Based on the Naviev-Stokes equations and the standard κ-ε turbulence model, this paper presents the derivation of the governing equations for the turbulent flow field in a draft tube. The mathematical model for the ...Based on the Naviev-Stokes equations and the standard κ-ε turbulence model, this paper presents the derivation of the governing equations for the turbulent flow field in a draft tube. The mathematical model for the turbulent flow through a draft tube is set up when the boundary conditions, including the inlet boundary conditions, the outlet boundary conditions and the wall boundary conditions, have been implemented. The governing equations are formulated in a discrete form on a staggered grid system by the finite volume method. The second-order central difference approximation and hybrid scheme are used for discretization. The computation and analysis on internal flow through a draft tube have been carried out by using the simplee algorithm and cfx-tasc flow software so as to obtain the simulated flow fields. The calculation results at the design operating condition for the draft tube are presented in this paper. Thereby, an effective method for simulating the internal flow field in a draft tube has been explored.展开更多
The application of a new type of moving bed reactor with draft tube for coal gasification was investigated. Successful coal gasification experiments were achieved using the coal gasifier. Product gas containing hydrog...The application of a new type of moving bed reactor with draft tube for coal gasification was investigated. Successful coal gasification experiments were achieved using the coal gasifier. Product gas containing hydrogen as high as 60% was obtained, and the calorific value of the product of 10 MJ·m-3 was obtained using air as oxidant. The reaction temperature of coal gasification in the moving bed was maintained at 870 °C which was comparatively low for coal gasification. Maximum coal gasification efficiency of 92% was obtained.展开更多
Solid-liquid suspension in an agitated tank with a draft tube was investigated witha newly developed infrared turbidimeter for measuring solid concentration.The diameter of theflared inlet transition tube and the dist...Solid-liquid suspension in an agitated tank with a draft tube was investigated witha newly developed infrared turbidimeter for measuring solid concentration.The diameter of theflared inlet transition tube and the distance from the inlet to the tank bottom are two importantparameters for draft tube design The NAX-4 impeller,developed in this study,is characterized byits high flow efficiency and low power consumption.Some modifications are made to the Bald′smodel by considering the effects of solid concentration and fluid viscosity on the critical speed forcomplete off-bottom suspension.The modified equation fits the experimental data satisfactority andcan be used in scale-up展开更多
The economy of the fishing industry is suffering from high fuel prices. Considerable efforts are invested in methods to increase the energy efficiency of fishing vessels and reducing the oil consumption per kilo of ca...The economy of the fishing industry is suffering from high fuel prices. Considerable efforts are invested in methods to increase the energy efficiency of fishing vessels and reducing the oil consumption per kilo of catch that may be as high as 0.6 to 0.7 liter oil per kilo catch. It is primarily the fact that sailing and fishing are on two very different speeds that cause these high fuel consumptions. This is called the two-speed problem and it is the trawlers that are hit hardest by it. The essence of the two-speed problem is that a hydraulic efficiency of only 28% can be expected in trawling speed, when it would be 67% if the ship is sailing at optimum speed all the time. Hydrodynamical analysis shows that an average hydraulic efficiency of only 41% can be expected for a trawler. There is no simple remedy for this, but it is possible to use a technology developed in the hydropower industry, i.e. a draft tube, or a diffuser, to recover energy that would otherwise be lost when trawling. A draft of tube the same length as the propellers diameter could mean fuel savings of 10%, a draft tube twice as long 20%. The difficulty is to find a way to get the draft tube out of the water during sailing with a vessel-specific mechanical design that is not a part of the fluid dynamics of the problem and not discussed in the paper.展开更多
