Mathematical modeling of NOx and soot emissions for diesel engines

The diesel engine is a type of internal combustion engines in which the fuel that is injected into combustion chamber is ignited by high temperature due to greatly compression of air. Only the air is compressed for diesel engines work. This causes the air to reach high temperatures inside the cylinder and atomized diesel fuel which is injected into the combustion chamber is ignited. Since 19th century, researchers have focused on diesel engines and they came into use with ships and submarines in early years of the 20th century. Then, diesel engines were seen for trucks, locomotives and heavy equipment. After a first quarter of the 20th century, they slowly began to be used in a few automobiles and the diesel engines play an important role in today's automotive world. Diesel engines have many advantages and plenty of drawbacks. When diesel engines and gasoline engines are compared, diesel engines burn less fuel than gasoline engines due to the engine's higher temperature of combustion and greater expansion ratio. Diesel engines have higher thermal efficiency than gasoline engines due to property of compression ignition. Due to this fact, diesel engines can convert over 45% of the chemical energy into mechanical energy while gasoline engines are typically 30% efficient. However, the most important disadvantage of diesel engines is that they emit more hazardous compounds for environment and human health than gasoline engines. Since the fuel in diesel engine is ignited by the heat of compressed air, the fuel had no time to be fully mixed with the air and it produces unburned HC, NOx and soot during the combustion process. Due to NOx and soot emissions, legislation concerning the pollutant gas emissions of diesel cars is becoming increasingly restrictive. Then, it requires many tests to reach the desired limits of the pollutant emissions. Testing with an engine results in long, expensive and inaccurate works. Therefore, it has needed to find a solution for reducing cost and time, also increasing test efficiency. Computer-aided engineering programs have been widely used with the developing computer technology and many engineering problems have been solved by using the computer-aided engineering programs. Some of these programs are developed by engineers to simulate the engine in the system order. Thus, computer aided engineering programs, which are referred as one-dimensional simulation programs in literature provide solution in the system order of an engine. Today, engineers are able to get through to detailed investigations of production engines from early studies of model engine by using one dimensional engine simulation programs. They provide very quick solutions when compared to three dimensional computational fluid dynamics programs. Also, they shorten test duration of engine dynamometer and provide further investigations for multi-parameter effects of engine performance parameters. One dimensional engine simulation programs are widely used by many automotive manufacturers due to the significant advantages described above. In one dimensional engine simulation programs, it is accepted that the axial velocity of the fluid is higher than the fluid velocity in other directions. Due to this reason, three dimensional conservation equations are reduced to one dimension. Continuity, momentum and energy equations are solved simultaneously by the model. All equations are solved in one dimension and all quantities are averaged across flow direction. The system is discretized into smaller volumes and volumes are connected by boundaries. Also, the scalar variables are calculated at the center of the volume and vector variables are calculated for each boundary. This type of discretization is referred as staggered grid. In literature, combustion of diesel engines are modeled with high accuracy by using one dimensional engine simulation. On the other hand, the emission modeling of diesel engines have been very challenging for researchers due to irregular chemistry of the exhaust gases. Apart from physical modeling, mathematical modeling is also commonly used. Mathematical modeling is very beneficial especially for the problems which cannot be explained by physical modeling. Therefore, mathematical modeling which is constructed according to measured data, could be very helpful to analyzed unknown systems. In accordance with this purpose, mathematical model can be used for prediction of exhaust gases. In this thesis study, mathematical model of NOx and soot emissions based on Gaussian Regression method is used for fast and accurate predictions. It is proved that NOx and soot emissions can be modeled mathematically with high accuracy for diesel engine. Experimental design is generated to collect training data for mathematical models. Instead of using conventional DoE methods, spacing filling DoE method is utilized. The results show that it's good enough to describe complex behaviors of the engine. Results are subdivided according to steady state and transient conditions. Firstly, steady state modeling is handled. Models using combustion input parameters are created to predict soot and NOx emissions. These parameters is directly or indirectly controlled by ECU. Optimization of the input parameters are performed to obtain highest results, and the model comprising of eight parameters are sufficient to predict soot and NOx emissions. Suggested model includes the parameters: engine speed, fuel rail pressure, total fuel quantity, start of main injection, start of pilot injection, mass air flow, intake manifold temperature and intake manifold pressure. Due to dependency of EGR rate to other model parameters, it is not required to add EGR rate parameter into the models. Controlling of pilot injection quantity have high errors, and thus its effect on modeling quality could not be observed. The models include combustion input and output parameters. However, some parameters cannot be measured directly on a dynamometer, and therefore 1D model of the engine is created. The values of these parameters are obtained by using 1D engine model. Effects of some combustion output parameters are also investigated in this thesis. Modeling improvement is aimed by using these parameters. Studies show that adding turbine inlet temperature into the models increases modeling quality of soot emissions. Also, it is obtained that using maximum cylinder pressure in the models increases the accuracy of validation data for steady state conditions, but it requires to use other combustion parameters such as turbine inlet pressure, burn duration 0-50%, burn duration 0-90% and burn duration 10-90%. In this thesis, it is also aimed to model emissions mathematically by using only outputs of the 1D engine model and to show its feasibility. Thus, optimum design of an engine can be obtained by using a coupled model of 1D engine model with a mathematical emission model. However, the results show that NOx emissions can be assessed during design optimization process but the same thing cannot be stated for soot emissions. The models including combustion input and output parameters are run in MATLAB to evaluate the model quality for transient conditions. World harmonized transient cycle (WHTC) is used for comparison of model and test data. The results show that mathematical emission models are capable of predicting transient results of emissions. The same model suggested for steady state conditions can be also used for transient conditions. However, there are some problems observed during analysis of transient results of the models. These problems are overestimation of soot emissions and time delay between model and test results. One of transient cycle points is out of range for training data of the models, and it results in overshooting of soot emissions. Setpoints of combustion variables are specified at the beginning of combustion by ECU, however, soot and NOx emissions are measured at engine outlet. This situation causes a delay between test and model results.