In this thesis, the theoretical and the experimental approaches were performed to study the trans... more In this thesis, the theoretical and the experimental approaches were performed to study the transitional characteristics of aerodynamic coefficients and flow field of the NACA 633-018 airfoil at Re ranging from 1.32×10E4 ~ 1.09×10E5. For theoretical approach, the catastrophe theory was applied to model the aerodynamic transition problem and to predict some aerodynamic characteristics undiscovered before. The so-called catastrophe theory describes the discontinuous phenomena with continuous functions based on the study of singularities of nonlinear functions. Results of aerodynamic loading measurement well verified the validity of the catastrophe theory on the aerodynamically transitional problems and flow visualization provided some physical essences of the flow field about the theory employed here. Finally, the aerodynamic transition of the airfoil was redefined and reexamined through the cusp catastrophe model. Combining the mathematical model and the experimental results, it can be deduced that the transition and sudden change of aerodynamic coefficients, in essence, is a phase-changing process of the topological structure of the flow field. The predicted sudden-changing points of the aerodynamic coefficients match very well with the experimental results within the error margin of α less than 0.5 degree and Re less than two thousand. It indicates that the lift or drag and Re as well as α actually constitutes a cubic hypersurface relationship during the transitional process, which is believed to be a new direction of related aerodynamic researches.
In order to prevent the spurious wave reflections and to improve the computational
efficiency in ... more In order to prevent the spurious wave reflections and to improve the computational efficiency in nanomechanical simulation, this dissertation performs a series of theoretical/numerical studies on the crystalline solid material, including nanomechanics of monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor list, and the application/simulation in laser-assisted nano-imprinting. Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are introduced, which is the foundation for the development of non-reflecting boundary condition and the simulation of corresponding nano materials. Based on the assumptions and the harmonic approximation for the utilized inter-atomic potential, the equation of motion as well as dispersive relation will be given. Furthermore, from the statistical properties of phonon and lattice energy, the thermal amplitude can be calculated and lattice temperature can be defined, which covers the result previously derived by other researchers at high temperatures. Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL) are two main philosophies to derive the generalized Langevin equation, which is a general form of non-reflecting boundary conditions. The general concepts of THK method, including the formulation, kernel generation, time convolution, application assessments and numerical verification, are given. Based on the Crump’s method to express the THK function in the exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from O(N 2 ) down to O(N). By applying the THK method in lattice relaxation and the system under external forcing or heating, it is demonstrated that the THK method indeed provides an isothermally non-reflecting boundary condition in nanomechanical computation. In ABL methods, two major mapping formulations are proposed and the corresponding performances are discussed analytically as well as verified numerically. Starting from the ω -mapping formulation, a series of extensive ABL methods are developed and investigated to improve the performance of wave absorption, and one ABL method is recommended due to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting boundary condition is addressed. Based on a rigorous definition of Verlet radius with respect to temperature and list-updating interval, this study gives an estimation formula of computation time, with which the best algorithm can be chosen according to different total number of atoms, system average density and system average temperature in the nanomechanical system. It has been shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm optimized with a list-updating interval and cell-dividing number is analyzed and shows the reduction of the computation time by 30% ~ 60%, which is verified by the molecular-dynamics simulation for a two-dimensional system. Finally, the molecular dynamics simulation accompanied with the isothermally non-reflecting boundary condition is performed to analyze the related material physics in laser-assisted nano-imprinting. Results show that the implemented boundary condition relax the lattice well, and eventually absorb the wave propagation of momentum/energy during heating and imprinting process. Besides, the temperature/force evolution in substrate, effect of the molding-demolding interval, and surface situation of mold are discussed
In this thesis, the theoretical and the experimental approaches were performed to study the trans... more In this thesis, the theoretical and the experimental approaches were performed to study the transitional characteristics of aerodynamic coefficients and flow field of the NACA 633-018 airfoil at Re ranging from 1.32×10E4 ~ 1.09×10E5. For theoretical approach, the catastrophe theory was applied to model the aerodynamic transition problem and to predict some aerodynamic characteristics undiscovered before. The so-called catastrophe theory describes the discontinuous phenomena with continuous functions based on the study of singularities of nonlinear functions. Results of aerodynamic loading measurement well verified the validity of the catastrophe theory on the aerodynamically transitional problems and flow visualization provided some physical essences of the flow field about the theory employed here. Finally, the aerodynamic transition of the airfoil was redefined and reexamined through the cusp catastrophe model. Combining the mathematical model and the experimental results, it can be deduced that the transition and sudden change of aerodynamic coefficients, in essence, is a phase-changing process of the topological structure of the flow field. The predicted sudden-changing points of the aerodynamic coefficients match very well with the experimental results within the error margin of α less than 0.5 degree and Re less than two thousand. It indicates that the lift or drag and Re as well as α actually constitutes a cubic hypersurface relationship during the transitional process, which is believed to be a new direction of related aerodynamic researches.
