Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation

Lieu, Binh K.; Moarref, Rashad; Jovanović, Mihailo R.

doi:10.1017/s002211201000340x

Cited by 57 publications

(72 citation statements)

References 20 publications

(36 reference statements)

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“…Despite initial successes of model-based feedback (Joshi et al 1997;Cortelezzi & Speyer 1998;Bewley & Liu 1998;Lee et al 2001;Högberg et al 2003a,b;Kim & Bewley 2007) and sensor-free (Fransson et al 2006;Jovanović 2008;Lieu et al 2010;Moarref & Jovanović 2012) control at low-Reynolds-numbers in wall-bounded flows many important challenges remain. One source of the problem is that, typically, sensing and actuation of the flow field is restricted to the surface of the domain.…”

Section: Model-based Flow Controlmentioning

confidence: 99%

Colour of turbulence

2017

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In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for colored-intime forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that colored-in-time excitation of the Navier-Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization, and control design.

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Section: Model-based Flow Controlmentioning

confidence: 99%

Colour of turbulence

2017

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“…A similar perturbation approach was successfully used in a non-modal study quantifying the effect of streamwise travelling waves on the transient energy growth in a channel flow Lieu et al 2010).…”

Section: Introductionmentioning

confidence: 99%

Second-order perturbation of global modes and implications for spanwise wavy actuation

et al. 2014

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Sensitivity analysis has successfully located the most efficient regions in which to apply passive control in many globally unstable flows. As is shown here and in previous studies, the standard sensitivity analysis, which is linear (1 st order) with respect to the actuation amplitude, predicts that steady spanwise wavy alternating actuation/modification has no effect on the stability of planar flows, because the eigenvalue change integrates to zero in the spanwise direction. In experiments however, spanwise wavy modification has been shown to stabilize the flow behind a cylinder quite efficiently.In this paper, we generalize sensitivity analysis by examining the eigenvalue drift (including stabilization/destabilization) up to 2 nd order in the perturbation, and show how the 2 nd order eigenvalue changes can be computed numerically by overlapping the adjoint eigenfunction with the 1 st order global eigenmode correction, shown here for the first time. We confirm the prediction against a direct computation, showing that the eigenvalue drift due to a spanwise wavy base flow modification is of 2 nd order. Further analysis reveals that the 2 nd order change in the eigenvalue arises through a resonance of the original (2D) eigenmode with other unperturbed eigenmodes that have the same spanwise wavelength as the base flow modification. The eigenvalue drift due to each mode interaction is inversely proportional to the distance between the eigenvalues of the modes (which is similar to resonance), but also depends on mutual overlap of direct and adjoint eigenfunctions (which is similar to pseudoresonance). By this argument, and by calculating the most sensitive regions identified by our analysis, we explain why an in-phase actuation/modification is better than an out-of-phase actuation for control of wake flows by spanwise wavy suction and blowing. We also explain why wavelengths several times longer than the wake thickness are more efficient than short wavelengths.

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“…Hence, in practice most flows are turbulent at sufficiently large Re. While the stability of laminar flow has been studied in great detail, little attention has been paid to the susceptibility of turbulence, the general assumption being that once turbulence is established it is stable.Many turbulence control strategies have been put forward to reduce the drag encountered in shear flows [7][8][9][10][11][12][13][14][15][16][17] . Recent strategies employ feedback mechanisms to actively counter selected velocity components or vortices.…”

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confidence: 99%

Destabilizing turbulence in pipe flow

et al. 2018

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Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities [1][2][3] , so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 90%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. Since neither the Reynolds number nor the shear stresses decrease (the latter often increase), these measures are not indicative of turbulence collapse. Instead, an amplification mechanism 4,5 measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.Flows through pipes and hydraulic networks are generally turbulent and the friction losses encountered in these flows are responsible for approximately 10% of the global electric energy consumption. Here turbulence causes a severe drag increase and consequently much larger forces are needed to maintain desired flow rates. In pipes, both laminar and turbulent states are stable (the former is believed to be linearly stable for all Reynolds number (Re) values; the latter is stable if Re > 2, 040 (ref. 6 )), but with increasing speed the laminar state becomes more and more susceptible to small disturbances. Hence, in practice most flows are turbulent at sufficiently large Re. While the stability of laminar flow has been studied in great detail, little attention has been paid to the susceptibility of turbulence, the general assumption being that once turbulence is established it is stable.Many turbulence control strategies have been put forward to reduce the drag encountered in shear flows [7][8][9][10][11][12][13][14][15][16][17] . Recent strategies employ feedback mechanisms to actively counter selected velocity components or vortices. Such methods usually require knowledge of the full turbulent velocity field. In computer simulations 7,8 , it could be demonstrated that under these ideal conditions, flows at a low Re number can even be relaminarized. In experiments, the required detailed manipulation of the time-dependent velocity field is, however, currently impossible to achieve. Other studies employ passive (for example, riblets) or active (oscillations or excitation of travelling waves) methods to interfere with the near-wall turbulence creation. Typically here drag reduction of 10 to 40% has been reported, but often the control cost is substantially higher than the gain, or a net gain can be achieved only in a narrow Re number regime.Instead of attempting to control or counter certain components of the complex fluctuating flow fields, we will show in the following that by appropriately dist...

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Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation

Cited by 57 publications

References 20 publications

Colour of turbulence

Colour of turbulence

Second-order perturbation of global modes and implications for spanwise wavy actuation

Destabilizing turbulence in pipe flow

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