A Zero-Dimensional Velocity-Composition-Frequency Probability Density Function Model for Compression-Ignition Engine Simulation

Numerical simulation of in-cylinder processes can significantly reduce the development and refinement costs of engines. While it can be argued that higher fidelity models improve accuracy of prediction, it comes at the expense of high computational cost. In this respect, a 3D analysis of in-cylinder processes may not be feasible for evaluating large number of design and operating conditions. The situation can be more foreboding for transient simulations. In the current work a phenomenological combustion modeling approach is explored that can be implemented in a lower fidelity modeling framework and can approach the accuracy of higher dimensional models with significant reduction in computational cost. The proposed model uses transported probability density function (tPDF) method within a 0D framework to provide a computationally efficient solution while capturing the essential physics of in-cylinder combustion. Scalar mixing is accounted for by a modified Euclidean Minimum Spanning Tree (EMST) mixing model. A new model has been formulated to calculate the mixing timescale using the velocity-composition-frequency (VCF) tPDF method. Numerical comparisons have been performed for two engines: one with a 3D-CFD simulated diesel engine to compare the in-cylinder composition and thermal stratification, and one with a diesel engine where measured data is available over a range of operating conditions encompassing a range of speed, load, and exhaust-gas recirculation (EGR). A 42-species chemical mechanism including thermal NO is used to represent the gas-phase chemistry. The proposed 0D-VCF model predicted pressure, heat-release-rate, equivalence-ratio vs temperature distribution, and NOx are compared to the 3D-CFD data, as well as to the experimentally measured data. The proposed model was able to capture the 3D-CFD trend of equivalence-ratio vs temperature distribution at different crank-angle degrees quite accurately. The 0D-VCF model computed pressure and heat-release-rate along with the NOx showed reasonable agreement with the experiment. In summary, the proposed 0D numerical model has the potential to provide a computationally less expensive alternative to a 3D numerical simulation for estimating engine performance and engine-out emission quantities when transient or large number of operating points are to be simulated.