Turbulence in pipe flows causes substantial friction and economic losses. The solution to appease the flow through pipelines might be, counterintuitively, to initially enhance turbulent mixing and get laminar flow in return.
Vast networks of pipes crisscross our cities, suburbs and rural areas. These pipe networks are often invisible, buried underground or tucked away in uninhabited areas. Yet they serve as essential circulatory systems that keep our society going, transporting water, oil, natural gas and other goods (Fig. 1a). Operating these networks is expensive, not least because a tremendous amount of energy is required to overcome the frictional losses generated by fluid flow in large-scale pipelines1. Generating this energy costs tens of billions of dollars each year globally. Given the scale of the problem, even a small reduction in friction has the potential to yield substantial economic and environmental benefits. Writing in Nature Physics, Jakob Kühnen and colleagues2 demonstrate an elegant approach for reducing frictional losses in pipes, and hence pumping-power requirements, by as much as 90%.
More specifically, Kühnen et al. have found a general method for suppressing turbulence in pipe flows. Compared to ordered laminar flow, turbulent flow generates, at a given flow rate, significantly more friction at the pipe walls. Ever since Osborne Reynolds’s landmark studies in the late nineteenth century3,4, it has been widely accepted that pipe flows transition from an ordered laminar state to a disordered turbulent state once a dimensionless quantity known as the Reynolds number exceeds a critical value. Most pipelines operate at Reynolds numbers far above this critical threshold. The real question then is how turbulence can be suppressed at these high Reynolds numbers.
It turns out that one must take a step back to move forward. In numerical simulations and experiments, Kühnen et al. show that turbulence can be suppressed over large sections of pipes by initially enhancing turbulent mixing. This counterintuitive measure leads to a more uniform flow across the pipe cross-section, which in turn causes the turbulence to die away (Fig. 1b).
To fully grasp why this procedure works, one must understand what fuels turbulence in the first place. The energetics of turbulent flows are perhaps best explained with a decomposition of the flow field into an average mean component and a fluctuating turbulent component. This decomposition is known as Reynolds-averaging4. In the Reynolds-averaged version of the governing Navier–Stokes equations, the turbulent fluctuations are sustained by energy transfers from the mean flow. This energy transfer arises due to interactions between the turbulent eddies and the gradient in mean velocity. In other words, the variation in the mean flow across the pipe cross-section fuels turbulence. For a more uniform mean flow field, this gradient disappears and the energy transfer pathway from the mean flow to the turbulence is closed off. And without a sustained energy input, the turbulence decays away.
To demonstrate this effect in numerical simulations, Kühnen and co-workers included an artificial forcing function in the governing equations that made the mean velocity profile more uniform. For appropriately chosen forcing, the turbulent fluctuations disappeared completely — the flow relaminarized. At the highest Reynolds numbers tested, the friction coefficient dropped by nearly 95% as a result.
In accompanying laboratory experiments, Kühnen et al. showcased how such turbulence suppression systems could be implemented in practice. To enhance turbulent mixing and create a more uniform mean flow profile, they employed multiple techniques, including stirring using rotors (Fig. 1b), injection of small jets of fluid from the wall and abruptly moving a small section of the pipe wall. In each case, a complete collapse of the turbulent flow was observed downstream of the forcing location. Also, this new laminar state persisted for a long distance, more than a hundred pipe diameters. The ensuing reduction in skin friction led to power savings ranging from 30% to 55% after accounting for the power required for generating the forcing.
The new methodology proposed does have its limitations, of course. For instance, even though the laminar state persists some distance downstream of the forcing location, the flow eventually transitions back to a turbulent state. This means that rotors or jet injectors used to make the mean profile more uniform have to be installed at regular intervals. Moreover, the transition to turbulence in pipe flow — a process that is still not fully understood5,6,7 — becomes increasingly sensitive to small disturbances (such as vibrations or surface imperfections) as the Reynolds number increases. While disturbances can be minimized in laboratory conditions, this is normally not possible in practical applications. Larger ambient disturbances in real-world systems would result in a quicker transition back to a turbulent state, limiting the energetic savings possible.
Active turbulence control for pipe flows is not a new idea. Yet few of the turbulence-control techniques proposed previously have moved beyond proof-of-concept laboratory experiments and simulations, and for good reasons. Many proposed techniques require control elements distributed along the entire pipe, either to suppress disturbances as they arise in laminar flows or to continuously tinker with energetic turbulent flow features. Such control systems are complex to engineer and expensive. The path suggested by Kühnen et al. — letting the flow transition to turbulence naturally and intermittently destabilizing this turbulent flow by changing the mean profile — is inherently simpler. Perhaps we will see something similar in a pipeline before long.
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