Ignition of a combustible mixture by a transient jet of hot reactive gas is important for safety of mines, prechamber ignition in IC engines, detonation initiation, and novel constant-volume combustors. The present work is a numerical study of the hot jet ignition process in a long constant-volume combustor (CVC) that represents a wave rotor channel. The hot jet of combustion products from a prechamber is injected through a converging nozzle into the main CVC chamber containing a premixed fuel-air mixture. Combustion in a two-dimensional analogue of the CVC chamber is modeled using a global reaction mechanism, a skeletal mechanism, or a detailed reaction mechanism for three hydrocarbon fuels: methane, propane, and ethylene. Turbulence is modeled using the two-equation SSTk-ωmodel, and each reaction rate is limited by the local turbulent mixing timescale. Hybrid turbulent-kinetic schemes using some skeletal reaction mechanisms and detailed mechanisms are good predictors of the experimental data. Shock wave traverse of the reaction zone is seen to significantly increase the overall reaction rate, likely due to compression heating, as well as baroclinic vorticity generation that stirs and mixes reactants and increases flame area. Less easily ignitable methane mixture is found to show slower initial reaction and greater dependence on shock interaction than propane and ethylene.