Pulsed detonation combustion is not a new research topic. However, since the detonation process was first observed in 1881, the interest in it grew substantially in the last decades. Because the gas turbines have reached their technological maturity, the scientific community has started looking into novel thermodynamic cycles, such as detonation-based cycles. Numerous studies have been recently published in the field of pulsed detonation combustion, both numerical and experimental and major breakthroughs have been achieved in understanding and controlling the phenomena. However, the topic remains of mostly academic interest, one of the reasons is that practical implementation of it is reliant turbomachinery that would efficiently convert the pulsed, high peak, pressure into useful work. The few studies conducted on classical, existing turbines, show an efficiency of around 50% when coupled with a PDC. The low efficiency has been directly connected with the shock wave losses. For this reason, the design of turbines with supersonic inlet, and associated performance assessments have been researched. This work, however, has supersonic steady inlet Mach number or sinusoidal pulsating conditions around an average subsonic value. No public literature exists on the performances of turbines operating at pulsating inlet conditions similar to the outlet of a PDC. The current paper tackles exactly this issue. The geometry for a turbine stator row was designed based on supersonic inlet design criteria. This geometry was then subjected to CFD numerical simulations. First, the pressure losses associated with a constant supersonic inlet were numerically determined to be a little over 26%. The next step was to assess the pressure losses of the same turbine row geometry in a transient approach. This time, the inlet conditions were set to be variable in time. The values were taken from a 1D in-house code computing the parameters at the outlet of a PDC working on hydrogen and air under stoichiometric conditions. This inlet conditions give a much better insight with respect to the flow within a turbine row when coupled with a PDC. It was observed that the pressure losses, computed as a time average for a period corresponding to the PDC functioning frequency were of 12%. This value is much less than that for a constant supersonic inlet, mostly due to the turbine being exposed to the shock waves for less time.