The minimal seed for transition to convective turbulence in heated pipe flow
arxiv(2024)
摘要
It is well known that buoyancy suppresses, and can even laminarise turbulence
in upward heated pipe flow. Heat transfer seriously deteriorates in this case.
Through a new DNS model, we confirm that the deteriorated heat transfer within
convective turbulence is related to a lack of near-wall rolls, which leads to a
weak mixing between the flow near the wall and centre of pipe. Having surveyed
the fundamental properties of the system, we perform a nonlinear nonmodal
stability analysis. it is found that, the minimal seed becomes thinner and
closer to the wall, with increase of buoyancy number C. Most importantly, we
show that the critical initial energy required to trigger shear-driven
turbulence keeps increasing, implying that attempts to artificially trigger it
may not be an efficient means to improve heat transfer at larger C. The new
minimal seed, found at C=6, is localised in streamwise direction and is active
in the centre of pipe. To find this branch of optimal, we took advantage of a
window of linear stability. While the nonlinear optimal causes transition to
convective turbulence directly at this and larger C, transition via the linear
instability passes via a travelling wave or periodic orbit solutions. Detailed
analysis of the periodic solution reveals three stages: growth of the unstable
eigenfunction, the formation of streaks, and the decay of streaks due to
suppression of the instability. Flow visualization at C up to 10 also show
similar features, suggesting that convective turbulence is sustained by these
three typical processes.
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