This paper describes a joint experimental and numerical study of a Constant Volume Combustion (CVC) chamber for propulsion engines. Combustion takes place in a constant volume vessel where gases are injected from a pressurized air inlet using valves. They are ignited using a spark and exhaust through a second set of valves. Like piston engines, CVC combustion raises multiple questions linked to the volumetric efficiency of the valves, the heat losses to the chamber walls, the ignition in a strongly turbulent flow, the influence of residual gases. These issues can compromise the potential gains associated to constant volume combustion. They are investigated in an experimental setup and compared to a full compressible LES. The major conclusion is the existence of significant cyclic variations which are observed in the experiment and analyzed in the LES: the local flow velocity at spark timing and the level of residuals are the major factors leading to cyclic variations. Cycles also appear to be coupled: combustion during cycle N directly affects cycle (N+1), more than in a piston engine. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.