Unsteady numerical studies on the internal shock structure of a cylindrical resonance tube

Abstract The present study numerically investigates the unsteady shock dynamics inside a resonance tube operating in the jet regurgitant mode. Unsteady simulations using a density-based solver were conducted to analyse the coupled interaction between the underexpanded nozzle jet and the cavity flow. The numerical model is validated with available experimental measurements by comparing the resonance frequency, cavity tip temperature and shock structure between the nozzle exit and cavity inlet. The predicted dominant frequency (∼1054 Hz) and wall temperature (∼408 K) show good agreement with experimental data, confirming the simulation’s ability to reproduce an experimentally observed resonance process. Numerical results show that the resonance process is dominated by periodic influx and efflux of the jet, accompanied by the formation, propagation and reflection of incident and reflected shock waves inside the cavity. Despite the longer duration and higher velocity influx phase, continuous near-wall outflow maintains nearly zero net mass exchange over each resonance cycle. The time spent in the influx phase is greater than that in the efflux phase. The results also show that the temperature rise inside the cavity is primarily due to shock irreversibility rather than compression of trapped gas alone. Multiple reflected shocks have been observed, and their merger is found to increase the wave speed and strengthen the pressure oscillations. A higher average speed of the incident shock wave compared to the reflected shock wave has been observed. The present study provides a detailed description of shock motion and heat generation mechanisms in cylindrical resonance tubes.