Modelling for turbulent autoignition with split fuel injection

Abstract

Split-injection is applied in automotive diesel engines in order to control heat release and pollution production. Injecting fuel prior to the main fuel injection, known as pilot injection, increases premixing and tends to reduce NOx emission. Injecting a portion of the fuel after the main injection has potential for reducing particulate emissions. In order to meet increasingly stringent emission and fuel consumption regulations, modern automotive diesel injectors have been developed with the capacity to deliver of the order of ten separate injection pulses during a single engine stroke. Simulation methods for split-injection engines are required in order to develop more advanced injection strategies with two or more separate fuel-injections. A range of additional combustion applications involve mixing and combustion between multiple streams such as Exhaust Gas Recirculation (EGR) and dual fuel injections. Modelling for the turbulent combustion interactions in multi-stream problems is developed in this thesis in the context of Conditional Moment Closure (CMC) methods.

The CMC approach provides modelling of chemical processes in turbulent flows by linking composition fluctuations to the variation of a small number of conditioning variables such as mixture fraction. In order to achieve good accuracy, the conditioning variables must be chosen to minimise compositional fluctuations around the conditional mean. Split-injection diesel engine operation results in complex combustion behaviour in which a single conditioning variable may be insufficient. However multiple-conditioned moment closures, or even double conditional moment closures (DCMC) have not been exploited previously. The objective of this study is to identify the most appropriate conditioning variables for modelling of split-injection diesel engines and to formulate, validate and demonstrate a practical implementation of the DCMC approach for engine-relevant simulations.

The thesis begins by developing a new formulation of the DCMC approach that is applicable to a general set of non-conserved conditioning variables, and a set of numerical solution approaches is demonstrated and verified. The choice of conditioning variables is then investigated through direct numerical simulations of autoignition in a turbulent flow with up to three separate fuel injections. In the case with a single injection, fluctuations around the mixture fraction-conditioned mean arise due to variation in mixture fraction dissipation rate affecting the progress of ignition differently at different points in space. In cases with multiple injections, the repeated addition of unreacted fuel also adds to fluctuations around the conditional mean. The high level of conditional fluctuations leads to large errors when employing singly-conditioned first-order conditional moment closure. Alternative doubly conditional moment closure approaches are tested using a priori and a posteriori analyses. Single conditioned first order closure gives extremely poor agreement with the DNS, and the study indicates that double conditioning on mixture fraction and progress variables, such as the sensible enthalpy, outperforms double conditioning on multiple mixture fractions.

The feasibility of the zero-dimensional DCMC approach for practical predictive design calculations is then assessed further through simulations of n-heptane spray ignition in constant volume research vessels with single or multiple injections. The experimental flows are simulated by coupling the zero-dimensional first order double conditional moment closure (0D-DCMC) with a commercial CFD code and an efficient Operator Splitting solution method is demonstrated. The predictions show the same trends as the experimental observations, however ignition delays and lift off lengths agree with the measurements only approximately. Reasons for the discrepancies include the uncertainty in the chemical modelling as well as in the ambient temperature surrounding the spray in the experiments. The modelling of conditional cross-scalar dissipation rate is also found to have a significant influence on the flame evolution, with the limiting cases of modelling corresponding to zero correlation or unity correlation between mixture fraction and progress variable giving unrealistic predictions. Conditional cross-dissipation rate modelling corresponding to negative unity correlation gives reasonable predictions, and an argument for why negative mixture fraction–progress variable correlation is expected to be dominant in autoignitive lifted jet flames involving multiple fuel injections is presented. Other aspects of modelling uncertainty with regard to conditional dissipation rates, presumed joint mixture fraction-progress variable probability density functions and first order source term closures will also contribute to the model error, and further development of models suitable for spray autoignition cases would be beneficial.

In comparison with the established three-dimensional singly-conditioned moment closure (3D-CMC), the 0D-DCMC model is a promising approach which is expected to be substantially faster than the 3D-CMC approach in most problems of engineering interest. Not withstanding the imperfect predictions, the ability of the zero-dimensional DCMC to describe the whole split-injection process and to provide new insight into the mechanisms involved is encouraging: this implies that only a few DCMC control volumes may be needed in order to model a wide range of flows involving very complex physics, of which split-injection is just one example, and the DCMC approach is therefore recommended for further development.

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Identifiers

ORCID for Edward Richardson: orcid.org/0000-0002-7631-0377

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