# A New Control-Oriented Semi-Empirical Approach to Predict Engine-Out NOx Emissions in a Euro VI 3.0 L Diesel Engine

^{1}

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## Abstract

**:**

## 1. Introduction

#### Contribution of the Present Study

_{b}

_{max,main}), the charge-to-fuel ratio, the injection pressure, the engine speed and the injected fuel mass. The evaluation of the temperature of the burned gases required the adoption of zero-dimensional predictive combustion model. Although the approach presented in [8,20] has been designed in order to have a low-throughput, it still requires a calculation time that is about 1.5 ms [8] when it is run on a rapid prototyping device, such as an ETAS ES910. The latter device is characterized by a computational performance which is 3–4 times faster than that of a modern ECU.

- It is based on MFB
_{50}(crank angle at which 50% of fuel-mass is burned), O_{2}(intake O_{2}concentration), N (engine speed) and q_{f}_{,inj}(total injected fuel quantity). In particular, it was found that MFB_{50}is a very robust metric that correlates well with the NOx formation. It will be shown that the MFB_{50}metric is able to account for the effects of injection timing and injection pressure simultaneously. - The model has not been designed in order to predict the absolute values of NOx emissions, but is based on the prediction of the deviations of NOx emissions, with respect the nominal engine-map calibration values, as a function of the deviations of MFB
_{50}and intake O_{2}concentration. This leads to several advantages. First, the variation range of the NOx deviations is much smaller than the variation range of the NOx absolute values. As a consequence, their prediction is more accurate, considering the high non-linearity of the NOx formation process. Second, the error of the model tends to zero when the deviations of the input parameters tend to zero, since the nominal NOx levels over the engine map are taken in this case. - Finally, it was demonstrated that the proposed method is physically consistent, since it maintains a high accuracy even when the number of points used for calibration is very low, and that it requires a much smaller computational time than the previous model proposed in [8].

## 2. Experimental Setup and Engine Conditions

_{T1}, T

_{T1}, p

_{T2}, T

_{T2}), compressor (p

_{C1}, T

_{C1}, p

_{C2}, T

_{C2}), and intercooler (p

_{IC1}, T

_{IC1}, p

_{IC2}, T

_{IC2}), in the intake manifold (p

_{int}, T

_{int}) and in the EGR circuit (T

_{EGR1}, T

_{EGR2}, p

_{EC2}, T

_{EC2}). The temperature was also acquired in each intake (T

_{i1}, T

_{i2}, T

_{i3}, T

_{i4}) and exhaust runner (T

_{e1}, T

_{e2}, T

_{e3}, T

_{e4}) by means of thermocouples.

_{cyl1}, p

_{cyl2}, p

_{cyl3}, p

_{cyl4}) manufactured by Kistler (Winterthur, Switzerland) are placed in glow-plug adapters to acquire for each cylinder, on a crank basis, the in-cylinder pressure time-histories. The in-cylinder pressure traces are pegged on the basis of the intake pressure that is measured by means of a high-frequency Kistler 4007C piezo-resistive transducer, located in front of cylinder 1 (p

_{i1,hf}). On the exhaust side, a high-frequency cooled Kistler 4049B piezo-resistive transducers is also installed (p

_{e1,hf}).

_{4}, NO

_{x}/NO, CO, CO

_{2}and O

_{2}both at the intake and exhaust manifolds. Finally, for the soot measurement an ‘AVL 415S’ smokemeter is used for steady-state tests whereas an AVL 439 opacimeter is adopted for transient tests. The measurement devices were controlled by the AVL PUMA OPEN 1.3.2 automation system.

#### Experimental Activity

- A full engine map including 123 points.
- EGR-sweep tests at fixed key-points, including 162 points. EGR rate was varied from 0 to 50% by setting different levels of trapped air mass with steps of 50 mg/cycle.
- Sweep tests of main injection timing (SOI
_{main}) and injection pressure (p_{f}) at fixed key-points, including 125 points. A SOI_{main}variation of ±6 crank angle degrees around the nominal values and a p_{f}variation of ±20% around the nominal values were set. A pilot-main injection strategy was adopted, in which the pilot quantity and the dwell-time between the pilot and main pulses was kept constant. The tests were carried out in “BMEP-control” mode. This means that, during the tests, the software of the test bench acted on the total injected quantity in order to maintain a constant value of BMEP corresponding to the desired target.