Optimization of draft tube position in a spouted bed reactor used for treatment of wastewater containing low concentration of heavy metals is investigated in this paper. Response surface methodology is used to optimiz...Optimization of draft tube position in a spouted bed reactor used for treatment of wastewater containing low concentration of heavy metals is investigated in this paper. Response surface methodology is used to optimize the draft tube height, the draft tube width and the gap between the bottom of the draft tube and the inlet nozzle. It is observed that the draft tube with a height of 60 millimeter, width of 12 millimeter and the gap of 13 millimeter between its bottom and inlet nozzle, results in optimum value of minimum spouting velocity, measured 45 cubic centimeter per second (2.7 Liter per minute) .展开更多
Draft tube vortex rope is considered a special cavitation flow phenomenon in tubular turbine units.Cavitation vortex rope is one of the most detrimental factors affecting the safety of hydraulic turbines.In this study...Draft tube vortex rope is considered a special cavitation flow phenomenon in tubular turbine units.Cavitation vortex rope is one of the most detrimental factors affecting the safety of hydraulic turbines.In this study,ANSYS CFX software was utilized to numerically simulate the internal cavitation flow of a hydraulic turbine draft tube.The evolution of the cavitation vortex core was characterized by vortex line distribution and vorticity transport equation.The shape and number of blades influenced the revolving direction and distribution characteristics of the vortex close to the runner cone,which formed a counterclockwise-clockwise-counterclockwise distribution pattern.Simultaneously,there were many secondary flows in the draft tube.Mutual cancellation and dissipation between the flows was one of the reasons for reduction in vorticity.When the cross-sectional shape of the draft tube was changed,the vorticity was distributed from the center of the vortex rope to all parts of the cross-sectional draft tube,with extreme values at the center and at the walls.The vortex stretching and dilatation terms played a major role in the change in vorticity,with the baroclinic torque having an effect at the center of the vortex rope,this study is helpful to understand the flow of water in the draft tube and guide the design and optimization of the draft tube in engineering application.展开更多
The three-dimensional unsteady turbulent flow is studied numerically in the whole flow passage of hydraulic turbine, and vortex flow in the draft tube is predicted accurately in this paper. The numerical prediction is...The three-dimensional unsteady turbulent flow is studied numerically in the whole flow passage of hydraulic turbine, and vortex flow in the draft tube is predicted accurately in this paper. The numerical prediction is based on the Navier-Stokes equations and Large-Eddy Simulation (LES) model. The SIMPLE algorithm with the body fitted coordinate and tetrahedroid grid system is applied for the solution of the discretization governing equations.展开更多
A new Reynolds-averaged Navier-Stokes (RANS) turbulence model is developed in order to correctly predict the mean flow field in a draft tube operating under partial load using 2-D axisymmetric simulations. It is sho...A new Reynolds-averaged Navier-Stokes (RANS) turbulence model is developed in order to correctly predict the mean flow field in a draft tube operating under partial load using 2-D axisymmetric simulations. It is shown that although 2-D axisymmetric simulations cannot model the 3-D unsteady features of the vortex rope, they can give the average location of the vortex rope in the draft tube. Nevertheless, RANS simulations underpredict the turbulent kinetic energy (TKE) production and diffusion near the center of the draft tube where the vortex rope forms, resulting in incorrect calculation of TKE profiles and, hence, poor prediction of the axial velocity. Based on this observation, a new k- c turbulence RANS model taking into account the extra production and diffusion of TKE due to coherent structures associated with the vortex rope formation is developed. The new model can successfully predict the mean flow velocity with significant improvements in comparison with the realizable k - c model. This is attributed to better prediction of TKE production and diffusion by the new model in the draft tube under partial load. Specifically, the new model calculates 31% more production and 46% more diffusion right at the shear layer when compared to the k - ~ model.展开更多
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 ...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.展开更多
