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
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 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
新能源随机性使得电力系统潮流复杂多变,加之大量新能源需要远距离输送消纳,输电阻塞问题日益严重。动态热定值(dynamic line rating,DTR)技术能够提升既有架空线路的输电能力,充分发挥系统的灵活调节能力。特别是在N-1事故场景下,采用...新能源随机性使得电力系统潮流复杂多变,加之大量新能源需要远距离输送消纳,输电阻塞问题日益严重。动态热定值(dynamic line rating,DTR)技术能够提升既有架空线路的输电能力,充分发挥系统的灵活调节能力。特别是在N-1事故场景下,采用DTR技术提升线路输送能力,能够缓解严重输电阻塞。然而,传统方法在考虑N-1事故时存在维数灾难问题,因此应用DTR技术仍然存在挑战性。为此,提出了一种两阶段分布鲁棒优化(distributionally robust optimization,DRO)方法以提升架空线路的输电能力。首先,构建了架空线路暂态温度计算模型并做适当简化处理,从而保证后续优化模型的凸性。随后,建立了考虑DTR和N-1安全准则的两阶段DRO模型以避免N-1事故下的持续停电,考虑无功与网损的线性化交流潮流模型能够更准确地计算线路潮流。最后,使用IEEE-24节点系统和IEEE-118节点系统验证了所提方法的有效性。展开更多
A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is proposed.The developed method is applied to solve problems governed b...A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is proposed.The developed method is applied to solve problems governed by the Sine–Gordon equation(SGE),the scalar wave equation and elasto-dynamics.Two methods are studied:one is a space-time formulation and the other is a semi-discrete method based on an implicit Runge–Kutta(RK)time integration.The methodology is implemented using the Tensorflow framework and it is tested on several numerical examples.Based on the results,the relative normalized error was observed to be less than 5%in all cases.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 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
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
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
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 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.
文摘新能源随机性使得电力系统潮流复杂多变,加之大量新能源需要远距离输送消纳,输电阻塞问题日益严重。动态热定值(dynamic line rating,DTR)技术能够提升既有架空线路的输电能力,充分发挥系统的灵活调节能力。特别是在N-1事故场景下,采用DTR技术提升线路输送能力,能够缓解严重输电阻塞。然而,传统方法在考虑N-1事故时存在维数灾难问题,因此应用DTR技术仍然存在挑战性。为此,提出了一种两阶段分布鲁棒优化(distributionally robust optimization,DRO)方法以提升架空线路的输电能力。首先,构建了架空线路暂态温度计算模型并做适当简化处理,从而保证后续优化模型的凸性。随后,建立了考虑DTR和N-1安全准则的两阶段DRO模型以避免N-1事故下的持续停电,考虑无功与网损的线性化交流潮流模型能够更准确地计算线路潮流。最后,使用IEEE-24节点系统和IEEE-118节点系统验证了所提方法的有效性。
基金the funds from the Department of Science and Technology(DST),Science and Engineering Research Board(SERB),India(No.SRG/2019/001581).
文摘A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is proposed.The developed method is applied to solve problems governed by the Sine–Gordon equation(SGE),the scalar wave equation and elasto-dynamics.Two methods are studied:one is a space-time formulation and the other is a semi-discrete method based on an implicit Runge–Kutta(RK)time integration.The methodology is implemented using the Tensorflow framework and it is tested on several numerical examples.Based on the results,the relative normalized error was observed to be less than 5%in all cases.
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.
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.
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.
