Application of Mode Decomposition in Supersonic S-Shaped Pipes with Multiple Bending Angles

Direct numerical simulations are employed to conduct modal analysis of supersonic flowfields in S-shaped pipes with a constant curvature ([Formula: see text]) and bending angles of [Formula: see text], [Formula: see text], and [Formula: see text]. The dynamic mode decomposition method is applicable to revealing the essential dynamic characteristics of the flow observables and quantitatively determining the frequency of each mode. The results show that the fluctuation field can be decomposed into dynamic modes consisting of periodic flow structures with varying frequencies, and low-frequency modes dominate the contribution to the fluctuations of velocity components and pressure in all modes. The S-shaped pipe with a bending angle of [Formula: see text] exhibits more pronounced changes in the downstream region than in the bend, with shock waves significantly increasing the turbulent kinetic energy of the upper boundary layer. The S-shaped pipe with a bending angle of [Formula: see text] generates flow separation and shock waves, resulting in strong pressure fluctuations at the junction between the first and second bends. The S-shaped pipe with a bending angle of [Formula: see text] is characterized by intense turbulent activities at the interface between the turbulent boundary layer and the mainstream. By comparison, the occurrence of separation has dominant contributions to thickening the boundary layer and enhancing turbulence.