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Physikalische Verbrennungsmodellierung bei Dieselmotoren
und Bewertung einer NOx-Kinetik für
Otto- Gas- und Dieselmotoren
Physical modeling of combustion for diesel engines and assessment of a NOx-kinetic for
gasoline, gas and diesel engines
Reza Rezaei, Friedrich Dinkelacker, Benjamin Tilch, Thaddäus Delebinski and Maximilian Brauer
Abstract
Enhancing the predictive quality of engine models, while maintaining an affordable computational cost is of great importance. In this study, a phenomenological com-bustion model for diesel combustion and a tabulated NOx kinetics model for me-thane, iso-octane and diesel fuel are presented. The combustion model uses physi-cal and chemical sub-models for local processes like injection, spray formation, igni-tion and combustion. Modeling of NOx formation is based on detailed tabulated chemistry methods. The applied combustion model accounts for the turbulence-controlled as well as the chemistry-controlled combustion in compression ignition engines. The phenomenological combustion model is first assessed for passenger car application, especially with multiple pilot injections and high EGR ratios for low load operating points. The validation results are presented for representative operat-ing conditions from a single-cylinder light-duty diesel engine and also a heavy-duty diesel engine.
In the second part of this study a novel approach for accurate and very fast modeling of NO formation in combustion engines is proposed. This approach is based on tabu-lation of detailed chemical kinetic and is validated against the detailed chemical reac-tion mechanism at all engine-relevant conditions with variation of pressure, tempera-ture, and air/fuel ratio under stationary and ramp-type transient conditions in a per-fectly-stirred reactor considering different fuels for gasoline, gas and diesel engines. Using this approach, a very good match to the results from calculations with the de-tailed chemical mechanism is observed. Finally, the tabulated NOx kinetic model is implemented in the combustion model for in-cylinder NOx prediction and compared with experimental engine measurement for instance a diesel engine.
Kurzfassung
Die Verbesserung der Vorhersagefähigkeit von Motormodellen unter Beibehaltung eines akzeptablen Rechenaufwands ist von großer Bedeutung. In dieser Arbeit wer-den ein phänomenologisches Verbrennungsmodell für Dieselmotoren und ein kenn-feldbasiertes NOx-Modell für Methan, Iso-Oktane und Dieselkraftstoff präsentiert. Das Verbrennungsmodell bildet lokale Prozesse wie Einspritzung, Spray-Ausbreitung, Zündung, Verbrennung sowie NOx-Bildung physikalisch ab. Das Ver-brennungsmodell berücksichtigt sowohl die turbulenz-gesteuerte als auch die che-misch-gesteuerte dieselmotorische Verbrennung. Das phänomenologische Verbren-nungsmodell wird zunächst für eine PKW-Anwendung, speziell für mehrere Pilotein-spritzungen und hohen AGR-Raten bei Niedriglasten bewertet. Es werden Validie-rungsergebnisse an repräsentativen Betriebspunkten eines PKW Einzylinders sowie eines Off-Road-Nfz-Dieselmotor dargestellt.
Im zweiten Teil dieser Arbeit wird eine neue Methode zur sehr schnellen Modellie-rung der NO-Bildung dargestellt und diskutiert. Die entwickelte kennfeldbasierte Re-aktionskinetik wird mittels detaillierten Reaktionmechanismus für alle motorrelevan-ten Bedingungen bedatet und validiert. Die Kinetik wird unter allen motorrelevanten Bedingungen durch die Variationen von Druck, Temperatur und Verbrennungsluft-verhältnis unter stationären und transienten Bedingungen (transiente Rampe) in ei-nem Reaktormodell für verschiedene Kraftstoffe für Otto-, Gas- und Dieselmotoren kalibriert. Das kennfeldbasierte NOx-Modell wird abschließend in das Verbren-nungsmodell zur Vorhersage der NOx-Bildung im Zylinder implementiert und mit ex-perimentellen Messergebnissen am Beispiel eines Dieselmotors angewendet und evaluiert.