## 3. Model Description

#### 3.1. NOx Formation Process and Recalls on the previously developed NOx Model

_{2}(nitrogen dioxide) emissions [20]. NO

_{2}emissions in diesel engines are generally around 10–30% of the total NOx emissions, especially at lower load conditions [31,32]. However, in the literature, only the NO emissions are generally modeled, and the values of predicted NO values are taken as representative of the total NOx emission levels [20]. The NO formation process mainly depends on several mechanisms: the thermal mechanism, which is temperature-dependent, the prompt mechanism [33] and the fuel-derived NO mechanism [20].

_{2}dissociation, and by the quantity of O

_{2}in the burning region. In general, the thermal mechanism leads to the predominant NOx formation contribution.

_{b}

_{max,main}’, the total mass of injected fuel (m

_{fuel}) (or, analogously, the total injected fuel volume quantity, ‘q

_{f}

_{,inj}’), the engine speed ‘N’, the injection pressure ‘p

_{f}’ and the stoichiometric in-cylinder charge-to-fuel ratio ‘${\alpha}_{st}^{u}$’. The NOx model reported in [20] needs to be coupled with a predictive combustion model, in order to estimate the temperature of the burned gases.

_{b}

_{max,main}’ was replaced by the ‘T

_{b}

_{,MFB50}’ term (i.e., the burned gas temperature evaluated at MFB

_{50}). The ‘T

_{b}

_{,MFB50}’ term is in fact easier to estimate, and its utilization does not lead to a deterioration of the model accuracy. Moreover, in [8] the stoichiometric in-cylinder charge-to-fuel ratio ${\alpha}_{st}^{u}$ was replaced by the intake oxygen concentration ‘O

_{2}’, since the two quantities are closely related to each other, but intake O

_{2}concentration can be evaluated more easily (it can even be measured by a sensor). However, the revised formulation proposed in [8] still requires the adoption of a predictive combustion model, in order to evaluate the ‘T

_{b}

_{,MFB50}’ term. Although the combustion model used by the authors in [8] has been developed with the aim of being suitable for control-oriented applications, it requires a computational time which is around 1.5 ms when it runs on an ETAS ES910 rapid prototyping device [8], which is characterized by a computational performance that is 3–4 higher than that of modern ECUs. This computational time may not be sufficient to realize a cycle-by-cycle model-based NOx control on a modern ECU. Moreover, the adoption of a thermodynamic combustion model leads to a highly physically consistent approach, but at the same time it makes the NOx model more sensitive to deviations in the input variables, with specific reference to the air and EGR mass, which are required by the combustion model. A 5% error in the trapped mass estimation can produce an error in the predicted NOx emissions which can be around 100% [23]. Therefore, a new semi-empirical NOx model has here been proposed, which does not require the use of a combustion model, with the consequence of being characterized by a much smaller computational time. Moreover, the new NOx model does not require the use of air or EGR mass, which may introduce a high uncertainty in the NOx prediction (typical biases of modern MAF sensors are of the order of 5% and their response over time is quite slow, while EGR mass is typically not measured). It will be shown that, instead, the intake O

_{2}concentration will be used. Recent studies [37] have in fact shown that intake O

_{2}sensors can be very accurate and capable of achieving a very fast response time (~10 ms), in order to realize an accurate NOx control in transient operation.

#### 3.2. Identification of the Input Parameters of the New Semi-Empirical NOx Model

- Combustion phasing ‘MFB
_{50}’ - Intake oxygen concentration ‘O
_{2}’ - Injected fuel volume quantity ‘q
_{f,inj}’ - Engine speed ‘N’.

_{main}/p

_{f}(see Figure 3), it was found that MFB

_{50}is a highly robust combustion metric that well correlates with engine-out NOx emissions. This is shown in Figure 4 and Figure 5. In particular, Figure 4 reports the contour plots of the measured NOx emissions as a function of injection pressure and SOI

_{main}, while Figure 5 reports the contour plots of the measured NOx emissions as a function of injection pressure and MFB

_{50}.

_{50}instead of SOI

_{main}. This means that MFB

_{50}is capable of explaining the effects, on NOx emission, of injection pressure and injection timing simultaneously. A slight deviation from the verticality trend is observed at high-load and low-speed conditions, in which injection pressure has a slight effect on NOx emissions even for a constant MFB

_{50}. It was hypothesized that, in these conditions, injection pressure highly affects the trends of heat release and burned gas temperatures, thus affecting NOx formation, even when keeping MFB

_{50}constant. This is due to the long energizing times of the injectors that are typically adopted in this engine area (high fuel quantities needs to be injected, but injection pressure levels are significantly smaller than those adopted at high engine speed). For the considered engine, the sensitivity of NOx emissions to injection pressure at constant MFB

_{50}is small, therefore injection pressure has not been included in the NOx model. However, if a different engine is considered, its effect needs to be checked.

