Global stability of 180-bend pipe flow with mesh adaptivity

The global stability of the flow in a spatially developing 180 degrees -bend pipe with curvature delta = R/Rc = 1/3 is investigated by performing direct numerical simulations to understand the underlying transitional mechanism. A unique application of the adaptive mesh refine-ment 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 approximate to 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, theta approximate to 15 degrees 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 degrees -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 degrees -bend and toroidal pipes by investigating the transition nature in a 180 degrees -bend pipe flow.