Figure 5 – Comparison of simulated (red line) and experimental
(blue crosses) outflow velocities in test #1 (left) and test #2
(right) where the simulations were calibrated by use of optimised values
for the five parameters mentioned in the legends.
In addition, it turns out that, even with reasonable guesses for these
three parameters, the outflow velocity calculated with Eq. (1.29) cannot
be made to match the outflow as measured in the tests. The way out was
to introduce two so-called flow resistance factors, denoted bya 1 and a 2 , with the view
of reducing the values of consolidation coefficientCe and release rate q , see Eqs. (1.18) and
(1.19), by dividing them by a 1 anda 2, respectively. Tests 1 and 2 were then used to
calibrate the expression model by systematically varying the above five
parameters within physically plausible ranges. Figure 5 presents for
these two tests the comparison between simulated and experimental
outflows as a function of time. The legends also show theR2 values which indicate a match which per test
is very good.
The two sets of optimised coefficients differ quite a bit, while the
only difference between the two tests is in the rate of pressure
increase. The discrepancies between the two sets may illustrate the
challenge of dealing with the experimental technicalities. The best
thing to do was to average the two sets to produce the following set
which will be used for the remainder of the tests of this paper:
The flow resistance factor a 1 = 2.7 may be
related to an over-prediction of cake permeabilityk 1 by Eq. (1.13): our own experiments showed an
over-prediction by a factor of 5. This also affects consolidation
coefficient, see Eq. (1.18). The value 42 for the flow resistance factora 2 may be due an over-estimation of both
agglomerate permeability k 2 and crystal diameterd c (which occurs squared). The value 0.59 for the
inter-aggregate solidosity looks a bit low, where Torquato et al.
[30], in a molecular dynamics study of hard spheres, report a
packing fraction of 0.64 for a maximally random jammed state. Figure 6
shows a comparison of simulation results obtained with the set of
optimised coefficients of Eq. (1.30) and experimental outflow velocities
for the same tests #1 and #2 as above. Compared to Figure 5, the
agreement is less good, with decrease values forR 2.