In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetso...In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.展开更多
A coupled supersonic inlet-fan Navier–Stokes simulation method was developed by using COMSOL-CFD code. The flow turning, pressure rise and loss effects across blade rows of the fan and the inlet-fan interactions were...A coupled supersonic inlet-fan Navier–Stokes simulation method was developed by using COMSOL-CFD code. The flow turning, pressure rise and loss effects across blade rows of the fan and the inlet-fan interactions were taken into account as source terms of the governing equations without a blade geometry by a body force model. In this model, viscous effects in blade passages can also be calculated directly, which include the exchange of momentum between fluids and detailed viscous flow close to walls. NASA Rotor 37 compressor test rig was used to validate the ability of the body force model to estimate the real performance of blade rows. Calculated pressure ratio characteristics and the distribution of the total pressure, total temperature, and swirl angle in the span direction agreed well with experimental and numerical data. It is shown that the body force model is a promising approach for predicting the flow field of the turbomachinery. Then, coupled axisymmetric mixed compression supersonic inlet-fan simulations were conducted at Mach number 2.8 operating conditions. The analysis includes coupled steady-state performance, and effects of the fan on the inlet. The results indicate that the coupled simulation method is capable of simulating behavior of the supersonic inlet-fan system.展开更多
In the process of China's modern social development, the demand for electric energy in various industries and people’s daily production and life has increased significantly. However, if we rely solely on thermal ...In the process of China's modern social development, the demand for electric energy in various industries and people’s daily production and life has increased significantly. However, if we rely solely on thermal power generation, it will inevitably cause pollution of the natural environment and substantial waste of fossil resources, which also makes the clean energy of solar power generation and wind power generation widely used. In order to further improve the application level of wind turbines, it is necessary to realize the effective distribution and power transmission through box substations. Based on this, this paper makes an in-depth research and Discussion on the foundation construction method of wind turbine substation, hoping to provide necessary reference for the foundation construction technology and comprehensive level improvement of wind turbine substation in China.展开更多
As the environmental problems become increasingly serious,distributed electrical propulsion systems with higher aerodynamic efficiency and lower pollution emission have received extensive attention in recent years.The...As the environmental problems become increasingly serious,distributed electrical propulsion systems with higher aerodynamic efficiency and lower pollution emission have received extensive attention in recent years.The distributed electrical propulsion usually employs the new aero-propulsion integrated configuration.A simulation strategy for internal and external flow coupling based on the combination of lifting line theory and body force method is proposed.The lifting line theory and body force method as source term are embedded into the Navier-Stokes formulation.The lift and drag characteristics of the aero-propulsion coupling configuration are simulated.The results indicate that the coupling configuration has the most obvious lift augmentation at 12°angle of attack,which can provide an 11.11%increase in lift for the airfoil.At 0°angle of attack,the pressure difference on the lip parts provides the thrust component,which results in a lower drag coefficient.Additionally,the failure impact of a ducted fan at the middle or edge on aerodynamics is investigated.For the two failure conditions,the lift of the coupling configuration is decreased significantly by 27.85%and 26.14%respectively,and the lip thrust is decreased by 70.74%and 56.48%respectively.展开更多
This paper focuses on aeroelastic prediction and analysis for a transonic fan rotor with only its“hot”(running)blade shape available,which is often the case in practical engineering such as in the design stage.Based...This paper focuses on aeroelastic prediction and analysis for a transonic fan rotor with only its“hot”(running)blade shape available,which is often the case in practical engineering such as in the design stage.Based on an in-house and well-validated CFD solver and a hybrid structural finite element modeling/modal approach,three main aspects are considered with special emphasis on dealing with the“hot”blade shape.First,static aeroelastic analysis is presented for shape transformation between“cold”(manufacturing)and“hot”blades,and influence of the dynamic variation of“hot”shape on evaluated aerodynamic performance is investigated.Second,implementation of the energy method for flutter prediction is given and both a regularly used fixed“hot”shape and a variable“hot”shape are considered.Through comparison,influence of the dynamic variation of“hot”shape on evaluated aeroelastic stability is also investigated.Third,another common way to predict flutter,time-domain method,is used for the same concerned case,from which the predicted flutter characteristics are compared with those from the energy method.A well-publicized axial-flow transonic fan rotor,Rotor 67,is selected as a typical example,and the corresponding numerical results and discussions are presented in detail.展开更多
