ANSYS FLUENT 12.0 Theory Guide - 15.4.6 Multicomponent Particle Definition (Law 7)

15.4.6 Multicomponent Particle Definition (Law 7)

Multicomponent particles are described in ANSYS FLUENT as a mixture of species within droplets/particles. The particle mass is the sum of the masses of the components

$m=\sum_{i}m_{i}$

(15.4-79)

The density of the particle $\rho_{p}$ can be either constant, or volume-averaged:

$\rho_{p}=\left(\sum_{i}\frac{m_{i}}{m\rho_{i}}\right)^{-1}$

(15.4-80)

For particles containing more than one component it is difficult to assign the whole particle to one process like boiling or heating. Therefore it can be only modeled by a law integrating all processes of relevance in one equation. The source terms for temperature and component mass are the sum of the sources from the partial processes:

$m_{p}c_{p}\left(\frac{dT_{p}}{dt}\right)=A_{p}\epsilon_{p}\s... ...}(T_{\infty}-T_{p})+\sum_{i}\frac{dm_{i}}{dt}(h_{i,p}-h_{i,g})$

(15.4-81)

$\left(\frac{dm_{i}}{dt}\right)=A_p M_{w,i}k_{c,i}(C_{i,s}-C_{i,\infty})$

(15.4-82)

The equation for the particle temperature consists of terms for radiation, convective heating (Equation 15.4-3) and vaporization. Radiation heat transfer to the particle is included only if you have enabled P-1 or Discrete-Ordinates (DO) radiation and you have activated radiation heat transfer to the particles using the Particle Radiation Interaction option in the Discrete Phase Model dialog box.

The mass of the particle components $m_{i}$ is only influenced by the vaporization (Equation 15.4-12), where $M_{w,i}$ is the molecular weight of species . The mass transfer coefficient $k_{c,i}$ of component is calculated from the Sherwood correlation (Equation 15.4-15). The concentration of vapor at the particle surface $C_{i,s}$ depends on the saturation pressure of the component.

Raoult's Law

The correlation between the vapor concentration of a species $C_{i,s}$ over the surface and its mole fraction in the condensed phase $X^L_{i}$ is described by Raoult's law:

$C_{i,s}=\frac{p_{i}}{RT}=\frac{X^L_{i}p}{RT}$

(15.4-83)

Peng-Robinson Real Gas Model

For the calculation of the vapor concentration of a species $C_{i,S}$ over the surface depends on whether the compressability of the vapor phase is taken into account:

$C_{i,S}={x_i}^V \frac{p}{{Z^V}RT}$

(15.4-84)

The data for the vapor pressure are no longer available, when a droplet material is chosen as the component of a mixture, because it is not necessary for the calculation.

Besides using Raoult's Law and 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 this section in the separate UDF Manual.

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