Dynamic decomposition and analysis of a supersonic impinging jet flow

Abstract

Impinging jets are commonplace in industrial applications, including rocket engines, needle-free-dug delivery or cold-gas-dynamic spray processes. In the aerospace industry, rocket launches represent a critical phase during which jet instabilities can lead to payload damage and loss of flight control. The dynamic of the impinging jet is clearly unsteady and turbulent. Typically, a feedback loop resonance between acoustic wave packages and shear-layer nozzle instabilities dominates the flow features: upstream travelling acoustic waves at the nozzle exit perturb the shear layer, triggering an intrinsic instability of the flow. These structures are then convected down the jet and induce motion in the shocks. This shock motion then generates a fluctuation in the wall jet, which in turn produces an upstream travelling wave which upon reaching the nozzle exit, closes the feedback loop [1-2]. Although the general features of the feedback loop are known, detailed interpretation on the physics involved is still an open problem. In this work, dynamic mode decomposition (DMD) and singular value decomposition (SVD) has been applied to provide information about this flow physics. DMD approach [3] enables the extraction of dynamic modes, which are spatial structures ranked by their dynamics and associated to different frequencies present in the flow. SVD produce an alternative decomposition of the flow based on level of energy. Both, decomposition are complementary and provide useful information about the relevant flow features. From a computational point of view these type of approaches construct a Krylov subspace using snapshots issued from a numerical simulation. The resulting space can be subsequently analyzed (e.g. Arnoldi technique) to obtain flow instability information related to the underlying Navier-Stokes operator. In the present study the non-steady dynamics of a jet with an impingement distance of 4 and a nozzle pressure ratio of 3.2 is considered. This configuration has been thoughtfully studied experimentally by [2]. The unsteady solutions or snapshot are extracted from an Implicit Large Eddy Simulation solver previously validated with the experimental results.