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Stability of flows in curved pipes

Time: Thu 2022-09-08 10.30 - 11.30

Location: Faxén, Teknikringen 8

Participating: Valerio Lupi (KTH Engineering Mechanics)

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Abstract: Curved pipes are ubiquitous in many industrial devices, and they are part of important biological apparatus, e.g. blood vessels and respiratory tracts. It is therefore of interest to investigate the stability properties and the route to turbulence of flows in curved pipes. In this talk, we first investigate the modal stability of the flow in a toroidal pipe for curvatures approaching zero, i.e. the straight pipe case, with the purpose of providing further evidence of the infinite linear stability threshold for a straight pipe. We find that the critical Reynolds number increases with decreasing curvature as a power law, confirming that it goes to infinity for a straight pipe.
The flow in a 90°-bend pipe is then studied, through both linear and nonlinear direct numerical simulations. The nonlinear simulations reveal a transition from a steady to an unsteady behaviour for 2500 < Re < 2550. This kind of flow differs from the one in a torus for being spatially developing. Therefore, three-dimensional global stability analysis needs to be carried out to detect the cause of the instability. We find a pair of complex conjugate unstable eigenvalues with symmetric eigenmodes. The structural stability analysis reveals the region on the outer wall of the bend as the one most receptive to spatially localized velocity feedbacks, also known as “wavemaker”, i.e. the core of the instability.