Abstract
For a water diversion hydropower system with a flat ceiling tail tunnel with high elevation, during transient states with relatively low tail water levels, free-surface-pressurized flow inevitably appears and its transient characteristics have obvious effects on the system’s operating stability. Using Newton–Raphson linearization in the characteristic implicit format for modeling of the free-surface-pressurized flow in the tail tunnel, the mathematical models for necessary boundary conditions were derived and linear algebraic equations with a band coefficient matrix were grouped for further transient simulation. Then, a unified mathematical model was established for hydraulic transient analysis of the hydropower system with free-surface-pressurized flow. Combined with experimental research and numerical simulation, the wave speed for the free-surface-pressurized flow was experimentally analyzed for further correctness in the unified model, and by comparative analysis the hydraulic characteristics of the free-surface-pressurized flow in the flat ceiling tail tunnel were investigated. It was found that the derived mathematical model can basically represent water behaviors in the water-surface-pressurized flow, the wave speed for the mixed water-surface-pressurized flow can be set to approximately 50m/s, and with this correctness the numerical results are in good agreement with the experimental results. Therefore, the obtained mathematical model combined with an experimental wave speed or a reference wave speed of 50 m/s for the free-surface-pressurized flow is preferable during the design stage of the hydropower system.
Highlights
FFoorr ththeededveevloeplompemnetnotf aowf aaterwdaivteerrsidoinvehrysdioronpohwyderrosptaotiwonerwsitthataionnunwdietrhgroaunndunpdoweregrrhoouunsde, paopwraecrthicoaulstey,pae pofratactilictaulntnyepleisoifnttraoildtuucnendeilnitso itnhteroladyuocuetddienstiognthoef alalyaorguet-sdceasliegtnaiol fsyastlaemrg.e-Insctahleisttaaiill ssyysstteemm., iInn otrhdisertatoilrseydsutecemt,hientaoirldtuernntoel’rsedexuccaevathtieontaailndturnoncekl’ms aesxscastvaabtiiloitny,atnheddriovcekrsmioanstsusntnaebliltihtya,t tohreigdinivaellrysisoenrvteudnndeulrtinhgatcoornisgtirnuacltliyonseirsvreeddedsuigrinnegdcaonndstrreuccotniosntruisctreeddeassigthneeddoawnndsrtreecaomnsptraurcttoedf tahse tthaeil dtuonwnnesltorefatmhephayrdtroofptohwe etarisl ytustnenmel(soefethFeighuyrder1o)p. ower system
If the tail water level is obviously lower than the top elevation of the tail tunnel outlet, the flat ceiling tail tunnel is always in free channel flow under both steady and transient states, and a unique interface between pressurized flow and free surface flow is located along the connecting tunnel
As the tail water level is slightly lower than the top elevation of tail tunnel outlet, the interface between the pressurized flow and the free surface flow is located along the flat ceiling tail tunnel under steady states, and possible mixed free-surface-pressurized flow will inevitably happen under transient states, with one or more air masses existing along the crown of the tail tunnel in some cases
Summary
FFoorr ththeededveevloeplompemnetnotf aowf aaterwdaivteerrsidoinvehrysdioronpohwyderrosptaotiwonerwsitthataionnunwdietrhgroaunndunpdoweregrrhoouunsde, paopwraecrthicoaulstey,pae pofratactilictaulntnyepleisoifnttraoildtuucnendeilnitso itnhteroladyuocuetddienstiognthoef alalyaorguet-sdceasliegtnaiol fsyastlaemrg.e-Insctahleisttaaiill ssyysstteemm., iInn otrhdisertatoilrseydsutecemt,hientaoirldtuernntoel’rsedexuccaevathtieontaailndturnoncekl’ms aesxscastvaabtiiloitny,atnheddriovcekrsmioanstsusntnaebliltihtya,t tohreigdinivaellrysisoenrvteudnndeulrtinhgatcoornisgtirnuacltliyonseirsvreeddedsuigrinnegdcaonndstrreuccotniosntruisctreeddeassigthneeddoawnndsrtreecaomnsptraurcttoedf tahse tthaeil dtuonwnnesltorefatmhephayrdtroofptohwe etarisl ytustnenmel(soefethFeighuyrder1o)p. ower system (see Figure 1). If the tail water level is obviously lower than the top elevation of the tail tunnel outlet, the flat ceiling tail tunnel is always in free channel flow under both steady and transient states, and a unique interface between pressurized flow and free surface flow is located along the connecting tunnel. As the tail water level is slightly lower than the top elevation of tail tunnel outlet, the interface between the pressurized flow and the free surface flow is located along the flat ceiling tail tunnel under steady states, and possible mixed free-surface-pressurized flow will inevitably happen under transient states, with one or more air masses existing along the crown of the tail tunnel in some cases. It is difficult to accurately simulate and clearly understand the transient characteristics of the tail system under these complex flow patterns or to clarify their effect on the hydropower system’s operating stability
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