Cédric Beaume

Applied Mathematician

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Transition to turbulence

Many flows encountered in industrial processes are turbulent and in most applications, turbulence is detrimental. Undesired effects include wall friction and drag increase, mixing enhancement and unsteadiness. Controlling these flows to delay transition to turbulence and preserve as much laminar unidirectional flow as possible represents a promising way to boost the profitability of many industries.

Our research deals with simple, yet representative, shear flows such as plane Couette (flow sheared by the opposite motion of parallel walls) and Poiseuille (flow down a circular pipe) flows. In these flows, the desired, laminar flow is stable and, therefore, large enough disturbances are necessary to trigger transition. In practice, the amplitude of these disturbances is not large and simple environmental vibrations such as those induced by a person walking into the room or a car driving by are sufficient to destabilize the system. These disturbances are naturally produced at specific locations, where the system is the most sensitive. Figure 1 shows a spatially localized disturbance in plane Couette flow showing the characteristic spatial structure of such disturbances: the central part of the domain is comprised of non-laminar features, here rolls undulating in the streamwise direction, while the outer parts of the domain contain laminar flow.

Figure 1: Spatially localized state of plane Couette flow triggered by the motion of the top and bottom walls in the streamwise direction, i.e., across the screen. The state is represented by isocontours of the streamwise velocity.

Once a localized disturbance is formed, transition to turbulence occurs by the progressive growth of the non-laminar region generated by the disturbance. Figure 2 shows such transition in plane Couette flow, where a localized disturbance of the type of that shown in figure 1 is initially imposed. The region containing the disturbance grows in time and, despite events where the flow locally relaminarises, ends up filling the domain.

Figure 2: Space-time plot representing the kinetic energy of the disturbance from the laminar flow represented as a function of the spanwise coordinate, z (corresponding to the horizontal axis in figure 1), and of the time, t. Blue (resp. red) indicates zero (resp. maximum) departure from the laminar flow.

The aim of our research is to prevent or aleviate the effects of transition to turbulence. To achieve this, we develop ways to decrease the turbulence contamination rate in situations like that in figure 2 or to simply suppress transition to turbulence by moving the corresponding critical flow rate to larger values.

Collaborations

Anton Pershin (University of Leeds, UK)

Steve Tobias (University of Leeds, UK)

© ~ 2011–2020 ~ Cédric Beaume