Computational optimization of split injections and EGR in a diesel engine using an adaptive gradient-based algorithm

Document Type

Conference Proceeding

Publication Date



Department of Computer Science; Department of Mathematical Sciences


The objective of this study is the development of a computationally efficient CFD-based tool for finding optimal engine operating conditions with respect to fuel consumption and emissions. The optimization algorithm employed is based on the steepest descent method where an adaptive cost function is minimized along each line search using an effective backtracking strategy. The adaptive cost function is based on the penalty method, where the penalty coefficient is increased after every line search. The parameter space is normalized and, thus, the optimization occurs over the unit cube in higher-dimensional space. The application of this optimization tool is demonstrated for the Sulzer S20, a central-injection, non-road DI diesel engine. The optimization parameters are the start of injection of the two pulses, the duration of each pulse, the duration of the dwell, the exhaust gas recirculation rate and the boost pressure. A zero-dimensional engine code is used to simulate the exhaust and intake strokes to predict the conditions at the closure of the inlet valves. These data are then used as initial values for the three-dimensional CFD simulation which, in turn, computes the the emissions and specific fuel consumption. Simulations were performed for two different cost functions with different emphasis on the fuel consumption. The best case showed that the nitric oxide and the particulates could be reduced by over 83% and almost 24%, respectively, below the EPA mandates while maintaining a reasonable value of specific fuel consumption. Moreover, the path taken by the algorithm from the starting point to the optimum has been investigated to understand the influence of each parameter on the process of optimization.

Publisher's Statement

Copyright © 2006 SAE International. Publisher’s version of record: https://doi.org/10.4271/2006-01-0059

Publication Title

SAE Technical Papers