An Advanced Optimization Methodology for Understanding the Effects of Piston Bowl Design in Late Injection Low-Temperature Diesel Combustion

An Advanced Optimization Methodology for Understanding the Effects of Piston Bowl Design in Late Injection Low-Temperature Diesel Combustion C. Genzale 1, D. Wickman 2 and R.D. Reitz 1 1 Engine Research Center, University of Wisconsin Madison, 1500 Engineering Dr., Madison, WI 53706, USA. E-mail: genzale@wisc.edu 2 Wisconsin Engine Research Consultants, LLC, 3983 Plymouth Cir., Madison, WI 53705, USA. Abstract. An integrated optimization methodology is presented that combines the use of a multi-objective genetic algorithm optimization tool and a non-parametric regression analysis tool in order to maximize understanding of piston bowl design for use in low-temperature diesel combustion. This methodology is specifically applied to a late injection, Modulated Kinetics (MK) type combustion in order to gain insight about the effect of bowl design under this type of operating condition. A multi-dimensional Computational Fluid Dynamics (CFD) code was employed with a newly developed automated grid generator and a multi-objective genetic algorithm to optimize eight piston bowl geometry parameters, start-of-injection timing and swirl ratio. The results indicate that bowl geometry and swirl ratio play an important supporting role in obtaining optimal emissions and fuel economy. Introduction In recent years, several engine modeling research groups have begun applying genetic algorithms to optimize complex engine design problems [1, 2, 3, 4]. This approach has shown a powerful ability to simultaneously optimize a large number of engine operating parameters at a relatively low computational cost. This technique has been especially successful in its ability to offer new insights and ideas that are assisting engine researchers in developing future strategies for emissions reductions and fuel conservation. By coupling genetic algorithms to CFD codes, researchers have found that a wide range of design options can be explored entirely theoretically without any concern of damaging engine components or implementing expensive experimental equipment. While these optimizations have yielded many interesting ideas, interpreting the meaning of the results is often difficult due to the large number of parameters being changed simultaneously. There have been many different approaches taken by researchers to better explain the results of these optimization problems. Liu et al. [1] undertook this task in an optimization of a multiple injection strategy for a high speed direct injection (HSDI) diesel engine by performing a parametric study around the resulting optimal design. In that study each design parameter was varied in order to gain a better understanding of the contribution each parameter gave to the optimal design. This approach successfully highlighted the important features in their optimal design, but could not fully illustrate the relative importance of each design parameter or the sensitivity of the design to changes in these parameters. De Risi et al. [2] were able to identify important but generalized piston bowl geometry requirements for optimal emissions in a HSDI diesel engine by using a multi-objective genetic algorithm. Because a multi-objective optimization method was used, a set of optimal solutions was found that simultaneously and individually optimized each of their design objectives. This set of solutions was used to identify important trends in the optimization of each objective. Using these trends, general piston bowl requirements for the optimization of each objective were able to be deduced, but the effect of individual design parameters was not obvious. Recently, Liu et al. [5] introduced a statistical regression method to fit a portion of the optimization data in their previous multiple injection strategy work. With this more rigorous technique, the contribution of each design parameter to the optimal design was quantified and the sensitivity of the optimal design to changes in design parameters was also illustrated. In this work, a multi-objective genetic algorithm similar to that used by De Risi et al. [2] is integrated with the statistical regression method used by Liu et al. [5] to maximize the interpretability of a piston bowl optimization using a new and highly flexible automated computational grid generator. This optimization is performed for a heavy duty direct injection diesel engine utilizing a late injection low-temperature combustion strategy. With a more meaningful methodology to interpret the optimization results, the role of bowl geometry and the effects of individual geometry features under these types of combustion regimes are illustrated. 1

