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.