This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse magneti...This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse magnetic case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.展开更多
In this paper, a numerical technique is proposed to obtain the solution for transient heat conduction equation of Copper. The copper element is characterized by many characteristics;the most important of which is its ...In this paper, a numerical technique is proposed to obtain the solution for transient heat conduction equation of Copper. The copper element is characterized by many characteristics;the most important of which is its high ability to conduct heat and electrical conductivity, in addition to being a flexible and malleable metal that is easy to form without being broken, making it one of the basic minerals that humans have benefited from for thousands of years, it is one of the first minerals. That has been discovered and extracted, and still plays a major role in the development of societies. The obtained solutions are compared with the available exact solutions and the obtained solutions using the finite difference method. The results indicate that the finite difference method is a highly effective method for obtaining approximate solutions for the thermal conductivity equation for copper. It is also clear from the numerical results from copper in the high conductivity of heat and electricity.展开更多
This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electri...This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electric case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.展开更多
The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the tra...The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.展开更多
The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-har...The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.展开更多
We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find...We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find that, in long histories, traces of the initial field would be present only in the exact analytical solutions. We conclude that the recovery of initial field is possible only if the equations could be solved analytically or only short time periods are involved. In practice, it is not possible to detect those traces by measurements or observations. If numerical procedures are used, truncation and discretization errors are always present. Fine-tuning of system parameters used or transforming time into another pseudo time frame may allow numerical integration to be carried out backward in time. But numerical instability is still a problem. Large spurious increases found by numerical procedures are most likely due to numerical inaccuracy and instability.展开更多
In recent years, metallurgical slags have been increasingly used as materials for the manufacture of cement, pavement and filling material. The transport of the molten slag to the receiving pots is carried out through...In recent years, metallurgical slags have been increasingly used as materials for the manufacture of cement, pavement and filling material. The transport of the molten slag to the receiving pots is carried out through open channels. The transient and steady-state flow of a molten slag in a rectangular open channel is numerically analyzed here. For the transient flow, the Saint-Venant equations were numerically solved. For the steady-state flow, the derivatives in time and space in the Saint-Venant equations were set equal to zero and a polynomial of degree 3 is obtained whose roots are the slag height values. It was assumed that the viscosity of the slag has an Arrhenius-type behavior with temperature. Four values of temperature values, namely 1723.15, 1773.15, 1823.15, 18873.15 ˚K, and five values of the angle of inclination of the channel, namely 1, 2, 3, 4, 5 degrees, are considered. Numerical results show that the steady-state values of the height and velocity of the molten slag depend strongly on the temperature of the slag and the angle of inclination of the channel. As the slag temperature and channel angle increase, the value of the steady-state slag height decreases. The value of the steady-state slag velocity increases as the slag temperature and channel inclination angle increase.展开更多
In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-...In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study’s results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors.展开更多
How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was der...How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.展开更多
We conducted a transient experimental investigation of steam–water direct contact condensation in the absence of noncondensible gas in a laboratory-scale column with the inner diameter of 325 mm and the height of 104...We conducted a transient experimental investigation of steam–water direct contact condensation in the absence of noncondensible gas in a laboratory-scale column with the inner diameter of 325 mm and the height of 1045 mm. We applied a new analysis method for the steam state equation to analyze the molar quantity change in steam over the course of the experiment and determined the transient steam variation. We also investigated the influence of flow rates and temperatures ofcooling water on the efficiency ofsteam condensation. Our experimental results show that appropriate increasing of the cooling water flow rate can significantly accelerate the steam condensation. We achieved a rapid increase in the total volumetric heat transfer coefficient by increasing the flow rate of cooling water, which indicated a higher thermal convection between the steam and the cooling water with higher flow rates. We found that the temperature ofcooling water did not play an important role on steam condensation. This method was confirmed to be effective for rapid recovering ofsteam.展开更多
We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from whic...We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design.展开更多
Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived usin...Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange＇s equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.展开更多
This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-mo...This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.展开更多
An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current...An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current density in the stator, is developed by means of a diffusion equation. A relationship between frequency of the conducting current, root of the characteristic function of Bessel equation and decay time in the armature is given. The skin depth in the helical stator is calculated and is compared with the approximate one which is widely used in the calculation of magnetic diffusion. Our analytical results are helpful to understanding the mechanism of the loss of magnetic flux in both the armature and stator and to suggesting an optimal design for improving performance of the helical flux compression generator.展开更多
