Hyder S. Husain

Elliptic jets. I: Characteristics of unexcited and excited jets

This paper summarizes experimental studies of incompressible elliptic jets of different aspect ratios and initial conditions, and effects of excitations at selected frequencies and amplitudes. Elliptic jets are quite different from the extensively studied plane and circular jets - owing mainly to the fact that the azimuthal curvature variation of a vortical structure causes its non-uniform self-induction and hence complex three-dimensional deformation. Such deformation, combined with properly selected excitation can substantially alter entrainment and other turbulence phenomena, thus suggesting preference for the elliptic shape in many jet applications. The dominance of coherent structures in the jet far field is evident from the finding that switching over of the cross-section shape continues at least up to 100 equivalent diameters D e . The locations and the number of switchovers are strongly dependent on the initial condition, on the aspect ratio, and, when excited, on the Strouhal number and the excitation level. We studied jets with constant exit momentum thickness θ e , all around the perimeter, thus separating the effects of azimuthal variations of θ e , (typical of elliptic jets) and of the shear-layer curvature. Also investigated are the instability characteristics, and enhanced entrainment caused by bifurcation as well as pairing of vortical structures. We discuss shear-layer and jet- column domains, and find the latter to be characterized by two modes : the preferred mode and the stable pairing mode - similar to those found in circular jets -both modes scaling on the newly-defined lengthscale D e . The paper documents some time- average measurements and their comparison with those in circular and plane jets.

Controlled excitation of elliptic jets

Studies of unexcited and excited elliptic jets reveal their characteristics to be noticeably different from circular jets, suggesting applications of excited elliptic jets for enhanced mixing and chemical reaction, and control of aerodynamic noise. The near‐field turbulence characteristics, jet spread, and locations of switching of major and minor axes of the jet cross section can be drastically altered by forcing. The preferred mode and the stable pairing mode of an elliptic jet scale with the exit equivalent diameter.

Elliptic jets, part 2. Dynamics of coherent structures: Pairing

The dynamics of the jet column mode of vortex pairing in the near field of an elliptic jet was investigated. Hot-wire measurements and flow visualization were used to examine the details of the pairing mechanism of nonplanar vortical elliptic structures and its effect on such turbulence measures as coherent velocities, incoherent turbulence intensities, incoherent and coherent Reynolds, stresses, turbulence production, and mass entrainment. It was found that pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane. In the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently, producing considerably greater entrainment and mixing than in circular or plane jets.

Elliptic jets. Part 3. Dynamics of preferred mode coherent structure

The dynamics of the preferred mode structure in the near field of an elliptic jet have been investigated using hot-wire measurements. A 2:1 aspect ratio jet with an initially turbulent boundary layer and a constant momentum thickness all around the nozzle exit perimeter was used for this study. Measurements were made in air at a Reynolds number Re D e (≡ U e D e / v ) = 3.5 × 10 4 . Controlled longitudinal excitation at the preferred mode frequency ( St D e ≡ fD e / U e = 0.4) induced periodic formation of structures, allowing phase-locked measurements with a local trigger hot wire. The dynamics of the organized structure are examined from educed fields of coherent vorticity and incoherent turbulence in the major and minor symmetry planes at five successive phases of evolution, and are also compared with corresponding data for a circular jet. Unlike in a circular jet, azimuthally fixed streamwise vortices (ribs) form without the aid of azimuthal forcing. The three-dimensional deformation of elliptic vortical structures and the rib formation mechanism have also been studied through direct numerical simulation. Differential self-induced motions due to non-uniform azimuthal curvature and the azimuthally fixed ribs produce greater mass entrainment in the elliptic jet than in a circular jet. The turbulence production mechanism, entrainment and mixing enhancement, and time-average measures and their modification by excitation are also discussed in terms of coherent structure dynamics and the rib-roll interaction. Various phase-dependent and time-average turbulence measures documented in this paper should serve as target data for validation of numerical simulations and turbulence modelling, and for design and control purposes in technological applications. Further details are given by Husain (1984).

Experiments on subharmonic resonance in a shear layer

The subharmonic resonance phenomenon is studied using hot-wire measurements and flow visualization in an initially laminar shear layer forced with two-frequencies for various choices of the fundamental frequency f and its subharmonic f /2 with controlled initial phase difference ϕ in between them. We explore the effects of the controlling parameters, namely: (i) forcing frequencies and their initial amplitudes, (ii) initial phase difference ϕ in , and (iii) detuning (i.e. when the second forcing frequency is slightly different from f /2). While several of our experimental observations support predictions based on weakly nonlinear theory, others do not. We explain our data in terms of vortex dynamics concepts.