The flow over a short intake is characterised by a strong interaction with the fan, that can only be captured when the rotor blades are modelled in the numerical simulations. In this paper, we use a coupled methodolog...The flow over a short intake is characterised by a strong interaction with the fan, that can only be captured when the rotor blades are modelled in the numerical simulations. In this paper, we use a coupled methodology to derive indications about relevant geometric variables affecting the high-incidence operation of an ultra-high bypass ratio turbofan intake with a length-to-diameter ratio of 0.35. By reproducing the effect of the fan through a body force model, we carry out a parametric study of the influence of the contraction ratio and the scarf angle at take-off conditions for a grid of 28 different three-dimensional shapes. The analysis of the selected performance metrics distributions at three angles of attack of 16., 24., and 28. reveals that a contraction ratio higher than 1.20 is needed to avoid separation at high incidence. While for an attached inlet the best performance is found with a moderate scarf angle, in presence of a developed separation the distortion level reduces as the scarf decreases up to negative values. We discuss the correspondence between the distortion indexes and the flow field, highlighting the origin of the detachment for the different geometries, according to the operating condition, and analysing the fan operation in the most distorted case. Finally, we assess the influence of modelling the rotor in the simulations, showing that its suppression effect on the separation at a given incidence depends on the intake geometric features.展开更多
Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constra...Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constraint and minimum mass was established based on the finite element method through these parameters.Then,the sequential quadratic programming algorithm was employed to search the optimal solutions.Several groups of value for initial design variables were chosen,for the purpose of not only finding much more local optimal results but also analyzing which discipline that the variables according to could be benefit for the convergence and robustness.Response surface method and Monte Carlo simulations were used to analyze whether the objective function and constraint function are sensitive to the variation of variables or not.Then the robust results could be found among a group of different local optimal solutions.展开更多
The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for ellipti...The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.展开更多
In this paper,stress states under corresponding condition of an aero-engine fan blade using finite element stress-strain analysis for three work cycles in the 900 h load spectrum are obtained.Through the nominal stres...In this paper,stress states under corresponding condition of an aero-engine fan blade using finite element stress-strain analysis for three work cycles in the 900 h load spectrum are obtained.Through the nominal stress method,we calculated the fatigue notch factor and combined the material characteristics of TC6 to correct the material curve to the fan blades curve. Finally,the fatigue life of a fan blade was estimated using the linear cumulative damage rule and nonlinear cumulative damage theory.展开更多
Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exac...Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.展开更多
Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are...Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.展开更多
基金Supported by BRNS of Bhaba Atomic Research Centre,Mumbai under Department of Atomic Energy,Government of India vide under Grant No.2012/37P/54/BRNS/2382
文摘In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.
基金support of National Natural Science Foundation of China (Nos. 51706008 and 51636001)China Postdoctoral Science Foundation (No. 2017M610742)Aeronautics Power Foundation of China (No. 6141B090315)
文摘A coupled supersonic inlet-fan Navier–Stokes simulation method was developed by using COMSOL-CFD code. The flow turning, pressure rise and loss effects across blade rows of the fan and the inlet-fan interactions were taken into account as source terms of the governing equations without a blade geometry by a body force model. In this model, viscous effects in blade passages can also be calculated directly, which include the exchange of momentum between fluids and detailed viscous flow close to walls. NASA Rotor 37 compressor test rig was used to validate the ability of the body force model to estimate the real performance of blade rows. Calculated pressure ratio characteristics and the distribution of the total pressure, total temperature, and swirl angle in the span direction agreed well with experimental and numerical data. It is shown that the body force model is a promising approach for predicting the flow field of the turbomachinery. Then, coupled axisymmetric mixed compression supersonic inlet-fan simulations were conducted at Mach number 2.8 operating conditions. The analysis includes coupled steady-state performance, and effects of the fan on the inlet. The results indicate that the coupled simulation method is capable of simulating behavior of the supersonic inlet-fan system.
文摘In the process of China's modern social development, the demand for electric energy in various industries and people’s daily production and life has increased significantly. However, if we rely solely on thermal power generation, it will inevitably cause pollution of the natural environment and substantial waste of fossil resources, which also makes the clean energy of solar power generation and wind power generation widely used. In order to further improve the application level of wind turbines, it is necessary to realize the effective distribution and power transmission through box substations. Based on this, this paper makes an in-depth research and Discussion on the foundation construction method of wind turbine substation, hoping to provide necessary reference for the foundation construction technology and comprehensive level improvement of wind turbine substation in China.
基金the funding support from the Taihang Laboratory,China(No.D2024-1-0201).
