Destabilizing turbulence in pipe flow

Abstract

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...

Upper edge of chaos and the energetics of transition in pipe flow

“…Furthermore, such perturbations may provide insights for control applications in order to eliminate turbulence. In agreement with the recent experimental observations of Kühnen et al [23], we find that highly-turbulent initial conditions with flat axial velocity profiles could lead to a complete laminarization. Via edge-tracking, we show that these initial conditions are indeed on the laminarizing side of the edge state's stable manifold.…”

“…Furthermore, ref. [23] measured transient growth due to the non-normality of the linearized Navier-Stokes operator assuming the mean profile to be the base flow. They found that the transient growth was substantially suppressed when the profile was flattened.…”

“…Marensi et al [21] showed that flattening the base profile in a pipe flow not only destabilizes the turbulence, as in the experiment of Kühnen et al [23], but it also enhances the nonlinear stability of the laminar flow. Minimal seed calculations were performed with a flattened base profile [23], namely…”

“…Recent experiments and numerical simulations by Kühnen et al [23] showed that flattening the flow profile by various control methods leads to the complete decay of turbulence for Reynolds numbers up to 40000. The main idea behind this was to disrupt the energy production in such a way that the turbulence cannot sustain itself.…”

“…The main idea behind this was to disrupt the energy production in such a way that the turbulence cannot sustain itself. Kühnen et al [23] attributed this to the linear part of the Navier-Stokes equations and used transient growth around a mean profile as a proxy for measuring this effect. Indeed, they found that the complete relaminarization is observed when the transient growth of a mean profile was below a certain level.…”