534
G. Kotalczyk and F. E. Kruis
Fig. 7 Resulting PSDs from the simulation of a test cases describing a binary, homogeneous
particle breakage function γ (v F , v P ) = 2/v P and a breakage rate b(v) = v (test case 1 in [43]) for
a monodisperse initial condition v 0 and the thus defined characteristic time t char = b(v 0 ) −1 . The
MC-simulations are compared with analytic solutions found in [46]
Table 3 Computational times required for the simulation of t = t char × 10 8 in dependency on the
used number of simulation particles
Simulation particles
NB
VB
VB-LV
1000
0.5 s
0.8 s
0.6 s
10,000
2.8 s
4.4 s
3.0 s
100,000
27.1 s
42.5 s
29.8 s
arithmetic standard deviation of the moments of the distributions performed for 100
different sets of random numbers is smaller than 1% of the mean value.)
3 Compartmental Population Balance Modelling
The modelling of flow-sheet simulations in the scope of an operator-splitting
approach (see e.g. [47]) requires a specific time step management, so that ongoing simulations processes can be forced to stop at specific simulation time points.
This issue is addressed first, in a second, longer paragraph, the implementation of
particle transport between single compartments by means of weighted MC particles
is introduced and some typical simulation scenarios are presented.
G. Kotalczyk and F. E. Kruis
Fig. 7 Resulting PSDs from the simulation of a test cases describing a binary, homogeneous
particle breakage function γ (v F , v P ) = 2/v P and a breakage rate b(v) = v (test case 1 in [43]) for
a monodisperse initial condition v 0 and the thus defined characteristic time t char = b(v 0 ) −1 . The
MC-simulations are compared with analytic solutions found in [46]
Table 3 Computational times required for the simulation of t = t char × 10 8 in dependency on the
used number of simulation particles
Simulation particles
NB
VB
VB-LV
1000
0.5 s
0.8 s
0.6 s
10,000
2.8 s
4.4 s
3.0 s
100,000
27.1 s
42.5 s
29.8 s
arithmetic standard deviation of the moments of the distributions performed for 100
different sets of random numbers is smaller than 1% of the mean value.)
3 Compartmental Population Balance Modelling
The modelling of flow-sheet simulations in the scope of an operator-splitting
approach (see e.g. [47]) requires a specific time step management, so that ongoing simulations processes can be forced to stop at specific simulation time points.
This issue is addressed first, in a second, longer paragraph, the implementation of
particle transport between single compartments by means of weighted MC particles
is introduced and some typical simulation scenarios are presented.