In the Wave and TAB spray models, droplet breakup is determined using a single diameter scale. The SSD model [24] treats breakup as a discrete random event resulting in a distribution of diameter scales over a range. With the SSD model, the probability of breakup is independent of the parent droplet size and the secondary droplet size is sampled from an analytical solution of the Fokker-Planck equation for the probability distribution. In addition, parameters for the size distribution are based on local conditions.

The initial diameter of the parcels injected into the domain is set in the DPM injection dialog box. The breakup model predicts the time at which breakup occurs and the number and properties of the new drops. Drops larger than a critical radius are subject to breakup:

(12–444)

where is the critical Weber number, which you will need to specify. The default value of the critical Weber number is 6.

The breakup time is defined as

(12–445)

where is the user-specified breakup constant, with a default value of 1.73.

Drops with a radius larger than the critical radius (derived from the critical Weber number) have their breakup times incremented. When the breakup time on the parcel is larger than the critical breakup time (locally calculated from conditions in the cell and on the parcel), breakup occurs.

When a parcel reaches breakup, it is destroyed and new parcels are created. The diameters of these child parcels are obtained by sampling a distribution function in the log of the diameter, :

(12–446)

where and are parameters of the model.

The parameter has a negative dimensionless value and must be set by you: is a typical factor by which child particles are smaller than the original parcel.

The parameter defines the variance, in logarithmic terms, of the distribution of child particles. It has a positive, dimensionless value, which should be significantly less than (to avoid child particles that are larger than the original). It is computed from .

When breakup occurs, enough parcels are created so that the number of drops represented by each parcel is approximately equal to a target number in the parcel (NP), which you set. Parcels are created, with diameters sampled randomly from the distribution, and provisionally given the target NP. This continues until the mass of the parent parcel is used up. A scaling factor is then applied to the number of drops in all the new parcels to conserve the mass of the parent parcel.

This methodology results in improved statistics and gives you control over error during a simulation. A smaller NP will mean more parcels but lower statistical error. However, there is a limit to the number of parcels that can be created during a single breakup event; the default value for this limit is 50. Therefore, the number of drops in each parcel will sometimes deviate significantly from the target NP.