文摘As the environmental problems become increasingly serious,distributed electrical propulsion systems with higher aerodynamic efficiency and lower pollution emission have received extensive attention in recent years.The distributed electrical propulsion usually employs the new aero-propulsion integrated configuration.A simulation strategy for internal and external flow coupling based on the combination of lifting line theory and body force method is proposed.The lifting line theory and body force method as source term are embedded into the Navier-Stokes formulation.The lift and drag characteristics of the aero-propulsion coupling configuration are simulated.The results indicate that the coupling configuration has the most obvious lift augmentation at 12°angle of attack,which can provide an 11.11%increase in lift for the airfoil.At 0°angle of attack,the pressure difference on the lip parts provides the thrust component,which results in a lower drag coefficient.Additionally,the failure impact of a ducted fan at the middle or edge on aerodynamics is investigated.For the two failure conditions,the lift of the coupling configuration is decreased significantly by 27.85%and 26.14%respectively,and the lip thrust is decreased by 70.74%and 56.48%respectively.
基金This study was supported by National Natural Science Foundation of China(No.11872212),China Postdoctoral Science Foundation Grant(No.2019M650112),Natural Science Foundation of Jiangsu Province,China(No.BK20190386)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China.
文摘This paper focuses on aeroelastic prediction and analysis for a transonic fan rotor with only its“hot”(running)blade shape available,which is often the case in practical engineering such as in the design stage.Based on an in-house and well-validated CFD solver and a hybrid structural finite element modeling/modal approach,three main aspects are considered with special emphasis on dealing with the“hot”blade shape.First,static aeroelastic analysis is presented for shape transformation between“cold”(manufacturing)and“hot”blades,and influence of the dynamic variation of“hot”shape on evaluated aerodynamic performance is investigated.Second,implementation of the energy method for flutter prediction is given and both a regularly used fixed“hot”shape and a variable“hot”shape are considered.Through comparison,influence of the dynamic variation of“hot”shape on evaluated aeroelastic stability is also investigated.Third,another common way to predict flutter,time-domain method,is used for the same concerned case,from which the predicted flutter characteristics are compared with those from the energy method.A well-publicized axial-flow transonic fan rotor,Rotor 67,is selected as a typical example,and the corresponding numerical results and discussions are presented in detail.
文摘The flow over a short intake is characterised by a strong interaction with the fan, that can only be captured when the rotor blades are modelled in the numerical simulations. In this paper, we use a coupled methodology to derive indications about relevant geometric variables affecting the high-incidence operation of an ultra-high bypass ratio turbofan intake with a length-to-diameter ratio of 0.35. By reproducing the effect of the fan through a body force model, we carry out a parametric study of the influence of the contraction ratio and the scarf angle at take-off conditions for a grid of 28 different three-dimensional shapes. The analysis of the selected performance metrics distributions at three angles of attack of 16., 24., and 28. reveals that a contraction ratio higher than 1.20 is needed to avoid separation at high incidence. While for an attached inlet the best performance is found with a moderate scarf angle, in presence of a developed separation the distortion level reduces as the scarf decreases up to negative values. We discuss the correspondence between the distortion indexes and the flow field, highlighting the origin of the detachment for the different geometries, according to the operating condition, and analysing the fan operation in the most distorted case. Finally, we assess the influence of modelling the rotor in the simulations, showing that its suppression effect on the separation at a given incidence depends on the intake geometric features.
文摘Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constraint and minimum mass was established based on the finite element method through these parameters.Then,the sequential quadratic programming algorithm was employed to search the optimal solutions.Several groups of value for initial design variables were chosen,for the purpose of not only finding much more local optimal results but also analyzing which discipline that the variables according to could be benefit for the convergence and robustness.Response surface method and Monte Carlo simulations were used to analyze whether the objective function and constraint function are sensitive to the variation of variables or not.Then the robust results could be found among a group of different local optimal solutions.
基金supported by the U.S.Department of Energy under Contract No.DE-AC02-98CH10886 and by the State of New York
文摘The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.
文摘In this paper,stress states under corresponding condition of an aero-engine fan blade using finite element stress-strain analysis for three work cycles in the 900 h load spectrum are obtained.Through the nominal stress method,we calculated the fatigue notch factor and combined the material characteristics of TC6 to correct the material curve to the fan blades curve. Finally,the fatigue life of a fan blade was estimated using the linear cumulative damage rule and nonlinear cumulative damage theory.
文摘Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.
文摘Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.
