| Tip-leakage vortex(TLV)cavitation is a common phenomenon in axial turbines.It will cause a decline in the performance of the hydraulic machinery,and accompanied with severe erosion and sharp rise in noise and vibration,which seriously impact security of the hydraulic machinery and the whole system.Thus,this paper combines the methodology of numerical simulation,experiment and theoretical analysis,aiming to solve the key scientific problems of TLV cavitating flow in the current generated by NACA0009 hydrofoil,which systematically investigates TLV evolution,characteristics of the TLV cavitating flow and methods to control TLV cavitation.The main contents and innovative results of this paper are as follows:(1)A Euler-Lagrangian cavitation model based on Rayleigh-Plesset equation considering the effect of nuclei is proposed.The model tracks the non-condensable gas in the liquid with the Discrete Phase Model(DPM),to obtain the distribution of non-condensable gas in the flow field.It is found that there is a significant increase in gas concentration near the vortex core.A new Eulerian-Lagrange cavitation model is obtained by quantitatively evaluating the influence of non-condensable gas enrichment in the vortex core on TLV cavitation process in the interphase mass transport equation,based on the equation of state for idea gas and law of partial pressure.The results show that the new cavitation model can predict the tip vortex cavitation and tip-leakage vortex(TLV)cavitation well,which will provide strong support for numerical research on this kind of flow.(2)Detailed analysis is conducted on the evolution characteristics and flow mechanism of TLV without cavitation.The results show that:(1)The gap size will have a significant impact on the stages of spatial evolution of TLV.When the gap is large,the influence of the gap wall is mild,in which case,the entire evolution of TLV can be divided into growth stage,fusion stage and viscous dissipation stage in sequence.As the gap gradually decreases,the influence of the wall starts to appear.The entire evolution stage can be divided into growth stage,fusion stage and dissipation stage due to the induced vortex.As the gap is further reduced,the influence of the gap wall is more significant.The induced vortex becomes more obvious in the gap region,and the entire evolution stage can be divided into growth stage,fusion stage,dissipation stage due to the induced vortex and dissipation stage due to friction of the gap wall;(2)Radius of the TLV is affected by its strength and the thickness of the hydrofoil boundary layer.Based on the experimental and numerical results,this paper analyzes the variation law of the TLV radius in detail,and proposes a new TLV radius prediction formula considering the characteristics of the vortex fusion process.This formula takes the contribution of vortex strength into account for the first time after considering the influence of the boundary layer on the vortex radius,which reflects the influencing factors of the TLV radius more comprehensively;(3)The strength of TLV is a key influencing factor for TLV cavitation.For this reason,this paper directly proceeds from Newton's second law and obtains the essential relationship between the ideal strength of TLV and the hydrofoil load change in the spanwise direction.The impact of different evolvement stages of TLV on its strength for different gap sizes is analyzed in detail,and a semi-empirical prediction framework for TLV strength is constructed.The TLV intensity of the simulation cases in the current paper is successfully forecasted,which provides an important reference for the prediction of TLV intensity in the future;(4)This paper also investigates the variation pattern of nuclei concentration in the TLV core.It is shown that there is obvious enrichment of non-condensable gas in the TLV core,and the concentration is highly correlated with the intensity of TLV.The greater the intensity of TLV,the larger concentration of non-condensable gas in the TLV core.(3)Considering all above,?v,a new cavitation number for TLV cavitation,is proposed in the present paper.Conventional cavitation number does not consider the influence of vortex strength,radius and non-condensable gas on vortex cavitation.On the basis of the research above,a new cavitation number?v is proposed in the present paper,which considers the influence of vortex strength,radius and non-condensable gas on vortex cavitation.The comparison with the experimental results shows that the new cavitation number can reflect the flow state of vortex cavitation more accurately.Based on?v,the interaction mechanism between cavitation and local flow in the tip-leakage vortex flow with three typical gap sizes is deeply analyzed.The results indicate that:(1)After cavitaton occurs,the intensity of TLV is mainly affected by the evolution behavior of sheet cavitation,while TLV cavitation has little effect on its own strength.Generally speaking,the smaller the gap is,the more unstable the sheet cavitation is,and the strength of TLV also presents corresponding quasi-periodic fluctuation.As the tip clearance enlarges,the strength of sheet cavitation gradually decreases with its instability reduced,and the intensity of TLV gradually returns to the level without cavitation,its fluctuation also decreases;(2)Cavitation has a significant influence on the nuclei distribution in the vortex core,and its influence depends on the spatial stability of TLV and the intensity of TLV cavitation after cavitation occurs.The more stable TLV itself is,the lower the intensity of TLV cavitation is,the less the effect of cavitation on nuclei distribution in the vortex core is;otherwise,cavitation is likely to significantly change the nuclei concentration distribution in the vortex core;(3)Cavitation has a significant influence on the radius of TLV.After cavitation occurs,the radius of TLV increases to a certain extent,and a“rigid body rotation”tangential velocity distribution is formed in the periphery of cavitation region,which is mainly caused by the expansion process induced by cavitation growth and the viscous effect of flow;(4)The occurrence of cavitation significantly changes the distribution of local vorticity and turbulence kinetic energy.The analysis based on the vorticity transport equation shows that the cavitation growth process is the reason for the continuous decrease of vorticity in the cavitating vortex;the analysis based on the turbulence kinetic energy transport equation shows that the transport term of turbulence kinetic energy is the main reason for the high turbulence kinetic energy in the cavitating vortex;(5)The boundary layer can weaken the intensity of TLV cavitation to a certain extent.The thicker the boundary layer is,the more significant its inhibition on TLV cavitation is.The research indicates that increasing the boundary layer thickness can weaken the tip-separation vortex(TSV),thus inhibiting the clearance cavitation to some extent.(4)A passive TLV cavitation suppression device,overhanging grooves cavitation suppressor,which can produce ideal effects in a large clearance range is proposed,and its specific suppression mechanism is illustrated.The results indicate that the device well combines the advantages of anti-cavitation lip and traditional groove treatment,thus producing ideal suppression effect on TLV cavitation in a large clearance range.On this basis,the key parameters are optimized by means of experiments in the present paper.Based on the numerical results,the mechanism of suppressing TLV cavitation is further analyzed.The results show that for small clearance,the device can significantly accelerate the dissipation of TSV and weaken the circulation of TLV,thus inhibiting TLV cavitation;for middle and large clearances,the device will hinder the fusion process of TLV and TSV,and increase the radius of TLV after fusion,thereby reducing the pressure drop at the vortex center and inhibiting TLV cavitation.The overhanging grooves device can effectively inhibit TLV cavitation under different tip clearance sizes,which is a potential suppression device for TLV cavitation in engineering practice. |
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