Numerical study of nozzle configuration effects on dynamic afterburning characteristics of rocket exhaust plume

A detailed method for analyzing the multifrequency energy distribution and flow structures of unsteady separated flows of rocket exhaust plume is developed to clarify the morphological and frequency-domain evolution of separation modes for different nozzle configurations. We performed large eddy simulations of the dynamic afterburning reaction flow within rocket exhaust plumes from the nozzle exit downstream. A spectral proper orthogonal decomposition reduced-order model tailored to supersonic exhaust plumes was constructed to extract joint space-frequency modes of flowfield fluctuations and quantify the evolution of coherent structures under multi-frequency energy weighting. We compared the separation-mode morphology and dominant frequency characteristics in the afterburning flow fields of identical exit area rectangular and circular nozzles and analyzed the mechanisms by which nozzle geometry modulates vortex-induced entrainment during afterburning. The results show that the rectangular nozzle yields greater plume expansion and stronger shear layer effects than those of circular nozzles. The plume core exhibits approximately 45° axis switching, and localized overexpansion occurs near the nozzle corners. For the circular nozzle, increasing azimuthal order yields progressively finer coherent structures with retained rotational symmetry; for the rectangular nozzle, the geometric asymmetry redistributes modal energy toward higher azimuthal wavenumbers, and physically meaningful structures arise from the coupling of multiple azimuthal modes. The pressure field exhibits an energy peak near St = 0.01. In the medium-frequency band ( St = 0.005–0.02, i.e., 500–2000 Hz), the modal energy of the rectangular nozzle is less than that of the circular nozzle, indicating a weaker influence of the Kelvin–Helmholtz instability. This study provides a systematic characterization of the dynamic afterburning behavior under different nozzle exit geometries, offering physical insight into how nozzle cross-sectional shape modulates the plume flow structures and spectral energy distribution.