_{2}, this choice was done in accordance with the previous NOx model [8,20]: intake O

_{2}concentration, in fact, has a significant impact on the NOx formation rate, according to the thermal mechanism. The adoption of the O

_{2}variable (instead of alternative parameters such as EGR or air mass) also increases the model robustness, as explained in the previous section, especially if an intake O

_{2}sensor is installed on the engine.

_{f}

_{,inj}’) have also been selected in accordance with the previous model presented in [8], as they are physically correlated to the NOx formation process. Engine speed in fact affects the in-cylinder charge motion and turbulence (and, therefore, the dilution of the burned gases generated by the combustion with the surrounding charge, with a consequent effect on the local temperatures and NOx formation/destruction processes), while the total injected fuel quantity is proportional to the mass of NOx that is formed inside the cylinder (see [20]) and is also correlated to the temperatures of the burned gases.

_{f}

_{,inj}’ parameter, since high engine load conditions are associated to high intake manifold pressure levels.

_{amb}’ and ambient humidity ‘H

_{abs}’ (which have a well known impact on the NOx formation) have been taken into account by means of the ISO recommended practices, as will be shown in the next section.

#### 3.3. Description of the Proposed Semi-Empirical Model

_{N}‘ which is emitted by the engine when it operates at nominal conditions (in terms of engine calibration parameters), and a NOx deviation ‘δNOx’, which occurs when MFB

_{50}or the intake O

_{2}concentration deviate with respect to the nominal values MFB

_{50N}and O

_{2N}. The nominal values of NOx emissions, of MFB

_{50}and of O

_{2}have been tabulated as a function of engine speed ‘N’ and total injected quantity ‘q

_{f}

_{,inj}’, and these tables are based on the measurements performed at steady-state conditions. More in detail, the NOx have been modeled as follows:

_{50}(i.e., a more delayed combustion) leads to a negative variation of NOx, and that a positive variation of O

_{2}leads to a positive variation of NOx. These assumptions can be considered reasonable for most of the operating conditions which occur in conventional diesel combustion.

_{amb}, H

_{abs}.

_{amb}’ and H

_{abs}’), the NOx are corrected according to the recommended practice proposed in [38].

_{abs}= 10.71 g/kg and T

_{amb}= 298 K, as follows:

_{amb}’, H

_{abs}’ are estimated as follows:

_{f}

_{,inj}’ and the engine speed ‘N’ are generally known quantities for the engine control unit. The intake O

_{2}concentration can be either measured with an intake O

_{2}sensor, or estimated by means of an O

_{2}model (the first option is in general expected to provide more accurate estimations). Analogously, MFB

_{50}can either be extracted from the in-cylinder pressure trace (if the engine is equipped with in-cylinder pressure transducers) or estimated by means of a heat release model. Concerning MFB

_{50}, both cases have been investigated in this paper, and the corresponding impact on the NOx model accuracy has been evaluated. The heat release predictive model that was used to estimate MFB50 is presented in the next section.

#### 3.4. Description of the Predictive Combustion Model

- Chemical energy release: it is estimated by means of a model which relies on the accumulated fuel mass approach [29]. The input data of the model are the injection parameters, the intake manifold thermodynamic conditions and the main engine operating parameters.
- In-cylinder pressure: the approach is based on a single-zone approach, which requires the net energy release. The net energy release is obtained as the difference between the chemical energy release and the heat exchanged between the charge and the cylinder walls. Polytropic evolutions are assumed to simulate the pressure during the compression phase and during the expansion phase. Several metrics can be extracted from the simulated in-cylinder pressure (e.g., Peak Firing Pressure (PFP) and IMEP (Indicated Mean Effective Pressure).
- Friction losses: the Chen-Flynn approach has been used to predict FMEP (Friction Mean Effective Pressure) on the basis of the engine speed and peak firing pressure; the simulation of friction losses allows BMEP (Brake Mean Effective Pressure) to be evaluated starting from IMEP.
- Pumping losses: the pumping losses (PMEP, i.e., Pumping Mean Effective Pressure) were simulated on the basis of a semi-empirical correlation, which is a function of the intake and exhaust manifold pressure levels, as well as of the engine speed.
- In-cylinder temperatures: the real-time 3-zone thermodynamic model proposed in [13] was used. This model was designed in order to be solved in closed form, so that it is suitable for control-oriented applications in terms of computational time.
- NOx emission levels: a semi-empirical correlation, that is a function of the burned gas temperature evaluated at MFB
_{50}(‘T_{b,}_{MFB50}’), intake oxygen concentration (‘O_{2}’), MFB_{50}, total injected fuel quantity (q_{f}_{,inj}), engine speed (‘N’) and injection pressure (‘p_{f}’), was used.

