Large Eddy Simulations of Swirling Nozzle‐Jet Flow Undergoing Vortex Breakdown

Abstract

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up-and downstream. Simulation methodologySwirling 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. In our group we developed a numerical tool to investigate swirling jet flow undergoing vortex breakdown (see [1] and references therein). For spatial derivatives we use high-order finite difference schemes [2] and a spectral method. The time integration scheme is a LDDRK method of fourth order [3]. We included a canonical nozzle with isothermal wall into our computational setup to account for more realistic inflow boundary conditions [4]. This modification is mainly motivated by the observation of [5] that the breakdown of the swirling jet interacts with the inflow boundary treatment leading to the possible prevention of naturally developing helical modes. We simulate a swirling jet at Re = R · u zc /ν c = 5000 At the inflow Dirichlet boundary conditions are applied to all five conservative variables supplemented with a sponge layer to prevent reflections of upstream travelling waves. A turbulent pipe flow profile is used for the axial velocity component, u z = 1 − r 7 and the radial velocity, u r , is identically zero. The fluid is in solid body rotation, u θ = S · r, within the nozzle and irrotational outside, where S = u θmax /u zmax = 1.0 is the swirl number. The pressure distribution is derived from the radial component of the Navier-Stokes equations in cylindrical coordinates and integrated numerically. The density is calculated from the equation of state thereafter. At the outflow and in the far-field non-reflecting boundary conditions are implemented [6]. Additionally a sponge layer is used in the far-field acting on the density ρ and pressure p to prevent a mean pressure drift. At the nozzle wall, which is of length 2.5R, all velocities u i and the temperature T are set according to the inflow profiles. The whole flow field is initialized according to the inflow profiles and random noise of small amplitude 10 −5 is added. Figure 1a shows an instantaneous snapshot of...

Dynamic Mode Decomposition for Swirling Jet Flow Undergoing Vortex Breakdown

“…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.…”