The Pelton turbine has been widely used to develop high-head water resources with sediments because of its advantages in life cycle costs.When a flood or monsoon season occurs,the sediment concentration in the river i...The Pelton turbine has been widely used to develop high-head water resources with sediments because of its advantages in life cycle costs.When a flood or monsoon season occurs,the sediment concentration in the river increases suddenly,causing severe erosion to the nozzle,needle,and runner of Pelton turbines.After decades of development,researchers have developed practical engineering experience to reduce the sediment concentration of the flow through the turbine and ensure the safety and efficiency of power generation.Research on the mechanism of sediment erosion,development of anti-erosion materials,and establishment of erosion prediction models have attracted scholarly interest in recent years.Extensive research has been conducted to determine a complete and valuable syndication erosion model.However,owing to the complexity of the flow and wear mechanisms,the influence of specific parameters of erosion and the syndication effect is still difficult to determine.Computational fluid dynamics and erosion monitoring technology have also been evaluated and applied.This paper presents a comprehensive review of the erosion of Pelton turbines,some of the latest technical methods,and possible future development directions.展开更多
We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1...We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1, q） are classified up to the equivalence of Hopf ＊-algebra structures.展开更多
We study Dorroh extensions of algebras and Dorroh extensions of coalgebras.Their structures are described.Some properties of these extensions are presented.We also introduce the finite duals of algebras and modules wh...We study Dorroh extensions of algebras and Dorroh extensions of coalgebras.Their structures are described.Some properties of these extensions are presented.We also introduce the finite duals of algebras and modules which are not necessarily unital.Using these finite duals,we determine the dual relations between the two kinds of extensions.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.52279083).
文摘The Pelton turbine has been widely used to develop high-head water resources with sediments because of its advantages in life cycle costs.When a flood or monsoon season occurs,the sediment concentration in the river increases suddenly,causing severe erosion to the nozzle,needle,and runner of Pelton turbines.After decades of development,researchers have developed practical engineering experience to reduce the sediment concentration of the flow through the turbine and ensure the safety and efficiency of power generation.Research on the mechanism of sediment erosion,development of anti-erosion materials,and establishment of erosion prediction models have attracted scholarly interest in recent years.Extensive research has been conducted to determine a complete and valuable syndication erosion model.However,owing to the complexity of the flow and wear mechanisms,the influence of specific parameters of erosion and the syndication effect is still difficult to determine.Computational fluid dynamics and erosion monitoring technology have also been evaluated and applied.This paper presents a comprehensive review of the erosion of Pelton turbines,some of the latest technical methods,and possible future development directions.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11171291）.
文摘We study the Hopf ＊-algebra structures on the Hopf algebra H（1, q） over C. It is shown that H（1, q） is a Hopf ＊-algebra if and only if ｜q｜ = 1 or q is a real number. Then the Hopf ＊-algebra structures on H（1, q） are classified up to the equivalence of Hopf ＊-algebra structures.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.12071412,11971418)Graduate Student Scientific Research Innovation Projects in Jiangsu Province(No.XKYCX18_036).
文摘We study Dorroh extensions of algebras and Dorroh extensions of coalgebras.Their structures are described.Some properties of these extensions are presented.We also introduce the finite duals of algebras and modules which are not necessarily unital.Using these finite duals,we determine the dual relations between the two kinds of extensions.
