Direct numerical simulations of a two-dimensional temporally-evolving ethylene-air non-premixed flame in a decaying turbulent flow are performed using a high-order compressible Navier-Stokes solver called S3D. Different models for fuel oxidation and soot formation/oxidation are presented and compared. The first model comprises a single step ethylene-air chemical mechanism with a semi-empirical soot model. Equidiffusion of species is assumed. The second model comprises a reduced mechanism derived from a detailed ethylene-air chemical kinetic mechanism that includes the reaction pathways for the formation of polycyclic aromatic hydrocarbons. The gas-phase chemistry is coupled with a semi-empirical soot model. The third model comprises the same reduced mechanism coupled with a detailed soot model based on the method of moments with interpolative closure. Differential diffusion of species is modeled. This paper presents a preliminary comparison of the models in the case of temporally evolving turbulent diffusion flames, with a particular focus on soot formation.