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Master equation,design equations and runaway speed of the Kaplan turbine

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Journal of Hydrodynamics 2021年第2期33卷 282-300页

作者： zh.zh.ng zh.W Zurch University of Applied ScienceZurichSwitzerland

To make the Kaplan turbine technology comparable to both the Pelton and the Francis turbine,the master equation for the Kaplan turbine has been established by analyses similar to that-for the Francis *** analysis begins with the descriptions of free vortex flows at the runner inlet and the swirl flow at the impeller *** considering the Euler equation for specific work and by further evaluating the most significant shock and swirling losses,the first and the second energy equations in the form of hydraulic efficiency were *** master equation is then established by combining both energy *** addition,three design equations and a new design parameter are *** master equation relates the turbine hydromechanics to the geometrical design of both the runner and the guide-vane *** enables the complete hydraulic characteristics of a given Kaplan turbine to be analytically and simply computed.A computation example demonstrates the functionality and applicability of the *** the reconstructed master equation,the runaway speed of the Kaplan turbine and its dependence on the guide-vane setting can be easily and precisely *** bulb turbines with guide vanes directly ahead of the turbine runner in the same tube,all computations are also applicable using another equivalent control parameter.

关键词： Kaplan turbine master equation design equations design parameter runaway speed hydraulic efficiency shock loss swirling loss bulb turbines

Master equation and runaway speed of the Francis turbine

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Journal of Hydrodynamics 2018年第2期30卷 203-217页

作者： zh.zh.ng Free Researcher Zurich Switzerland

The master equation of the Francis turbine is derived based on the combination of the angular momentum（Euler） and the energy laws. it relates the geometrical design of the impeller and the regulation settings（guide vane angle and rotational speed） to the discharge and the power output. The master equation, thus, enables the complete characteristics of a given Francis turbine to be easily computed. While applying the energy law, both the shock loss at the impeller inlet and the swirling loss at the impeller exit are taken into account. These are main losses which occur at both the partial load and the overloads and, thus, dominantly influence the characteristics of the Francis turbine. They also totally govern the discharge of the water through the impeller when the impeller is found in the standstill. The computations have been performed for the discharge, the hydraulic torque and the hydraulic efficiency. They were also compared with the available measurements on a model turbine. Excellent agreement has been achieved. The computations also enable the runaway speed of the Francis turbine and the related discharge to be determined as a function of the setting angle of the guide vanes.

关键词： Francis turbine master equation runaway speed hydraulic efficiency shock loss swirling loss streamline similarity method

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Journal of Hydrodynamics 2018年第1期30卷 140-152页

作者： zh.zh.ng Free Researcher Zurich Switzerland

An analytical method is presented, which enables the non-uniform velocity and pressure distributions at the impeller inlet of a pump to be accurately computed. The analyses are based on the potential flow theory and the geometrical similarity of the streamline distribution along the leading edge of the impeller blades. The method is thus called streamline similarity method（SSM）. The obtained geometrical form of the flow distribution is then simply described by the geometrical variable G（s） and the first structural constant G_Ⅰ. As clearly demonstrated and also validated by experiments, both the flow velocity and the pressure distributions at the impeller inlet are usually highly non-uniform. This knowledge is indispensible for impeller blade designs to fulfill the shockless inlet flow condition. By introducing the second structural constant G_Ⅱ, the paper also presents the simple and accurate computation of the shock loss, which occurs at the impeller inlet. The introduction of two structural constants contributes immensely to the enhancement of the computational accuracies. As further indicated, all computations presented in this paper can also be well applied to the non-uniform exit flow out of an impeller of the Francis turbine for accurately computing the related mean values.

关键词： Pumps streamline similarity method flow distribution shock loss structural constant

SUBSTRUCTURE PRECONDiTiONERS FOR NONCONFORMiNG PLATE ELEMENTS

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Journal of Computational Mathematics 1998年第4期16卷 289-304页

作者： Shi, ZC Xie, zh Chinese Acad Sci ICMSEC State Key Lab Sci & Engn Comp Beijing 100080 Peoples R China Chinese Acad Sci Inst Atmospher Phys LASG Beijing 100080 Peoples R China

in this paper, we consider the problem of solving finite element equations of biharmonic Dirichlet problems. We divide the given domain into non-overlapping subdomains, construct a preconditioner for Morley element by substructuring on the basis of a function decomposition for discrete biharmonic functions. The function decomposition is introduced by partitioning these finite element functions into the low and high frequency components through the intergrid transfer operators between coarse mesh and fine mesh, and the conforming interpolation operators. The method leads to a preconditioned system with the condition number bounded by C(1 + log(2) H/h) in the case with interior cross points, and by C in the case without interior cross points, where H is the subdomain size and h is the mesh size. These techniques are applicable to other nonconforming elements and are well suited to a parallel computation.