Optimization Methodology Multi-Objective Micro-Genetic Algorithm A genetic algorithm is a type of optimization method that conducts an evolutionary or genetic-based search related to the Darwinian idea of survival of the fittest. It is a global search technique that utilizes the ideas of evolution to create new and better designs using the fittest attributes of the designs that the search has previously found. The genetic algorithm chosen for this work is the multi-objective micro-genetic algorithm of Coello Coello and Pulido [6]. The multi-objective micro-genetic algorithm evaluates the strength of an individual design by a concept known as dominance, illustrated in Fig. 1. In Fig. 1, the 8 points Figure 1: Illustration of Pareto optimality plotted represent the performance of 8 individuals in the objective space, where 2 objectives are identified to be optimized. There exists no individual that outperforms point A in the minimization of both objectives simultaneously, so it is therefore a dominant or non-dominated design. The same argument holds true for points B-D. All non-dominated points form a set of optimal designs termed the Pareto optimal set or the Pareto front. It can be seen that each of these points represents a simultaneous optimization of both objectives with varying weights given to each objective. Points A-D could each be considered optimal by different designers, depending on whether objective 1 or objective 2 was more important for their application. In the multi-objective optimization approach, all of these designs are kept as a set of optimal solutions for the user to choose from once the optimization process is complete. Non-Parametric Regression Method A non-parametric regression (NPR) method was used in this work as a post-optimization data analysis tool [7]. This method is a curve fitting technique that can be applied to an irregular set of data where the functional form of the data is unknown. Unlike parametric regression techniques, where an assumption must be made regarding the form of the data (i.e. the assumption of a straight line in a least squares type regression), the primary task of a nonparametric regression model is to determine the response function that best fits the data. The response function in a non-parametric model is simply assumed to belong to some infinitely dimensional collection of functions, subject only to qualitative constraints (i.e., requiring the function to be continuous or differentiable). A recently developed method for determining the unknown model parameters of an NPR, the Component Selection and Smoothing Operator (COSSO), was applied in this work. In COSSO, the response function is determined using a cross validation technique and is based on a smoothing spline analysis of variance (SS-ANOVA) framework [7]. In this technique, 5% of the data is withheld from the regression fit and then later used to test and improve the predicted response. Further details of the method are outlined in [8]. Numerical Models CFD Code The CFD code is a version of KIVA-3V with improvements in various physical and chemistry models developed at the Engine Research Center, University of Wisconsin-Madison. The major model improvements include the spray atomization [9, 10], drop-wall impingement [11], ignition and combustion [12] and soot formation and oxidation models [13]. The extended Zel dovich mechanism, as presented by Heywood [14], was used to calculate the NO formation. Automated Grid Generation A newly developed Kwick Grid mesh generation technique was utilized to both parameterize the bowl geometry and automate the grid generation. Kwick grid produces bowl-in-piston sector meshes for use with the KIVA-3V CFD code. The grid generation methodology is based on that of Wickman [15], where the grid structure is decoupled from the geometry allowing large changes in geometry to occur without adversely affecting the grid 2

Table 1: Engine and fuel injector specifications [16] Table 2: Engine operating conditions and baseline performance structure. Up to 5 parameters are used to describe the overall shape of the piston bowl. Up to 8 additional parameters can be used to control the details of the bowl profile. The profile of the bowl is controlled using cubic Bezier curves. The technique is capable of handling re-entrant as well as open-type piston bowls. Description of Current Optimization Engine Description and Operating Conditions A single-cylinder, direct-injection, 4-stroke diesel research engine, based on a Cummins N-series production engine, was modeled in this investigation. The engine is an optically-accessible heavy-duty research