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The paper considers a two-dimensional flow in a channel, which consists ofstraight inlet and outlet branches and a circularly 90-degree curved bend. Anincompressible viscous fluid flows through the elbow under the action of aconstant pressure gradient between the inlet and outlet. Navier-Stokesequations were solved numerically using a high-fidelity spectral/hp elementmethod. In a range of Reynolds numbers, an adaptive selective frequency dumpingmethod was used to get a steady-state flow. It was found that three separationbubbles and vortex shedding can exist in the bend. The modal stability of two-and three-dimensional perturbations was investigated. Critical Reynolds numberof the two-dimensional disturbances was found as extrapolation by lowerReynolds number results. It is much greater than three-dimensional one, but thetwo-dimensional flow could subcritically unstable with respect to the imposedsmall-amplitude white noise. For three-dimensional perturbations, thedependence of the critical Reynolds numbers on the bending radius is obtained.For a case of a moderate bending radius the neutral curve is provided andeigenfunctions are studied in detail: three-dimensional instability can becaused by periodic or monotonically growing mode, these unstable modes regardto the recirculation bubbles that occur after the bend.

Linear stability of flow in a 90-degree bend