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Vortex breakdown in a hydropower turbine draft tube swirling jet

Artur Gesla and Eunok Yim

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Phys. Rev. Fluids 11, 094701 – Published 3 September, 2026

DOI: https://doi.org/10.1103/38kd-t5ym

Abstract

The swirling flow in a Francis type hydropower turbine is known to be susceptible to the formation of a large helical structure, commonly referred to as a vortex rope. This vortex rope can be interpreted as an unstable mode associated with vortex breakdown. This perspective is adopted here in a simplified laminar flow setting. The helical vortex rope mode is shown to bifurcate supercritically from an axisymmetric base flow in a Hopf bifurcation within a turbine draft tube. When wall friction effects are neglected, a large recirculation region at the axis can form and a range of subcritical solutions is identified for a flow regime corresponding to partial load of the turbine. The existence of these subcritical solutions promotes the emergence of a hysteresis loop. We further describe a regular dynamics of a formation of recirculation bubble at the axis and its destruction due to the emergence of a helical vortex rope at its periphery. Increasing the axial flow discharge towards the regime corresponding to nominal turbine load leads to an unfolding of the steady solutions branch in a transcritical bifurcation. This bifurcation takes place at finite Reynolds number and complements existing evidence of transcritical bifurcation of the swirling jet flows, previously reported in the inviscid limit.

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Outline

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Phys. Rev. Fluids 11, 094701– Published 3 September, 2026
  • Received 20 February 2026
  • Accepted 24 July 2026
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