engine with a central, vertical common rail injector and a simple flat bottomed bowl that allows for maximum optical access [16]. Due to compromises necessary to implement optical access in the engine, the geometric compression ratio is only 11.2:1, compared to 16:1 in the production engine. As a result, elevated intake air temperatures and pressures are used to yield charge conditions at TDC typical of those in the production engine. The main geometric specifications of the engine and the fuel injector details are summarized in Table 1. A late injection low-temperature combustion condition was chosen to be optimized in this work and is summarized in Table 2. This condition was selected based on an experimental investigation by Singh et al. [16], where three different low-temperature premixed-type combustion strategies were evaluated via optical measurements. Note that the intake temperature and pressure in Table 2 is significantly higher than typical for production engines. As discussed previously, this is due to the lower geometric compression ratio in this research engine and is required to achieve charge conditions at TDC similar to those of a production engine. The chosen operating condition involves a late injection at TDC, which occurs in a highly dilute environment of 12.6% oxygen by volume. Under this condition, the ignition delay is approximately as long as the injection duration, which results in a premixed type of combustion. This condition is similar to the MK (modulated kinetics) combustion strategy proposed by Kimura et al. [17]. Optimization Parameters and Objectives The optimization parameters and objectives chosen for this work were selected with the primary motivation of this research in mind, viz., understanding the role of the piston bowl geometry in low-temperature premixed-type combustion regimes. To facilitate this goal, the piston bowl profile was parameterized into 8 adjustable features and the piston profile was optimized to achieve minimum NOx emissions, soot emissions and fuel consumption. The piston bowl geometry features varied in this optimization are illustrated in Fig. 2. Note that in this optimization, the bore, stroke, squish height and compression ratio were all held constant as the bowl profile was varied. In addition to optimizing the bowl profile, the start of injection timing was allowed to vary ±5 CAD from the 3

Figure 2: Piston bowl geometry optimization parameters Table 3: List of optimization parameters and ranges baseline timing shown in Table 2 to optimize spray targeting for a given bowl shape. To compliment these parameters, swirl ratio was included in the set of optimization variables. Previous work by Miles et al. [18] has shown that swirl ratio can have a significant impact on emissions and fuel consumption behavior in late injection combustion systems, through the formation of bulk flow structures. Since swirl ratio and bowl geometry features are both responsible for bulk flow formation, it is likely that they interact in interesting ways and so they were chosen to be simultaneously optimized in this study. The complete set of design parameters optimized in this study, and the ranges over which they were allowed to vary are shown in Table 3. Results and Discussion Analysis of the Pareto Front The previously outlined genetic algorithm was used in an optimization of the piston bowl geometry, spray targeting and swirl ratio of the late injection combustion condition described in Table 2. As the optimizations progressed, the position of the Pareto front in the objective space and the number of citizens contained in the Pareto front were monitored. After 200 generations, the optimization was concluded since the Pareto front had stopped making appreciable advances and the number of citizens contained in the Pareto front had largely stopped increasing. A plot of the citizens produced by the optimization and the Pareto front solution is shown in Fig. 3. The Pareto front contains 73 designs with varying NOx, soot and gross indicated specific fuel consumption (gisfc) performance. In selecting an optimal solution from these 73 designs, one might simply scan through the performance of each design and pick out those of interest for further investigation. However, there is also important information contained in the evolution of the designs along the Pareto front. As it can be seen in Fig. 3, the multi-objective optimization approach optimizes each objective separately and produces a solution set with a range of designs that perform at both high and low levels of each objective. By examining this range of designs, trends be noted and a better understanding can be gained regarding which design parameters