The advisability of the use of matrix methods of equations rearrangement for the investigated system which allows writing a secular equation is considered in this article. This approach greatly simplifies the analysis...The advisability of the use of matrix methods of equations rearrangement for the investigated system which allows writing a secular equation is considered in this article. This approach greatly simplifies the analysis of performance of transient response in complicated multi-coupled electrical system at small perturbations.展开更多
Transient analysis of 33 KV power transmission line stability of Egi communi-ty is considered in this research work with the aim of reducing the frequency of fault occurrence and voltage collapse in the network. The s...Transient analysis of 33 KV power transmission line stability of Egi communi-ty is considered in this research work with the aim of reducing the frequency of fault occurrence and voltage collapse in the network. The supply is taken from Egi generating station located at Total Nigeria Limited Gas Plant Obite at voltage level of 33 KV to Egi communities. This work focuses on the transient nature of network stability since transient fault is the most dangerous in elec-trical systems. The swinging of the generator rotor in the event of transient three-phase short circuit fault can be monitored by the circuit breakers and the protective relays which causes mal-functioning of the circuit breakers and pro-tective relays leading to abnormal behavior of the network. Therefore, data obtained from the power station were used as a case study of Independent Power Producer (IPP) in Nigeria. For investigation of the power angle, angular velocity, rotor angle differential changes, and angular velocity differential changes, an electrical transient analyzer tool was employed (ETap version 16.00) for circuit breaker and protective relay time setting of (0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60). The work used the Trapezoidal numerical technique for data analysis. The graphs were plotted using Matlab R2015a and the results obtained showed that when a symmetrical three-phase short circuit fault occur at one or any of the feeders, the fault must be cleared as quick as possible through the coordination of the circuit breakers and protective relays. For this research work, 17 cycles corresponding to relay time setting of t = 0.34 s were recommended and at each cycle, changes in time with respect to changes in rotor angle, angular velocity, rotor differential and angular velocity differential were calculated on the power network simultaneously. The results demonstrated that the Trapezoidal method is numerically stable, accurate and has faster respond time when compared to Modified Euler and swing equation techniques in event of fault occurrence in network.展开更多
The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural ...The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural gas pipeline network requires more strictly on the calculation efficiency of transient simulation.To this end,this paper proposes a new method for the transient simulation of natural gas pipeline networks based on fracture-dimension-reduction algorithm.Firstly,a pipeline network model is abstracted into a station model,inter-station pipeline network model and connection node model.Secondlly,the pressure at the connection node connecting the station and the inter-station pipeline network is used as the basic variable to solve the general solution of the flow rate at the connection node,reconstruct the simulation model of the inter-station pipeline network,and reduce the equation set dimension of the inter-station pipeline network model.Thirdly,the transient simulation model of the natural gas pipeline network system is constructed based on the reconstructed simulation model of the inter-station pipeline network.Fnally,the calculation accuracy and efficiency of the proposed algorithm are compared and analyzed for the two working conditions of slow change of compressor speed and rapid shutdown of the compressor.And the following research results are obtained.First,the fracture-dimension-reduction algorithm has a high calculation accuracy,and the relative error of compressor outlet pressure and user pressure is less than 0.1%.Second,the calculation efficiency of the new fracture-dimension-reduction algorithm is high,and compared with the nonlinear equations solv ing method,the speed-up ratios under the two conditions are high up to 17.3 and 12.2 respectively.Third,the speed-up ratio of the fracture-dimension-reduction algorithm is linearly related to the equation set dimension of the transient simulation model of the pipeline network system.The larger the equation set dimension,the higher the speed-up ratio,which means the more complex the pipeline network model,the more remarkable the calculation speed-up effect.In conclusion,this new method improves the calculation speed while keeping the calculation accuracy,which is of great theoretical value and reference significance for improving the calculation efficiency of the transient simulation of complex natural gas pipeline network systems.展开更多
This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for exam...This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.展开更多
文摘This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse magnetic case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
文摘In this paper, a numerical technique is proposed to obtain the solution for transient heat conduction equation of Copper. The copper element is characterized by many characteristics;the most important of which is its high ability to conduct heat and electrical conductivity, in addition to being a flexible and malleable metal that is easy to form without being broken, making it one of the basic minerals that humans have benefited from for thousands of years, it is one of the first minerals. That has been discovered and extracted, and still plays a major role in the development of societies. The obtained solutions are compared with the available exact solutions and the obtained solutions using the finite difference method. The results indicate that the finite difference method is a highly effective method for obtaining approximate solutions for the thermal conductivity equation for copper. It is also clear from the numerical results from copper in the high conductivity of heat and electricity.