_{50}metric, which is one of the inputs that is required by the newly proposed NOx model.

#### Estimation of the Chemical Energy Release Q_{ch} and of MFB_{50}

_{pil}

_{,j}and τ

_{pil}

_{,j}are the combustion rate coefficient and the ignition delay coefficient, respectively, and Q

_{fuel}

_{,pil,j}is the chemical energy of the mass of fuel which is injected.

_{fuel}term is estimated as follows:

_{SOI}indicates the start of the injection time, t

_{EOI}the end of the injection time, H

_{L}is the lower heating value of the fuel and ${\dot{m}}_{f,inj}$ is the fuel mass rate.

_{SOI}and ρ

_{SOC}indicate the in-chamber densities evaluated at the start of injection or combustion, respectively, and are expressed in kg/m

^{3}. The injection pressure p

_{f}is expressed in bar, the engine speed N in rpm, the total injected fuel quantity q

_{f}

_{,inj}in mm

^{3}/cyc/cyl, the total injected fuel quantity of the pilot shots q

_{pil}

_{,tot}in mm

^{3}/cyc/cyl and finally the intake oxygen concentration O

_{2}in %. p

_{int}indicates the intake manifold pressure.

_{50}is finally estimated as the crank angle at which the 50% of the maximum chemical energy has been released.

#### 3.5. Considerations Concerning Model Recalibration for Different Engines

- A full engine map with baseline operating parameters: this map is used in order to derive the nominal values of the NOx emissions, intake O
_{2}concentration and MFB_{50}used in the model (see Equations (2)–(4)). - Sweep tests of intake O
_{2}concentration and injection parameters (e.g., SOI_{main}, p_{rail}) at fixed key-points: these tests are required in order to identify the correlation of the NOx deviations (Equation (3)). The key-points should be located in the engine area in which a high accuracy in the NOx prediction is required.

## 4. Evaluation of the Uncertainty of the Measured NOx and of the Predicted NOx

_{i}variables, the associated variance ${u}_{c}^{2}(y)$ is obtained as follows:

_{i}is defined as the “coefficient of sensitivity” of ‘y’ with respect to the i-th independent variable ‘x

_{i}’.

_{c}of the measured NOx concentration had already been carried out in [20], and is reported here for the sake of completeness. This uncertainty mainly depends on two contributions: the uncertainty of the NOx concentration of the span gas included in the calibration cylinders and the accuracy of the NOx measuring instrument (i.e., the CLD device). Two ranges (low-NOx/high-NOx) were used for the calibration of the CLD device that was used for the measurement of the NOx concentration in the exhaust gases: the low-NOx calibration range was realized using a calibration cylinder with a NOx concentration of 150 ppm in the span gas, while the high-NOx calibration range was realized using a calibration cylinder with a NOx concentration of 1000 ppm in the span gas. Table 4 reports the uncertainty of the NOx concentration in the span gas included in the calibration cylinders (Table 4a), the accuracy specifications of the CLD device (Table 4b) and the uncertainty of the measured NOx emissions considering four different levels (Table 4c).

## 5. Model Calibration

_{50}terms are in line with the observations reported in Section 3.3, while the positive exponent of the ‘q

_{f}

_{,inj}’ term means that the NOx deviation range increases with engine load. The effect of engine speed is, instead, less significant than that of the injected fuel quantity, and opposite for positive or negative variations of MFB

_{50}.

## 6. Results and Discussion

_{50}, intake O

_{2}concentration, engine speed and total injected fuel quantity.

_{50}can be either derived from the in-cylinder pressure trace (if the engine is equipped with pressure transducers), or estimated by a predictive heat release model (i.e., Equations (9)–(18)), both cases have been considered for the model assessment. With reference to the case in which MFB

_{50}is extracted from the in-cylinder pressure trace, the values of MFB

_{50}used in the model are the result of the average over the last consecutive 100 cycles for the steady-state tests, while they derive from a cycle-by-cycle acquisition in the transient tests. The intake O

_{2}concentration used in the model was taken from the measurements of the gas analyzer (an intake O

_{2}sensor was not available), while engine speed and total injected quantity were taken from the test bench measurements.