contribute to the optimization of each objective. GISFC [g/kw-hr] 212 208 204 200 196 192 0.2 0.3 0.4 NOx [g/kgf] 0.5 All Citizens Produced Pareto Citizens 0.6 Figure 3: Pareto front solution of the optimization 0.3 0.4 0.5 0.7 0.6 Soot [g/kgf] 4 A set of designs from the Pareto front (Fig. 3), which perform with a range of NOx emissions, soot emissions and fuel consumption, are presented in Fig. 4. The profile of the baseline piston is shown as the dashed grey line for comparison with each optimized geometry. An idealized spray trajectory is shown as a dashed arrow to indicate the spray targeting at the start of injection timing, as optimized for each piston geometry. In comparing the designs that result in a range of NOx emissions on the Pareto front, some trends may be noted. First, there is a trend of decreasing swirl with decreasing NOx. This trend does not behave in a linear manner, however, as the change in swirl ratio from the high NOx design to the midrange NOx design is only 0.1. This indicates that the production of NOx emissions could be more sensitive to swirl ratio as the level of swirl is increased. It might also indicate that a different,

Figure 4: Designs along the Pareto front that optimize each objective more subtle, element of the design is contributing to the increase in NOx. Trends in the piston bowl geometry are more difficult to ascertain, but a trend towards a smaller diameter, deeper bowl may be noted as NOx emissions decrease. Although it can be challenging to make a strong conclusion at this level of analysis, the trends, in general, indicate that low swirl and a smaller diameter, deeper bowl contribute to lower NOx emission. Figure 4 also shows some interesting trends over the range of Pareto front designs that optimize soot emission performance. First, there is a nearly linear increase in the swirl ratio as soot emissions decrease. Also, a trend towards a shallower, wider bowl for reduced soot emissions can be noted. Especially interesting is the fact that the Pareto front design that resulted in the lowest NOx emissions is also the design that results in the highest soot emissions. Even under this low-temperature combustion condition, a soot-nox trade-off is still evident. The Pareto front designs in Fig. 4 that optimize gisfc are seen to closely follow the trend in designs for optimizing soot emissions. Like the effect of swirl ratio on soot emissions, there is a distinct trend of increasing swirl ratio with decreasing fuel consumption. A trend in bowl shapes is also evident that varies from a deeper, smaller bowl to a wider, more shallow bowl as fuel consumption is decreased. Furthermore, the mid-range and high soot performance designs also result as the mid-range and high fuel consumption designs. This result indicates that the physical mechanisms provided by these bowl shapes might affect soot emissions and fuel consumption performance similarly. From the trends in the designs along the Pareto front, a very general sense of the important design parameters can be obtained. As discussed, however, it is difficult to understand whether these general trends function independently of other design changes. A more robust analysis technique is required to decouple to effects of each design parameter. In this work, a statistical regression method was applied in order to quantify these independent effects. Regression Analysis of Optimization Data As previously discussed, in Fig. 4 it was difficult to ascertain whether bowl geometry or swirl ratio contributed more heavily to reduction of NOx emissions. It was also observed that similar variations in bowl geometry and swirl ratio resulted in the reduction of both soot emissions and fuel consumption. To gain a more concrete understanding of these effects, COSSO was used to fit a surface over the optimization data set. Three response surfaces were constructed using the NOx emissions, soot emissions and fuel consumption, respectively, as the response variables. The resulting NOx response, soot response and fuel consumption response to changes in swirl ratio, bottom bowl diameter (B in Fig. 2), central pip height (A in Fig. 2) and bowl diameter (D in Fig. 2) are shown in Fig. 5. The swirl ratio, central pip height and bowl diameter of the baseline configuration are shown as the circled values on the horizontal scales. It should be noted that a baseline value for the diameter of the bottom of the bowl is not shown since the baseline configuration has a flat bottom, making its value ambiguous. The responses are plotted with the same vertical scale so that the relative effects of each parameter can be compared. In comparing the relative magnitudes of the response curves in Fig. 5, it can be seen that changes in the swirl ratio have a significant impact on NOx, soot and fuel consumption. Changes in the bowl diameter are also seen to have a significant effect on NOx emissions and fuel consumption, but not on soot emissions. Pip height and the 5

