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To calculate soot source terms a new soot model is applied to study the formation and oxidation of soot particles in turbulent flames. The model is based on a detailed description of the chemical and physical processes leading to the formation of soot. It can be subdivided into the growth of polycyclic aromatic hydrocarbons (PAHs) in the gas phase reactions and the processes of particle inception, condensation, surface growth, and oxidation. Two different parts are developed about the growth of PAHs in the gas phase reaction. The first step towards the formation of soot is the formation of benzene and the second step is how to form PAH from benzene. In particle inception and condensation stages Smoluchowski's equation is deduced and PAH size distribution equations are obtained. In surface growth and oxidation process Hydrogen Abstraction - Carbon Addition (HACA) mechanism is modified due to the finding that the bound between the acetylene and the soot surface can be broken at high temperature in the experiment. Finally the analysis about soot source terms are used in turbulent combustion and different calculated results are obtained for different soot source terms. Acetylene, soot and OH densities are discussed and soot spatial distributions in the cylinder for different crank angle degree are carried out in 4JB1 diesel engine. It gives the theory and method about calculating soot exactly in diesel engine.