The ability of turbulence model to accurately describe the complex characteristics of the flow field and the fuel spray is of great importance in the optimum design of diesel engine. The numerical simulations of the flow field and the spray characteristics within the combustion chamber of direct injection model entgine are performed to examine the applicability of turbulence model. The turbulence models used are the RNG $varepsilon$ model and the modified $varepsilon$ model which included the compressibility effect due to the compression/expansion of the charges. In this study, the predicted results in the quiescent condition of direct injection model engine show reasonable trends comparing with the experimental data of spray characteristics, i. e., spray tip penetration, spray tip velocity. The results of eddy viscosity obtained using the $varepsilon$ model in the spray region is significantly larger than that obtained using the RNG $varepsilon$ model. The application of the RNG model seems to have some potential for the simulations of the spray characteristics, e. g., spray tip penetration, spray tip velocity, droplets distribution over the $varepsilon$ model.