NOx Response (g/kgf) Soot Response (g/kgf) GISFC Response (g/kw-hr) swirl ratio pip height (% bowl depth) swirl ratio pip height (% bowl depth) swirl ratio pip height (% bowl depth) bottom bowl diam. (% bowl diam.) bowl diam. (% bore) bottom bowl diam. (% bowl diam.) bowl diam. (% bore) = baseline configuration bottom bowl diam. (% bowl diam.) bowl diam. (% bore) Figure 5: Optimization data response surface shapes (horizontal axis shows some of the main design parameters considered in the optimization and vertical axis indicates corresponding response) diameter of the bottom of the bowl are shown to have little effect on the three objectives. By using the COSSO regression technique, the important parameters are not only able to be identified, but they can be ranked according to their influence. As it was proposed in the Pareto front analysis, swirl ratio and bowl diameter are both shown to be important parameters that lead to variations in NOx, but with the COSSO regression curves it is also found that the bowl diameter is more influential than the swirl ratio. The fuel consumption response curves reveal that changes in swirl ratio and changes in bowl diameter have equal impact on fuel consumption performance, which is again in line with the Pareto front analysis, but yields an understanding of their relative effect which could not be observed previously. The soot response curves indicate that swirl ratio is the only design parameter to have a significant effect on soot emissions. This is in contrast to the previous observations in the Pareto front analysis and is an especially important result. From the Pareto front analysis, it had appeared that changes in bowl geometry and swirl ratio affected soot emissions and fuel consumption performance similarly. The COSSO analysis instead reveals that the change in bowl shapes from a deep, small diameter bowl to a wide, shallow bowl is only significant in improving fuel consumption. The physical mechanism provided by this change in bowl shape, which results in improved fuel consumption, does not result in improved soot emissions. The shape of the response curves can also reveal additional insight regarding the effects of the design parameters. Focusing on the NOx response curves in Fig. 5, the response curve which results from changes in bowl diameter confirms that small bowl diameters contribute to lower NOx, as proposed in the Pareto front analysis. The shape also reveals that there is a diameter at which a maximum NOx occurs and further increases in diameter result in reducing NOx. The shape of the NOx response due to changes in swirl ratio shows that swirl ratio has little effect on NOx over a range from 0.5 to 2.5, but then tends to increase NOx at higher swirl ratios. This is consistent with the previous observation obtained from the Pareto front analysis that NOx emissions appeared to be more sensitive to swirl ratio as the swirl ratio was increased. Looking at the soot response curves of Fig. 5, the response curve which results from changes in swirl ratio behaves in a mostly linear fashion. Thus, increases in swirl ratio are seen to cause a nearly linear decrease in soot emissions. This confirms the previous Pareto front analysis observation where soot performance was seen to improve from a high level to a mid-range level to a low level with an almost linear increase in swirl ratio. From the Pareto front analysis, it was observed that wider bowls and higher swirl ratios resulted in reduced fuel consumption, but the COSSO analysis yields an additional and important result. The fuel consumption response shapes of Fig. 5 show that increasing swirl and increasing bowl diameter do result in improved fuel consumption, but only until an optimal swirl and bowl diameter are reached. At swirl ratios higher than approximately 3.0 and bowl diameters larger than 75% of the bowl diameter, fuel consumption is seen to increase. This phenomenon would be difficult to extract from a simple analysis of the Pareto front and is clearly revealed through the use of this technique. Summary and Conclusions A new approach for implementing and analyzing optimization results for engine design has been developed. Specifically, a multi-objective micro-genetic algorithm is combined with a statistical regression analysis methodology that enables us to better analyze the results of the optimization. By combining these two methods, it 6

