### 6.8.3. Energy Transfer to and from the Wall Film

The total heat transfer to a single wall film droplet is found from the following energy balance:

| (6–186)

#### 6.8.3.1. Conductive Heat Transfer

is the heat conducted from the wall, as given by:

| (6–187)

where is the conductive heat transfer coefficient and is the wall area covered by the particle. This term is always included in the energy equation for wall particles.

##### 6.8.3.1.1. Non-flooded Regime

In the non-flooded regime, is assumed to be equal to the drop diameter. The wall contact area is computed from .

##### 6.8.3.1.2. Flooded Regime

In the flooded regime, is set equal to the wall film thickness, . The wall contact area is computed from , with being the volume of the particle and the wall film thickness that was computed at the previous time step.

#### 6.8.3.2. Convective Heat Transfer

The heat transferred from the gas to the film, , is given by:

| (6–188)

where is the area covered by a wall particle, is the conservative gas temperature at the particle position, and is the film heat transfer coefficient.

This term is always included in the energy equation for wall particles.

##### 6.8.3.2.1. Non-flooded Regime

For the non-flooded regime, and are computed as:

| (6–189)

The Nusselt number used for the calculation of is computed using the Ranz-Marshall correlation for a sphere:

| (6–190)

##### 6.8.3.2.2. Flooded Regime

In the flooded regime, is set equal to the transfer coefficient for energy computed by the flow solver.

Note: The energy transfer coefficient is only available for turbulent flows. A physics check is added to the tracker setup phase to make sure that you set the flow type to turbulent.

#### 6.8.3.3. Calculation of the Average Wall Film Temperature

The average wall film temperature (that is, the temperature of all wall particles associated to a boundary vertex) is computed by using the particle vertex machinery, by adding up contributions of wall particles (particles that already exist and new particles that turn into wall particles). This is done as a postprocessing step after all particles have been tracked.

#### 6.8.3.4. Evaporation from Film

accounts for the energy that is removed from the wall film particle, as it evaporates into the surrounding medium:

| (6–191)

is the latent heat of vaporization, is the rate of evaporation.

##### 6.8.3.4.1. Non-flooded Regime (Non-boiling)

The mass transfer rate for a single droplet is computed using the Liquid Evaporation Model. For particles below the boiling point, the following relation is used:

| (6–192)

The transfer coefficient, , is defined as:

| (6–193)

The Sherwood number is calculated using the Ranz-Marshall correlation for a sphere as:

##### 6.8.3.4.2. Flooded Regime (Non-boiling)

The mass transfer rate of a particle component, , into the coupled Euler phase can be determined by considering species mass balances on control surfaces on either side of the phase interface:

| (6–194)

is the mass fraction of the particle component at the film surface, and is the surface diffusive mass flux.

The surface mass flux can be expressed in terms of a mass transfer coefficient, , as:

| (6–195)

is the mass fraction of the volatile particle component as obtained from the flow field solution. The transfer coefficient, , is set equal to the transfer coefficient for scalars as computed by the flow solver.

Inserting Equation 6–195 into Equation 6–194 and solving for , gives:

| (6–196)

##### 6.8.3.4.3. Flooded and Non-flooded Regime (Boiling Particles)

For particles above the boiling point this relation is used:

| (6–197)

where and is given by Equation 6–187 and Equation 6–188 respectively. is computed in the same way as for regular particles.

Release 18.2 - © ANSYS, Inc. All rights reserved.