Multicomponent particles are described in Ansys Fluent as droplet particles containing a mixture of several components or species. The particle mass is the sum of the masses of the components

(12–160)

The density of the particle can be either constant, or volume-averaged:

(12–161)

The multicomponent droplet vaporization rate is calculated as the sum of the vaporization rates of the individual components.

For the diffusion-controlled vaporization model, the vaporization rate of component is given by Equation 12–162

(12–162)

while for the convection/diffusion controlled model, it is given by:

(12–163)

For the single-rate thermolysis model [67], the vaporization rate of component is given by:

(12–164)

A simplified constant rate thermolysis model is also available:

(12–165)

Note that the Thermolysis model rate applies to the individual droplet component of the multicomponent particle.

The equation for the multicomponent particle temperature consists of terms for radiation, convective heating and vaporization, and is cast similarly to the single component particle energy equation (Equation 12–70). Radiation heat transfer to the particle is included only if you have enabled P-1 or Discrete-Ordinates (DO) radiation heat transfer to the particles using the Particle Radiation Interaction option in the Discrete Phase Model dialog box.

The energy equation is written for the multicomponent particle as follows:

(12–166)

When radiation heat transfer is active, the boiling rate calculated by Equation 12–168, is augmented by the radiation term,

(12–167)

When the total vapor pressure at the multicomponent droplet surface exceeds the cell pressure, Ansys Fluent applies a boiling rate equation ([346], [498], [13]). The total vapor pressure is computed as where is the partial pressure of component .

An equation for the boiling rate for component can be formulated from the overall energy balance by setting following the assumption that the particle temperature is changing very slowly in the boiling regime:

(12–168)

Where

(12–169)

(12–170)

The fractional vaporization rate is computed as the normalized mass fraction of the species at the particle surface:

(12–171)

where is known from the vapor-liquid equilibrium (VLE) expression.

In the above equations, the following notation is used:

 

12.4.6.1. Raoult’s Law

The correlation between the vapor concentration of a species over the surface and its mole fraction in the condensed phase is described by Raoult’s law:

(12–172)

Raoult’s law assumes that the vapor phase is an ideal gas and the liquid particle mixture is an ideal mixture. Liquid mixtures close to ideal are those of similar chemical species (for example, n-pentane/n-hexane, or benzene/toluene). Raoult’s law may also be valid when approaches 1 for the solvent species when a non-volatile component (small mass fraction) is dissolved in a volatile solvent (large mass fraction). Refer to Vapor Liquid Equilibrium Theory for more details on the assumptions and the derivation of Raoult’s law. Note that Equation 12–172 is not applied for the components that have been defined as immiscible-not-vaporizing.

 

12.4.6.2. Peng-Robinson Real Gas Model

In the Peng-Robinson Real Gas Model, the vapor concentration of each species at the surface is deduced from the calculations of vapor mole fraction and compressibility:

(12–173)

These calculations are described in Vapor Liquid Equilibrium Theory. The vapor-liquid equilibrium is deduced from the inputs for the Peng-Robinson model in the evaporating vapor species, so it is not necessary to specify vapor pressure separately.

Note that Equation 12–173 is not applied for the components that have been defined as immiscible-not-vaporizing.

Instead of using Raoult’s Law or the Peng-Robinson equation of state, you can define your own user-defined function for delivering the vapor concentration at the particle surface. For more information, see DEFINE_DPM_VP_EQUILIB in the Fluent Customization Manual.