In the framework of an optimization study of a Zero-Net-Mass-Flux fluidic, synthetic jet actuator, based on a multi-objective optimization formulation, the consideration of optimization parameters such as the actuator location and the outlet design implies a re-meshing procedure that adds complexity. It is still the case even if the actuator is modeled with simple boundary conditions at the jet orifice exit since, locally, the re-mesh is still required. This strongly impacts the global computational cost, in particular if the considered geometry is complex. In a previous study, we proposed an alternative method to model Zero-Net Mass Flux synthetic jet actuators through the implementation of volumetric reduced-order models (ROM) as additional source terms. The previous reduced-order model consisted in a simplified ROM model where a constant-in-space momentum quantity was imposed in the ROM formulation and the compressible effects were neglected. In this paper, we propose to extend the previous work in an attempt to apply this ROM strategy to higher Mach number flows, where compressibility effects at the outlet of the pulsed jets can no more be neglected, while improving the early interaction of the pulsed jet with the surrounding flow by considering the starting jet influence when the actuators are operated in a pulsed manner.
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