Dynamic Mode Decomposition for Swirling Jet Flow Undergoing Vortex Breakdown

Abstract

Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical shear layer and a large recirculation zone around the jet axis. We performed Large-Eddy Simulations (LES) of compressible swirling jet flows at Re=5000, Ma=0.6 in the high swirl number regime (S=1). A nozzle is included in our computational setup to account for more realistic inflow conditions. The obtained velocity fields are analyzed by means of temporal and spatial dynamic mode decomposition (DMD) to get further insight into the characteristic structures dominating the flow. We present eigenvalue spectra for the case under consideration and discuss the stability behaviour in time and space. LES of swirling jet flow undergoing vortex breakdownWe performed Large-Eddy Simulations (LES) of swirling jet flow undergoing vortex breakdown, see [1] for a review. We solve the compressible Navier-Stokes equations on a cylindrical grid using high-order temporal and spatial discretisation schemes, see [2] and the references therein for details. The Reynolds number is set to Re = ρ cl r in u z cl /µ cl = 5000 and the Mach number to Ma = 0.6 using the centerline values at the inflow plane of the computational domain. The flow medium is air. We capture the fundamental physics of the flow configuration under investigation, namely a large recirculation zone at the centerline of the jet, a strong bursting behind the nozzle lip and helical instabilities dominating the flow, see [3] and Fig. 1. To get further insight into the structures dominating the flow we apply the Dynamic Mode Decomposition method (DMD) to the simulation results. Dynamic Mode Decomposition of LES resultsThe Dynamic Mode Decomposition (DMD) is a relatively new method to get insight into coherent structures dominating the dynamics of a flow in time and space. It is based on snapshot sequences of either experimental or numerical time-and spaceresolved data (see [4] for a detailed description of the method and first applications). The present investigation is based on 1000 snapshots in time and 75 snapshots in space. Criteria of [5] are applied where possible. Data is sampled in a cylindrical 3D region of the computational domain of the LES shown in Fig. 1 (right). We apply DMD to all three velocity components u r , u θ , u z one after the other and restrict ourselves here to presenting results for the azimuthal velocity u θ only for the sake of brevity. Data is sampled after 100tu cl /r in dimensionless time units for a time interval of 25tu cl /r in . The maximum resolved Strouhal number in the snapshot basis is St = 20 and the maximum resolved streamwise wave number k/r in = 9.5. With the snapshot basis used in the present investigation the residual converged over 4 orders of magnitude.Figure 2 (left) shows the temporal spectrum of the flow with the unstable region shaded in grey. Since transitional processes are still going on during sampling of the flow most of th...

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“…Considering both the variation of the shapes and the distributions of transient velocity streamlines with the increment of b z , we deduce that the kinetic energy in the jet region is weakened with the spiral flow intensity increasing gradually. Comparing the numerical results shown in Figures 3 and 6 with previous results [20][21][22][23][24], with b z = 0 the ordinary jet flow is clearly modified by the toroidal lf which transfers it into swirling jet flow. For example, as shown in Figure 6, when |b z | increases from 0 to 60 µT, the shapes of the transient velocity streamlines change in the whole fluid domain.…”