Formation of nuclei and soot particles is computed following the empirical models of Tesner et al. [45]. The source terms are formulated in terms of particle number concentrations for nuclei:

(7–140)

and soot particles:

(7–141)

Where [part/mol] is Avogadro’s number and:

(7–142)

is the mass of a soot particle and are the density and the mean diameter of the soot particles, respectively. With the above definitions, the source terms for nuclei and soot formation can be modeled as (Tesner et al. [45]):

(7–143)

(7–144)

In the nuclei equation, the spontaneous formation of radical nuclei from the fuel, , is modeled using the Arrhenius approach,

(7–145)

where is the mass fraction of carbon in the fuel material. is a linear branching coefficient, is a linear termination coefficient, and is a coefficient of linear termination or radical nuclei on soot particles. In the soot equation, and are constants. The default values for all of the soot model parameters are summarized in the following table:

Most references list the coefficients using the absolute particle number [part] in the physical dimensions. However, for numerical, reasons CFX is using [mol] instead. To convert from the [part] system into the [mol] system, coefficients and have to be multiplied by Avogadro’s number [part/mol], and the coefficient must be divided by . All other coefficients remain unchanged.