_{2}concentration, the values used in the model were the result of an average over the last 60 s for the steady-state tests (an engine stabilization time of 30–60 s is carried out before the measurement of each steady-state point). For the transient tests, the instantaneous intake O

_{2}concentration was used in the model, in which the acquisition frequency was equal to 20 Hz.

_{2}estimation on the accuracy of the predicted NOx levels. Finally, Section 6.6 is focused on the results concerning the required computational time on the ETAS ES910 rapid prototyping device.

#### 6.1. Model Assessment at Steady-State Conditions

_{50}is estimated from the in-cylinder pressure sensor, Figure 7b reports the results of the NOx model when MFB

_{50}is estimated by the predictive heat release model (Equations (9)–(18)), and finally Figure 7c reports the results of the previous NOx model reported in [8].

^{2}) and by the Root Mean Squared Error (RMSE), which are reported in each figure.

_{50}is estimated through the pressure sensor, and of the order of 44 ppm when MFB

_{50}is estimated by the heat release model. In both cases, the accuracy is of the same order as that of the previously developed model [8], i.e., 38 ppm.

#### 6.2. Model Validation over Transient Conditions

_{50}was estimated through the in-cylinder pressure sensor, Figure 9b reports the predicted NOx trends using the NOx model, in which MFB

_{50}is estimated by the predictive heat release model, and finally Figure 9c reports the predicted NOx levels using the previous NOx model reported in [8].

_{c}= 5 s. This filtering is necessary for the comparison with the experimental trends, since the latter are obtained from the measurements of the gas analyzer, which suffers from a certain degree of smoothing and delaying (compared to the actual engine-out NOx levels over the transient), due to the mixing of the exhaust gases in the pipes that connect the engine to the gas analyzer. This effect had already been observed in [8]. In order to have an experimental measurement of the NOx emissions that is more representative of the actual dynamics which occurs in the engine exhaust manifold, a NOx sensor with high frequency response (not available for the considered tests) should be installed in the engine.

_{50}is not extracted from the in-cylinder pressure sensor, but is estimated by the predictive heat release model (see Figure 9b).

#### 6.3. Model Calibration with Limited Number of Experimental Tests

#### 6.4. Analysis of the NOx Model Uncertainty

_{50}, O

_{2}, N, q

_{f}

_{,inj}), in general, is in fact characterized by a variance, which determines an uncertainty in the predicted NOx levels.

_{50}and O

_{2}lead to the highest contribution in the uncertainty of the predicted NOx emissions, while the contribution of N and q

_{f}

_{,inj}is smaller (the maximum error of the encoder is of the order of 0.00075 N, while the error of the fuel meter is of the order of 0.1% of the measured value).

- Case 1: MFB
_{50}is estimated from the in-cylinder pressure sensor. - Case 2: MFB
_{50}is estimated by the predictive heat release model.

_{50}that is associated to case 1 was derived using the information related to the accuracy of the pressure transducer, while the standard deviation of MFB

_{50}that is associated to case 2 was obtained by means of a statistical analysis of the heat release model accuracy.

_{2}concentration, the standard deviation was obtained on the basis of the accuracy of the Paramagnetic Oxygen Detector (POD) device that is installed in the gas analyzer, and on the basis of the uncertainty in the gas concentration of the calibration cylinders.

_{c}’ (i.e., NOx + U

_{c}and NOx − U

_{c}). Figure 10a refers to case 1 (MFB

_{50}from pressure sensor), while Figure 10c refers to case 2 (i.e.,

_{MFB50}from heat release model). The values of the standard deviation of MFB

_{50}and O

_{2}are reported on the top of each chart. For the same two cases, Figure 10b,d report the statistical distributions of the relative expanded uncertainty of the predicted NOx emissions.

_{50}(with a standard deviation σ = 0.1°) can lead to a relative uncertainty in the predicted NOx emissions that is between 2 and 8%, while the use of the heat release model to estimate MFB

_{50}(with a standard deviation σ = 0.8°) leads to a relative uncertainty that is between 5% and 25%.

_{50}from pressure sensor, Figure 11a) and case 2 (i.e., MFB

_{50}from heat release model, Figure 11b).

_{50}(with a standard deviation σ = 0.1°) can lead to a relative uncertainty in the predicted NOx emissions that is between 3% and 7%, while a broader distribution of uncertainty occurs if a heat release model is used to estimate MFB

_{50}(with a standard deviation σ = 0.8°).

