Auto-igniting n-heptane sprays have been studied experimentally in a high pressure, high temperature constant volume combustion chamber with optical access. Ignition delay and the total pressure increase due to combustion are highly 50 Flow Turbulence Combust (2010) 84:49-78 repeatable whereas the ignition location shows substantial fluctuations. Simulations have subsequently been performed by means of a first-order fully elliptic Conditional Moment Closure (CMC) code. Overall, the simulations are in good agreement with the experiment in terms of spray evolution, ignition delay and the pressure development. The sensitivity of the predictions with respect to the measured initial conditions, the spray modelling options as well as the chemical mechanism employed have been analysed. Strong sensitivity on the chemical mechanism and to the initial temperature on the predicted ignition delay is reported. The primary atomisation model did not affect strongly the predicted auto-ignition time, but a strong influence was found on the ignition location prediction.