Criterion for the linear convective to absolute instability transition of a jet in crossflow: The countercurrent viscous and round mixing-layer analogy (original) (raw)
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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.
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.
Local stability analysis of an inviscid transverse jet
Journal of Fluid Mechanics, 2007
A local linear stability analysis is performed for a round inviscid jet with constant density that is injected into a uniform crossflow of the same density. The baseflow is obtained from a modified version of the inviscid transverse jet near-field solution of Coelho & Hunt (J. Fluid Mech. vol. 200, 1989, p. 95) which is valid for small values of the crossflow-to-jet velocity ratio λ. A Fourier expansion in the azimuthal direction is used to couple the disturbances with the three-dimensional crossflow. The spatial growth rates of the modes corresponding to the axisymmetric and first helical modes of the free jet as λ → 0 increase as λ increases. The diagonal dominance of the dispersion relation matrix is used as a quantitative criterion to estimate the range of velocity ratios (0 < λ < λ c ) within which the transverse jet instability can be considered to have a structure similar to that of the free jet. Further, we show that for λ > 0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.
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.
Effects of controlled vortex generation and interactions in transverse jets
Physical Review Fluids
This experimental study examined the effects of controlled vortex generation and interactions created by axisymmetric excitation of a transverse jet, with a focus on the structural and mixing characteristics of the flow. The excitation consisted of a double-pulse forcing waveform applied to the jet, where two distinct temporal square-wave pulses were prescribed during a single forcing period. The two distinct pulses produced vortex rings of different strength and celerity, the strategic selection of which promoted vortex ring interactions or collisions in the near field to varying degrees. Jet flow conditions corresponding to a transitionally convectively and absolutely unstable upstream shear layer (USL) in the absence of forcing, at a jet-to-cross-flow momentum flux ratio of J = 10, and to an absolutely unstable USL at J = 7, were explored for a jet Reynolds number of 1800. Acetone planar laser-induced fluorescence imaging was utilized to quantify the influence of different prescribed temporal waveforms. All forcing conditions enhanced the spread, penetration, and molecular mixing of the jet as compared to the unforced jet, though to differing degrees. Interestingly, when the jet was convectively unstable, forcing which promoted vortex collisions provided the greatest enhancement in molecular mixing, whereas the absolutely unstable jet produced the greatest enhancement in mixing when the vortex rings did not interact, with important implications for optimized jet control.
Numerical Simulations of Global Instability In Separated Flows At High Mach Number
30th AIAA Applied Aerodynamics Conference, 2012
The global stability or instability of supersonic ramp flow and of a jet in supersonic crossflow is investigated. The three-dimensional Navier-Stokes equations are solved directly with no model applied. Ramp flow is studied at Mach number 4.8 and Reynolds numbers 6,843 and 3,422, based on inflow boundary layer displacement thickness and freestream velocity. The laminar base flows are stable in two-dimensions. Simulations in three-dimensions show that the high Reynolds number case is globally unstable, while the flow is stable at the lower Reynolds number, suggesting that a critical Reynolds number for instability exists between these two Reynolds numbers. A spanwise wavelength of 12 times the incoming boundary layer displacement thickness is found to be the most unstable for the ramp flow with Reynolds number of 6,843. Similar conclusions are found for a sonic jet injected into a Mach 6.7 crossflow, which is stable at low jet momentum flux ratios (Jp), but becomes globally unstable as Jp increases. Streamwise vortices are observed in the unstable jet cases and a spanwise wavelength of 8 times the incoming boundary layer displacement thickness is found to be the preferred mode of global instability.
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.
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.