Dynamic behavior of the counter-flow jet for drag reduction in hypersonic laminar flow under short penetration mode

Abstract

Depending on the counter-flow jet (CFJ) injection characteristics, the flow field can be classified into the short penetration mode (SPM) and the long penetration mode. Although SPM is generally considered stable, the pressure drag coefficient exhibits significant fluctuations exceeding 10%, which cannot be explained by penetration length alone. Numerical simulations in a hypersonic laminar regime, combined with fast Fourier transform and multi-resolution dynamic mode decomposition (mrDMD) analyses, suggest that the dominant oscillatory behavior is closely associated with the dynamic evolution of the extended jet layer within a coupled system of shock, shear-layer, and recirculation dynamics. The mrDMD analysis further indicates that the interaction between the extended jet layer, unsteady shock structures, and surface pressure distribution forms a self-sustained feedback loop governing the oscillatory CFJ behavior. The motion of the extended jet layer enables the prediction of maximum and minimum drag states, demonstrating that the pressure drag coefficient undergoes a quasi-periodic, sine-like oscillation that can be decomposed into six characteristic steps. Furthermore, the mrDMD results show that this six-step feedback process is organized across multiple temporal scales, with slow background modes interacting with fast shock–jet oscillations. These findings provide new physical insight into the oscillatory mechanism of the SPM by identifying the coherent flow structures associated with drag fluctuations beyond the conventional interpretation based solely on penetration characteristics.