Simcenter STAR-CCM+ Modelling Solid Dissolution with LMP + self-verification

2024-08-01T14:10:08.000-0400
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Summary

An example of salt dissolution implemented using the Lagrangian particle devolatilization model is provided and verified in a small kitchen experiment.

Details

 Attachments:

This example aims to encourage implementation of your own models. Especially for multiphase mass transfer the multiphase reaction models can be used for many combinations of phases.

The verification of such models ideally uses exact results from academic papers.

Modelling Dissolution Rate

As with many mass transfer models the rate of dissolution is driven to a thermodynamic equilibrium and limited by a mass transfer coefficient.

1. The driving force is the equilibrium concentration minus the salt concentration in the water.
This is also called solubility and can be found on the internet for salt in water. Be aware that is a dependence on the temperature.
2. The mass transfer coefficient is dependent on the diffusivity and Reynold number and can be estimated using Sherwood correlations.
The Ranz-Marshall correlation is used in many places in Simcenter STAR-CCM+ for particle mass and energy transfer.

The resulting equation for the mass transfer rate is given as

EQ1:   ∂m/∂t = kAparticle (Cequilibrium - Cgas)

with the mass transfer coefficient k and mass concentration C.

Implementation in Simcenter STAR-CCM+

The mass transfer is implemented as a particle devolatilization (reaction) from solid salt to dissolved salt in water with a user reaction rate.

Equation 1 is used with one additional step.
The reaction rate is defined in [kmol/s]. Therefore the dissolution (mass) rate has to be multiplied by the molar mass of salt.

Ranz-Marshall implementation:

2*(1+0.3*pow(\${ParticleReynoldsNumber},1/3)*pow(\$Sc, 1/2))

Calculating the mass transfer coefficient:

\${Sh_ranzMarshall}*\${DynamicViscosity}/\${Sc}/\${ParticleDiameter}/\${Density}

Mass transfer Rate:

\${massTransferCoefficient}*(\${x_eq_NaCl}-\${MoleFractionsalty})

Reaction rate for devolatilization model:

\${dissolutionMassTransfer}*\${MolecularWeightsalty}

Please find all the details for the implementation in the attached simulation.

Self-Verification

For verification purposes a small kitchen experiment was performed.

Two table salt brands were tested in a drop test and the dissolution compared. The particle size distribution (PSD) is very different as can be seen in the following picture (coarse on the left and fine salt on the right).
The PSD was evaluated using pictures and an OpenCV circle detection algorithm - an example shown below.

The median particle diameter is ~0.71 mm for the coarse salt and ~0.42 mm for the fine salt.

The salt was dropped into a ~60cm water bottle and filmed. In the simulation the water column is 1m in height.
The PSD is applied as a CDF in the Lagrangian injector and the particles are allowed to free fall.

Results

Please find the videos of the small experiments and simulations attached.

Fine Salt

• The coarse particles fall faster and reach the bottom (60 cm) at ~6 seconds in the experiment. This matches the depth in the simulation although they are allowed to fall more. The coarse particles also reach the 1 m bottom in the experiment.
• The fine particles hardly reach the bottom in the experiment. The same can be seen in the simulation, they are completely dissolved at the end of the water collumn.

These results seem to match qualitatively well and thereby verify the implemented dissolution model.
Of course for an exact verification more detailed measurements need to be taken into account.

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