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Modeling of Gate Tunneling Current for Nanoscale MOSFETs with High-k Gate Stacks
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作者 王伟 孙建平 顾宁 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2006年第7期1170-1176,共7页
A quantum model based on solutions to the Schrodinger-Poisson equations is developed to investigate the device behavior related togate tunneling current for nanoscale MOSFETs with high-k gate stacks. This model can mo... A quantum model based on solutions to the Schrodinger-Poisson equations is developed to investigate the device behavior related togate tunneling current for nanoscale MOSFETs with high-k gate stacks. This model can model various MOS device structures with combinations of high-k dielectric materials and multilayer gate stacks,revealing quantum effects on the device performance. Comparisons are made for gate current behavior between nMOSFET and pMOSFET high- k gate stack structures. The results presented are consistent with experimental data, whereas a new finding for an optimum nitrogen content in HfSiON gate dielectric requires further experimental verifications. 展开更多
关键词 high- k gate current quantum model
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羊心浦肯野纤维钠泵活动与动作电位长度关系
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作者 韩大英 《首都医学院学报》 1991年第2期98-104,共7页
采用羊心浦肯野纤维标本,间断地施以快速刺激,用普通玻璃微电极与离子选择电极同时记录细胞动作电位(AP)、细胞内 Na^+ 活度(a_(Na)~i)及细胞间 K^+ 活度(a_k^0).或者,在固定频率刺激下将标本短时间置于无 K^+ 液中作预处理,以提高 a_(N... 采用羊心浦肯野纤维标本,间断地施以快速刺激,用普通玻璃微电极与离子选择电极同时记录细胞动作电位(AP)、细胞内 Na^+ 活度(a_(Na)~i)及细胞间 K^+ 活度(a_k^0).或者,在固定频率刺激下将标本短时间置于无 K^+ 液中作预处理,以提高 a_(Na)~i,刺激钠泵活动.目的在于观察细胞膜钠泵活动及跨膜被动K^+ 流在 APD 变化中的调控作用.结果表明,在心率的生理范围内(60~150次/min),致电钠泵电流在总复极电流中占12%~15%。 展开更多
关键词 浦肯野纤维 钠泵 动作电位 K^+
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The Conformally Symmetric K-Contact Manifolds
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作者 郭震 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期5-10,共6页
In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvatu... In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds. 展开更多
关键词 Conformally symmetric Contact Structure Killing vector field
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Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump 被引量:16
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作者 吴波 汪西力 +1 位作者 LIU Hui 徐海良 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第8期3008-3016,共9页
Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of... Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump. 展开更多
关键词 slurry pump solid-liquid two-phase flow unsteady flow 3-D full passage numerical simulation
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Computational fluid dynamics simulation of gas-liquid two phases flow in 320 m^3 air-blowing mechanical flotation cell using different turbulence models 被引量:3
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作者 沈政昌 陈建华 +2 位作者 张谌虎 廖幸锦 李玉琼 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第6期2385-2392,共8页
According to the recently developed single-trough floating machine with the world's largest volume(inflatable mechanical agitation flotation machine with volume of 320 m3) in China, the gas-fluid two-phase flow in... According to the recently developed single-trough floating machine with the world's largest volume(inflatable mechanical agitation flotation machine with volume of 320 m3) in China, the gas-fluid two-phase flow in flotation cell was simulated using computational fluid dynamics method. It is shown that hexahedral mesh scheme is more suitable for the complex structure of the flotation cell than tetrahedral mesh scheme, and a mesh quality ranging from 0.7 to 1.0 is obtained. Comparative studies of the standard k-ε, k-ω and realizable k-ε turbulence models were carried out. It is indicated that the standard k-ε turbulence model could give a result relatively close to the practice and the liquid phase flow field is well characterized. In addition, two obvious recirculation zones are formed in the mixing zones, and the pressure on the rotor and stator is well characterized. Furthermore, the simulation results using improved standard k-ε turbulence model show that surface tension coefficient of 0.072, drag model of Grace and coefficient of 4, and lift coefficient of 0.001 can be achieved. The research results suggest that gas-fluid two-phase flow in large flotation cell can be well simulated using computational fluid dynamics method. 展开更多
关键词 computational fluid dynamics (CFD) simulation flotation cell gas-liquid two-phases flow
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Effect of pumping chamber on performance of non-overload centrifugal pump 被引量:2
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作者 谷云庆 牟介刚 +5 位作者 代东顺 郑水华 吴登昊 蒋兰芳 施瀚昱 WANG Evan 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第8期2989-2997,共9页
In order to specify the characteristics of un-overloaded centrifugal pumps, the IH100-65-200 pump was chosen as the model pump. Different calculation models for centrifugal pumps were established under different pumpi... In order to specify the characteristics of un-overloaded centrifugal pumps, the IH100-65-200 pump was chosen as the model pump. Different calculation models for centrifugal pumps were established under different pumping chamber sectional parameters. In the numerical simulation of the centrifugal pumps flow field, the shaft power, head, efficiency, and the changes of the internal flow field under different sectional areas and sectional shapes were studied with the RNG k-ε turbulence model, and the influence of the pumping chamber section characteristics of the non-overloaded centrifugal pumps were analyzed. The results show that sectional areas have a significant impact on the non-overload characteristics of centrifugal pumps. The shaft power and head of centrifugal pump are increasing with a lager sectional area, by which the gradient of head curves decreases. The efficiency is improved under a large flow rate condition, but the head and the efficiency are reduced at a small flow rate. It is also observed that the sectional shapes have less influence on the shaft power, the hydraulic performance and flow field characteristics of a centrifugal pump. 展开更多
