Calculating ffrac from volume fractions

[marbris]

I've been reading through the code and I've found a few things that seem inconsistent. Please let me know if I'm misunderstanding what the code is supposed to do.

ffrac is the overall filling fraction of the electrode. In mod_cell.py Lines 166-179 ffrac is calculated with

$$ffrac = dx \sum_{v} \sum_{p} \bar{c}_{v,p} V_{v,p}$$

This equation seems to treat $V_{v,p}$ as the particle volume as a fraction of the electrode volume $dx$. However, the $V_{v,p}$ is the particle volume as a fraction of the total particle volume in the electrode volume (configuration.py Line 669). This is only equivalent when each electrode volume contains the same total particle volume. This is not the case when the particle size distribution is randomized.

Instead, lines 166-179 could be replaced with something like

# Define the overall filling fraction in the electrodes
for trode in trodes:
    eq = self.CreateEquation("ffrac_{trode}".format(trode=trode))
    eq.Residual = self.ffrac[trode]()
    tmp = 0
    Vol_fracs = config["psd_vol"][trode] / config["psd_vol"][trode].sum(axis=None)
    for vInd in range(Nvol[trode]):
        for pInd in range(Npart[trode]):
            Vj = Vol_fracs[vInd,pInd]
            tmp += self.particles[trode][vInd,pInd].cbar() / config[trode,'csmax'] * Vj
    eq.Residual -= tmp