Numerical simulations of diesel sprays in a constant-volume vessel have been performed with the conditional moment closure (CMC) combustion model for a broad range of conditions. On the oxidizer side these include variations in ambient temperature (800-1100 K), oxygen volume fraction (15-21%) and density (7.3-58.5 kg/m₃) and on the fuel side variation in injector orifice diameter (50-363 μm) and fuel pressure (600-1900 bar); in total 22 conditions. Results are compared to experimental data by means of ignition delay and flame lift-off length (LOL). Good agreement for both quantities is reported for the vast majority of conditions without any changes to model constants: the variations relating to the air side are quantitatively accurately predicted; for the fuel side (viz. orifice diameter and injection pressure) the trends are qualitatively well reproduced. For the reference case, three different n-heptane chemical mechanisms (with 22, 29 and 67 species) have further been compared with respect to the ignition process and the subsequent flame stabilization and the flame structure is compared to conceptual models presented in the literature. At those conditions all three mechanisms showed comparable results. Based on the findings reported, CMC is seen as a highly promising approach to model spray combustion for a very broad range of diesel engine relevant conditions.