Local stability analysis of an inviscid transverse jet (original) (raw)
Related papers
Journal of Fluid Mechanics, 2008
The dominant non-dimensional parameter for isodensity transverse jet flow is the mean jet-to-crossflow velocity ratio, R. In Part 1 (Megerian et al., J. Fluid Mech., vol. 593, 2007, p. 93), experimental results are presented for the behaviour of transverse-jet near-field shear-layer instabilities for velocity ratios in the range 1 < R 10. The nominally axisymmetric mode is found to be the most unstable mode in the transverse-jet shear-layer near-field region, upstream of the end of the potential core. The overall agreement of theoretical and experimental results suggests that convective instability occurs in the transverse-jet shear layer for jet-to-crossflow velocity ratios above 4, and that the instability is strengthened as R is decreased.
2021
The jet in crossflow, or a transverse jet, eventually undergoes a linear transition from convectively to absolutely/globally unstable as the crossflow to jet velocity ratio increases. This flow field, however, has an extremely complex dynamics. Hence, determining this transition location is not a trivial task. It has long been known that this transition is associated with the upstream shear layer connected to the near field Kelvin-Helmholtz vortex ring, but it was only recently that the most unstable global mode and wave maker were located there as well. These findings led to the realization that an inviscid and planar linear stability analysis of the local velocity profile extracted from the jet in the crossflow upstream shear layer was strongly correlated with its transition to absolute/global instability. It is shown in this paper that such an analysis can be turned into an accurate predictive tool with the use of a viscous (instead of inviscid) and round (instead of planar) mixing layer. In other words, replacing an inviscid analysis of a planar mixing layer with counterflow by a viscous analysis of a round coaxial jet with outer nozzle suction leads to an accurate prediction of the jet in crossflow convective to an absolute instability transition.
Stability of a jet in crossflow
Physics of Fluids, 2011
We have produced a fluid dynamics video with data from Direct Numerical Simulation (DNS) of a jet in crossflow at several low values of the velocity inflow ratio R. We show that, as the velocity ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behavior, before finally exhibiting asymmetric chaotic motion. We also perform a stability analysis just above the first bifurcation, where R is the bifurcation parameter. Using the overlap of the direct and the adjoint eigenmodes, we confirm that the first instability arises in the shear layer downstream of the jet orifice on the boundary of the backflow region just behind the jet.
Absolute instability of an annular jet: local stability analysis
Meccanica, 2020
The paper presents parametric studies of the first and second azimuthal absolute modes in annular non-swirling and swirling jets. The spatio-temporal linear stability analysis is applied to investigate an influence of governing parameters including axial velocity gradients in inner and outer shear layers, back-flow velocity, swirl number and shape of the azimuthal velocity. A new base flow is formulated allowing a flexible variation of the shape of axial and azimuthal velocity profiles. It is shown that the first helical absolute mode is governed mainly by the back-flow velocity and swirl intensity. A steepness of the inner shear layer can control the absolute mode frequency. The velocity gradient in the outer shear layer and the shape of the azimuthal velocity have rather limited impact on the absolute mode characteristics. Finally, it is shown that the second helical absolute mode can dominate the flow with a stronger swirl intensity.
Global stability of a jet in crossflow
Journal of Fluid Mechanics, 2009
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie licentiatexamen torsdagen den 05 juni 2008 kl 14.00 i D41, Kungliga Tekniska Högskolan, Lindstedtsvägen 17, 1tr, Stockholm.
Temporal and spatial instability of an inviscid compound jet
Rheologica Acta, 1996
This paper examines the linear hydrodynamic stability of an inviscid compound jet. We perform the temporal and the spatial analyses in a unified framework in terms of transforms. The two analyses agree in the limit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analysis, there are two growing modes, stretching and squeezing. Thin film asymptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstable for small jet velocities and admits a convec-tively growing instability for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spatial growth rate. Predictions of both the temporal and the spatial theories compare well with experiment.
Experiments on a jet in a crossflow in the low-velocity-ratio regime
Journal of Fluid Mechanics, 2019
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.
Shear Layer Instabilities in Low Density Transverse Jets
2009
Shear layer instabilities associated with the gaseous, isodensity jet in crossflow have been explored in detail in recent experimentsfootnotetextMegerian, et al., JFM, 593, pp. 93-129, 2007, indicating that the jet shear layer is globally unstable when the jet-to-crossflow velocity ratio, R, is less than 3.2 for a flush injected jet. Low density jets in quiescent surroundings are also known to become globally unstable for jet-to-ambient density ratios below approximately 0.6-0.7. It is thus of interest to explore the nature of changes in the character of shear layer instabilities for the low density jet in crossflow, with special focus on the influence of jet-to-crossflow momentum flux ratios at which instabilities are altered. A specially designed mixing device is utilized for exploration of helium and nitrogen jet mixtures. Calibration of the mixing device is accomplished using an acoustic waveguide capable of exploring alterations of standing wave frequencies with different gas mixtures. A range of flow conditions are explored, and alterations in the jet's spectral character suggesting transition to absolute instability are quantified.