文摘This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electric case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
文摘The 1/3 subharmonic solution for the Duffing’s equation is investigated by using the methods of harmonic balance and numerical integration. The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied. Over and above, the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method. Finally, asymptotical stability of the pure subharmonic oscillations element is inspected.
基金Project supported by the National Natural Science Foundation of China (No.50275024)
文摘The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
文摘We investigate under what conditions transient simulation could be used to integrate backward in time so that the initial field could be recovered from later histories. In this paper we use realistic examples and find that, in long histories, traces of the initial field would be present only in the exact analytical solutions. We conclude that the recovery of initial field is possible only if the equations could be solved analytically or only short time periods are involved. In practice, it is not possible to detect those traces by measurements or observations. If numerical procedures are used, truncation and discretization errors are always present. Fine-tuning of system parameters used or transforming time into another pseudo time frame may allow numerical integration to be carried out backward in time. But numerical instability is still a problem. Large spurious increases found by numerical procedures are most likely due to numerical inaccuracy and instability.
文摘In recent years, metallurgical slags have been increasingly used as materials for the manufacture of cement, pavement and filling material. The transport of the molten slag to the receiving pots is carried out through open channels. The transient and steady-state flow of a molten slag in a rectangular open channel is numerically analyzed here. For the transient flow, the Saint-Venant equations were numerically solved. For the steady-state flow, the derivatives in time and space in the Saint-Venant equations were set equal to zero and a polynomial of degree 3 is obtained whose roots are the slag height values. It was assumed that the viscosity of the slag has an Arrhenius-type behavior with temperature. Four values of temperature values, namely 1723.15, 1773.15, 1823.15, 18873.15 ˚K, and five values of the angle of inclination of the channel, namely 1, 2, 3, 4, 5 degrees, are considered. Numerical results show that the steady-state values of the height and velocity of the molten slag depend strongly on the temperature of the slag and the angle of inclination of the channel. As the slag temperature and channel angle increase, the value of the steady-state slag height decreases. The value of the steady-state slag velocity increases as the slag temperature and channel inclination angle increase.
文摘In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study’s results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors.
基金This work was financially supported by Key Program of the National Natural Science Foundation of China(No.50639020)the National High Technology Research and Development Program of China(863Program)(No.2006AA09Z332)
文摘How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.
文摘We conducted a transient experimental investigation of steam–water direct contact condensation in the absence of noncondensible gas in a laboratory-scale column with the inner diameter of 325 mm and the height of 1045 mm. We applied a new analysis method for the steam state equation to analyze the molar quantity change in steam over the course of the experiment and determined the transient steam variation. We also investigated the influence of flow rates and temperatures ofcooling water on the efficiency ofsteam condensation. Our experimental results show that appropriate increasing of the cooling water flow rate can significantly accelerate the steam condensation. We achieved a rapid increase in the total volumetric heat transfer coefficient by increasing the flow rate of cooling water, which indicated a higher thermal convection between the steam and the cooling water with higher flow rates. We found that the temperature ofcooling water did not play an important role on steam condensation. This method was confirmed to be effective for rapid recovering ofsteam.
基金supported by the Program for New Century Excellent Talents in Universities(No.NCET-12-0625)the Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province(No.SBK2014010134)+2 种基金the Fundamental Research Funds for Central Universities(No.NE2013101)the National Natural Science Foundation of China(No.11232007)a project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘We study the effects of mechanical nonlinearity arising from large thickness-shear deformation on the transient process of an AT-cut quartz plate resonator. Mindlin＇s two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained. Numerical solutions by the Runge-Kutta method show that in common operating conditions of quartz resonators the nonlinear effect varies from noticeable to significant. As resonators are to be made smaller and thinner in the future with about the same power requirement, nonlinear effects will become more important and need more understanding and consideration in resonator design.
基金Project supported by the National Natural Science Foundation of China (No. 10572150)the Natural Science Foundation of Naval University of Engineering (No. HGDQNJJ008)
文摘Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange＇s equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.
