Ignition quality tester (IQT) is a standard experimental device to determine ignition delay time of liquid fuels in a controlled environment in the absence of gas exchange. The process involves fuel injection, spray breakup, evaporation and mixing, which is followed by auto-ignition. In this study, three-dimensional computational fluid dynamics (CFD) is used for prediction of auto-ignition characteristics of diethyl ether (DEE) and ethanol. In particular, the sensitivity of the ignition behavior to different injection rate profiles is investigated. Fluctuant rate profile derived from needle lift data from experiments performs better than square rate profile in ignition delay predictions. DEE, when used with fluctuant injection rate profile resulted in faster ignition, while for ethanol the situation was reversed. The contrasting results are attributed to the difference in local mixing. The fluctuant injection profile yields larger spray velocity variations promoting fuel evaporation and local turbulent mixing. The suitable ignition conditions were reached earlier for DEE with fluctuant injection profile, whereas ethanol exhibits pseudo-homogeneous mixing due to its lower cetane number. Ignition was faster for square rate profile due to ignition in end tube for ethanol. The fluctuant injection leads to a better homogeneity for ethanol due to longer time available for mixing. The nature of heat release rate, auto-ignition and combustion were altered by the fluctuant injection rate profile when compared to square rate injection profile.