Conclusions Mathematical methods and models1

54 algorithms demonstrates the practical application of these methods for calibration of phenomenological models. An excellent agreement between the measured and simulated ROHR characteris- tics is shown, inspite of the wide range of engine and operating condition setups used in this study. Furthermore, considering the heavy-duty engine calibrated model as example, the general applicability of the ROHR model is confirmed with blind trials on both the automotive and the marine diesel engines. Despite the deviations in absolute values, both blind trials correctly reproduce the variations among single operating conditions, and can be adjusted to yield correct absolute values using basic knowledge of the tested engine or a few experimental operating conditions for a recalibration. An advanced fuels survey further shows, that both the re-calibrated and the blind try ROHR models are capable of predicting the effects of water-in-diesel emulsions and diesel-butylal blended fuels on ROHR characteristics correctly. ϕ SOC ϕ 10 ϕ 50 ϕ 90 O p ti mized Pearson’s Correlation Coefficient r [-] 0.9214 0.9538 0.9252 0.6655 Linear Regression Slope m [-] 0.83 0.91 1.01 0.58 Linear Regression Intercept b [-] 0.46 0.79 0.26 13.93 B lind Try Pearson’s Correlation Coefficient r [-] 0.8918 0.9161 0.8876 0.6070 Linear Regression Slope m [-] 0.74 0.81 0.91 0.52 Linear Regression Intercept b [-] 0.36 0.82 0.18 14.21 Tab. 4.5 Heavy-Duty Advanced Fuels ROHR Model Statistics for the EA Optimized and the Heavy-Duty Blind Try Case 55 5 E MISSIONS OF N ITROGEN O XIDE Based on the ROHR model proposed in Chapter 4, a phenomenological model to determine the emissions of nitrogen oxide is given below. Combined with the soot emissions model presented in Chapter 6, one of the most pressing topics in current diesel engine research development can be addressed: the simultaneous reduction of both nitrogen oxide and soot emissions to meet stringent emission regulations.

5.1 Model Description

Collectively referred to as emissions of nitrogen oxide NO x , nitric oxide NO nominally accounts for approximately 90 of the total NO x emissions during reg- ular diesel engine operation. However, for light-load, low-speed operating condi- tions, the share of nitrogen dioxide NO 2 formed may increase up to 30 of the total amount of NO x emissions [44]. Given the low content of nitrogen in commercial fuels and the predominantly dif- fusion controlled combustion in standard diesel engines, the governing source for nitric oxide formation is the oxidation of molecular nitrogen contained in the com- bustion air a.k.a. thermal NO formation. Moreover, for cases with high energy release fractions during the premixed combustion phase, or for cases with NO x emission concentrations lower than 100 [ppm], prompt nitrogen oxide formation a.k.a. Fenimore NO x becomes a significant source for nitrogen oxide. When fast calculations are to be made across an entire engine operating map, a computationally reliable and efficient mechanism for the exhaust gas NO concentra- tion is needed. Because of both the complexity of the reaction scheme and thus increase in computation time and the low impact of the Fenimore NO x formation mechanism on the total NO x emissions, the present study follows a commonly used restriction and considers only thermal NO formation. Weisser [102] shows for various operating conditions of a 4-stroke medium-size, medium-speed Common-Rail DI diesel engine, that reducing the mechanism com- plexity results in a decrease in prediction accuracy for NO emissions as well as a sub- stantial reduction in computational time especially for the 0-dimensional models. The present model calculates the NO concentration using the established and computationally efficient extended Zeldovich reaction mechanism [109] along with a CHEMKIN [54] chemical equilibrium solver. This novel implementation links the characteristic in-cylinder temperature traces driving the NO formation to a repre- sentative airfuel ratio function in a consistent way c.f. Section 5.1.2, Figure 5.1. 56

5.1.1 Inputs Outputs

Intended as an emission submodel in an engine process simulation program, the NO model uses the temporal state of the process ROHR, temperature, pressure, etc., the reaction chemistry kinetics Section 5.1.3 and a representative airfuel ratio function Section 5.1.2 as inputs. As an output, the model provides the temporal NO formation and reduction rates.

5.1.2 Variable Virtual Combustion Zones

By means of a “virtual” combustion zone with variable stoichiometry computed in the thermodynamic combustion process simulation, the dominant localized NO formation phenomena, such as hot spots in the fuel-lean post-combustion gases, are captured. As an attempt to include the nitrogen oxide emissions resulting from the fuel-rich components next to the flame front position, a richer-than-stoichiometric phase in the representative airfuel ratio function is used during initial stages of combustion Figure 5.1 a. After the initial constant airfuel ratio λ start from ϕ SOC to ζ start , the presented model uses an airfuel ratio proportional to the increasing combustion progress to account for characteristic diesel combustion effects e.g. transition of unburned fuel- rich to burned fuel-lean gases. The final phase of the representative airfuel ratio function is modeled as a crank angle proportional leaning maximum λ global of burned gases until the exhaust valves open at λ EO and ϕ EO . The associated interme- diate temperature trace T λ NO , which lies between the thermodynamic maximum process temperature T λ stoichiometric and the mean process temperature T λ global , is determined using the rate of heat release analysis software WEG, based on the variable representative airfuel ratio function Figure 5.1. A list of the seven model parameters used to model the representative airfuel ratio function is given in Table 5.1. a b Fig. 5.1 Variable representative airfuel ratio function and associated in- cylinder temperature trace for NO formation λ N O [- ] Combust ion Progress ζ [ -] Crank Angle ϕ [ ° CA] ϕ EO ζ start λ EO λ end λ start 1 ζ end c ROHR c CA ϕ SOC λ N O [- ] Combust ion Progress ζ [ -] Crank Angle ϕ [ ° CA] ϕ EO ζ start λ EO λ end λ start 1 ζ end c ROHR c CA ϕ SOC T e m p e ra tu re [K ] Crank Angle ϕ [ ° CA] T λ stoichiometric T λ NO T λ global T e m p e ra tu re [K ] Crank Angle ϕ [ ° CA] T λ stoichiometric T λ NO T λ global