Validation of a numerical quasi one-dimensional model for wave rotor turbines with curved channels

A wave rotor is a shock-driven pressure exchange device that, whilst relatively rarely studied or indeed, employed, offers significant potential efficiency gains in a variety of applications including refrigeration and gas turbine topping cycles. This paper introduces a quasi one-dimensional wave action model implemented in MATLAB for the computation of the unsteady flow field and performance characteristics of wave rotors of straight or cambered channel profiles. The purpose here is to introduce and validate a rapid but reliable method of modelling the performance of a power-generating wave rotor where little such insight exists in open literature. The model numerically solves the laminar one-dimensional Navier-Stokes equations using a two-step Richtmyer TVD scheme with minmod flux limiter. Additional source terms account for viscous losses, wall heat transfer, flow leakage between rotor and stator endplates as well as torque generation through momentum change. Model validation was conducted in two steps. First of all, unsteady and steady predictive capabilities were tested on three-port pressure divider rotors from open literature. The results show that both steady port flow conditions as well as the wave action within the rotor can be predicted with good agreement. Further validation was done on an in-house developed and experimentally tested four-port, three-cycle, throughflow micro wave rotor turbine featuring symmetrically cambered passage walls aimed at delivering approximately 500 W of shaft power. The numerical results depict trends for pressure ratio, shaft power and outlet temperature reasonably well. However, the results also highlight the need to accurately measure leakage gaps when the machine is running in thermal equilibrium.