关键词 centrifugal pumps sectional area sectional shape non-overload characteristics numerical simulation
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Correlation of Cooperatively Localized Rearrangement on the "Fluidized Domain" of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp
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作者 刘颖 宋名实 +2 位作者 金艳 胡桂贤 吴大鸣 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2010年第1期45-64,I0001,共21页
Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” ... Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu- tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts (K-W-W) stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established. 展开更多
关键词 Heterophrase fluctuation model Kinetics of aging Dynamics of de-aging Creep and stress relaxation K-W-W decay function Fluidized domain constituent chain
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Numerical simulation of the hydrodynamics within octagonal tanks in recirculating aquaculture systems 被引量:16
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作者 柳瑶 刘宝良 +2 位作者 雷霁霖 关长涛 黄滨 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2017年第4期912-920,共9页
A three-dimensional numerical model was established to simulate the hydrodynamics within an octagonal tank of a recirculating aquaculture system. The realizable k-e turbulence model was applied to describe the flow, t... A three-dimensional numerical model was established to simulate the hydrodynamics within an octagonal tank of a recirculating aquaculture system. The realizable k-e turbulence model was applied to describe the flow, the discrete phase model (DPM) was applied to generate particle trajectories, and the governing equations are solved using the finite volume method. To validate this model, the numerical results were compared with data obtained from a full-scale physical model. The results show that: (1) the realizable k-e model applied for turbulence modeling describes well the flow pattern in octagonal tanks, giving an average relative error of velocities between simulated and measured values of 18% from contour maps of velocity magnitudes; (2) the DPM was applied to obtain particle trajectories and to simulate the rate of particle removal from the tank. The average relative error of the removal rates between simulated and measured values was 11%. The DPM can be used to assess the self-cleaning capability of an octagonal tank; (3) a comprehensive account of the hydrodynamics within an octagonal tank can be assessed from simulations. The velocity distribution was uniform with an average velocity of 15 cm/s; the velocity reached 0.8 m/s near the inlet pipe, which can result in energy losses and cause wall abrasion; the velocity in tank corners was more than 15 cm/s, which suggests good water mixing, and there was no particle sedimentation. The percentage of particle removal for octagonal tanks was 90% with the exception of a little accumulation of 〈5 mm particle in the area between the inlet pipe and the wall. This study demonstrated a consistent numerical model of the hydrodynamics within octagonal tanks that can be further used in their design and optimization as well as promote the wide use of computational fluid dynamics in aquaculture engineering. 展开更多
关键词 recirculating aquaculture systems octagonal tanks hydrodynamic simulation rate of particle removal
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Numerical investigation of confined swirling gas-solid two phase jet
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作者 金晗辉 夏钧 +1 位作者 樊建人 岑可法 《Journal of Zhejiang University Science》 CSCD 2002年第1期82-85,共4页
This paper presents a \%k\|ε\|k\-p\% multi\|fluid model for simulating confined swirling gas\|solid two phase jet comprised of particle\|laden flow from a center tube and a swirling air stream entering the test secti... This paper presents a \%k\|ε\|k\-p\% multi\|fluid model for simulating confined swirling gas\|solid two phase jet comprised of particle\|laden flow from a center tube and a swirling air stream entering the test section from the coaxial annular. A series of numerical simulations of the two\|phase flow of 30 μm, 45 μm, 60 μm diameter particles respectively yielded results fitting well with published experimental data. 展开更多
关键词 k\|ε\|k\%\-p multi\|fluid model two phase flow confined swirling jet
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COMPUTATION OF TURBULENCE FLOW ON HYBRID GRIDS USING k-ω TURBULENCE MODEL AND OSHER SCHEME
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作者 LIUXue-qiang WUYi-zhao 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2004年第2期94-97,共4页
An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-... An unstructured Reynolds-averaged Navier-Stokes flow solver using the finite volume method is studied. The spatial discretisation is based on the Osher approximate Riemann solvers. A two-equation turbulence model (k-ω model) is also developed for hybrid grids to compute the turbulence flow. The turbulence flow past NACA0012 airfoil and the double ellipsolids are computed, and the numerical results show that the above methods are very efficient. 展开更多
