Global stability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>180</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math>-bend pipe flow with mesh adaptivity
Daniele Massaro, Valerio Lupi, Adam Peplinski, Philipp Schlatter
Abstract
We explore the global stability of flow in a U-bend (180${}^{\ensuremath{\circ}}$-bend) and compare the results with those in an elbow (90${}^{\ensuremath{\circ}}$-bend) and toroidal pipes. These findings may have relevance for piping systems as well as bends in blood vessels. We identify a Hopf bifurcation at Re${}_{b}$=2528, which is consistent with the elbow flow but significantly lower than the torus, suggesting different underlying transition mechanisms in developing and periodic geometries. In our numerical approach, we utilize a novel method that employs adaptive meshes individually designed for the base flow, direct and adjoint disturbances, optimized for both efficiency and accuracy.