1. Introduction
Numerical simulation methods are utilized as a standard tool for the description of internal combustion engine processes, and for the optimization to fulfill future emis-sion standards, fuel consumption reduction and improved safety and drivability, see e.g. Heywood [1]. A predictive model that accounts for several engine processes such as combustion and emission formation plays a decisive role in powertrain de-velopment, including optimization of engine components as well as development, testing, and model-based calibration of combustion and aftertreatment control strat-egies [2].
Fast empirical combustion models, e.g. Vibe function [3], often suffer from a lack of predictability. Phenomenological models have the advantage of being both easy to handle and computationally efficient. In addition, they are capable of predicting sev-eral effects of important parameters on the combustion process and emission for-mation.
In recent years, multiple modeling approaches have been studied by various investi-gators. For instance, the approach proposed by Chmela et al. [4, 5] is a global model based on a single-zone description of the combustion chamber. It does not require subdividing of the combustion chamber into zones of different compositions and temperatures. Therefore, it offers a fast and computationally efficient modeling. This
is categorized as a phenomenological combustion model, since it relates the burning rate to the engine characteristic parameters (e.g. the injection rate as a time-dependent input parameter) [6, 7]. The main issue of this model is the hypothesis that the rate of fuel combustion is determined by the rate of air-fuel mixing. The rate of air-fuel mixing depends on the injection rate as well as turbulent kinetic energy.
More detailed models are generally less computational efficient. For example the so-called packet model from Hiroyasu et al. [8, 9] can be mentioned, in which the com-pression stroke is modeled with one zone, while the injection spray is discretized into small packets in axial and radial directions. Other authors follow this concept, e.g. [10, 11, 12]. Stiesch and Merker [12] modified this model so that the maximum burn-ing rate of each packet depends not only on the vaporized fuel and the available air but also on the maximum chemical reaction rate. Barba [7] proposed an empirical and a phenomenological combustion model. The phenomenological combustion model accounts for premixed and also the diffusion combustion in combination with an ignition delay model.
2. Combustion model formulation
As the focus of the current study is set on highly efficient modeling of combustion, the approach of Chmela et al. [5] for single-zone modeling of spray and combustion is used as basis of the development while the spray is not modeled with the packet approach. The time evolution of spray characteristics are governed by mass and momentum conservation equation of the spray control volume. The model is inte-grated as a user subroutine in the simulation software GT-Power [13] accounting for two-zone description of the cylinder thermodynamics. The working fluid consists of an unburned zone and a burned zone with energy and mass interactions between themselves. For each zone, the thermodynamic properties such as temperature, gas composition, etc. are calculated separately. For brevity, only the highlights of the combustion model for modeling the multiple pilot injections for passenger car appli-cation under low load and high exhaust gas recirculation ratio are described here. More detail about the physical sub-models such as injection, spray formation, and combustion can be found in [14].
2.1 Ignition model
The applied ignition model employs semi-empirical models for both physical and chemical sub-processes accounting for ignition delay. Modeling of the chemical igni-tion delay is performed by a least-square fitted ignition model of Weisser [15] that enables the capture of the low temperate and high temperature ignition behavior, including the negative temperature (NTC) region in between, Figure 1. In order to consider the effect of physical sub-processes on ignition delay, a simple formulation used by Barba [7] is used to describe the physical ignition delay.
Ign
itio
n d
ela
y
[ms]
0.01
0.1
1
10
100
1000/T [1/K]
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Ciezki et al., measured 3 bar Ignition Model 3 barCiezki et al., measured 13 bar Ignition model 13 bar
Patel et al., ERC mech. 40 barCiezki et al., measured 40 bar Ignition model 40 bar
Figure 1: Comparison of the ignition delay sub-model with experimental measure-ments of Ciezki et al [16] and the reduced reaction kinetic mechanism of Patel et al.
[17]
2.2 Premixed and diffusion combustion modeling
The combustion model is principally a laminar-and-turbulent characteristic-time com-bustion model which is frequently used in CFD models for diesel engine combustion [18] with improvements accounting for the premixed, diffusion, and burn-out combus-tion [14]. This handles the two extremes of combustion, reactions limited by kinetics and those limited by mixing.
