Formation of Secondary Vortices in Turbulent Square-Duct Flow

Bottaro, Alessandro; Soueid, Houssam; Galletti, Bernardo

doi:10.2514/1.17327

Cited by 30 publications

(18 citation statements)

References 32 publications

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“…The main peak scales on external units with an optimal spanwise wavelength λ z ∼ 3 h, while the secondary peak, which scales in inner (wall) units, is found at λ + = 100 and is associated with typical near wall streaks. To explain the formation of secondary vortices in a turbulent square duct Bottaro, Souied & Galletti (2006) have computed the linear optimals, using a mixing length model for the eddy viscosity.…”

Section: Introductionmentioning

confidence: 99%

Optimal transient growth and very large–scale structures in turbulent boundary layers

2009

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We are interested in the optimal energy growth of perturbations sustained by a zero pressure gradient turbulent boundary layer. We use the mean flow proposed by Monkewitz et al. (2007), the turbulence dynamics being modeled by an eddy viscosity added in the disturbance equations following the approach of delÁlamo and Jiménez (2006), or in the turbulent channel flow case. Although all the considered turbulent mean profiles are linearly stable, they support transient energy growths due to the non-normality of the operator. We find that the most amplified perturbations are streamwise uniform and correspond to streamwise vortices evolving into streamwise streaks.Consistently with the study of delÁlamo and Jiménez (2006), we find that two distinct peaks of the optimal growth exist for sufficiently large Reynolds numbers: a primary one scaling in outer units and a secondary one scaling in wall units. The optimal structures associated with the peak scaling in wall units correspond well to the most probable streaks observed in the buffer layer and their moderate energy growth is independent of the Reynolds number. The energy growth associated with the peak scaling in outer units is larger than that of the inner peak. The optimal perturbations associated with this primary peak consist in very large-scale structures with a spanwise wavelength of the order of 8 δ.Since such very large-scale structures have not been observed yet in turbulent shear flows, preliminary experiments aiming at forcing such structures and studying their growth have been conducted. We find that large-scale turbulent streaks can be forced using well-shaped roughness elements embedded in the boundary layer. Their amplitude can reach about 13.5% of the free-stream velocity before decaying.

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Section: Introductionmentioning

confidence: 99%

Optimal transient growth and very large–scale structures in turbulent boundary layers

2009

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“…The transient growth of disturbance energy and the subsequent formation of streamwise streaks was referred to as a likely early stage of transition in square duct flow. A subsequent attempt to link the algebraic growth to the formation of the large scale turbulent vortices met with mixed success (Bottaro et al 21 ).…”

Section: Introductionmentioning

confidence: 99%

Coherent flow states in a square duct

et al. 2008

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The flow in a square duct is considered. Finite amplitude approximate travelling wave solutions, obtained using the self-sustaining-process approach introduced by Waleffe [Phys. Fluids 9, 883 (1997)], are obtained at low to moderate Reynolds number and used as initial conditions in direct numerical simulations. The ensuing dynamics is analysed in a suitably defined phase space. Only one among the travelling wave solutions found is capable to survive for long time, with the flow trajectory forming quasi-regular loops in phase space. Eventually, also this trajectory escapes along the manifold of a chaotic saddle and relaminarisation ensues.

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“…Countless studies have been devoted to the formation of secondary vortices in the turbulent regime (see Gavrilakis (1992) for a direct numerical simulation approach) and, more recently, an attempt has been made to link the appearance of such large-scale coherent states to the vortices appearing during the initial, optimal transient phase of disturbance growth (Galletti & Bottaro (2004); Bottaro et al (2006)). The longitudinal laminar flow velocity component has an analytic form U (y, z) available, for example, in Tatsumi & Yoshimura (1990), with y and z cross-stream axes.…”

Section: Model Configurationmentioning

confidence: 99%

Transition to turbulence in duct flow

2008

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The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path to turbulence. Initially the so-called 'linear optimal perturbation problem' is formulated and solved, yielding optimal disturbances in the form of longitudinal vortices. Such optimals, however, fail to elicit a significant response from the system in the nonlinear regime. Thus, streamwise-inhomogeneous, sub-optimal disturbances are focussed upon; nonlinear quadratic interactions are immediately evoked by such initial perturbations and an unstable streamwise-homogeneous large amplitude mode rapidly emerges. The subsequent evolution of the flow, at a value of the Reynolds number at the edge between fully developed turbulence and relaminarization, shows the alternance of patterns with two pairs of large scale vortices near opposing parallel walls. Such edge states bear a resemblance to optimal disturbances.

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Formation of Secondary Vortices in Turbulent Square-Duct Flow

Cited by 30 publications

References 32 publications

Optimal transient growth and very large–scale structures in turbulent boundary layers

Optimal transient growth and very large–scale structures in turbulent boundary layers

Coherent flow states in a square duct

Transition to turbulence in duct flow

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