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Designing a minimal baffle to destabilise turbulence in pipe flows

Published online by Cambridge University Press:  13 August 2020

Elena Marensi Open the ORCID record for Elena Marensi [Opens in a new window] ,
Zijing Ding Open the ORCID record for Zijing Ding [Opens in a new window] ,
Ashley P. Willis Open the ORCID record for Ashley P. Willis [Opens in a new window]  and
Rich R. Kerswell
Elena Marensi*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, SheffieldS3 7RH, UK
Zijing Ding
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, CambridgeCB3 0WA, UK
Ashley P. Willis
Affiliation:
School of Mathematics and Statistics, University of Sheffield, SheffieldS3 7RH, UK
Rich R. Kerswell
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, CambridgeCB3 0WA, UK
*
†Email address for correspondence: elena.marensi@ist.ac.at
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Abstract

Motivated by the results of recent experiments (Kühnen et al., Flow Turbul. Combust., vol. 100, 2018, pp. 919–943), we consider the problem of designing a baffle (an obstacle to the flow) to relaminarise turbulence in pipe flows. Modelling the baffle as a spatial distribution of linear drag ${\boldsymbol {F}}(\boldsymbol {x},t)=-\chi (\boldsymbol {x})\boldsymbol {u}_{tot}(\boldsymbol {x},t)$ within the flow ($\boldsymbol {u}_{tot}$ is the total velocity field and $\chi \ge 0$ a scalar field), two different optimisation problems are considered to design $\chi$ at a Reynolds number $Re=3000$. In the first, the smallest baffle defined in terms of a $L_1$ norm of $\chi$ is sought which minimises the viscous dissipation rate of the flow. In the second, a baffle which minimises the total energy consumption of the flow is treated. Both problems indicate that the baffle should be axisymmetric and radially localised near the pipe wall, but struggle to predict the optimal streamwise extent. A manual search finds an optimal baffle one radius long which is then used to study how the amplitude for relaminarisation varies with $Re$ up to $15\,000$. Large stress reduction is found at the pipe wall, but at the expense of an increased pressure drop across the baffle. Estimates are then made of the break-even point downstream of the baffle where the stress reduction at the wall due to the relaminarised flow compensates for the extra drag produced by the baffle.

JFM classification

Instability: Transition to turbulence Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A31
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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