Experiments on a jet in a crossflow in the low-velocity-ratio regime

Abstract

The hairpin instability of a jet in a crossflow (JICF) for low jet-to-crossflow velocity ratio is investigated experimentally for a velocity ratio range of R ∈ (0.14, 0.75) and crossflow Reynolds numbers Re D ∈ (260, 640). From spectral analysis, we characterize the Strouhal number and amplitude of the hairpin instability as a function of R and Re D . We demonstrate that the dynamics of the hairpins is well described by the Landau model, and hence that the instability occurs through Hopf bifurcation, similarly to other hydrodynamical oscillators such as wake behind different bluff bodies. Using the Landau model, we determine the precise threshold values of hairpin shedding. We also study the spatial dependence of this hydrodynamical instability, which shows a global behaviour.

Global linear analysis of a jet in cross-flow at low velocity ratios

“…In figure 6 the streamwise velocity and spanwise vorticity in the symmetry plane are shown for both the stable and the unstable case. Those figures are qualitatively similar to the experimental results by Klotz et al (2019, figure 7). They show the same distinct shape of the recirculation area behind the jet and below the shear layer.…”

“…At Re D = 495 and δ * /D = 0.3603, the stability limit is found slightly above R = 0.35 with the pipe fully meshed. The neutral curve found here is close to the experimental results from Klotz et al (2019) who studied a similar range of parameters, although in their experiments the boundary layer was thinner, with δ * /D ranging from 0.26 to 0.3. A comparison with a very low velocity ratio case in Cambonie & Aider (2014), at R = 0.16 is also made.…”

“…These observations are also consistent with the transition scenario proposed by Cambonie & Aider (2014). However, a more recent experimental study by Klotz, Gumowski & Wesfreid (2019), focusing on low Reynolds numbers and velocity ratios, finds a steady state at very low velocity ratio, and an unsteady flow dominated by hairpin vortices when the velocity ratio is increased. Ilak et al (2012) performed a global linear stability analysis of the jet in cross-flow and found a Hopf bifurcation at peak velocity ratio R = 0.625.…”

“…As a consequence, the shape of the velocity profile was different from the complete flow computed here, with a larger top velocity. In the present direct numerical simulations (DNS), the velocity profile at the pipe exit, shown in figure 2, appears significantly bent by the cross-flow, a feature that was also observed by Klotz et al (2019). In particular, a stationary recirculation vortex can be seen in the upstream part of the pipe exit, consistent with the inner vortex described in Bidan & Nikitopoulos (2013).…”

“…On the other hand, the slightly higher values of critical jet velocity ratio presented here compared to those recently reported by Klotz et al (2019) are better explained by a different velocity profile exiting the pipe. They report a flatter velocity profile with thinner shear layers in the absence of a cross-flow.…”