Wave rotors are periodic-flow devices that provide dynamic pressure exchange and efficient energy transfer through internal pressure waves generated due to fast opening and closing of ports. Wave turbines are wave rotors with curved channels that can produce shaft work through change of angular momentum from inlet to exit. In the present work, conservation equations with averaging in the transverse directions are derived for wave turbines, and quasi-one-dimensional model for axial-channel non-steady flow is extended to account for blade curvature effects. The importance of inlet incidence is explained and the duct angle is optimized to minimize incidence loss for a particular boundary condition. Two different techniques are presented for estimating the work transfer between the gas and rotor due to flow turning, based on conservation of angular momentum and of energy. The use of two different methods to estimate the shaft work provides confidence in reporting of work output and confirms internal consistency of the model while it awaits experimental data for validation. The extended wave turbine model is used to simulate the flow in a three-port wave rotor. The work output is calculated for blades with varying curvature, including the straight axial channel as a reference case. The dimensional shaft work is reported for the idealized situation where all loss-generating mechanisms except flow incidence are absent, thus excluding leakage, heat transfer, friction, port opening time, and windage losses. The model developed in the current work can be used to determine the optimal wave turbine designs for experimental investment.