The Schmehl breakup model [580] distinguishes between three breakup regimes:

These regimes differ by the Weber number, which is a measure of strength of aerodynamic forces relative to surface tension forces:

(12–464)

and the Ohnesorge number, which assesses the damping effect of viscous friction in the droplet against surface tension:

(12–465)

In Equation 12–464 and Equation 12–465:

= gas density

= relative droplet-gas-velocity

= diameter of the droplet before breakup

= droplet liquid density

= surface tension of droplet liquid

The transition between different breakup mechanisms are modeled by the following functions depending on the local Weber number:

The three breakup mechanisms use different normal velocities, breakup time-points, and volume distribution of child droplets.

In all regimes, the breakup process is subdivided into two stages:

The Schmehl breakup model uses the deformation and disintegration mechanism suggested by Pilch and Erdman [518]. The droplet deformation period, drag coefficient, reference area for drag, and drag force are computed according to Equation 12–448 through Equation 12–454 (see Madabhushi Breakup Model for details).

The total breakup time is dependent on the local Weber number and is determined by the following correlations:

The child droplet velocity due to the rim expansion is calculated by Equation 12–456 (see Figure 12.25: Child Droplet Velocity). The magnitude of the normal velocity in a plane normal to the parent droplet velocity is dependent on the breakup regime:

Like for the Madabhushi model, the normal velocity direction angle is randomly chosen in the range [0, 2π] for each of the child droplets (see Figure 12.25: Child Droplet Velocity). The number of child droplets is not fixed to five as in the Madabhushi model. By default, it is set to 1, but can be changed in the GUI as described in Breakup in the Fluent User's Guide.

In the Bag Breakup and Multimode Breakup regimes, the target volumetric distribution of child droplets after breakup is given by the root-normal distribution Equation 12–458 known from the Madabhushi breakup model (see Figure 12.26: Madabhushi Diameter Distribution).

In the Bag Breakup regime, the total mass of the parent droplet parcel is uniformly distributed over the child droplets parcels. In the Shear Breakup regime, 20 % of the total mass of the parent droplet parcel remains in the parent droplet parcel, and only 80 % is uniformly distributed over the child droplets parcels. The Multimode Breakup regime is in between the Bag Breakup and the Shear Breakup regimes. This regime computes the shed mass using a linear interpolation between the two other regimes based on the Weber numbers that define the breakup regimes and .

In the Multimode Breakup regime (), the mass remaining in the parent droplet parcel is calculated as:

(12–470)

Accordingly, the mass uniformly distributed over the child droplets parcels is computed as:

(12–471)

Finally, the remaining parent droplet parcel is adapted based on the new diameter following the target volumetric distribution of its child droplets after breakup and also the new flow rate and the number in parcel, which are calculated based on .

In the Shear Breakup regime, the volume distribution of child droplets is characterized by a bimodal density function with a maximum in the region of small droplet diameters and a second maximum in the region of large droplet diameters. The fine fraction of the droplet fragments represents approximately 80% of the total mass of the parent droplet parcel . These droplets result from film fragments stripped off the disc-shaped droplet by shear forces. The remaining 20% in the large diameter region represents the contribution of the core droplet fragments formed by the stripping process. The diameter of this core droplet is estimated from the critical Weber number at flow conditions at the instant of breakup as:

(12–472)

The target volumetric distribution of the stripped child droplets after breakup is given by the same root-normal distribution as for the Madabhushi breakup model Equation 12–458 (see Figure 12.26: Madabhushi Diameter Distribution); however, here, the mass media diameter is taken as:

The remaining parent droplet parcel is then adapted according to the new diameter:

(12–476)

and also the new flow rate and the number in parcel, which are calculated based on . Since may be lager than the original parent droplet diameter depending on the critical Weber number , the maximum diameter of the remaining droplet parcel is restricted to the original parent droplet parcel diameter before the breakup process.

If the number of breakup parcels is set to one, a statistical breakup is complete, and no child droplet parcels are shed. The parent droplet parcel is adapted according to the new diameter, the new flow rate, and the number in parcel as follows:

The new parent droplet diameter relates to the target Sauter mean diameter after breakup as:

(12–480)

The deformation and disintegration mechanism as well as the velocity adjustment due to the rim expansion of the parent droplet parcel is applied as described above.