#### 6.5. Impact of Intake O_{2} Error on the NOx Prediction Accuracy

_{2}concentration.

_{2}leads to a variation of NOx emissions that is of the order of 200 ppm.

_{2}estimation is high, the analysis carried out in the previous section has been repeated by assuming a standard deviation σ

_{O2}= 0.5%. This standard deviation can be representative of the accuracy of intake O

_{2}models typically adopted in ECUs. The results are reported in Figure 13. In particular, Figure 13a,c report, for the steady-state tests of Figure 3, the upper and lower values bands of the predicted NOx emissions taking into account the expanded uncertainty ‘U

_{c}’ (i.e., NOx + U

_{c}and NOx − U

_{c}). Figure 13a refers to the case in which MFB

_{50}is estimated from the pressure sensor, while Figure 13c refers to the case in which MFB

_{50}is estimated by the heat release model. The values of the standard deviation σ are reported, for MFB

_{50}and O

_{2}, on the top of each chart. For the same two cases, Figure 13b,d report the statistical distribution of the relative expanded uncertainty of the predicted NOx emissions.

_{2}is equal to 0.5%, the relative uncertainty of the predicted NOx emissions increases in a range between 5 and 25% if MFB

_{50}is estimated by the pressure sensor (Figure 13b), while it increases in a range between 5 and 35% if MFB

_{50}is estimated by the heat release model (Figure 13d).

_{2}sensor with high accuracy is recommended in order to have an accurate estimation of NOx emissions. An analysis of the current state of the art in the development of intake O

_{2}sensors suggests that it is possible to achieve very high levels of accuracy which are stable over time. For example, the intake O

_{2}sensor developed in [40] is characterized by a maximum relative error that is of the order of 2% (which corresponds to a standard absolute deviation σ

_{O2}= 0.2% for a measured value of intake O

_{2}concentration equal to 20%, assuming that the maximum error has a coverage factor of 95%). This standard deviation is not far from that of the POD device that was used to validate the model in this paper (see the uncertainty analysis in the previous section).

#### 6.6. Required Computational Time on ETAS ES910

_{50}is estimated by a pressure sensor or from the heat release model. This can be explained by the fact that the 3-zone thermodynamic model included in the predictive combustion model is highly time-consuming (see also [8]).

## 7. Conclusions

_{50}’. The model also takes into account the effects of engine speed, total injected quantity, and ambient temperature and humidity.

_{2}concentration is measured with a sufficiently level of accuracy (e.g., with a standard deviation of 0.15%).

## Author Contributions

## Conflicts of Interest

## Abbreviations

BMEP | Brake Mean Effective Pressure |

c | Coefficient of sensitivity |

CA | Crank angle |

CFD | Computer fluid-dynamics |

CLD | Chemiluminescence detector |

DT | Dwell-time |

ECU | Engine control unit |

EGR | Exhaust gas recirculation |

EOI | End of injection |

EVO | Exhaust valve opening |

FPT | Fiat powertrain technologies |

H_{abs} | Absolute humidity of the air |

HCCI | Homogeneous charge compression ignition |

H_{L} | Lower heating value of the fuel |

ICEAL-PT | Internal Combustion Engines Advanced Laboratory at the Politecnico di Torino |

IMEP | Indicated mean effective pressure |

IMEP360 | Gross indicated mean effective pressure |

IMEP720 | Net indicated mean effective pressure |

IVC | Intake valve closing |

K | Combustion rate coefficient |

m | Mass |

MAF | Mass airflow sensor |

m_{fuel} | Total injected fuel mass per cycle/cylinder |

${\dot{m}}_{f,inj}$ | Fuel injection rate |

MFB_{50} | Crank angle at which 50% of the fuel mass fraction has burned |

N | Engine rotational speed |

O_{2} | Intake charge oxygen concentration |

p | Pressure |

PCCI | Premixed charge compression ignition |

p_{exh} | Exhaust manifold pressure |

p_{f} | Injection pressure |

PFP | Peak firing pressure |

p_{int} | Intake manifold pressure |

PMEP | Pumping mean effective pressure |

POD | Paramagnetic oxygen detector |

q | Injected fuel volume quantity |

Q_{ch} | Chemical heat release |

q_{f}_{,inj} | Total injected fuel volume quantity per cycle/cylinder |

Q_{fuel} | Chemical energy associated with the injected fuel |

Q_{net} | Net heat release |

q_{pil} | Injected fuel volume quantity of the pilot injection |

q_{pil,tot} | Total injected fuel volume quantity of the pilot injections |

R^{2} | Squared correlation coefficient |

RMSE | Root mean square error |

SOC | Start of combustion |

SOI | Electric start of injection |

SOI_{main} | Electric start of injection of the main pulse |

t | Time |

T | Temperature |

T_{amb} | Ambient temperature |

T_{b}_{max,main} | Maximum temperature of the burned gas zone during the combustion of the main pulse |