For the reaction kinetics limit, the laminar time scale, l is calculated according to
Kong et al. [18],
)/exp(][][ 5.1
2
75.0 RTEOfuelAl
(1)
The effects of exhaust gas recirculation and oxygen concentration as well as fuel concentration in the mixture are taken into account.
Combustion limited by mixing is the other extreme, if the chemical time scales are negligibly small compared to the turbulent mixing time scales. For instance, the Eddy Break-Up (EBU) model assumes the resulting effective reaction rate to be propor-tional to the reciprocal of the turbulent time scale [19]. In fact, the entire spectrum of combustion regimes can be found in diesel engine combustion. This means that at any time, there may be a partial burning in either a kinetically-limited or mixing-limited way, while the overall combustion often lies somewhere in between these extremes. The developed combustion model accounts for both laminar and turbulent time scales.
For passenger car applications, there are considerable amount of low-load points in the engine map which are operated in the New European Driving Cycle (NEDC). These points may have moderate or high EGR rates with multiple pilot injections and therefore a major portion of the combustion is premixed and chemically controlled. The combustion model is improved here in order to calculate the ignition delay con-sidering the low temperature, NTC ignition, and the high temperature ignition which
may happen by an early pilot injection, late main, or a post injection. The ignition de-lay is calculated for each injection event. The spray model calculates the mixture preparation for each event individually. The effect of air-entrainment and dilution of mixture before and after combustion have an important effect on ignition and pre-mixed combustion afterwards. This is considered in the spray model, providing the mass fraction of the mixed fuel above a certain relative air-fuel ratio as a function of mixing time, and this crucial input is used by the combustion model for each injection event separately.
3. Test engines
The combustion model is validated using measurement data of different diesel en-gines, from passenger car up to heavy-duty applications, utilizing EGR and various injection strategies. For brevity, only two validation engines are presented here.
3.1 Light-duty passenger car diesel engine
The presented combustion model is modified for passenger car light-duty application with relatively high EGR ratios and multiple pilot injections with focus on part and low-load cases which are relevant for the European exhaust-emission legislation in the NEDC cycle. The thermodynamic measurements are conducted on a passenger car single-cylinder engine with a displacement of approximately 536 cm
3. The engine
has an eight-hole nozzle with a common-rail injection system. All relevant pressures and temperatures (intake air, EGR, exhaust gas, lubricant, coolant) are controlled externally by the test bench. The main engine parameters are listed in Table 1:
Bore 83 mm
Stroke 99 mm
Compression ratio 16.2
Max. peak firing pressure 220 bar
Number of nozzle holes 8
Nozzle hydraulic flow rate 710 cm3 / min @ 100bar
Table 1: Specifications of the passenger car single-cylinder test engine
3.2 Heavy duty diesel engines
The second validation engine is a heavy-duty diesel engine, certified for the non-road Tier 4i emission standard. It has a displacement of approximately 2000 cm
3 for each
cylinder and an eight-hole nozzle equipped with a common-rail injection system. No EGR is applied at this engine. All points on the engine map are considered, Figure 2.
Torq
ue r
atio [
%]
10
33
55
78
100
Engine speed [1/min]
600 1000 1400 1800 2200
Heavy-duty diesel engine
Figure 2: The investigated engine operating points of the heavy-duty diesel engine
4. Validation of the phenomenological combustion model
4.1 Light-duty passenger car diesel engine
For the light-duty passenger car engine, at first, a full load operating point is selected for validation of the combustion model with variation of the rail-pressure. For the two part load operating points, a start of injection (SOI) variation and an EGR variation are carried out. As given in Table 2, the engine speed differs for the part and full load cases. GT-Power is used as simulation platform and the integrated combustion model is used for modeling of heat release rate with the same parameters for all op-erating points.
Operating point
Engine speed [1/min]
Mean effective pressure [bar]
Rail-pressure [bar]
EGR rate [%]
A 3700 14.9-17.4 1600-2200 0
B 1200 6.2-6.5 800 34-38
C 1200 6.2-6.3 800 0-41
Table 2: Investigated operating points using the passenger car single-cylinder engine
Figure 3 compares the simulated in-cylinder pressure with the measurement. Shifting the start of injection to an earlier time, increases the maximum cylinder pressure and the pressure gradient, which are both reproduced properly by simulation. A good match is observed between simulation and measurement in Figure 3.
