Modeling unsteady turbulent flame development in lifted spray flames is important as a strong correlation exists between pollutant formation and the transient flame features such as auto-ignition, flame propagation and flame stabilization. Detailed chemistry mechanisms with large number of species are required to resolve the chemical kinetics accurately. These factors make high-fidelity simulation of engine combustion computationally expensive. In this work, a turbulent combustion model is proposed based on tabulation of flamelets. The aim is to develop a comprehensive combustion modeling approach incorporating detailed chemistry mechanisms, turbulence models and highly resolved grids leveraging the computational cost advantage of tabulation. A novel technique of implementing unsteady flamelet libraries without the use of progress variables is implemented for igniting sprays called Tabulated Flamelet Model (TFM). These flamelet libraries use residence time of each flamelet as one of the independent variables to incorporate unsteadiness in the chemistry tabulation. The proposed combustion model is then validated within a Reynolds Averaged Navier-Stokes (RANS) framework against an igniting n-dodecane spray flame under diesel engine conditions using experimental data from the Engine Combustion Network (ECN), specifically, Spray A condition. For these constant volume simulations, 4D flamelet libraries based on scalar dissipation rate, residence time, mixture fraction variance and mixture fraction are generated using a parallel code for a 106 species and 420 reactions chemistry mechanism (for n-dodecane). The results are compared against the results from the multizone homogeneous reactor combustion model with the same chemistry mechanism. The numerical results show good agreement with experimental measurements for ignition delay and flame lift-off length across a wide range of ambient temperature, oxygen and injection pressure conditions. This RANS framework together with the TFM approach is further extended to simulate combustion of methyl decanoate in a full 360-degree optical direct injection engine geometry. A 5D flamelet library, with an additional dimension of pressure is generated using a 115 species 460 reactions mechanism. The heat release rate and flame lift-off from the model show agreement with the measurements from the optical engine. Effect of numerical parameters such as number of injected flamelets, flamelet table resolution, and mesh size are analyzed. Overall, the TFM approach is able to capture the experimental trends well, both quantitatively and qualitatively.