Leonardo Alves

Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio

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. A local linear stability analysis is presented in this paper for the subrange R >4, using two different base flows for the transverse jet. The first analysis assumes the flow field to be described by a modified version of the potential flow solution of Coelho & Hunt ( J. Fluid Mech ., vol. 200, 1989, p. 95), in which the jet is enclosed by a vortex sheet. The second analysis assumes a continuous velocity model based on the same inviscid base flow; this analysis is valid for the larger values of Strouhal number expected to be typical of the most unstable disturbances, and allows prediction of a maximum spatial growth rate for the disturbances. In both approaches, results are obtained by expanding in inverse powers of R so that the free-jet results are obtained as R →∞. The results from both approaches agree in the moderately low-frequency regime. Maximum spatial growth rates and associated Strouhal numbers extracted from the second approach both increase with decreasing velocity ratio R , in agreement with the experimental results from Part 1 in the range 4 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

(Received 18 August 2006 and in revised form 4 January 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 0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.

Control of Vorticity Generation in an Acoustically Excited Jet in Crossflow

*† ‡ § ** , This paper provides an overview of recent research activities pertaining to the control of penetration, spread, and mixing associated with the forced jet in crossflow or transverse jet. Experimental research at UCLA has in the past focused on acoustical forcing via feedforward control of the transverse jet at relatively low jet-to-crossflow velocity ratios R, and the optimization of jet penetration and spread via square wave forcing at specific frequencies and temporal pulse widths. Yet recent experimental as well as theoretical studies of the nearfield shear layer instabilities associated with the transverse jet suggest that the nature of the jet instability is different for lower values of R (below 5) than higher values of R (6 and above). These studies indicate that the transverse jet at higher R values is convectively unstable, while the transverse jet at lower R values demonstrates the presence of self-excited global oscillations, a behavior related to an absolute instability of the jet shear layer. The implications of these findings explain differences observed in forced transverse jet behavior and suggest strategies for the application of forcing in its control.

A uniformly valid asymptotic solution for a transverse jet and its linear stability analysis

An expansion in terms of the ratio λ of the characteristic crossflow velocity U∞ to jet velocity Uj, where λ=U∞/Uj≪1, is used to obtain a representation of the basic three-dimensional steady flow in the nearfield of a transverse jet at large Reynolds numbers and to study its dominant instability. The inviscid vortex sheet analysis of Coelho and Hunt is extended so as to include asymptotic analysis of the viscous shear layers forming along the boundaries of the jet. These not only allow for continuity of the velocity components but also create vorticity whose advection induces an O(λ) axial flow in the direction of the jet. A uniformly valid solution is then constructed for use in a stability analysis that concentrates on the effect of crossflow upon the dominant mode of the free jet. Both the characteristic frequency and growth rate of this mode are found to increase with λ, in qualitative agreement with recent experimental observations.

Control of Transverse Jet Shear Layer Instabilities

*† ‡ § This paper describes experimental results pertaining to the nature and control of shear layer instabilities associated with the single jet in crossflow or transverse jet, a flowfield widely used in propulsive devices. These studies suggest that the character of the jet’s nearfield shear layer instability can be significantly different for the transverse jet as compared with the free jet. For transverse jets, the instabilities can be initiated much closer to the jet orifice, for either flush or elevated jet injection, and are much stronger, with earlier development of subharmonic and higher harmonic modes. For the case of flush injection, the nature of the transverse jet instability also differs significantly for lower values of the jet-to-crossflow velocity ratio R (below 3.5) as compared to jets at higher R; in the case of flush injection, there is a rapid initiation of strong, distinct modes that are not affected by external sinusoidal forcing. No such behavior at low R values is observed for the elevated jet. These findings help to explain differences observed in strongly forced transverse jet behavior and suggest strategies for the application of jet forcing in the control of its mixing and penetration .