Diesel Engine Simulations with Multi-Dimensional Conditional Moment Closure

First-order elliptic Conditional Moment Closure (CMC), coupled with a computational fluid dynamics (CFD) solver, has been employed to simulate combustion in a direct-injection heavy-duty diesel engine. The three-dimensional structured finite difference CMC grid has been interfaced to an unstructured finite volume CFD mesh typical of engine modelling. The implementation of a moving CMC grid to reflect the changes in the domain due to the compression and expansion phases has been achieved using an algorithm for the cell addition/removal and modelling the additional convection term due to the CMC cell movement. Special care has been taken for the boundary conditions and the wall heat transfer. An operator splitting formulation has been used to integrate the CMC equations efficiently. A CMC domain reduction of the three-dimensional problem to two- and zero-dimensions through appropriate volume integration of the CMC equation has been explored in terms of accuracy and computational time. Additional considerations have been reported concerning the initialization of the CMC domain in conserved scalar space during transient calculations where the probability density function of the mixture fraction changes drastically with time as during fuel injection. Predictions compare favourably with the experimental pressure traces for tests at full and half load. A balance of terms in the CMC equation allows conjectures on the structure of the flame and its expansion across the spray after autoignition.

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