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Combustion in direct-injection diesel engines occurs in a lifted, turbulent diffusion flame mode. Numerous studies indicate that the combustion and emissions in such engines are strongly influenced by the lifted flame characteristics, which are in turn determined by fuel and air mixing in the upstream region of the lifted flame, and consequently by the liquid breakup and spray development processes. From a numerical standpoint, these spray combustion processes depend heavily on the choice of underlying spray, combustion, and turbulence models. The present numerical study investigates the influence of different chemical kinetic mechanisms for diesel and biodiesel fuels, as well as Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) turbulence models on predicting flame lift-off lengths (LOLs) and ignition delays. Specifically, two chemical kinetic mechanisms for n-heptane (NHPT) and three for biodiesel surrogates are investigated. In addition, the RNG k-ε (RANS) model is compared to the Smagorinsky based LES turbulence model. Using adaptive grid resolution, minimum grid sizes of 250 μm and 125 μm were obtained for the RANS and LES cases respectively. Validations of these models were performed against experimental data from Sandia National Laboratories in a constant volume combustion chamber. Ignition delay and flame lift-off validations were performed at different ambient temperature conditions. The LES model predicts lower ignition delays and qualitatively better flame structures compared to the RNG k-ε model. The use of realistic chemistry and a ternary surrogate mixture, which consists of methyl decanoate, methyl 9-decenoate, and NHPT, results in better predicted LOLs and ignition delays. For diesel fuel though, only marginal improvements are observed by using larger size mechanisms. However, these improved predictions come at a significant increase in computational cost.