ABSTRACT 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 higherdimensional 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。84611

INTRODUCTION

Over the years, engine research has focused on improving the engine performance by optimizing various design and operating parameters。 For diesel engines, the common rail injection system in conjunction with other injection strategies, such as the split injection, (e。g。 [1–7]), have contributed to the reduction of fuel consumption as well as emissions。 These injection techniques in combination with exhaust gas recirculation (EGR) (e。g。 [8–10]) and water injection strategies (e。g。 [11–13]) have been investigated in many experimental and computational studies。 The above cited studies have identified a variety of engine parameters which influence the formation of pollutants such as soot, (i。e。 particulates PM), and nitric oxide (NOx)。 Unfortunately, different parameters influence the behavior of these pollutants differently。 Typically, a reduction in nitric oxide is associated with an increase in the soot formation, referred to as the soot-NOx trade-off, which usually occurs at the expense of the fuel consumption。 In view of this complex dependence of the engine input and output data, and due to the fact that changes in the experimental setup can be very costly, computational techniques seem to be a natural choice for finding optimal engine operating conditions。 The search for optimal engine operating conditions leads to an optimization problem, where an appropriate cost function is minimized over a high-dimensional parameter space which reflects the engine’s input data。 In order to obtain accurate emission values, the computations are generally performed by means of a CFD code which simulates the engine’s compression and combustion phase。 This simulation is computationally very expensive and is the main contribution to the overall computational costs of the optimization process。 A well-suited optimization method for input-output systems with unknown dynamics, is based on the genetic algorithm (GA)。 GAs are modeled on the principle of natural selection, where an optimal state is determined over many generations of successful outcomes, subject to possible mutations (cf。 [14])。 If iterated over enough generations, GAs are likely to produce global optima。 However, pure GA methods require thousands of cost function evaluations and are therefore too expensive for CFD-based engine optimization。 A variation of the GA, called the micro-genetic-algorithm (μGA), has successfully been developed and applied in engine optimizations by Reitz and co-workers (cf。 [15–21])。 The main feature of the μGA is the effcient selection process used in the determination of the next generation, which allows a drastic reduction in the population size。 Typically, the population can be reduced from at least thirty, as required by the standard GA, down to as low as five。 Consequently, the number of costly engine simulations is greatly reduced, which makes the μGA applicable to engine optimization using present-day computers。 In the aforementioned computations, NOx and soot emissions in conjunction with fuel consumption have been optimized with respect to a variety of engine parameters。 These parameters include various patterns of pulsed injections, start of injection, combustion chamber geometry and others。 The cost function used in the μGA is derived from the widely used penalty method in constrained optimization problems。 In this approach, the quantities which need to be optimized, i。e。 emissions and fuel consumption, are combined in one expression which then is minimized。 A different approach to the evaluation of the performance criteria is taken by the multi-objective GAs。 In these algorithms, the optimal performance is determined by extreme points of an associated set, called the Pareto set, and the selection of the new generations involves a special type of fitness or cost function。 Multi-objective μGAs have been used by de Risi et al。 [22] in the optimization of engine combustion chamber geometries using a three-dimensional CFD code。 Also, a multi-objective μGA utilizing a phenomenological engine model has been developed and implemented in the study of Hiroyasu et al。 [23]。 The big disadvantage of GA-based optimization methods is their enormous computational costs, especially in the context of CFD engine simulations。 More efficient approaches are gradient-based minimization methods。 In gradient-based methods, an optimum is obtained by minimizing the cost function along a sequence of search directions。 These methods approach their target monotonically and, therefore, are computationally much more efficient than GA-based strategies。 The main drawback of gradient methods is the fact that they are less likely to reach a global minimum in the presence of local minima。 In such situations, the obtained minimum is determined by the starting point。 The efficiency of gradient-based optimization often outweighs their drawback of only finding a local minimum。 In an experimental study of Lee and Reitz [24], a response surface method has been successfully utilized to find optimal engine operating conditions。 In response surface methods, the gradient is determined from a plane which is fitted through neighboring points of a pivot using a least squares approach。 The determination of the gradient by this method is necessary because the engine optimization parameters are subject to experimental fluctuations, which can adversely influence the cost function evaluation。 In previous studies by these authors (cf。 [25, 26]), a conjugate gradient method in conjunction with a backtracking algorithm had been introduced and tested for an experimental, non-road Sulzer S20 DI diesel engine utilizing a KIVA-3-based CFD code [27]。 The first study [25] explored the effect of using different cost function weights, when the conventional injection parameters were optimized with respect to fuel consumption and emissions。 The second paper [26] was a preliminary investigation of a two pulse split injection strategy and its effect on emissions reduction。 Both studies showed that the conjugate gradient method is computationally extremely efficient and that considerable improvements in terms of emissions can be achieved。 However, this approach suffered from the disadvantage that the monotonic cost function descent could lead to very low emissions but an unacceptably high fuel consumption。 In the present study, an adaptive steepest descent method in conjunction with a modified backtracking strategy in the associated line search is used。 The standard backtracking algorithm is modified to use a dynamic first step, depending upon the steepness of the search direction。 The idea is to reduce the number of steps taken along the line search。 The entire optimization has been performed on a normalized unit cube in n-dimensional space, i。e。, the range of each optimization parameter is mapped onto the interval [0,1]。 In this study, a Sulzer S20 stationary diesel engine has been optimized for two different cost function formulations。 The three-dimensional engine simulations used to predict the emissions and the SFC have been performed from the closure of the inlet valves to the opening of the exhaust valves with a KIVA-3-based code。 A zero-dimensional engine code has been used to simulate the exhaust and inlet strokes to predict the equilibrium conditions at inlet valve closure for the CFD code。 The parameters that are optimized are the start of injection of the first pulse, injection duration of the first pulse, duration of dwell, injection duration of the second pulse, EGR rate and the boost pressure。 The emission mandates used are the ones prescribed by the United States Environmental Protection Agency (EPA) for stationary engines [28]。