T_{b}_{,MFB50} | Temperature of the burned gas zone at MFB_{50} |

T_{int} | Intake manifold temperature |

u^{2} | Variance |

U_{c} | Expanded combined uncertainty |

VGT | Variable Geometry Turbine |

VPM | Virtual Pressure Model |

Greek symbols | |

${\alpha}_{st}^{u}$ | Stoichiometric charge-to-fuel ratio |

ρ | Density |

ρ_{SOI} | In-chamber ambient density evaluated at the SOI instant |

ρ_{SOC} | In-chamber ambient density evaluated at the SOC instant |

σ | Standard deviation |

τ | Ignition delay coefficient |

Subscripts | |

air | Made of air |

EGR | Made of EGR |

main | Main pulse |

pil | Pilot pulse |

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**Figure 1.**FPT F1C 3.0 L Euro VI diesel engine installed on the highly dynamic test bench at the Politecnico di Torino. The EATS ES910 rapid prototyping device can be observed on the right side.

**Figure 4.**Contour plots of measured NOx emissions as a function of injection pressure and SOI

_{main}, for the points indicated by the black squares.

**Figure 5.**Contour plots of measured NOx emissions as a function of injection pressure and MFB

_{50}, for the points indicated by the black squares.

**Figure 6.**Scheme of the predictive combustion model reported in [8].

**Figure 9.**Predicted and experimental trends of engine-out NOx emissions for the analyzed transient test. The predicted NOx trace has been filtered using a time constant of 5 s, as reported in [8]. (

**a**) new model, MFB

_{50}from pressure sensor; (

**b**) new model, MFB

_{50}from heat release model; (

**c**) previous model presented in [8].

**Figure 10.**Results of the uncertainty analysis of the NOx model for the steady-state tests of Figure 3, adopting a standard deviation σ

_{O2}= 0.15% (O

_{2}from gas analyzer). (

**a**,

**c**) upper and lower values bands of the predicted NOx emissions taking into account the expanded uncertainty ((

**a**) MFB

_{50}from pressure sensor, (

**c**) MFB

_{50}from heat release model); (

**b**,

**d**) statistical distribution of the relative expanded uncertainty of the predicted NOx emissions ((

**b**) MFB

_{50}from pressure sensor, (

**d**) MFB

_{50}from heat release model).

**Figure 11.**Results of the uncertainty analysis of the NOx model for the transient test of Figure 8, adopting a standard deviation σ

_{O2}= 0.15% (O

_{2}from gas analyzer). The statistical distribution of the relative expanded uncertainty of the predicted NOx emissions is reported ((

**a**) MFB

_{50}from pressure sensor, (

**b**) MFB

_{50}from heat release model).

**Figure 12.**Measured NOx emissions as a function of the measured intake O2 concentration for the EGR sweep tests reported in Figure 3.

**Figure 13.**Results of the uncertainty analysis of the NOx model for the steady-state tests of Figure 3, assuming a standard deviation σ

_{O2}= 0.5% (e.g., O

_{2}from model). (

**a**,

**c**): upper and lower values bands of the predicted NOx emissions taking into account the expanded uncertainty ((

**a**) MFB

_{50}from pressure sensor, (

**c**) MFB

_{50}from heat release model); (

**b**,

**d**): statistical distribution of the relative expanded uncertainty of the predicted NOx emissions ((

**b**)

_{MFB50}from pressure sensor, (

**d**) MFB

_{50}from heat release model).