was shown that more information can be obtained regarding the influence of each design parameter and the sensitivity of optimal designs to changes in each design parameter. The new approach was applied in an optimization of piston bowl geometry in a heavy duty direct injection diesel engine under a late injection lowtemperature combustion condition. In the analysis of the optimization it was shown that general information about piston bowl geometry requirements and swirl ratio for optimal emissions and fuel consumption performance could be extracted by analyzing the designs along the Pareto front. From this analysis, it was observed that increases in swirl ratio resulted in increased NOx and decreased soot emissions and fuel consumption. It was also observed that a general trend in bowl shapes could be detected where a shallow, wider bowl was preferred for reduced fuel consumption and that a deeper, small diameter bowl was preferred for reduced NOx emissions. The use of a non-parametric regression analysis tool, which fitted a surface over the entire optimization data set, allowed for further information to be gained regarding the importance and effect of each design parameter on the emissions and fuel consumption performance. The preference of deeper, small diameter bowls for reduced NOx was confirmed in this analysis. Higher swirl ratios were also confirmed to provide high NOx and low soot and fuel consumption performance. The response curves further revealed that an optimal swirl ratio and bowl diameter exist for reducing fuel consumption. It was also shown that bowl diameter had little effect on soot emissions, which was not a conclusion that could be made based on the Pareto front analysis of the results. Acknowledgments Support for this research was provided by Catepillar, Inc. and DOE/Sandia National Labs. References [1] Liu Y. and Reitz R.D. (2005) Optimizing HSDI Diesel Combustion and Emissions Using Multiple Injection Strategies. SAE paper 2005-01-0212. [2] De Risi A., Donateo T. and Laforgia D. (2003) Optimization of the Combustion Chamber of Direct Injection Diesel Engines. SAE paper 2003-01-1064. [3] Hiroyasu T., Miki M., Kim M., Watanabe S., Hiroyasu H. and Miao H. (2004) Reduction of Heavy Duty Diesel Engine Emission and Fuel Economy with Multi-Objective Genetic Algorithm and Phenomenological Model. SAE paper 2004-01- 0531. [4] Senecal P.K., Pomraning E. and Richards K.J. (2002) Multi-Mode Genetic Algorithm Optimization of Combustion Chamber Geometry for Low Emissions. SAE paper 2002-01-0958. [5] Liu Y., Lu F. and Reitz R.D. (2005) The use of non-parametric regression to investigate the sensitivities of high-speed direct-injection diesel emissions and fuel consumption to engine parameters. International Journal of Engine Research. [6] Coello Coello C.A. and Pulido G.T. (2001) A Micro-Genetic Algorithm for Multiobjective Optimization. First International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science: no 1993: pp 126-140. [7] Gu C. (2002) Smoothing Spline ANOVA Models. Springer-Verlag. [8] Lin Y. and Zhang H.H. (2003) Component Selection and Smoothing in Smoothing Spline Analysis of Variance Models. Institute of Statistics Mimeo Series 2556, NUCS. [9] Beale J.C. and Reitz R.D. (1999) Modeling Spray Atomization with the Kelvin-Helmholtz/Rayleigh-Taylor Hybrid Model. Atomization and Sprays: vol 9: pp 623-650. [10] Reitz R.D. (1987) Modeling Atomization Processes in High-Pressure Vaporization Sprays. Atomization and Spray Technology: vol 3: pp 309-337. [11] Naber J.D. and Reitz R.D. (1988) Modeling Engine Spray/Wall Impingement. SAE paper 880107. [12] Kong S.-C., Han Z. and Reitz R.D. (1995) The Development and Application of a Diesel Ignition and Combustion Model for Multidimensional Engine Simulation. SAE paper 950278. [13] Hampson G.J. and Reitz R.D. (1998) Two-Color Imaging of In-Cylinder Soot Concentration and Temperature in a Heavy- Duty DI Diesel Engine with Comparison to Multidimensional Modeling for Single and Split Injections. SAE paper 980524. [14] Heywood J.B. (1998) Internal Combustion Engine Fundamentals. McGraw-Hill Company. [15] Wickman D.D. (2003) Ph.D. Dissertation, Department of Mechanical Engineering, University of Wisconsin-Madison. [16] Singh S., Reitz R.D. and Musculus M.P.B. (2005) 2-Color Thermometry Experiments and High Speed Imaging of Multi- Mode Diesel Engine Combustion. SAE paper 2005-01-3842. [17] Kimura S., Aoki O., Ogawa H., Muranaka S. and Enomoto Y. (1999) New Combustion Concept for Ultra-Clean and High- Efficiency Small DI Diesel Engines. SAE paper 1999-01-3681. [18] Miles P.C. (2000) The Influence of Swirl on HSDI Diesel Combustion at Moderate Speed and Load. SAE paper 2000-01- 1829. 7