关键词 turbulence model hybrid grids AIRFOIL Navier-Stokes equations
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Numerical Simulation of the Stokes Wave for the Flow around a Ship Hull Coupled with the VOF Model
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作者 Shengtao Chen Jingjun Zhong Peng Sun 《Journal of Marine Science and Application》 CSCD 2015年第2期163-168,共6页
The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method (FVM) is applied to solve Reynolds ... The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method (FVM) is applied to solve Reynolds averaged Navier-Stokes (RANS) equation. The realizable k-e turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid (VOF) method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull's movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattem and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull's heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships' movement, wave and hydrodynamics. 展开更多
关键词 phase flow Stokes wave ship hull numerical tank freesurface wave artifical beach volume of fluid (VOF) finite volumemethod (FVM)
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Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions
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作者 ZHENGYu-Ming FUCHSChristian +4 位作者 FAESSLERAmand SHEKHTERKirril SRISAWADPornrad KOBDAJChinorat YANYu-Peng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第5期746-750,共5页
The influence of the chiral mean field on the in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture... The influence of the chiral mean field on the in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization, which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the in-plane flow. 展开更多
关键词 kaon in-plane flow kaon mean field covariant kaon dynamics heavy ion collision
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Numerical Simulation and Kinetic Analysis of Turbine Sail
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作者 Hu Yihuai Wang Taiyou Luan Yongli 《Journal of Energy and Power Engineering》 2017年第2期127-134,共8页
This paper firstly introduces the structure and working principle of turbine sail. Numerical model of a turbine sail is established with Gambit software. The aerodynamic characteristics of the turbine sail are describ... This paper firstly introduces the structure and working principle of turbine sail. Numerical model of a turbine sail is established with Gambit software. The aerodynamic characteristics of the turbine sail are described with RNG k-e turbulence model and the numerical simulation is carded out with Fluent software. The influence of sail's structure is analyzed including plate, separation type and height/width ratio. The lift coefficients and drag coefficients of the simulated turbine sail are calculated under different rotation angles, suction intensity and separation plate position. The calculated results are compared with the wind tunnel experimental results, which verifies the feasibility of the numerical results and establishes a foundation for the optimal design of turbine sails. 展开更多
关键词 Turbine sail aerodynamic characteristics fluent calculation wind tunnel test.
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A dual-scale turbulence model for gas–liquid bubbly flows 被引量:1
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作者 管小平 李兆奇 +2 位作者 王丽军 李希 成有为 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2015年第11期1737-1745,共9页
A dual-scale turbulence model is applied to simulate cocurrent upward gas-liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubbl... A dual-scale turbulence model is applied to simulate cocurrent upward gas-liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubble- induced turbulence. Single-phase standard k-e model is used to compute shear-induced turbulence and another transport equation is added to model bubble-induced turbulence. In the latter transport equation, energy loss due to interface drag is the production term, and the characteristic length of bubble-induced turbulence, simply the bubble diameter in this work, is introduced to model the dissipation term. The simulated results agree well with experimental data of the test cases and it is demonstrated that the proposed dual-scale turbulence model outperforms other models. Analysis of the predicted turbulence shows that the main part of turbulent kinetic en- ergy is the bubble-induced one while the shear-induced turbulent viscosity predominates within turbulent vis- cosity, especially at the pipe center. The underlying reason is the apparently different scales for the two kinds of turbulence production mechanisms: the shear-induced turbulence is on the scale of the whole pipe while the bubble-induced turbulence is on the scale of bubble diameter. Therefore, the model reflects the multi-scale phe- nomenon involved in gas-liquid bubbly flows. 展开更多
关键词 Two-fluid modelDual-scale turbulence modelShear-induced turbulenceBubble-induced turbulenceBubbly flow
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Effect of Inlet Guide Vanes on the Performance of Small Axial Flow Fan 被引量:4
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作者 LIU Yang LIN Zhe +3 位作者 LIN Peifeng JIN Yingzi Toshiaki Setoguchi Heuy Dong Kim 《Journal of Thermal Science》 SCIE EI CAS CSCD 2017年第6期504-513,共10页
