Experiments on the stability of streamwise streaks in plane Poiseuille flow

Elofsson, Per; Kawakami, Mitsuyoshi; Alfredsson, P. Henrik

doi:10.1063/1.869962

Cited by 68 publications

(45 citation statements)

References 28 publications

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“…[4][5][6][7] These studies confirmed that the instability is of inflectional type and that the dominating instability appears as spanwise ͑sinuous͒ oscillations of the streaks. For zero-pressure-gradient boundary layers, the spatial response of a single low-speed streak submitted to a time-harmonic excitation of sinuous or varicose type has been more recently examined experimentally by Asai et al 8 The growth of the sinuous mode was observed to evolve into a train of quasi-streamwise vortices with vorticity of alternate sign.…”

Section: Introductionsupporting

confidence: 67%

“…17 and 18, presented at the European Fluid Mechanics Conference 6 ͑EFMC6͒ in June of 2006, reveals that the streak amplitude is not the relevant parameter for the breakdown: Streaks of the same amplitude do not always undergo breakdown. Linear stability analysis predicted threshold streak amplitudes of 35% in the plane channel 6 and 26% in boundary-layer flow, 9 values considered higher than those one would expect from experiments. However, Waleffe 25 showed the subcritical nature of streak instability in channel flows.…”

Section: Introductionmentioning

confidence: 90%

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Streak interactions and breakdown in boundary layer flows

Brandt

Lange

2008

Physics of Fluids

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The objective of this paper is to show that the interaction of streamwise velocity streaks of finite length can lead to turbulent breakdown in the flat-plate boundary layer flow. The work is motivated by previous numerical and experimental studies of transitional flows where the high-frequency oscillations leading to turbulence are seen to form in the region of strongest shear induced by streaks in relative motion. Therefore, a model for the interaction of steady and unsteady ͑i.e., slowly moving in the spanwise direction͒ spanwise periodic streaks is proposed. The interaction of two subsequent streaks is investigated for varying collision parameters. In particular, the relative spanwise position and angle are considered. The results show that the interaction is able to produce both a symmetric and asymmetric breakdown without the need for additional random noise from the main stream. Velocity structures characteristic of both scenarios are analyzed. Hairpin and ⌳ vortices are found in the case of symmetric collision between a low-speed region and an incoming high-speed streak, when a region of strong wall-normal shear is induced. Alternatively, when the incoming high-momentum fluid is misaligned with the low-speed streak in front, single quasi-streamwise vortices are identified. Despite the different symmetry at the breakdown, the detrimental interaction involves for both cases the tail of a low-speed region and the head of a high-speed streak. Further, the breakdown appears in both scenarios as an instability of three-dimensional shear layers formed between the two streaks. The streak interaction scenario is suggested to be of relevance for turbulence production in wall-bounded flows.

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Section: Introductionsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 90%

Streak interactions and breakdown in boundary layer flows

Brandt

Lange

2008

Physics of Fluids

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“…In particular, it has been observed that streaks of high amplitude become susceptible to secondary inflectional instability leading to breakdown to turbulence. [23][24][25] The aim of this paper is therefore to investigate for the first time the non-modal stability of particle-laden channel flows for different particle mass fraction and relaxation time. Although modal stability analysis shows a stabilization of the flow in the presence of particles, an effective delay of the turbulent onset in channel flows requires also damping of non-modal growth mechanisms.…”

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confidence: 99%

Modal and non-modal stability of particle-laden channel flow

2011

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Modal and non-modal linear stability analysis of channel flow with a dilute particle suspension is presented where particles are assumed to be solid, spherical, and heavy. The two-way coupling between particle and fluid flow is therefore modeled by the Stokes drag only. The results are presented as function of the particle relaxation time and mass fraction. First, we consider exponentially growing perturbations and extend previous findings showing the potential for a significant increase of the critical Reynolds number. The largest stabilization is observed when the ratio between the particle relaxation time and the oscillation period of the wave is of order one. By examining the energy budget, we show that this stabilization is due to the increase of the dissipation caused by the Stokes drag. The observed stabilization has led to the hypothesis that dusty flows can be more stable. However, transition to turbulence is most often subcritical in canonical shear flows where non-modal growth mechanisms are responsible for the initial growth of external disturbances. The non-modal analysis of the particle-laden flow, presented here for the first time, reveals that the transient energy growth is, surprisingly, increased by the presence of particles, in proportion to the particle mass fraction. The generation of streamwise streaks via the lift-up mechanism is still the dominant disturbance-growth mechanism in the particle laden flow; the length scales of the most dangerous disturbances are unaffected, while the initial disturbance growth can be delayed. These results are explained in terms of a dimensionless parameter relating the particle relaxation time to the time scale of the instability. The presence of a dilute solid phase therefore may not always work as a flow-control strategy for maintaining the flow as laminar. Despite the stabilizing effect on modal instabilities, non-modal mechanisms are still strong in internal flows seeded with heavy particles. Our results indicate that the initial stages of transition in dilute suspensions of small particles are similar to the stages in a single phase flow.

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“…Brandt et al (2003) found that the instability of optimal streaks is convective and that the streaks behave as amplifiers of external noise. The secondary instabilities and the associated modes can be calculated through linear Floquet analyses of the streak base flow extracted from DNS or experiential results (Elofsson, Kawakami & Alfredsson 1999;Ricco, Luo & Wu 2011).…”

Section: Secondary Instabilities Of Streaksmentioning

confidence: 99%

Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade

et al. 2017

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Flow past a NACA 65 blade at chord-based Reynolds number 138 500 is studied using stability analysis, generalized (spatially weighted) transient growth analysis and direct numerical simulations (DNS). The mechanisms of transition on various sections of the blade observed in previous work by Zaki et al. (J. Fluid Mech., vol. 665, 2010, pp. 57-98) are examined, with a focus on the pressure side around the leading edge. In this region, the linearly most energetic perturbation has spanwise wavenumber 40π (five boundary-layer thicknesses) and is tilted against the mean shear to take advantage of the Orr mechanism. In a DNS, the nonlinear development of this optimal perturbation induces Λ structures, which are further stretched to hairpin vortices before breaking down to turbulence. At higher spanwise wavenumber, e.g. 120π, a free-stream optimal perturbation is obtained upstream of the leading edge, in the form of streamwise vortices. During its nonlinear evolution, this optimal perturbation tilts the mean shear and generates spanwise periodic high-and low-speed streaks. Then through a nonlinear lift-up mechanism, the low-speed streaks are lifted above the high-speed ones. This layout of streaks generates a mean shear with two inflectional points and activates secondary instabilities, namely inner and outer instabilities previously reported in the literature.

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Experiments on the stability of streamwise streaks in plane Poiseuille flow

Cited by 68 publications

References 28 publications

Streak interactions and breakdown in boundary layer flows

Streak interactions and breakdown in boundary layer flows

Modal and non-modal stability of particle-laden channel flow

Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade

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