In this study, the transient numerical simulation of the flow in a fluidic oscillator has been performed. The proposed device includes several geometrical modifications of a previously patented apparatus intended for the synthesis of ozone-rich bubbles in an oxygen plasma. Prior to the experimental construction of the proposed fluidic oscillator, the present work performs a numerical study of the internal flow in the proposed design, aimed to determine its feasibility. The unsteady simulations are based on the unsteady Reynolds averaged Navier–Stokes equations coupled to the transition Shear Stress Transport (transition SST) turbulence model due to the low Reynolds numbers considered (3500 and 5000 based on flow bulk velocity). The behavior of the complex fluid flow inside the device, where four main vertical structures develop and interact, along one cycle is described in detail including the turbulent kinetic energy and intermittency in the analysis. Moreover, the effect of increasing the Reynolds number on the pressure oscillation frequency and amplitude is analyzed. In particular, the frequency is increased around a 38% and the amplitude a 100% when switching from a Reynolds number of 3500–5000. The numerical results obtained are encouraging, and the evaluated fluidic oscillator design will be fabricated and analyzed in an upcoming experimental study.