Abstract Pressure gain combustors (PGC) exploit either their isochoric or detonative combustion increasing the theoretical thermal efficiency of a gas turbine cycle. On this basis, a constant-volume combustor (CVC) is developed operating with rotary valves while the chamber is fed with mixture of air and liquid iso-octane. This work describes the numerical design of a new exhaust section after the CVC. First, the design parametrization of the transition duct and the resulting design of experiments (DOE) of 81 samples are introduced. Every case is numerically tested and the election of the best sample is based on the pressure losses and the oscillations characterization. In the last part, the LS89-VKI vane is added at the aft part of the best transition duct and the ensemble exhaust system is analyzed with the help of transient CFD analysis. Every component is evaluated in terms of pressure losses and oscillations, while the operation of the vane is investigated in details. The results of the stator's performance are discussed and compared with steady experimental data. During a CVC period, the cycle average outlet flow angle remains close to the outlet metal angle denoting promising results for the future numerical analysis of the subsequent rotor.