Inj. R
ate
[m
g/s
]In
j. R
ate
[m
g/s
]In
j. R
ate
[m
g/s
]
Cylin
der
pre
ssure
[bar]
0
40
80
120
160
200
pRail = 1600 bar
Measurement Combustion model Injection rate
A
Cylin
der
pre
ssure
[bar]
0
20
40
60
80
100 B
SOI = - 6.8 °CA
Cylin
der
pre
ssure
[bar]
0
20
40
60
80
100
Crank angle [°CA ATDC]
-20 0 20 40 60
C
EGR = 0 %
Crank angle [°CA ATDC]
-20 0 20 40 60
C
EGR = 31 %
B
SOI = - 9.2 °CA
pRail = 1800 bar
A
pRail = 2000 bar
A
B
SOI = - 11.4 °CA
Crank angle [°CA ATDC]
-20 0 20 40 60
C
EGR = 38 %
Crank angle [°CA ATDC]
-20 0 20 40 60
C
EGR = 41 %
B
SOI = - 14.0 °CA
pRail = 2200 bar
A
Figure 3: Comparison of the simulated in-cylinder pressure with measurement. Op-erating points A, B, and C correspond to n=3700, 1200, and 1200 1/min
4.2 Heavy-duty diesel engine
Additionally, the phenomenological combustion model is investigated on a heavy-duty diesel engine. Calibration of the combustion model parameters is carried out for nine representative operating points and then used with the same parameters for the entire engine map.
Three important engine speeds of 1200, 1500, and 1900 1/min with engine load of 25%, 50%, 75%, and 100% are selected for plotting in Figure 4. The simulated heat release rate is compared with results obtained from the thermodynamic analysis of the measured cylinder pressure. A good concordance between simulation and measurement is obtained for all the full and part load cases.
Inj. R
ate
[m
g/s
]In
j. R
ate
[m
g/s
]In
j. R
ate
[m
g/s
]
Measurement Combustion model Injection rate
Heat
rele
ase [
1/°
CA
]
0.00
0.04
0.07
0.11
0.14A: 25%
Heat
rele
ase [
1/°
CA
]
0.00
0.04
0.07
0.11
0.14B: 25%
Heat
rele
ase [
1/°
CA
]
0.00
0.04
0.07
0.11
0.14
Crank angle [°CA ATDC]
-20 0 20 40 60
C: 25%
Crank angle [°CA ATDC]
-20 0 20 40 60
C: 50%
A: 50%
B: 50% B: 75%
Crank angle [°CA ATDC]
-20 0 20 40 60
C: 75%
Crank angle [°CA ATDC]
-20 0 20 40 60
C: 100%
A: 100%
B: 100%
A: 75%
Figure 4: Heat release rate obtained from the combustion model and thermodynamic analysis of experimental investigation. Operating points A, B, and C correspond to n=1200, 1500, and 1900 1/min with 25%, 50%, 75%, and 100% load respectively
5. Tabulated NOx Kinetic Model
The extended Zeldovich mechanism [20] is a common reaction kinetic to model the thermal NO formation and is often used in 1-D as well 3-D simulation tools, employ-ing three kinetic reactions and assuming further equilibrium reactions. These equilib-rium reactions are required to calculate the H, O, and OH radicals for the three slow-er kinetic reactions, determining the NO concentration.
In this study, an analytical investigation of NOx formation kinetics in all engine-relevant conditions is carried out, using the detailed chemical reaction mechanism GRI-Mech 3.0 [21] with 325 reactions and 53 species for different fuels. Figure 5 shows the investigated operating conditions from 2000 to 3000 K as well as various relative air-fuel ratios from 0.4 to 3.0. Each of these operating conditions is simulated in a perfectly-stirred and adiabatic reactor. The reactor pressure and temperature are defined as constant values at start of the simulation. The mole fraction of each spe-cies, O, H, OH, etc. is initialized equal to its mole fraction in the equilibrium condition by the given pressure, temperature, and air-fuel ratio, assuming that combustion is very fast compared to the NO kinetic and the combustion products are in equilibrium state at the start of the reactor simulation. The Composition of each investigated fuel is considered in the combustion products initialized in the equilibrium condition at the start of reactor simulations.