In terms of gas holdup,liquid velocity,and volumetric mass transfer coefficient for oxygen(KLa),the hydrodynamic behavior of four configurations of an airlift reactor(ALR)with a net draft tube(NDT)of different net mes...In terms of gas holdup,liquid velocity,and volumetric mass transfer coefficient for oxygen(KLa),the hydrodynamic behavior of four configurations of an airlift reactor(ALR)with a net draft tube(NDT)of different net mesh sizes(ALR-NDT-3,6,12,and ALR)have been numerically simulated for a range of inlet air flow rates.The effect of various levels of ratio of height(H)to inner tube diameter(D)of the net draft tube(H/D:9.3,10.7,17.5,and 20)and ratio of inner cross-sectional area of the riser(Ar)to the inner cross sectional area of the downcomer(Ad)(Ad/Ar:1.3 and 7)for different air flow rates is also evaluated for each reactor configuration operating with an air-water system.The two-fluid formulation coupled with the k-εturbulence model is used for computational fluid dynamics(CFD)analysis of flow with Eulerian descriptions for the gas and liquid phases.Interactions between air bubbles and liquid are taken into account using momentum exchange and drag coefficient based on two different correlations.Trends in the predicted dynamical behavior are similar to those found experimentally.A good agreement was achieved suggesting that geometric effects are properly accounted for by the CFD model.After a comparison with experimental data,numerical simulations show significant enhanced gas holdup,liquid velocity,and Kta for the ALR-NDTs compared with the conventional ALR.Higher gas holdup values are achieved for ALR-NDT-3 than that for the other ALRs because it acts like a bubble column reactor as the holes present in the NDT are large.Maximum liquid velocities are seen in ALR-NDT-12,which operates like a conventional ALR.Moreover,the interaction between the NDT and upward gas flow leads to cross flow through the net,small bubbles,and high interfacial area as well as good mass transfer.This was significant in ALR-NDT-6 with maximum Kta value of 0.031 s-1.The applied methodology provides an insightful understanding of the complex dynamic behavior of ALR-NDTs and may be helpful in optimizing the design and scale-up of reactors.展开更多
Open-sided draft tubes provide an optimal gas distribution through a cross flow pattern between the spout and the annulus in conical spouted beds.The design,optimization,control,and scale-up of the spouted beds requir...Open-sided draft tubes provide an optimal gas distribution through a cross flow pattern between the spout and the annulus in conical spouted beds.The design,optimization,control,and scale-up of the spouted beds require precise information on operating and peak pressure drops.In this study,a multi-layer perceptron(MLP)neural network was employed for accurate prediction of these hydrodynamic characteristics.A relatively huge number of experiments were accomplished and the most influential dimensionless groups were extracted using the Buckingham-pi theorem.Then,the dimensionless groups were used for developing the MLP model for simultaneous estimation of operating and peak pressure drops.The iterative constructive technique confirmed that 4-14-2 is the best structure for the MLP model in terms of absolute average relative deviation(AARD%),mean square error(MSE),and regression coefficient(R^(2)).The developed MLP approach has an excellent capacity to predict the transformed operating(MSE=0.00039,AARD%=1.30,and R^(2)=0.76099)and peak(MSE=0.22933,AARD%=11.88,and R2=0.89867)pressure drops.展开更多
Numerical simulations of the flow in the draft tube of a Francis turbine are carried out in order to elucidate the effects of tangential velocity on flow stability.Influence of the location of the maximum tangential v...Numerical simulations of the flow in the draft tube of a Francis turbine are carried out in order to elucidate the effects of tangential velocity on flow stability.Influence of the location of the maximum tangential velocity is explored considering the equality of the total energy at the inlet of the draft tube.It is found that the amplitude of the pressure fluctuation decreases when the location of the maximum of the tangential velocity moves from the centre to the wall on the cross section.Thus,the stability of the flow in the draft tube increases with the moving of the location of the maximum tangential velocity.However,the relative hydraulic loss increases and the recovery coefficient of the draft tube decreases slightly.展开更多
Elbow draft-tubes are widely used in large- and medium-sized hydropower stations in many countries. During the application, handling the somatotype of elbow tubes has been found challenging: in order to maintain the ...Elbow draft-tubes are widely used in large- and medium-sized hydropower stations in many countries. During the application, handling the somatotype of elbow tubes has been found challenging: in order to maintain the designed shape of draft tube and to meet the requirement of construction lofting, the configuration of reinforcing bars and the fabrication of templates, the geometry of elbow tubes has to be accurately calculated to draw engineering graphics. Based on the derived equations in this paper, the motion of elbow tube curve envelope is simulated by using computers, which shows directly the smoothness of the curve and provides dynamic simulation for the study and optimization of the design and construction of elbow draft tubes, along with the front view and bottom view.展开更多
