The engine includes a stator including an inlet to admit a compressed gaseous oxidant flow, and an exhaust to discharge burnt gases; and a rotor mounted in the stator in a fluid-tight manner and rotatable with respect to the stator around a rotation axis. The rotor has an inlet orifice oriented in the axial direction and faces the inlet opening in a manner to receive the compressed air flow, a combustion chamber communicating with the inlet orifice, and an exhaust duct which leads in a transverse direction from the combustion chamber to the periphery of the rotor for discharging burnt gases through the exhaust. The inlet, the combustion chamber and the exhaust duct are arranged in fluid communication with each other during the rotor rotation, without the interposition of valve members. Seal members seal the inlet orifice and the exhaust duct when they face the internal surface of the stator.