Summary Comparative Algorithm Study
44
absolute values of the start of combustion
ϕ
SOC
and the positions of 10 and 50
energy release
ϕ
10
,
ϕ
50
. Otherwise, the differences between the measured and simulated positions of 90 energy release
ϕ
90
are up to 10 °CA. As a result of the small energy release rates near the end of combustion, minor inaccuracies in the
energy release cause significant deviations in the temporal locations, e.g. an error of ± 1 in absolute energy released changes the location by almost 5 °CA.
The correlation statistics for
ϕ
SOC
,
ϕ
10
,
ϕ
50
, and
ϕ
90
given in Table 4.2 con- firm the “graphical” interpretations from Figure 4.8. Whereas the
ϕ
SOC
,
ϕ
10
, and
ϕ
50
correlation coefficients are of the order of 0.9 for both calibration and verifica- tion, the
ϕ
90
coefficients are significantly lower approximately 0.7 and 0.8 respec- tively. Furthermore, the linear regression slope m smaller than unity and the
intercept b larger than zero indicate the slightly reduced sensitivity of the simula- tion data on operating condition variations during both calibration and verification.
To illustrate the broad range of operating conditions used, the heat release traces from six operating conditions, arbitrarily selected from the 39 heavy-duty engine
operating conditions given in Table A.2, are compared in Figure 4.9. Although the
a b
Fig. 4.8 Heavy-Duty Diesel ROHR Model Calibration Verification:
a Sequential Operating Conditions Plot, b “1-to-1” Scatter Plot
ϕ
SOC
ϕ
10
ϕ
50
ϕ
90
C alibra
tio n
Pearson’s Correlation Coefficient r
[-] 0.8970
0.9248 0.9005
0.7111
Linear Regression Slope m
[-] 0.84
0.86 0.85
0.67
Linear Regression Intercept b
[-] -0.08
0.31 1.65
11.75
Verif icati
on Pearson’s Correlation Coefficient r
[-] 0.9465
0.9194 0.9174
0.8178
Linear Regression Slope m
[-] 0.95
0.82 0.77
0.62
Linear Regression Intercept b
[-] 0.01
0.71 2.83
14.17 Tab. 4.2
Heavy-Duty Engine ROHR Model Statistics
C ra
n k
A n
g le
ϕ [°
C A
a T
D C
]
350 360
370 380
390 400
410 420
Heavy-Duty Operating Conditions [-] 5
10 15
20 25
30 35
40
Verificat ion Calibrat ion
ϕ
SOC
Sim Meas
ϕ
10
Sim Meas
ϕ
50
Sim Meas
ϕ
90
Sim Meas
ϕ
S im
u la
ti o
n [°
C A
a T
D C
]
350 360
370 380
390 400
410 420
ϕ Measurment [° CA aTDC] 350
360 370
380 390
400 410
420
Calibrat ion Verificat ion Start of Combust ion
10 Energy Release 50 Energy Release
90 Energy Release