NO is initialized as zero and is formed in this perfectly-stirred reactor until reaching its value at the equilibrium condition. The rate constants of the Zeldovich mechanism are used as given by Bowman [22]. The same initial conditions such as temperature, pressure and species concentration are implied for both the detailed kinetic and Zeldovich mechanism at the start of reactor simulation.
Te
mp
era
ture
[K
]
2000
2200
2400
2600
2800
3000
Case [-]
0 10 20 30 40 50 60 70 80 90 100 110 120 130
La
mb
da
[-]
0.6
1.0
1.4
1.8
2.2
2.6
3.0
Figure 5: Temperature and pressure variation for each reactor simulation case
In order to evaluate the Zeldovich mechanism, NO concentrations at the different representative times after start of NO formation are compared with values from the detailed kinetic as well as their values in the equilibrium condition for tetradecane, Figure 6.
NO
[p
pm
]
0
6000
12000
18000
24000
30000
36000
Case [-]
0 10 20 30 40 50 60 70 80 90 100 110 120 130
NO in equilibrium state Detailed GRI-Mech 3.0 at t=0.1 ms Zeldovich mechanism at t=0.1 ms
NO
[p
pm
]
0
6000
12000
18000
24000
30000
36000 NO in equilibrium state Detailed GRI-Mech 3.0 at t=1.6 ms Zeldovich mechanism at t=1.6 ms
Figure 6: Comparison of the NO concentration in a perfectly-stirred reactor at 0.1 ms and 1.6 ms after start of NO formation for various operating conditions for tetrade-
cane
The selected post-processing time of 1.6 ms in Figure 6, corresponds to e.g. 12 °CA at 1250 1/min, which is an important time scale for combustion and emission for-mation.
As Figure 6 illustrates, large deviation between the calculated NO by the Zeldovich mechanism and the detailed GRI-Mech 3.0 mechanism is observed during the for-mation phase. Depending on operating conditions and completeness of NO for-mation, an inaccuracy factor of about approximately 2 is observed in the formation phase. This correlates with an uncertainty factor of 2 for NO formation reactions [1].
It can be concluded here that the Zeldovich mechanism with a big deviation in pre-diction of the NO formation phase, could be a source of inaccuracy in simulation of NOx emissions in combustion engines. However a direct implementation of a detailed reaction mechanism like GRI-Mech 3.0 or even a reduced mechanism with fewer reactions as proposed e.g. by Yoshikawa and Reitz [23], is computationally not af-fordable for a fast-running phenomenological combustion model.
For improving the accuracy and computational time, a tabulated chemistry method for modeling the NO formation, based on the characteristic chemical time scale is proposed. This is similar to the proposed model of Kong et al. [18] for modeling the premixed combustion,
chem
iii YY
t
Y
*~~~
(2)
Here, for NO formation, chem is taken as the characteristic formation time scale and *~
iY as the NO concentration in the equilibrium state. Solving the above differential
equation with initial conditions of 0.00 tNO leads to:
chem
t
eNONOtNO
** (3)
In order to calculate the NO concentration using (3), the characteristic chemical time,
chem and the NO concentration in equilibrium condition, *NO are required. These val-
ues can be calculated from the GRI-Mech 3.0 detailed chemical reaction mechanism in a perfectly-stirred reactor for various temperatures and air-fuel ratios and are pro-vided as look-up tables. A temperature range from 2000 to 3000 K and different gas compositions according to relative air-fuel ratios from 0.4 to 3.0 at a constant pres-sure of 80 bar, are selected for tabulation of the required parameters.
