Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model
Table 1
Calibration parameters and error of simulation using different numbers of classes in discretised solution method for PBM at different velocity gradients.
Number of classes
Ratio of breakage rate coefficient and collision efficiency, (m−1⋅s−1)
Average error of volume
Computational time (s)
Dimensionless number , D
Note
s−1
24 (k = 2.0)
1032
0.0247
13.8
0.0900
The total simulation time at which the steady-state PSD can be obtained was 5400 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)
1045
0.0235
18.7
0.0980
35 (k = 1.6)
1025
0.0181
30.4
0.0760
48 (k = 1.4)
1052
0.0163
61.5
0.0977
88 (k = 1.2)
1050
0.0128
213.3
0.0900
s−1
24 (k = 2.0)
2602
0.0243
7.6
0.0900
The total simulation time at which the steady-state PSD can be obtained was 3000 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)
2598
0.0231
10.1
0.1020
35 (k = 1.6)
2617
0.0165
14.6
0.0640
48 (k = 1.4)
2611
0.0150
25.5
0.0770
88 (k = 1.2)
2626
0.0123
89.4
0.0900
s−1
24 (k = 2.0)
4267
0.0287
5.5
0.0900
The total simulation time at which the steady-state PSD can be obtained was 2500 s. The possible values of the parameter were chosen in the range of , and a constant step-length 1 was applied in the exhaust algorithm for parameter calibration.
28 (k = 1.8)
4185
0.0268
8.2
0.1130
35 (k = 1.6)
4228
0.0214
10.3
0.0842
48 (k = 1.4)
4226
0.0185
18.7
0.0959
88 (k = 1.2)
4199
0.0149
55.6
0.0900
: the cumulative volume percentage distribution was first calculated from the simulated PSD using different numbers of classes and then interpolated at the pivots of the measured PSD grid. Finally, the average error of volume percentage was recalculated by comparing with the measured PSD. : a dimensionless number; : relating error and computational time; see (10).
