71
6.3 Model Study on Different Engine Sizes
Similar to the model studies on different engine sizes for the ROHR and NO models in the previous chapters, the proposed soot model is applied to the heavy-duty, auto-
motive and marine diesel engine in order to evaluate the general applicability of the approach. The heavy-duty engine is again used as the reference engine. In addition to
the engine specific model calibrations for the automotive and marine diesel engine, the heavy-duty model is applied to both engines without modifications blind try.
6.3.1 “Heavy-Duty” Diesel
Figure 6.4 shows the results using an Evolutionary Algorithm with a population size n
pop
of 50 n
parent
= 25, n
offspring
= 75 to calibrate the eight parameters of the soot
model c.f. Table 6.1. Given a mean calculation time of one third of a second, the calibration based on the 19 operating conditions takes approximately 6 hours.
Figure 6.4 indicates that the correlation, or rather linear regression statistics, for both the calibration and verification are not as good as those for the NO emission
model Figure 5.4. While the correlation coefficient r for the calibration indicates a good qualitative agreement between measured and simulated soot emission values
r 0.9, the low linear regression slope m 0.8 is a sign of the low sensitivity of the two step soot model Table 6.2. The model over- and underestimates low and
high experimental soot emissions, respectively, even if the experimental uncertain- ties of ± 0.03 [gkWh] Section 3.5.2 are taken into account.
Despite the deficiencies in quantitative terms, the model correctly reproduces the trends i.e. qualitative variations among individual operating conditions, such as the
characteristic decrease of soot emissions for an increase in injection pressures shown for the operating conditions 4, 5, and 6 400, 700, and 1000 [bar], respectively.
a b
Fig. 6.4 Heavy-Duty Diesel Soot Model Calibration Verification:
a Sequential Operating Conditions Plot, b “1-to-1” Scatter Plot
S o
o t
E m
is si
o n
s [
g k
W h
]
0. 0 0. 1
0. 2 0. 3
0. 4 0. 5
Heavy-Duty Operating Conditions [-] 5
10 15
20 25
30 35
40
Measurement Simulation
Verificat ion Calibrat ion
S o
o t
S im
u la
ti o
n s
[ g
k W
h ]
0. 0 0. 1
0. 2 0. 3
0. 4 0. 5
Soot Measurements [ g kWh] 0. 0
0. 1 0. 2
0. 3 0. 4
0. 5
Calibrat ion Verification
72
6.3.2 “Automotive” Diesel
The identical Evolutionary Algorithm implemented in Section 6.3.1 n
pop
= 50, n
par- ent
= 25, n
offspring
= 75 is used to calibrate the soot model based on 20 out of the 57
representative automotive diesel engine operating conditions given in Table A.2. Except for the overestimation of low experimental values for high load, no EGR
operating conditions BMEP 11 [bar] and EGR 0.5 []; 8, 11, 27, 33, 3839, and 4546, a good correlation between the measured and calculated soot emissions
for both calibration and verification cases is observed c.f. Figure 6.5. Furthermore the absolute deviations between measured and calculated soot emissions observed
for the verification operating conditions back up the low model sensitivity men- tioned in Section 6.3.1. However, trends among different operating conditions are
still correctly reproduced for both the calibration and verification cases.
To illustrate the low model sensitivity, Figure 6.6 and Table 6.3 provide a sample of six out of the 57 automotive operating conditions, showing a variation in engine
load BMEP, injection pressure p
Inj
and EGR rate at a constant piston speed c
m
. Whereas the simulation slightly underestimates the experimental values for the low
engine load with low injection pressure - and thus high soot emissions - operating conditions 34 - 36, it overestimates the values for the high engine load, high
injection pressure and low EGR rate operating conditions 37 - 39 significantly.
CALIBRATION VERIFICATION Pearson’s Correlation Coefficient r
[-] 0.9181
0.8216
Linear Regression Slope m
[-] 0.79
0.49
Linear Regression Intercept b
[-] 0.05
0.04 Tab. 6.2
Heavy-Duty Soot Model: Calibration Verification Statistics
Fig. 6.5 Automotive Diesel Soot Model Calibration Verification
Verification Calibration
S o
o t
E m
is si
o n
s [
g k
W h
]
0. 0 0. 2
0. 4 0. 6
0. 8 1. 0
1. 2 1. 4
1. 6
Automotive Operating Conditions [-] 5
10 15
20 25
30 35
40 45
50 55
Measurement Simulation
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