Steady-blowing jet control of a finite-length square cylinder at high reynolds number: Turbulence characteristics and DRL-based adaptive drag reduction

This study systematically investigates the turbulence characteristics and drag-reduction mechanisms of steady wall-normal blowing control on a three-dimensional square cylinder at Re = 22000 using a large-eddy simulation (LES) with the Smagorinsky subgrid-scale model. Four jet positions at the cylinder corners—the windward face (Jet 1), the two lateral faces (Jets 2 and 3), and the leeward face (Jet 4)—are first compared under a fixed mass-flow-rate ratio of Q i = 5%. The results reveal that the leeward jet (Jet 4) yields the best performance: the time-averaged recirculation bubble contracts markedly, the leeward-face pressure recovers, and the coherence of the Kármán vortex street is disrupted, achieving a 25.4% drag reduction. In contrast, windward and lateral jets produce limited benefits or even increase drag. Further analysis using Q-criterion vortex identification, wake topology and oscillation patterns, and spectral proper orthogonal decomposition (SPOD) clarifies the underlying mechanism: Jet 4 injects momentum directly into the vortex-formation region, thereby shrinking the reversed-flow zone, suppressing free-end downwash, and converting large-scale coherent vortex shedding into broadband small-scale fluctuations. Based on these findings, a TD3-based deep-reinforcement-learning framework is developed at the Jet 4 location. The adaptive policy is trained on a reduced LES mesh and then frozen and tested on the high-resolution mesh, where it dynamically adjusts the jet velocity under the constraint Q i ≤5%. After 2000 training episodes, the learned policy achieves a 29.5% drag reduction in deterministic high-resolution testing. These results demonstrate that leeward “direct-action” steady-blowing jets combined with DRL-based adaptive control constitute an effective strategy for drag reduction of bluff bodies at high Reynolds numbers, offering a practical reference for flow control of analogous engineering structures.