Calibration of the proposed reaction mechanism and calculation of both parameters for each simulation case is performed by minimization of error using the particle swarm optimization solver [24]. Figure 7 compares the NO formation at 80 bar and temperature of 2700 K for different relative air-fuel ratios.
A very good match between the proposed NOx kinetic model and results obtained from the detailed GRI-Mech 3.0 mechanism with 325 reactions and 35 species is obtained. In order to assess the accuracy of the proposed kinetic, the deviation from the simulated NO by the detailed mechanism during the formation phase is calculat-ed and the relative error (in percent) is given by (4).
%.100
dttNO
dttNOtNOerrorRelative
t_equil.
0mech.Detailed
t_equil.
0mech.DetaliedModelTab.
(4)
NO
[ppm
]
0
3000
6000
9000
12000
15000
18000
Time [ms]
0.0 0.2 0.4 0.6 0.8 1.0
Detailed mechanism GRI-Mech 3.0 Tabulated NOx kinetic model
Lambda=1.4
Lambda=1.0
Lambda=0.8
Figure 7: Validation of the tabulated NOx kinetic model for NO formation in a perfect-ly-stirred reactor at 2700 K and 80 bar for different relative air/fuel ratios for tetrade-
cane
Figure 8, right side, shows that the relative error for the majority of simulated cases is lower than one percent. For some points with low temperature and rich mixture, a higher relative error is observed; however, as shown at the left side of Figure 8, the NO concentration for this region is lower than 5 ppm, so overall a very good match is reached for the tetradecane as a reprehensive diesel fuel. With this very fast model-ing approach neither kinetics nor equilibrium reactions need to be solved. Conse-quently the computational speed is significantly improved without loss in accuracy which enables this approach even for engine control unit (ECU) applications.
La
mb
da
[-]
0.5
1.0
1.5
2.0
2.5
3.0
Temperature [K]
2000 2200 2400 2600 2800 3000
5 10
3000025000
2000015000
10000
7500
5000
2500
12500
17500
2250027500
32500
500 100020050
3470032800310002920027400257002400022300207001910017600162001480013500122001100098808820783069106050
5 10
3000025000
2000015000
10000
7500
5000
2500
12500
17500
2250027500
32500
500 100020050
NO in equilibrium state [ppm]
Temperature [K]
2000 2200 2400 2600 2800 3000
5.025.0
1.0
0.50.5
0.5
0.60.60.60.60.50.50.40.40.30.20.10.10.20.50.70.70.60.50.30.20.1
5.025.0
1.0
0.50.5
0.5
Percent error [%]
Relative error [%]
Figure 8: Evaluation of the tabulated NOx kinetic model for NO formation in a perfect-ly-stirred reactor at various temperatures and air-fuel ratios for the tetradecane fuel
An important parameter which is investigated in this study is the effect of NO concen-tration at the start of the reactor simulation on the chemical time constant. In engine simulation, in the early phase of combustion with relatively high temperature, NO is formed in the burned zone and in the later phase of combustion, because of fast mix-ing with the unburned mixture, the temperature is reduced. Therefore, it may happen that the local concentration of NO is higher than the NO concentration in the equilib-
rium condition of the corresponding temperature and thus a backward reaction oc-curs.
In order to evaluate the ability of the proposed kinetic in such conditions, all men-tioned operating conditions, temperature, and air-fuel ratio variations are simulated with a start value of NO concentration equal to the NO concentration of the corre-sponding equilibrium conditions plus 2000 ppm.
It is observed that a modification of the chemical reaction time scale is necessary. In order to reach the best match, the chemical time can be given as an additional look-up table or be correlated as:
1337.5,2599.7,4568.5
, 02000
ECandECEC
CCTCT
T
ppmTppm
(5)
Where ppm0 is the chemical time scale for calculation of NO concentration when the
instantaneous value of NO concentration is lower than the equilibrium value of NO by the corresponding temperature and air-fuel ratio, otherwise the correlated time scale,
ppm2000 , can be used.