Control of vortex breakdown by addition of near-axis swirl

We present a new method for controlling vortex breakdown (VB) via addition of co- or counter-rotation near the axis. Co-rotation is adequate to totally suppress VB, whereas counter-rotation increases the number and size of VB “bubbles” and makes the flow unsteady. We study these effects in a closed cylindrical container, in which a rotating end disc drives the base flow; an independently rotating central rod (with rod radius≪disk radius) is employed to control VB. This flow, being free of ambient disturbances, is well suited for understanding both the VB mechanism and its control; the present work appears to be the first to study VB control. We develop and explain our control strategy using flow visualization and simple analytical reasoning. Our results suggest that an additional co- or counter-rotation, applied near the vortex axis, can be effective in suppressing or enhancing VB in practical flows.

The elliptic whistler jet

Elliptic jets have decided advantages for technological applications over circular jets; this paper explores further advantages achieved by jet forcing due to self-excitation. Using hot-wire measurements and flow visualization, we have studied an elliptic whistler (i.e. self-excited) air jet of 2:1 aspect ratio which, in contrast to an elliptic jet issuing from a contoured nozzle, displays no axis switching, but significantly increased spread in the major-axis plane. Its near-field mass entrainment is considerably higher (by as much as 70%) than that of a non-whistling jet. Flow visualization reveals unexpected dynamics of the elliptic vortical structures in the whistler jet compared to that in the non-whistling jet. Vortices rolled up from the lip of the elliptic pipe impinge onto the collar, producing secondary vortices; interaction of these two opposite-signed vortices is shown to cause the different behaviour of the whistler jet.

Subharmonic Resonance in a Shear Layer

The initiation, growth, interaction, breakdown and regeneration of coherent structures in turbulent shear flows are the manifestations of a hierarchy of flow instability mechanisms. After the initial roll up of the shed vortex sheet into discrete vortices, the most common interaction that a shear layer undergoes is pairing of two neighboring vortices. The pairing process, i.e. the growth of the subharmonic, is a consequence of what has come to be known as subharmonic resonance -- the nonlinear interaction between a wave of frequency f and a subharmonic wave of frequency f/2, producing an f/2 component which is capable of reinforcing the subharmonic. Such reinforcement depends on excitation parameters such as the phase between the fundamental and the subharmonic, and the critical fundamental amplitude[1, 2].

The Complementary Roles of Experiments and Simulation in Coherent Structure Studies

The past two decades’ vigorous studies of coherent structures (CS) have failed to produce a consensus on what CS are, let alone a CS-based turbulence theory or even an objective, mathematical definition of CS. What started out as a promise for a mechanistic explanation for fluid turbulence—as researchers found or reinvented CS in their ‘search for order in disorder’ and presumed to have discovered a deterministic, tractable route to turbulence phenomena—has unfolded itself as a Pandora’s box. Successive studies of CS continue to raise more questions than they answer. Thus, even though we understand more about turbulence via CS concepts, we have become painfully even more aware of how complex turbulence is. CS are not the panacea they were initially presumed to be, nor are they as simple as we all had hoped. Despite some progress through CS research, the secrets of turbulence remain ever impenetrable.

Nonlinear Instability of Free Shear Layers: Subharmonic Resonance and Three-Dimensional Vortex Dynamics

The subharmonic resonance phenomenon in a free shear layer is studied experimentally and numerically. Excitation using both fundamental and subharmonic at an initial phase difference (ϕin shows stable pairing for a wide range of ϕin. However, for a narrow range of ϕin, either ‘shredding’ occurs or pairing is temporarily suppressed and occurs downstream without periodicity. Under detuned excitation, which is more representative of feedback-driven subharmonic growth, amplitude and phase modulations produce multiple sideband frequencies reflecting variations in the pairing location and occasional nonpairings. In direct numerical simulations (DNS) of a temporal shear layer, we uncover and analyze a new mechanism of transition, based on excitation of the ‘bulging’ instability by pairing of spanwise vortices (‘rolls’) with out-of-phase spanwise undulations. This 3D pairing generates strong internal core dynamics, consisting of core size oscillation driven by oscillating cells of spanwise flow within the rolls. Core dynamics amplify due to instability, can grow alongside streamwise vortices (‘ribs’), and eventually initiate mixing transition at a lower initial 3D disturbance level than that required for transition by ribroll interaction alone. We emphasize that the limitations of traditional perturbation analysis in understanding of the nonlinear and 3D aspects of instability and transition need to be overcome by new approaches such as vortex dynamics and topology.