Modal Analysis of Supersonic Flow Separation in Nozzles

Abstract: Operating a convergent-divergent nozzle under overexpanded conditions can lead to supersonic flow separation in the divergent section of the nozzle. In this case, an attached oblique shock wave forms at the separation base. The sudden pressure rise across the shock wave can cause damaging lateral pressure forces, or side-loads, to act on the nozzle if the separation line is asymmetric. Such asymmetry can be caused by downstream instabilities stemming from turbulence, external excitation or periodic modes. In this thesis the applicability of applying modal decomposition methods to supersonic nozzle flows was investigated. Axisymmetric RANS and URANS simulations of nozzle flows were investigated using the Arnoldi algorithm and the Dynamic Mode Decomposition,respectively. The Arnoldi method relies on a linearized flow solver and has the advantage of being able to detect asymmetric modes on two dimensional grids. The DMD, however, is a snapshot-based algorithm which needs no explicit linearization of the flow dynamics. Results show that these methods can successfully be applied to supersonic nozzle flows with separation and strong shocks. For example, the Arnoldi method predicted a helical screeching mode with impressive accuracy and The DMD analysis on perturbed 2D URANS flow field was able to detect modes linked to transonic resonance. Finally, Detached Eddy Simulations (DES) on a separated flow inside a Truncated Ideal Contoured Nozzle were performed for two separate nozzle pressure ratios (NPR’s). The simulated sideload were lower than experimentally measured values but within uncertainty range. A three dimensional DMD analysis was performed on the DES data and revealed a strong ovalization mode at the lower NPR and a helical mode which could be linked to a peak in side-load spectrum at the higher NPR.