Investigation On Vortex Characteristics In Francis Turbine Operating At Part Load Conditions

Hydropower units will undoubtedly undertake a more arduous and urgent task of peak regulation and frequency modulation due to the integration of an increasing amount of renewable energy resources with intermittent nature into the power system.In such a case,hydropower units has to more frequently work at part load conditions in order to meet the load demand of the system In a Francis turbine,precessing vortex rope in draft tube and inter-blade cavitation vortex are two kinds of particular cavitation flowing phenomenon resulting from the unfavorable part-load conditions.Subsequently,the turbines are inevitably subject to the dynamic load imbalance due to the development of vortex structures which introduces more complex spectrum composition to the pressure fluctuation and negatively influence the stability of the turbine.In this study,the aim is to clarify the instability characteristics caused by vortex flowing at part load condition in a Francis turbine.The spatio-temporal evolution of the precessing vortex rope and inter-blade cavitation vortex as well as their influence on the hydraulic vibration characteristics were investigated jointly using of high-precision numerical simulation and experiments.The main findings are presented as follows.(1)Different vortex identification methods including the pressure iso-surface method,Q criterion,?2 criterion,? criterion and Liutex criterion are evaluated for the proper identification of the vortex structures arising from the part-load condition in Francis turbine.The results show that the flow in the draft tube is predominated by the inertia force while the viscous force has a noticeable influence on the flow in the runner.The occurrence of precessing vortex rope in the draft tube is clearly identified using the Q criterion and ?2 criterion.However,the above two methods have inferior performance in the proper identify the inter-blade cavitation vortex structures,which is attributed to the fact that the two criteria tend to overestimate the rate-of-strain.In comparison,the Q criterion and Liutex criterion have more favorable capability to identify the occurrence of both of the precessing vortex rope in the draft tube and the inter-blade cavitation vortex,which contributes to the improved prediction accuracy of the vortex evolution in the turbine.(2)The spatio-temporal evolution of vortex structures in the turbine is investigated by analyzing the vapor volume in the time and frequency domains.The results show that a periodical and low-frequency oscillation of the vapor volume is captured under the operating conditions of precessing vortex rope and inter-blade cavitation vortex.The dominant frequency of vapor volume is 0.3 times of the rotational frequency at the precessing vortex rope condition,and its varies from 1.0 times to 1.5 times of the rotational frequency at the inter-blade cavitation vortex condition.The change of vortex volume is accompanied by the behaviors of elongate and shorten of the precessing vortex rope in the draft tube when it is intensified.The evolution of inter-blade cavitation in the runner presents a dynamic cycle that is associated with the cavitation vortex incipient,development,local collapse and disappearance as well as cavitation vortex re-formation in the blade channels.In the process of vortex evolution,the vortex structure attaches up to the runner hub all the time and the most pronounced collapse of cavitation is observed at the intersection of trailing edge and the runner shroud on the suction sides,which tends to cause observable variations in the flow field and finally results in undesirable hydraulic performance of the turbine.(3)The physical mechanism of vorticity production in hydraulic turbine is investigated through the relative vorticity transport equation that describes the coupling relationship between the vortex and cavitation.The results indicate that the vortex stretching term and Coriolis force term always play a significant role in the vorticity production.Meantime,the distribution of vorticity development in the cavitation region,is governed by the dilatation term and baroclinic torque term.The topology analysis in the runner shows that abrupt change from streamwise to sapnwise occurs in the friction lines on the suction side of the runner blade,which creates a distinct separation line and leads the flow to converge towards the separation line.The analyses suggest that the flow separation on the runner hub induced by negative incident angle at the leading edge of the runner plays the foremost role in the formation of the inter-blade cavitation vortex.(4)The influence of evolution process of vortex structure on the hydraulic vibration of the hydraulic turbine is clarified by time and frequency domain analysis of the pressure fluctuations.The results confirm that the amplitudes of pressure fluctuation in the turbine are significantly magnified due to the patio-temporal evolution of precessing vortex rope in the draft tube and inter-blade cavitation vortex.The inter-blade cavitation not only has a global influence on the distribution of pressure fluctuation in the whole turbine,but also locally amplify the amplitude of pressure fluctuation in the suction side of the runner blade.Furthermore,the enhancement of amplitude in the vicinity of the runner shroud is attributed to the collapse and regeneration at the trailing of the vortex structure,while it is influenced importantly by the flow separation with high strength near the runner hub.(5)The relationship between the transient characteristics of the unsteady pressure fluctuation signals and spatial-temporal evolution of the vortex structure is established combining the one-dimensional theory of cavitation and the three-dimensional turbulence numerical calculation.The results show that the instantaneous pressure fluctuation is proportional to the acceleration of the vapor volume,which firmly evidence that the spatio-temporal evolution of the vortex structure is the fundamental cause of high-amplitude pressure fluctuation.Base on the above conclusions,an counter measurement by air admission from the vaneless space is implemented to alleviate the vortex structure successfully,which improves the flow separation and energy dissipation and prevents excessive amplitudes of pressure fluctuation in the turbine.