基金Supported by the National Natural Science Foundation of China(10162002) the Key Project of Chinese Ministry Education (204138) the Sci-ence Foundation of Yunnan Education Bureau(5Y0020A)
文摘Based on the Naviev-Stokes equations and the standard κ-ε turbulence model, this paper presents the derivation of the governing equations for the turbulent flow field in a draft tube. The mathematical model for the turbulent flow through a draft tube is set up when the boundary conditions, including the inlet boundary conditions, the outlet boundary conditions and the wall boundary conditions, have been implemented. The governing equations are formulated in a discrete form on a staggered grid system by the finite volume method. The second-order central difference approximation and hybrid scheme are used for discretization. The computation and analysis on internal flow through a draft tube have been carried out by using the simplee algorithm and cfx-tasc flow software so as to obtain the simulated flow fields. The calculation results at the design operating condition for the draft tube are presented in this paper. Thereby, an effective method for simulating the internal flow field in a draft tube has been explored.
文摘The application of a new type of moving bed reactor with draft tube for coal gasification was investigated. Successful coal gasification experiments were achieved using the coal gasifier. Product gas containing hydrogen as high as 60% was obtained, and the calorific value of the product of 10 MJ·m-3 was obtained using air as oxidant. The reaction temperature of coal gasification in the moving bed was maintained at 870 °C which was comparatively low for coal gasification. Maximum coal gasification efficiency of 92% was obtained.
文摘Solid-liquid suspension in an agitated tank with a draft tube was investigated witha newly developed infrared turbidimeter for measuring solid concentration.The diameter of theflared inlet transition tube and the distance from the inlet to the tank bottom are two importantparameters for draft tube design The NAX-4 impeller,developed in this study,is characterized byits high flow efficiency and low power consumption.Some modifications are made to the Bald′smodel by considering the effects of solid concentration and fluid viscosity on the critical speed forcomplete off-bottom suspension.The modified equation fits the experimental data satisfactority andcan be used in scale-up
文摘The economy of the fishing industry is suffering from high fuel prices. Considerable efforts are invested in methods to increase the energy efficiency of fishing vessels and reducing the oil consumption per kilo of catch that may be as high as 0.6 to 0.7 liter oil per kilo catch. It is primarily the fact that sailing and fishing are on two very different speeds that cause these high fuel consumptions. This is called the two-speed problem and it is the trawlers that are hit hardest by it. The essence of the two-speed problem is that a hydraulic efficiency of only 28% can be expected in trawling speed, when it would be 67% if the ship is sailing at optimum speed all the time. Hydrodynamical analysis shows that an average hydraulic efficiency of only 41% can be expected for a trawler. There is no simple remedy for this, but it is possible to use a technology developed in the hydropower industry, i.e. a draft tube, or a diffuser, to recover energy that would otherwise be lost when trawling. A draft of tube the same length as the propellers diameter could mean fuel savings of 10%, a draft tube twice as long 20%. The difficulty is to find a way to get the draft tube out of the water during sailing with a vessel-specific mechanical design that is not a part of the fluid dynamics of the problem and not discussed in the paper.
文摘Optimization of draft tube position in a spouted bed reactor used for treatment of wastewater containing low concentration of heavy metals is investigated in this paper. Response surface methodology is used to optimize the draft tube height, the draft tube width and the gap between the bottom of the draft tube and the inlet nozzle. It is observed that the draft tube with a height of 60 millimeter, width of 12 millimeter and the gap of 13 millimeter between its bottom and inlet nozzle, results in optimum value of minimum spouting velocity, measured 45 cubic centimeter per second (2.7 Liter per minute) .
