A Frequency Selection Criterion in Spatially Developing Flows

Chomaz, Jean‐Marc; Huerre, Patrick; Redekopp, L. G.

doi:10.1002/sapm1991842119

Cited by 191 publications

(209 citation statements)

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“…The complex GinzburgLandau ͑CGL͒ equation is chosen as a model of open flows since families of linear and nonlinear wave solutions are readily determined analytically. As summarized below, the study of CGL models has been found to lead to linear frequency selection criteria 6 that remain applicable for the Navier-Stokes equations. 7 The same approach is adopted here in the fully nonlinear context.…”

Section: ͓S1070-6631͑98͒00410-3͔mentioning

confidence: 99%

“…In the linear approximation, global frequency selection in doubly infinite domains is dictated by saddle point conditions 6,7 imposed on the local linear dispersion relation. Such a criterion predicts remarkably well the vortex shedding frequency behind blunt edged plates.…”

Section: ͓S1070-6631͑98͒00410-3͔mentioning

confidence: 99%

“…6. In the fully nonlinear regime, soft global modes with an overall slowly varying spatial envelope have been identified and described in Ref.…”

Section: The Purpose Of This Letters Section Is To Provide Rapid Dissmentioning

confidence: 99%

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Steep nonlinear global modes in spatially developing media

et al. 1998

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International audienceA new frequency selection criterion valid in the fully nonlinear regime is presented for extended oscillating states in spatially developing media. The spatial structure and frequency of these modes are dominated by the existence of a sharp front connecting linear to nonlinear regions. A new type of fully nonlinear time harmonic solutions called steep global modes is identified in the context of the supercritical complex Ginzburg-Landau equation with slowly varying coefficients. A similar formulation is likely to be applicable to fully nonlinear synchronized global oscillations in spatially developing free shear flows

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Section: ͓S1070-6631͑98͒00410-3͔mentioning

confidence: 99%

Section: ͓S1070-6631͑98͒00410-3͔mentioning

confidence: 99%

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Steep nonlinear global modes in spatially developing media

et al. 1998

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“…The pocket of subcriticality was, however, anticipated by Benjamin [19], who analyzed subcritical flows and concluded that the existence of a sufficiently large region of subcriticality was a necessary condition for vortex breakdown onset. The result is reminiscent of the criterion that a sufficiently large pocket of absolute instability is necessary for a flow to become globally unstable [20]. In both cases, the determination of the pocket of subcriticality or absolute instability is problem dependent and difficult to estimate, in particular when the flow cannot be reasonably approximated as parallel.…”

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Vortex-Breakdown-Induced Particle Capture in Branching Junctions

et al. 2016

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We show experimentally that a flow-induced, Reynolds number-dependent particle-capture mechanism in branching junctions can be enhanced or eliminated by varying the junction angle. In addition, numerical simulations are used to show that the features responsible for this capture have the signatures of classical vortex breakdown, including an approach flow aligned with the vortex axis and a pocket of subcriticality. We show how these recirculation regions originate and evolve and suggest a physical mechanism for their formation. Furthermore, comparing experiments and numerical simulations, the presence of vortex breakdown is found to be an excellent predictor of particle capture. These results inform the design of systems in which suspended particle accumulation can be eliminated or maximized. DOI: 10.1103/PhysRevLett.117.084501 Flows through branching junctions are common in everyday piping systems, industrial applications, and even physiological flows. Despite the prevalence of branching flows and the breadth of studies of these systems, recent discoveries demonstrate new features that have not been studied. For example, for flow through a T junction in which flow enters the base of the T and splits between the two symmetric outlets, it is natural to believe that suspended particles entering the system will find the junction to be a kinematically unstable stagnation region and be swept downstream through the outlets. However, it has been shown that, in fact, bubbles can be trapped in these regions within flow features that resemble vortex breakdown [1,2], which refers to a phenomenon where internal stagnation points develop, followed by regions of reversed flow with limited axial extent [3].Despite the fact that this capture mechanism depends strongly on the swirling motion of flow in the junction through the interplay of centrifugal, pressure gradient, and drag forces [1], the effect of varying the junction angle has not been explored. We introduce this geometric change, systematically varying the junction angle θ, which introduces significant changes in the secondary swirl velocities [4,5] (Fig. 1). As the Reynolds number Re is increased (while the flow remains laminar), the flow field undergoes qualitative changes involving the formation of internal stagnation regions with strong swirl. We use numerical simulations to show how these features originate and evolve as Re and θ are varied, and we show that the physical mechanism for their development is the same as for classical bubble-type vortex breakdown. Finally, we use experiments to demonstrate that the particle capture in two-phase flows is caused by these vortex breakdown features identified in our single-phase simulations.

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“…In particular, the CGL model has proven to be accurate in determining global frequency criteria in both the hnear (Chomaz et al 1991) and nonlinear (Pier et al 1998) regimes. Moreover, because the CGL model roughly captures the streamwise structure of the system eigenfunctions and the variation of the complex frequency of these eigenmodes with Reynolds number, the CGL model has also allowed quantitative predictions of the effects of proportional feedback control on the actual flow system in several previous studies (Monkewitz 1989(Monkewitz , 1993Monkewitz et al 1991;Roussopoulos & Monkewitz 1996).…”

Section: The Ginzburg-landau Model Of Weakly Nonparallel Flowsmentioning

confidence: 99%