The soot model used in Ansys Forte is the two-step soot model consisting of competing formation and oxidation steps. The Hiroyasu soot formation [36] and Nagle and Strickland-Constable oxidation [61] models were used. The governing equations for the soot model are as follows:

(2–46)

(2–47)

(2–48)

(2–49)

where p is pressure, n is a constant, M _s is soot mass, with an additional subscript f for "formation" or o for "oxidation". M _pre is the mass of the soot precursor, K _f is the soot formation rate, A _sf is the pre-exponential factor for the global soot-formation reaction, E _f is the activation energy for soot formation, MW _c is the molecular weight of carbon, ρ _s is soot density, D _s is the assumed soot particle diameter, and R _total is the Nagle and Strickland-Constable oxidation rate. More details about the soot model are given by Vishwanathan and Reitz [100] . The default values of model constants used in FORTÉ are: n=0.5, Asf = 40 cm3/mol-s, Ef =12,500 cal/mol, ρ s=2 g/cm3, and Ds=25 nm.