基金the National Natural Science Foundation,China(Grant No.52079118)Key Research and Development Plan of Sichuan Provincial Department of Science and Technology(Grant No.2023YFQ0021)+1 种基金Qinghai Province“Kunlun Talents High-end Innovation and Entrepreneurship Talent Program”Qinghai University of Science and Technology talent introduction of scientific research special grants,Central leading local(scientific and technological innovation base construction)project XZ202201YD0017CJiangsu South-North Water Diversion Science and Technology R&D Project(Grant No.JSNSBD202303).
文摘Draft tube vortex rope is considered a special cavitation flow phenomenon in tubular turbine units.Cavitation vortex rope is one of the most detrimental factors affecting the safety of hydraulic turbines.In this study,ANSYS CFX software was utilized to numerically simulate the internal cavitation flow of a hydraulic turbine draft tube.The evolution of the cavitation vortex core was characterized by vortex line distribution and vorticity transport equation.The shape and number of blades influenced the revolving direction and distribution characteristics of the vortex close to the runner cone,which formed a counterclockwise-clockwise-counterclockwise distribution pattern.Simultaneously,there were many secondary flows in the draft tube.Mutual cancellation and dissipation between the flows was one of the reasons for reduction in vorticity.When the cross-sectional shape of the draft tube was changed,the vorticity was distributed from the center of the vortex rope to all parts of the cross-sectional draft tube,with extreme values at the center and at the walls.The vortex stretching and dilatation terms played a major role in the change in vorticity,with the baroclinic torque having an effect at the center of the vortex rope,this study is helpful to understand the flow of water in the draft tube and guide the design and optimization of the draft tube in engineering application.
基金Project supported by the National Natural Science Foundation of China (Grant No :50179021) and the Youth Scienceand Technology Foundation of Sichuan (Grant No :05ZQ026-07) .
文摘The three-dimensional unsteady turbulent flow is studied numerically in the whole flow passage of hydraulic turbine, and vortex flow in the draft tube is predicted accurately in this paper. The numerical prediction is based on the Navier-Stokes equations and Large-Eddy Simulation (LES) model. The SIMPLE algorithm with the body fitted coordinate and tetrahedroid grid system is applied for the solution of the discretization governing equations.
基金funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award Numbers DE-EE0002667 (the DOE/PSU Graduate Student Fellowship Program for Hydropower Research)DE-EE0002668 (The HRF Fellowship)the Hydro Research Foundation
文摘A new Reynolds-averaged Navier-Stokes (RANS) turbulence model is developed in order to correctly predict the mean flow field in a draft tube operating under partial load using 2-D axisymmetric simulations. It is shown that although 2-D axisymmetric simulations cannot model the 3-D unsteady features of the vortex rope, they can give the average location of the vortex rope in the draft tube. Nevertheless, RANS simulations underpredict the turbulent kinetic energy (TKE) production and diffusion near the center of the draft tube where the vortex rope forms, resulting in incorrect calculation of TKE profiles and, hence, poor prediction of the axial velocity. Based on this observation, a new k- c turbulence RANS model taking into account the extra production and diffusion of TKE due to coherent structures associated with the vortex rope formation is developed. The new model can successfully predict the mean flow velocity with significant improvements in comparison with the realizable k - c model. This is attributed to better prediction of TKE production and diffusion by the new model in the draft tube under partial load. Specifically, the new model calculates 31% more production and 46% more diffusion right at the shear layer when compared to the k - ~ model.
基金supported by the National Natural Science Foundation of China(Grant No.51076077)National Key Technology R&D Program of China(Grant No.2008BAC48B02)
文摘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.
