Vortex breakdown in a hydro turbine draft tube swirling jet
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912915743834112 |
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| author | Gesla, Artur Yim, Eunok |
| author_facet | Gesla, Artur Yim, Eunok |
| contents | 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 baseflow 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 only in the inviscid limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18278 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vortex breakdown in a hydro turbine draft tube swirling jet Gesla, Artur Yim, Eunok Fluid Dynamics 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 baseflow 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 only in the inviscid limit. |
| title | Vortex breakdown in a hydro turbine draft tube swirling jet |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2602.18278 |