Modal Decomposition of Separated Nozzle Flow

Licentiatavhandling, 2014

The applicability of two different eigenvalue algorithms coupled with an axisymmetric RANS solver to predict the eigenmodes of separated supersonic flow inside an axisymmetric convergent-divergent nozzle was investigated. These are the Arnoldi and the Dynamic Mode Decomposition (DMD) algorithms, respectively. The Arnoldi method relies upon an explicit linearization of the flow dynamics, a linearized flow solver, to successively build up an orthogonal Krylov projection basis to project the flow dynamics onto. A disadvantage of using the linearized flow solver is that it does not include a turbulence model. However, it has an advantage in that its equations can be formulated to detect asymmetric modes. The DMD is a snapshot-based algorithm, which needs no explicit linearization of the flow dynamics. It can thus incorporate influence from the modeled turbulence and nonlinearities. The results show that the frequency range of the least damped modes, in the Arnoldi analysis, was within the frequency range to which experiments and numerical simulations have shown the flow to be most sensitive. Comparison of the DMD and Arnoldi modes showed that in some cases, the two methods provide almost identical modes, particularly in the case of the least damped modes, which are of most importance. An investigation of a nozzle geometry known to experience transonic resonance was carried out applying the DMD algorithm to a set of URANS simulation snapshots. The results indicate that the method is capable of predicting the transonic resonance frequencies with reasonable accuracy and, as a consequence, analyzing the DMD modes provides insight into the fundamental resonance mechanism.