Draft tube vortex is one of the main causes of hydraulic instability in hydraulic reaction turbines,in particular Francis turbines.A method of cavitation calculations was proposed to predict the pressure fluctuations induced by draft tube vortices in a model Francis turbine,by solving RANS equations with RNG k-turbulence model and ZGB cavitation model,with modified turbulence viscosity.Three cases with different flow rates at high head were studied.In the study case of part load,two modes of revolutions with the same rotating direction,revolution around the axis of the draft tube cone,and revolution around the core of the vortex rope,can be recognized.The elliptical shaped vortex rope causes anisotropic characteristics of pressure fluctuations around the centerline of the draft tube cone.By analyzing the phase angles of the pressure fluctuations,the role of the vortex rope as an exciter in the oscillating case can be recognized.An analysis of Batchelor instability,i.e.instability in q-vortex like flow structure,has been carried out on the draft tube vortices in these three cases.It can be concluded that the trajectory for study case with part load lies in the region of absolute instability(AI),and it lies in the region of convective instability(CI)for study case with design flow rate.Trajectory for study case with over load lies in the AI region at the inlet of the draft tube,and enters CI region near the end of the elbow.
A set of circulation indices are defined and calculated to characterize monthly mean polar vortex at 10 hPa geopotential height chart in the Northern Hemisphere,including area–(S),intensity–(P) and center position (λc,φc)–indices by use of 1948–2007 NCEP/NCAR 10 hPa monthly height data.These indices series are used to investigate the seasonal variation and interannual anomaly of polar vortex,along with the relations with global warming,ozone anomaly and Arctic Oscillation (AO).The results show that (1) there is anticyclonic (cyclonic) from Jun.to Aug.(from Sep.to Mar.).The change of spring circulation pattern is slower than that of autumn.(2) S can be replaced by P due to the interannual synchronal variations of the intensity and area for polar vortex.The interannual (interdecadal) variations of P are significant in Jan.(Jul.).(3) The anomalies of system center position in Jan.are more evident than that in Jul.(4) The variations of mean temperature at mid-stratosphere in the vicinity of pole zone in Jan.are different from that in Jul.,but they are synchronal with the corresponding P and not significant correlation with the trend of global warming.However,the relationship between P and total O3 in Jul.are obvious.(5) There is so notable correlation between P and AO that P can represent AO.