Effects of the inlet guide vanes on the static characteristics, aerodynamic noise and internal flow characteristics of a small axial flow fan are studied in this work. The inlet guide vanes with different outlet angle... Effects of the inlet guide vanes on the static characteristics, aerodynamic noise and internal flow characteristics of a small axial flow fan are studied in this work. The inlet guide vanes with different outlet angle are designed, which are mounted on the casing and located at the upstream of the impeller of the prototype fan. Both steady and unsteady flow simulations arc performed. The steady flow is simulated by the calculations of Navier-Stokes equa- tions coupled with RNG k-epsilon turbulence model, while the unsteady flow is computed with large eddy simu- lation. According to the theoretical analysis, the inlet guide vanes with outlet angle of 60° are regarded as the op- timal inlet guide vanes. The static characteristic experiment is carried out in a standard test rig and the aerody- namic noise is tested in a semi-anechoic room. Then, performances of the fan with optimal inlet guide vanes are compared with those of the prototype fan. The results show that there is reasonable agreement between the simu- lation results and the experimental data. It is found that the static characteristics of small axial flow fan is im- proved obviously after installing the optimal inlet guide vanes. Meanwhile, the optimal inlet guide vanes have effect on reducing noise at the near field, but have little effect on the noise at the far field. 展开更多
关键词 small axial flow fan inlet guide vanes static characteristics aerodynamic noise internal flow characteristics
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Simulation and Experiment Research of Aerodynamic Performance of Small Axial Fans with Struts 被引量:2
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作者 CHU Wei LIN Peifeng +4 位作者 ZHANG Li JIN Yingzi WANG Yanping Heuy Dong Kim Toshiaki Setoguchi 《Journal of Thermal Science》 SCIE EI CAS CSCD 2016年第3期216-222,共7页
Interaction between rotor and struts has great effect on the performance of small axial fan systems. The small axial fan systems are selected as the studied objects in this paper, and four square struts are downstream... Interaction between rotor and struts has great effect on the performance of small axial fan systems. The small axial fan systems are selected as the studied objects in this paper, and four square struts are downstream of the rotor. The cross section of the struts is changed to the cylindrical shapes for the investigation: one is in the same hy- draulic diameter as the square struts and another one is in the same cross section as the square struts. Influence of the shape of the struts on the static pressure characteristics, the internal flow and the sound emission of the small axial fans are studied. Standard K-s turbulence model and SIMPLE algorithm are applied in the calculation of the steady fluid field, and the curves of the pressure rising against the flow rate are obtained, which demonstrates that the simulation results are in nice consistence with the experimental data. The steady calculation results are set as the initial field in the unsteady calculation. Large eddy simulation and PISO algorithm are used in the transient calculation, and the Ffowcs Williams-Hawkings model is introduced to predict the sound level at the eight monitoring points. The research results show that: the static pressure coefficients of the fan with cylindrical struts increase by about 25% compared to the fan with square strum, and the efficiencies increase by about 28.6%. The research provides a theoretical guide for shape optimization and noise reduction of small axial fan with struts. 展开更多
关键词 STRUTS SHAPE INTERACTION aerodynamic performance
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K-Theory and the Quantization Commutes with Reduction Problem
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作者 Nigel HIGSON Yanli SONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2014年第5期703-732,共30页
The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They ... The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula. 展开更多
关键词 Symplectic reduction QUANTIZATION K-THEORY K-HOMOLOGY CompactLie groups
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Numerical simulation of air entrainment and suppression in pump sump 被引量:1
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作者 QIAN Zhong Dong WU Peng Fei +1 位作者 GUO Zhi Wei HUAI Wen Xin 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2016年第12期1847-1855,共9页
The dynamics of air entrainment and suppression schemes in a pump sump are investigated. Four different turbulence models(standard k-ε model, realizable k-ε model, renormalization group(RNG) k-ε model and shear-str... The dynamics of air entrainment and suppression schemes in a pump sump are investigated. Four different turbulence models(standard k-ε model, realizable k-ε model, renormalization group(RNG) k-ε model and shear-stress transport(SST) k-ω model) and the volume of fluid(VOF) multiphase model are employed to simulate the three-dimensional unsteady turbulent flow in a pump sump. The dynamic processes of air entrainment are simulated under conditions of relatively high discharge and low submergence; the mechanism of air entrainment is discussed in detail. Then suppression means for air entrainment is adopted by placing a circular plate on the intake pipe at three different heights. The results show: the position and structure of the free-surface vortices, sidewall-attached vortices, back wall-attached vortices, and floor-attached vortices calculated by SST k-ω turbulence model agree well with the experimental data. The two main contributors for air entrainment are pressure difference and vortex strength. By placing a circular plate in the middle of the intake pipe under water, air entrainment is suppressed because vortex strength is reduced. 展开更多
关键词 air entrainment suppression schemes pump sump VOF
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