Compound engine system with rotary engine

A compound engine system (8) comprises a rotary engine (10) having a volumetric compression ratio lower than its volumetric expansion ratio. A recess (38) defined in the peripheral wall (28) of the rotor (24) in each of the chambers (32) has a volume of more than 5% of the displacement volume of the chamber (32). The expansion in a turbine section (13) of the system compensates for the relatively low expansion ratio of the rotary engine (10).