关键词： substructure preconditioner biharmonic equation nonconforming plate element

MULTiGRiD METHODS FOR MORLEY ELEMENT ON NONNESTED MESHES

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Journal of Computational Mathematics 1998年第5期16卷 385-394页

作者： Shi, ZC Xie, zh Chinese Acad Sci ICMSEC State Key Lab Sci & Engn Comp Beijing 100080 Peoples R China Chinese Acad Sci Inst Atmospher Phys LASG Beijing 100080 Peoples R China

in this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the W-cycle and a uniform condition number estimate for the variable V-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements.

关键词： multigrid method Morley element nonnested meshes

Laser and Fluorescence Properties of Organic Dye DCM Doped Sol-Gel-Derived Solid-State Materials

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Journal of Materials Science & Technology 1999年第6期15卷 563-566页

作者： zh.ng, QY Jiang, zh Tongji Univ Pohl Inst Solid State Phys Shanghai 200092 Peoples R China Chinese Acad Sci Shanghai Inst Opt & Fine Mech Shanghai 201800 Peoples R China

Two kinds of new Ormosil xerogels derived from GPTMS (3-glycidyl propyl trimethoxisilane) and TEOS (tetraethoxysilane) or GPTMS and Ti(OBu)4 (tetrabutoxytitanate) were synthesized viathe sol-gel method as dye laser host. Their optical properties, microstructure characteristics and sudece laser damage thresholds have been reported. The effects of dye matrix combination on the fluorescence emission, slope efficiency, photostability and tunable bandwidth were *** oscillation was easily achieved near 620 nm with a slope efficiency of 29% from DCM dopedSiO2-Ormosil pumped by a frequency-doubled radiation from a Q-switched Nd:YAG laser. The laser wavelength was tunable over 59 nm, and the laser output energy had only a 10% reduction after 2.5× 104 pulses at a pump repetition rate of 1Hz and a pump intensity of 1

关键词： GPTMS DCM EtOH

Magneto-rheological elastomer (MRE) based composite structures for micro-vibration control

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Earthquake Engineering and Engineering Vibration 2010年第3期9卷 345-356页

作者： YQ Ni ZG Ying zh.Chen Department of Civil and Structural Engineering The Hong Kong Polytechnic University Hung Horn Kowloon Hong Kong China Department of Mechanics Zhejiang University Hangzhou 310027 China

Magneto-rheological elastomers （MiLEs） are used to construct composite structures for micro-vibration control of equipment under stochastic support-motion excitations. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. Frequency-domain solution methods for stochastic micro-vibration response analysis of the MRE-based structural systems are developed to derive the system frequency-response function matrices and the expressions of the velocity response spectrum. With these equations, the root-mean-square （RMS） velocity responses in terms of the one-third octave frequency band spectrum can be calculated. Further, the optimization problem of the complex moduli of the MRE cores is defined by minimizing the velocity response spectra and the RMS velocity responses through altering the applied magnetic fields. Simulation results illustrate the influences of MRE parameters on the RMS velocity responses and the high response reduction capacities of the MRE-based structures. in addition, the developed frequency-domain analysis methods are applicable to sandwich beam structures with arbitrary cores characterized by complex shear moduli under stochastic excitations described by power spectral density functions, and are valid for a wide frequency range.

关键词： magneto-rheological elastomer (MRE) micro-vibration control equipment composite structure sandwich beam stochastic excitation

investigation of the Surface Properties of Vinyl Ethers – Sodium 2-Acrylamido-2-Methylpropanesulfonate Copolymers

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Advances in Materials Physics and Chemistry 2012年第4期2卷 177-180页

作者： S. Kh. Khussain E. M. Shaikhutdinov N. zh. Seitkaliyeva A. zh. zh.nisova Department of applied chemistry Kazakh National Technical University named after Kanysh Satpaev Almaty Kazakhstan

The surface properties of water soluble copolymers vinyl ethers of monoethanolamine and ethylene glycol with sodium 2-acrylamido-2-methyl-propanesulfonate were investigated by studying adsorption at the aqueous solution – air interface. it is found that copolymers have considerably higher surface activity in comparison with poly- sodium 2-acrylamido-2-methyl-propanesulfonate.

关键词： Surface Active Copolymers Adsorption interface Standard Free Energy of Adsorption

Solid liquid Mixed Casting of Al-Si Alloy

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Journal of Central South University 2000年第3期12卷 133-135页

作者： Chen, zh.Kang, ZT Cent S Univ Technol Dept Mat Sci & Engn Changsha 410083 Peoples R China

The paper presents a novel material preparation technology—Solid liquid mixed casting technology. in the technology, large amounts of homogeneous alloy powder or heterogenous powder with perfect wettability are added into the superheated melt. After strong agitation, the mixed melt can be cast or hot processed. Applying solid liquid mixed casting, three kinds of Al Si alloys were investigated. The results show that, when the mass of powder accession to alloy melt is about 1, the mean size of primary Si in hyper eutectic alloy can be controlled at less than 5 μm; and the mean grain size of α phase in hypo eutectic alloy is less than 10 μm. This technology has the advantage of preparing material with very fine microstructure by fairly simple casting process, and may be a new practicable and valuable metal preparation technology.

关键词： solid liquid mixed casting powder melt Document code:A