flamelet Generated Manifold (FGM) and the Conditional Source-term Estimation approach to predict the ignition and flame propagation on an autoigniting n-dodecane spray flame is assessed. Simulations are performed on a single-hole injection of n-dodecane under a wide range of Engine Combustion Network’s “Spray A” conditions within a Reynolds-averaged Navier-Stokes (RANS) framework. Results from parametric sweeps of ambient temperature and oxygen concentration are qualitatively validated against experimental data from the literature and compared against predictions from an industry standard well-stirred reactor model. The efficacy of the CSE-FGM RANS approach in predicting flame characteristics is evaluated and further compared with high fidelity CSE-FGM simulations using the Large Eddy Simulation (LES) turbulence model. Overall, it was found that the CSE-FGM RANS model was able to capture global flame properties — showing particular strength in predicting auto-ignition events in the low temperature region. The model was also able to satisfactorily capture details of the two-stage ignition process. The results were shown to be consistent with those of the CSE-FGM LES model, demonstrating the adaptability of the CSE-FGM approach to different turbulence modelling paradigms.

In this article, different manifold reduction techniques are implemented for the post-processing of Particle Image Velocimetry (PIV) images from a Spark Ignition Direct Injection (SIDI) engine. The methods are proposed to help make a more objective comparison between Reynolds-averaged Navier-Stokes (RANS) simulations and PIV experiments when Cycle-to-Cycle Variations (CCV) are present in the flow field. The two different methods used here are based on Singular Value Decomposition (SVD) principles where Proper Orthogonal Decomposition (POD) and Kernel Principal Component Analysis (KPCA) are used for representing linear and non-linear manifold reduction techniques. To the authors’ best knowledge, this is the first time a non-linear manifold reduction technique, such as KPCA, has ever been used in the study of in-cylinder flow fields. Both qualitative and quantitative studies are given to show the capability of each method in validating the simulation and incorporating CCV for each engine cycle. Traditional Relevance Index (RI) and two other previously developed novel indexes: the Weighted Relevance Index (WRI) and the Weighted Magnitude Index (WMI), are used for the quantitative study. The results indicate that both POD and KPCA show improvements in capturing the main flow field features compared to ensemble-averaged PIV experimental data and single cycle experimental flow fields while capturing CCV. Both methods present similar quantitative accuracy when using the three indexes. However, challenges were highlighted in the POD method for the selection of the number of POD modes needed for a representative reconstruction. When the flow field region presents a Gaussian distribution, the KPCA method is seen to provide a more objective numerical process as the reconstructed flow field will see convergence with an increasing number of modes due to its usage of Gaussian properties. No additional criterion is needed to determine how to reconstruct the main flow field feature. Using KPCA can, therefore, reduce the amount of analysis needed in the process of extracting the main flow field while incorporating CCV.

Accurate modeling of the initial transient period of spray development is critical within diesel engines, as it impacts on the amount of vapor penetration and hence the combustion characteristics of the spray. In addition, in multiple injection schemes shorter injections will be mostly, if not totally, within the initial transient period. This paper investigates how two different commercially available Computational Fluid Dynamics (CFD) codes (hereafter noted as Code 1 and Code 2) simulate transient diesel spray atomization, in a non-combusting environment. The case considered for comparison is a single-hole injection of n-dodecane representing the Engine Combustion Network’s ‘Spray A’ condition. It was identified that the different spray break-up models used by the codes (Reitz-Diwakar for Code 1, Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) for Code 2) had a significant impact on the transient liquid penetration. From differing initial base setups, Code 1’s case was then matched as closely as possible to Code 2’s case, applying the KH-RT break-up model in Code 1 with the same constants for the break-up and turbulence models as in Code 2. Despite the nominal equivalence between the two simulations, there existed a discrepancy in liquid length prediction throughout injection between codes. This was thought to be caused by differing implementations of the KH-RT model in both codes. Therefore, a new implementation of the KH-RT model was input into Code 1 in order to allow correct matching of the liquid length to experimental data throughout the injection period. This was achieved utilizing a numerical switch based on the Ohnesorge number. Results from the new model are shown and compared to the previous implementation, showing an improved ability to match to experimental data. Differences between the results from the modified KH-RT model in Code 1 and the standard implementation in Code 2 are also discussed.

A novel combustion modelling approach is proposed here to study the transient effects of diesel spray. Conditional Source-term Estimation (CSE) is a combustion model which invokes the Conditional Moment Closure (CMC) hypothesis to provide an approximation of the mean chemical source term in an averaged transport equation. Unlike CMC, where transport equations are solved for conditional moments, CSE recovers these conditional moments through the solution of an inverse problem. Integral equations are inverted for the conditional moments, by assuming spatial homogeneity in the conditional averages where Tikhonov regularisation is applied. Previous CSE studies have shown that the model is able to predict the flame characteristics successfully for both premixed and non-premixed combustion modes. However, most of these investigations were based on methane flames. This study will be the first successful application of CSE to a complex hydrocarbon fuel, n-dodecane, under the Engine Combustion Network's (ECN) ‘Spray A’ conditions. Detailed chemistry is included in tabulated form using the Flamelet Generated Manifold (FGM) methodology. The predictions of this study include both the Favre averaged conditional mass fraction of reactive species and temperature. The results are compared with available experimental data and previous numerical results. Both RANS and LES simulations are performed under the same condition. The objectives of the paper are (i) assessment of the application of CSE on igniting diesel spray (ii) comparison of the CSE numerical results with available experimental results and previous numerical simulations. Overall, the combination of a chemical mechanism that has been tuned to predict ‘Spray A’ conditions with the CSE-FGM model is able to successfully predict autoignition delay time and lift-off length of n-dodecane spray within the scatter of the experimental data. CSE-FGM offers a feasible tool for detailed combustion analysis of diesel spray flames. Both RANS and LES can give reasonably good global predictions of the flame.

This article considers the application and refinement of artificial neural network methods for the prediction of NO x emissions from a high-speed direct injection diesel engine over a wide range of engine operating conditions. The relative computational cost and performance of two backpropagation algorithms, Levenberg–Marquardt and Bayesian regularization, for this application are compared, with the Levenberg–Marquardt algorithm demonstrating a significant cost advantage. This work also assesses the performance of two alternative filtering approaches, a p-value test and the Pearson correlation coefficient, for reducing the required number of input variables to the model. The p-value test identified 32 input parameters of significance, whereas the Pearson correlation test highlighted 14 significant parameters while additionally providing a ranking of their relative importance. Finally, the article compares the predictive performance of the models generated by the two filtering methods. Overall, both models show good agreement to the experimental data with the model created using the Pearson correlation test showing improved performance in the low-NO x region.