基金supported by the National Natural Science Foundation of China(No.11372140)
文摘This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr- Somrnerfeld and Squire （OSS） equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re- orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes （N-S） equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro- posed. The algorithm is then applied to a one-dimensional base flow （the plane Poiseuille flow） and a two-dimensional base flow （the plane Poiseuille flow with a low-speed streak） in a channel. For one-dimensional cases, the effects of the spanwise width of the chan- nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character- ized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross- check method.
基金Project supported by the National Natural Science Foundation of China （Grant No 0475012） and partially by Technology ＆ Science Foundation of China Academy of Engineering ＆ Physics （Grant No 20040210）.
文摘An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current density in the stator, is developed by means of a diffusion equation. A relationship between frequency of the conducting current, root of the characteristic function of Bessel equation and decay time in the armature is given. The skin depth in the helical stator is calculated and is compared with the approximate one which is widely used in the calculation of magnetic diffusion. Our analytical results are helpful to understanding the mechanism of the loss of magnetic flux in both the armature and stator and to suggesting an optimal design for improving performance of the helical flux compression generator.
文摘The advisability of the use of matrix methods of equations rearrangement for the investigated system which allows writing a secular equation is considered in this article. This approach greatly simplifies the analysis of performance of transient response in complicated multi-coupled electrical system at small perturbations.
文摘Transient analysis of 33 KV power transmission line stability of Egi communi-ty is considered in this research work with the aim of reducing the frequency of fault occurrence and voltage collapse in the network. The supply is taken from Egi generating station located at Total Nigeria Limited Gas Plant Obite at voltage level of 33 KV to Egi communities. This work focuses on the transient nature of network stability since transient fault is the most dangerous in elec-trical systems. The swinging of the generator rotor in the event of transient three-phase short circuit fault can be monitored by the circuit breakers and the protective relays which causes mal-functioning of the circuit breakers and pro-tective relays leading to abnormal behavior of the network. Therefore, data obtained from the power station were used as a case study of Independent Power Producer (IPP) in Nigeria. For investigation of the power angle, angular velocity, rotor angle differential changes, and angular velocity differential changes, an electrical transient analyzer tool was employed (ETap version 16.00) for circuit breaker and protective relay time setting of (0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60). The work used the Trapezoidal numerical technique for data analysis. The graphs were plotted using Matlab R2015a and the results obtained showed that when a symmetrical three-phase short circuit fault occur at one or any of the feeders, the fault must be cleared as quick as possible through the coordination of the circuit breakers and protective relays. For this research work, 17 cycles corresponding to relay time setting of t = 0.34 s were recommended and at each cycle, changes in time with respect to changes in rotor angle, angular velocity, rotor differential and angular velocity differential were calculated on the power network simultaneously. The results demonstrated that the Trapezoidal method is numerically stable, accurate and has faster respond time when compared to Modified Euler and swing equation techniques in event of fault occurrence in network.
文摘The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural gas pipeline network requires more strictly on the calculation efficiency of transient simulation.To this end,this paper proposes a new method for the transient simulation of natural gas pipeline networks based on fracture-dimension-reduction algorithm.Firstly,a pipeline network model is abstracted into a station model,inter-station pipeline network model and connection node model.Secondlly,the pressure at the connection node connecting the station and the inter-station pipeline network is used as the basic variable to solve the general solution of the flow rate at the connection node,reconstruct the simulation model of the inter-station pipeline network,and reduce the equation set dimension of the inter-station pipeline network model.Thirdly,the transient simulation model of the natural gas pipeline network system is constructed based on the reconstructed simulation model of the inter-station pipeline network.Fnally,the calculation accuracy and efficiency of the proposed algorithm are compared and analyzed for the two working conditions of slow change of compressor speed and rapid shutdown of the compressor.And the following research results are obtained.First,the fracture-dimension-reduction algorithm has a high calculation accuracy,and the relative error of compressor outlet pressure and user pressure is less than 0.1%.Second,the calculation efficiency of the new fracture-dimension-reduction algorithm is high,and compared with the nonlinear equations solv ing method,the speed-up ratios under the two conditions are high up to 17.3 and 12.2 respectively.Third,the speed-up ratio of the fracture-dimension-reduction algorithm is linearly related to the equation set dimension of the transient simulation model of the pipeline network system.The larger the equation set dimension,the higher the speed-up ratio,which means the more complex the pipeline network model,the more remarkable the calculation speed-up effect.In conclusion,this new method improves the calculation speed while keeping the calculation accuracy,which is of great theoretical value and reference significance for improving the calculation efficiency of the transient simulation of complex natural gas pipeline network systems.
文摘This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.