In order to reduce the amount of tabulated data and increase the computational speed, only one constant pressure of 80 bar is considered and the effect of the reac-tor pressure is treated as the next step. A variation of reactor pressure from 80 to 200 bar is carried out for all of the above mentioned temperatures and air-fuel ratios. It is observed from the pressure variation, that the value of the NO in equilibrium condition does not change significantly with pressure. But for the characteristic chemical time scale, a simple correlation for considering of the effect of pressure is proposed in (6).
1,2400;3089.22
1,2400;4196.15
140
6285.0
140
5538.0
KTp
KTpp
bar
bar
(6)
The best correlation for the pressure variation from 80 bar to 200 bar is obtained if 140 bar is taken as the basis pressure. For brevity, the deviation analysis is not plot-ted for all investigated pressures. When using (6), the average error is lower than one percent for each pressure, considering all temperatures and air-fuel ratios.
All of the above mentioned investigations are carried out with stationary reactor simu-lation. Evaluation of the developed kinetic in transient conditions is performed, first in a perfectly-stirred reactor with a ramp-type temperature increase. Figure 9 illustrates the temperature ramp in the reactor and compares the NO concentration from the proposed kinetic to the simulated value using the detailed mechanism. The calculat-ed NO in the reactor by the tabulated kinetic model correlates well with results of the detailed mechanism.
As the final step for evaluation of the developed reaction kinetic, the calculated NOx emissions are compared with the results from the detailed GRI-Mech 3.0 mechanism under different engine operating points of a diesel engine. Both GRI-Mech 3.0 and the developed NOx kinetic are coupled with the same combustion model and two-
zone temperature model for calculating the burned and unburned temperatures. Fig-ure 10 compares the NOx calculated by the detailed mechanism with the results ob-tained from the tabulated kinetic model using tetradecane for different engine speeds of the heavy-duty diesel engine with 55% load.
NO
[p
pm
]
0
600
1200
1800
2400
3000
Time [ms]
0 1 2 3 4 5
Detailed mechanism GRI-Mech 3.0 Tabulated NOx kinetic model
Te
mp
era
ture
[K
]
2000
2150
2300
2450
2600
Time [ms]
0 1 2 3 4 5
Reactor temperature
Figure 9: Evaluation of the tabulated NOx kinetic model for NO formation in a perfect-ly-stirred reactor and a transient temperature ramp using tetradecane fuel
NO
x /
NO
x,m
ax [
-]
0.40
0.60
0.80
1.00
1.20
Engine speed [1/min]
700 950 1200 1450 1700 1950 2200
Detailed mechanism GRI-Mech 3.0 Tabulated NOx kinetic model
Figure 10: Comparison of the simulated NOx emissions by the detailed GRI-Mech 3.0 mechanism and the tabulated kinetic model for the heavy-duty diesel engine
with 55% load and tetradecane fuel
As is depicted in Figure 10, a very good match between the NOx calculated by the detailed mechanism and the proposed kinetic model with a transient variation of temperature, pressure, and air-fuel ratio in the burned zone under real diesel engine operating conditions for various engine speeds is obtained.
Finally, the tabulated NOx kinetic model is implemented in the phenomenological combustion model. Both NOx and combustion models are coupled to the GT-Power software for simulation of combustion and in-cylinder NOx emissions. The combus-tion model calculates the burning rate, and the NOx model, with the new kinetic mechanism, calculates the NOx in the burned zone. Calculation of the burned zone temperature is simply based on the two-zone modeling approach commonly used in computationally efficient phenomenological models. Figure 11 illustrates the calcu-lated and measured NOx emissions obtained from the new NOx kinetic coupled with the above mentioned phenomenological combustion model for the heavy-duty diesel engine. Both the simulated and measured NOx emissions are normalized by the same reference value. A relatively good match between the measured and simulated NOx is obtained.
It should be noted that an accurate calculation of in-cylinder NOx emissions strongly depends on the calculation of the burned zone temperature and the mixing rate be-
tween the burned and unburned zone. The crucial information about spray formation, turbulent kinetic energy, ignition delay, and distribution of the air-fuel mixture in the combustion chamber can be provided by a phenomenological combustion model, which enhances the accuracy of temperature calculation and consequently the pre-dictability of the NOx model. However, the focus of this study is the development of an improved NOx kinetic mechanism. Further improvement of the two-zone mixing model of the diesel engine combustion with help of the combustion model is a focus of future works.