Engine Specifications | |
---|---|

Engine type | FPT F1C Euro VI diesel engine |

Number of cylinders | 4 |

Displacement | 2998 cm^{3} |

Bore × stroke | 95.8 mm × 104 mm |

Rod length | 160 mm |

Compression ratio | 17.5 |

Valves per cylinder | 4 |

Turbocharger | VGT type |

Fuel injection system | High pressure Common Rail |

ETAS ES910 Device | |
---|---|

Main processor | Freescale PowerQUICC^{TM} III MPC8548 with 800 MHz clock Double precision floating point unit |

Memory | 512 MByte DDR2-RAM (400 MHz clock) |

64 MByte Flash | |

128 kByte NVRAM |

Property | Units | Diesel EN 590 |
---|---|---|

Cetane number | - | 53.1 |

Flash Point | °C | 70 |

Density at 15 °C | kg/m^{3} | 844 |

Viscosity at 40 °C | mm^{2}/s | 2.860 |

Lower heating value | MJ/kg | 43.4 |

**Table 4.**(

**a**) Uncertainty of NOx calibration cylinders. (

**b**) Main sources of error of the CLD device. (

**c**) Expanded uncertainty of the measured NOx for different measured values.

(a) | ||

Measuring Range | NOx Concentration in the Span-Gas of the Calibration Cylinder | Relative Expanded Uncertainty U_{c} |

low-NOx | 150 ppm | 2% |

high-NOx | 1000 ppm | 2% |

(b) | ||

Error type | Error | |

Linearity | ≤2% of measured value (10–100% of full scale range) | |

≤1% of full scale range whichever is smaller | ||

Drift 24 h | ≤1% of full scale range | |

Reproducibility | ≤0.5% of full scale range | |

(c) | ||

Measured NOx | U_{c} | Relative U_{c} |

50 ppm | 1.6 ppm | 3.1% |

100 ppm | 2.5 ppm | 2.5% |

500 ppm | 16 ppm | 3.3% |

1300 ppm | 33 ppm | 2.5% |

**Table 5.**Values of RMSE related to the prediction of NOx emissions, as a function of the percentage of data used for the model calibration, when applying the model to the steady-state tests reported in Figure 3.

% of Tests Used for Calibration | NOx RMSE (MFB_{50} from Pressure Sensor) | NOx RMSE (MFB_{50} from Heat Release Model) |
---|---|---|

100 | 34 ppm | 44 ppm |

50 | 34 ppm | 44 ppm |

25 | 36 ppm | 46 ppm |

20 | 37 ppm | 45 ppm |

15 | 38 ppm | 45 ppm |

10 | 40 ppm | 46 ppm |

5 | 46 ppm | 53 ppm |

**Table 6.**Values of RMSE related to the prediction of NOx emissions, as a function of the percentage of data used for the model calibration, when applying the model to the transient test reported in Figure 8.

% of Tests Used for Calibration | NOx RMSE (MFB_{50} from Pressure Sensor) | NOx RMSE (MFB_{50} from Heat Release Model) |
---|---|---|

100 | 17 ppm | 22 ppm |

50 | 16 ppm | 23 ppm |

25 | 14 ppm | 27 ppm |

20 | 14 ppm | 27 ppm |

15 | 15 ppm | 25 ppm |

10 | 13 ppm | 28 ppm |

5 | 18 ppm | 18 ppm |

**Table 7.**Standard deviation of MFB

_{50}and O

_{2}for the evaluation of the uncertainty of the NOx model.

Input Parameter | Case 1 (MFB_{50} from Pressure Sensor) | Case 2 (MFB_{50} from Heat Release Model) |
---|---|---|

MFB50 | σ = 0.1° | σ = 0.8° |

O_{2} | σ = 0.15% | σ = 0.15% |

**Table 8.**Average computational time required by the NOx models, when implemented on the ETAS ES910 RP device.

New NOx (MFB_{50} from Pressure Sensor) | New NOx Model (MFB_{50} from Heat Release Model) | NOx Model Presented in [8] |
---|---|---|

<50 μs | ~200–300 μs | ~1500 μs |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Finesso, R.; Hardy, G.; Maino, C.; Marello, O.; Spessa, E.
A New Control-Oriented Semi-Empirical Approach to Predict Engine-Out NOx Emissions in a Euro VI 3.0 L Diesel Engine. *Energies* **2017**, *10*, 1978.
https://doi.org/10.3390/en10121978

**AMA Style**

Finesso R, Hardy G, Maino C, Marello O, Spessa E.
A New Control-Oriented Semi-Empirical Approach to Predict Engine-Out NOx Emissions in a Euro VI 3.0 L Diesel Engine. *Energies*. 2017; 10(12):1978.
https://doi.org/10.3390/en10121978

**Chicago/Turabian Style**

Finesso, Roberto, Gilles Hardy, Claudio Maino, Omar Marello, and Ezio Spessa.
2017. "A New Control-Oriented Semi-Empirical Approach to Predict Engine-Out NOx Emissions in a Euro VI 3.0 L Diesel Engine" *Energies* 10, no. 12: 1978.
https://doi.org/10.3390/en10121978