文摘In terms of gas holdup,liquid velocity,and volumetric mass transfer coefficient for oxygen(KLa),the hydrodynamic behavior of four configurations of an airlift reactor(ALR)with a net draft tube(NDT)of different net mesh sizes(ALR-NDT-3,6,12,and ALR)have been numerically simulated for a range of inlet air flow rates.The effect of various levels of ratio of height(H)to inner tube diameter(D)of the net draft tube(H/D:9.3,10.7,17.5,and 20)and ratio of inner cross-sectional area of the riser(Ar)to the inner cross sectional area of the downcomer(Ad)(Ad/Ar:1.3 and 7)for different air flow rates is also evaluated for each reactor configuration operating with an air-water system.The two-fluid formulation coupled with the k-εturbulence model is used for computational fluid dynamics(CFD)analysis of flow with Eulerian descriptions for the gas and liquid phases.Interactions between air bubbles and liquid are taken into account using momentum exchange and drag coefficient based on two different correlations.Trends in the predicted dynamical behavior are similar to those found experimentally.A good agreement was achieved suggesting that geometric effects are properly accounted for by the CFD model.After a comparison with experimental data,numerical simulations show significant enhanced gas holdup,liquid velocity,and Kta for the ALR-NDTs compared with the conventional ALR.Higher gas holdup values are achieved for ALR-NDT-3 than that for the other ALRs because it acts like a bubble column reactor as the holes present in the NDT are large.Maximum liquid velocities are seen in ALR-NDT-12,which operates like a conventional ALR.Moreover,the interaction between the NDT and upward gas flow leads to cross flow through the net,small bubbles,and high interfacial area as well as good mass transfer.This was significant in ALR-NDT-6 with maximum Kta value of 0.031 s-1.The applied methodology provides an insightful understanding of the complex dynamic behavior of ALR-NDTs and may be helpful in optimizing the design and scale-up of reactors.
文摘Open-sided draft tubes provide an optimal gas distribution through a cross flow pattern between the spout and the annulus in conical spouted beds.The design,optimization,control,and scale-up of the spouted beds require precise information on operating and peak pressure drops.In this study,a multi-layer perceptron(MLP)neural network was employed for accurate prediction of these hydrodynamic characteristics.A relatively huge number of experiments were accomplished and the most influential dimensionless groups were extracted using the Buckingham-pi theorem.Then,the dimensionless groups were used for developing the MLP model for simultaneous estimation of operating and peak pressure drops.The iterative constructive technique confirmed that 4-14-2 is the best structure for the MLP model in terms of absolute average relative deviation(AARD%),mean square error(MSE),and regression coefficient(R^(2)).The developed MLP approach has an excellent capacity to predict the transformed operating(MSE=0.00039,AARD%=1.30,and R^(2)=0.76099)and peak(MSE=0.22933,AARD%=11.88,and R2=0.89867)pressure drops.
基金supported by the open fund of State Key Laboratory of Hydroscience and Engineer of Tsinghua University(No.sklhse-2013-E-02)the Special Major Project of Science and Technology of Zhejiang province(No.2013C 01139)
文摘Numerical simulations of the flow in the draft tube of a Francis turbine are carried out in order to elucidate the effects of tangential velocity on flow stability.Influence of the location of the maximum tangential velocity is explored considering the equality of the total energy at the inlet of the draft tube.It is found that the amplitude of the pressure fluctuation decreases when the location of the maximum of the tangential velocity moves from the centre to the wall on the cross section.Thus,the stability of the flow in the draft tube increases with the moving of the location of the maximum tangential velocity.However,the relative hydraulic loss increases and the recovery coefficient of the draft tube decreases slightly.
基金Supported by Open Fund of Key Laboratory of Ministry of Education of Hydraulic and Waterway Engineering of Chongqing Jiaotong University Province and Department Construction together(SLK2009A04)
文摘Elbow draft-tubes are widely used in large- and medium-sized hydropower stations in many countries. During the application, handling the somatotype of elbow tubes has been found challenging: in order to maintain the designed shape of draft tube and to meet the requirement of construction lofting, the configuration of reinforcing bars and the fabrication of templates, the geometry of elbow tubes has to be accurately calculated to draw engineering graphics. Based on the derived equations in this paper, the motion of elbow tube curve envelope is simulated by using computers, which shows directly the smoothness of the curve and provides dynamic simulation for the study and optimization of the design and construction of elbow draft tubes, along with the front view and bottom view.