Motivation and Objectives Mathematical methods and models1

2

1.2 Common-Rail DI Diesel Engines

Despite the significant contributions to local and global air quality problems, as well as the potential health effects, commercial applications are almost exclusively pow- ered by direct injection diesel engines. In addition, due to the high efficiency, supe- rior drivability, low life-cycle costs, the share of diesel powered passenger cars in western Europe increased from 13.8 in 1990 to 48.2 in 2004 [1]. In order to controlreduce the negative impacts on the environment, emission regulations specify and enforce the maximum amount of pollutants allowed to be emitted by an internal combustion engine. For common diesel engines, generally the particulate matter PM 1 , the nitrogen oxide NO x 2 , the hydrocarbons HC, and the carbon monoxide CO emissions are regulated, whereas the carbon dioxide CO 2 emissions for example are subject to voluntary agreements between adminis- trations and manufacturers. Facing the increasingly stringent emission regulations, major engine research and development focuses on the simultaneous reduction of fuel consumption and exhaust emissions of diesel engines by combustion and cycle efficiency improve- ments [45]. According to [10], the various technologies developed and implemented in modern diesel engines can be classified - in a non exhaustive list - as follows: • FUEL INJECTION AND AIR MANAGEMENT variable-rate fuel injection systems e.g. Common-Rail, exhaust gas recircu- lation, variable nozzlegeometry turbocharger, two-stage turbocharging, four-valve cylinder heads, variable swirl, variable valve train actuation, etc. • FUEL COMPOSITION MODIFICATIONS low sulphur fuels, water-in-diesel fuel emulsions, oxygenated and hydrogen enriched fuels, etc. • EXHAUST GAS AFTERTREATMENT oxidation catalysts, diesel particulate filters, nitrogen oxides adsorber cata- lysts, selective catalytic reduction systems, etc. • COMBUSTION CONCEPT Homogeneous Charge Compression Ignition HCCI, Low Temperature Combustion LTC, etc. 1. Particulate Matter PM - both solid and liquid particles of 1 nanometre to 100 micrometres in diameter suspended in the air. IC engine PM emission mainly consist of elemental carbon soot, unburned fuel hydrocarbons, and various acids, with a soot content that varies from 25 to 95 depending on the fuel, operating condition and type of engine used [3]. 2. Nitrogen Oxide NO x - generic term for the various nitrogen oxides produced during combus- tion, such as nitric oxide NO, nitrogen dioxide NO 2 , or nitrous oxide N 2 O. Nitrogen oxide formation is promoted by high temperatures and excess of oxygen. 3

1.2.1 Combustion Analysis and Modeling

Given that in engineering “modeling a process” has become a synonym for develop- ing and using an appropriate combination of assumptions and equations that permit critical features of a process to be analyzed [44]. Internal combustion engine models thus range from zero-dimensional empirical model, to three-dimensional computa- tional reactive fluid dynamic models. An experimental combustion analysis generally includes the interpretation of global engine operating characteristics, such as performanceefficiency measures and exhaust emissions, as well as time resolved temperature and in-cylinder pres- sure data.

1.2.2 Exhaust Emissions

Diesel exhaust is a complex mixture of gases, vapors, liquid aerosols and substances made up of particles i.e. fine particles, that has the potential to cause a range of seri- ous health problems. Despite the controversy about the epidemiology studies used to develop health risk assessments of diesel exhaust, long-termchronic inhalation exposure is likely to pose a lung cancer hazard to humans and short-termacute exposures can cause irritation and inflammatory symptoms [21]. Among the more than 40 substances emitted by diesel engines that are listed as hazardous air pollutants by the U.S. Environmental Protection Agency EPA, the nitrogen oxide and particulate matter soot emissions are the most important ones. Whereas the nitrogen oxide emissions along with unburned hydrocarbons and sun- light make for the formation of ground-level ozone 1 and contribute to the forma- tion of acid rain, particulate matter emissions are mainly associated with the serious health effects mentioned above.

1.2.3 Optimization

During the IC engine design process, optimization methods are used for example, to calibrate numerical models [100], to reduce engine exhaust emissions in automated test-bed systems i.e. electronic control unit calibration [95], or to find the best fuel propulsion systems in life cycle analysis studies [64]. The optimization techniques employed range from gradient-free methods, such as evolutionary algorithms or coordinate strategies, to first and second-order gradient methods, such as conjugate gradient or Newton’s method c.f. Section 2.4 and [69]. 1. Ozone O 3 - an allotrope of oxygen O 2 consisting of three oxygen atoms, a powerful oxidizing agent, highly corrosive and poisonous.