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Global stability of 180∘-bend pipe flow with mesh adaptivity

Daniele Massaro1,*, Valerio Lupi1, Adam Peplinski1, and Philipp Schlatter1,2

  • 1SimEx/FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden
  • 2Institute of Fluid Mechanics (LSTM), Friedrich–Alexander–Universität Erlangen–Nürnberg (FAU), Erlangen 91058, Germany

  • *dmassaro@kth.se
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Phys. Rev. Fluids 8, 113903 – Published 20 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.113903

Abstract

The global stability of the flow in a spatially developing 180∘-bend pipe with curvature δ=R/Rc=1/3 is investigated by performing direct numerical simulations to understand the underlying transitional mechanism. A unique application of the adaptive mesh refinement technique is used during the stability analysis for minimizing the interpolation and quadrature errors. Independent meshes are created for the direct and adjoint solutions, as well as for the base flow extracted via selective frequency damping. The spectrum of the linearized Navier-Stokes operator reveals a pair of complex conjugate eigenvalues, with frequency f≈0.233. Therefore, the transition is attributed to a Hopf bifurcation that takes place at Reb,cr=2528. A structural sensitivity analysis is performed by extracting the wavemaker. We identify the primary source of instability located on the outer wall, θ≈15∘ downstream of the bend inlet. This region corresponds to the separation bubble on the outer wall. We thus conclude that the instability is caused by the strong shear resulting from the backflow, similar to the 90∘-bend pipe flow. We believe that understanding the stability mechanism and characterizing the base flow in bent pipes is crucial for studying various biological flows, like blood vessels. Hence, this paper aims to close the knowledge gap between a 90∘-bend and toroidal pipes by investigating the transition nature in a 180∘-bend pipe flow.

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Phys. Rev. Fluids 8, 113903– Published 20 November, 2023
  • Received 9 June 2023
  • Accepted 25 October 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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