Sim
ula
ted N
Ox /
NO
x,
ref [-
]
0.0
0.2
0.4
0.6
0.8
1.0
Measured NOx / NOx, ref [-]
0.0 0.2 0.4 0.6 0.8 1.0
Figure 11: Comparison of NOx emissions using the developed kinetic for tetradecane with measurement results for the heavy-duty diesel engine in overall operating points
The proposed method for tabulation of NOx kinetic for diesel engine is generalized for simulation of gasoline as well as natural gas engines. Iso-octane (C8H18) is con-sidered as the representative fuel for gasoline and methane (CH4) is investigated for natural gas engines.
Similar to the above described approach, for each fuel, the reactor pressure and temperature are varied and the values in eq. 3 are calculated for each reactor condi-tion. The relative error and NO in the equilibrium condition are plotted for the iso-octane and methane fuels, Figure 12.
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Figure 12: Evaluation of the tabulated NOx kinetic model in a perfectly-stirred reactor at various temperatures and air-fuel ratios for the iso-octane (top) and methane (bot-
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As shown in Figures 12 for both fuels the relative error in the NO formation phase for the majority of simulated cases is lower than one percent. For some points with low temperature and rich mixture, a higher relative error is observed; however, as shown at the left side of Figure 12, the NO concentration for this region is low. Overall a very good match is reached for the tetradecane as a reprehensive diesel fuel as well for methane and iso-octane as representative fuels for natural gas and gasoline en-gines.
6. Conclusion
A phenomenological combustion model with a novel NOx reaction kinetic model has been developed. The combustion model exhibits a good predictability for different combustion systems and engine sizes from passenger car to heavy-duty diesel en-gines, under different operating conditions. The combustion model has a high com-putational speed and can provide a good platform for evaluation of control strategies as well as engine transient cycles when integrated in the simulation software GT-Power.
The tabulated kinetic model enables fast execution as it relies on a single equation and does not require any equilibrium reaction for NO calculation. This enables the model to be used in a detailed 3-D CFD simulation or even for NOx calculation in en-gine control units with low computational capacity. The proposed NOx kinetic shows very good accuracy in comparison with the detailed GRI-Mech 3.0 mechanism in sta-tionary as well as in transient conditions in a perfectly-stirred reactor and also in combination with the phenomenological combustion model under real-engine operat-ing conditions.
7. Acknowledgement
The authors would like to thank colleagues at IAV GmbH, Mrs. H. Puschmann, Mr. E. Neumann, and Mr. J. Seebode as well as Mr. K. Kuppa from the Institute for Tech-nical Combustion at the University of Hanover, for their valuable help and technical support.
8. References
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[8] Hiroyasu, H.; Kadota, T.; Arai, M.: Development and Use of a Spray Combus-tion Modeling to Predict Diesel Engine Efficiency and Pollutant Emission, Part 1: Combustion Modeling, Bulletin of the JSME, Vol. 26, 1983
[9] Hiroyasu, H.; Kadota, T.; Arai, M.: Development and Use of a Spray Combus-tion Modeling to Predict Diesel Engine Efficiency and Pollutant Emission, Part 2: Computational Procedure and Parametrical Study, Bulletin of the JSME, Vol. 26, 1983
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[17] Patel, A.; Kong, S.C.; Reitz, R.D.: Development and validation of a reduced reaction mechanism for HCCI engine simulations, SAE Technical Paper Series No. 2004-01-0558, 2004
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Autoren / The Authors:
Dr.-Ing. Reza Rezaei, IAV GmbH, Gifhorn
Prof. Dr.-Ing. Friedrich Dinkelacker, Institut für Technische Verbrennung, Leibniz Universität Hannover
Dipl.-Ing. Benjamin Tilch, IAV GmbH, Gifhorn
Dr.-Ing. Thaddäus Delebinski, IAV GmbH, Berlin
Dr.-Ing. Maximilian Brauer, IAV GmbH, Berlin
