Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

Abstract

Vortex breakdown of swirling, round jet flows is investigated in the compressible, subsonic regime by means of Direct Numerical Simulation (DNS). This is achieved by solving the compressible Navier–Stokes equations on a cylindrical grid using high-order spatial and temporal discretization schemes. The Reynolds number is Re=ρc∘wc∘R∘/μc∘=5000 and the flow is moderately compressible with Mach number Ma=wc∘/γRair∘Tc∘=0.6. The integral swirl number at the inflow is Sint=0.85. The parameters are chosen properly so as to make comparisons with existing experiments at lower Mach numbers possible while still enabling a study of compressible and baroclinic effects. Different from previous numerical investigations, a nozzle immersed in the fluid is included in the computational domain and is modelled as an isothermal no-slip wall, either rotating with the mean azimuthal flow direction or kept at rest. The present investigation aims to clarify the role played by the nozzle wall motion for the vortex breakdown of the swirling jet. We study the nozzle flow as well as the swirling jet flow simultaneously, a novelty for numerical investigations of vortex breakdown in swirling jets. Depending on the nozzle wall motion, the flow differs significantly upstream of the vortex breakdown: for the rotating nozzle, the flow inside the nozzle is purely laminar and the azimuthal boundary layer at the outer nozzle wall gives rise to the axisymmetric mode n=0 and a single-helix type instability with azimuthal wave number n=1. With the nozzle at rest, a transitional flow is observed within the nozzle where a helical instability with azimuthal wave number n=12 dominates, growing in the boundary layer at the nozzle wall. For both nozzle setups, the helical instabilities observed for the nozzle flow interact with the developing vortex breakdown and the conical shear-layer downstream of the nozzle. For the nozzle at rest, this interaction results in a vortex breakdown configuration which is shifted in the upstream direction and which has a smaller radial and streamwise extent compared to the rotating nozzle case and the recirculation intensity is higher. The dominant frequency is highly influenced by the flow upstream of the vortex breakdown and is substantially higher for the nozzle at rest. Although the nozzle flow field differs for the two configurations and therefore alters the vortex breakdown downstream, a single-helix type instability n=1 governing the vortex breakdown is found for both cases. This provides strong evidence for the robustness of the instability mechanisms leading to vortex breakdown.