In order to prevent the spurious wave reflections and to improve the computational
efficiency in ... more In order to prevent the spurious wave reflections and to improve the computational efficiency in nanomechanical simulation, this dissertation performs a series of theoretical/numerical studies on the crystalline solid material, including nanomechanics of monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor list, and the application/simulation in laser-assisted nano-imprinting. Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are introduced, which is the foundation for the development of non-reflecting boundary condition and the simulation of corresponding nano materials. Based on the assumptions and the harmonic approximation for the utilized inter-atomic potential, the equation of motion as well as dispersive relation will be given. Furthermore, from the statistical properties of phonon and lattice energy, the thermal amplitude can be calculated and lattice temperature can be defined, which covers the result previously derived by other researchers at high temperatures. Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL) are two main philosophies to derive the generalized Langevin equation, which is a general form of non-reflecting boundary conditions. The general concepts of THK method, including the formulation, kernel generation, time convolution, application assessments and numerical verification, are given. Based on the Crump’s method to express the THK function in the exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from O(N 2 ) down to O(N). By applying the THK method in lattice relaxation and the system under external forcing or heating, it is demonstrated that the THK method indeed provides an isothermally non-reflecting boundary condition in nanomechanical computation. In ABL methods, two major mapping formulations are proposed and the corresponding performances are discussed analytically as well as verified numerically. Starting from the ω -mapping formulation, a series of extensive ABL methods are developed and investigated to improve the performance of wave absorption, and one ABL method is recommended due to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting boundary condition is addressed. Based on a rigorous definition of Verlet radius with respect to temperature and list-updating interval, this study gives an estimation formula of computation time, with which the best algorithm can be chosen according to different total number of atoms, system average density and system average temperature in the nanomechanical system. It has been shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm optimized with a list-updating interval and cell-dividing number is analyzed and shows the reduction of the computation time by 30% ~ 60%, which is verified by the molecular-dynamics simulation for a two-dimensional system. Finally, the molecular dynamics simulation accompanied with the isothermally non-reflecting boundary condition is performed to analyze the related material physics in laser-assisted nano-imprinting. Results show that the implemented boundary condition relax the lattice well, and eventually absorb the wave propagation of momentum/energy during heating and imprinting process. Besides, the temperature/force evolution in substrate, effect of the molding-demolding interval, and surface situation of mold are discussed
Uploads
Papers by James D.B. Wang
633-018 airfoil at Re ranging from 1.32×10E4 ~ 1.09×10E5. For theoretical approach, the catastrophe theory was applied to model the aerodynamic transition problem and to predict
some aerodynamic characteristics undiscovered before. The so-called catastrophe theory describes the discontinuous phenomena with continuous functions based on the study of
singularities of nonlinear functions. Results of aerodynamic loading measurement well verified the validity of the catastrophe theory on the aerodynamically transitional problems and flow visualization provided some physical essences of the flow field about the theory employed here. Finally, the aerodynamic transition of the airfoil was redefined and reexamined through the cusp catastrophe model.
Combining the mathematical model and the experimental results, it can be deduced that the transition and sudden change of aerodynamic coefficients, in essence, is a
phase-changing process of the topological structure of the flow field. The predicted sudden-changing points of the aerodynamic coefficients match very well with the experimental results within the error margin of α less than 0.5 degree and Re less than two thousand. It indicates that the lift or drag and Re as well as α actually constitutes a cubic hypersurface relationship during the transitional process, which is believed to be a new direction of related aerodynamic researches.
efficiency in nanomechanical simulation, this dissertation performs a series of
theoretical/numerical studies on the crystalline solid material, including nanomechanics of
monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor
list, and the application/simulation in laser-assisted nano-imprinting.
Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are
introduced, which is the foundation for the development of non-reflecting boundary condition
and the simulation of corresponding nano materials. Based on the assumptions and the
harmonic approximation for the utilized inter-atomic potential, the equation of motion as well
as dispersive relation will be given. Furthermore, from the statistical properties of phonon
and lattice energy, the thermal amplitude can be calculated and lattice temperature can be
defined, which covers the result previously derived by other researchers at high temperatures.
Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL)
are two main philosophies to derive the generalized Langevin equation, which is a general
form of non-reflecting boundary conditions. The general concepts of THK method, including
the formulation, kernel generation, time convolution, application assessments and numerical
verification, are given. Based on the Crump’s method to express the THK function in the
exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from O(N 2 ) down to O(N). By applying the THK method
in lattice relaxation and the system under external forcing or heating, it is demonstrated that
the THK method indeed provides an isothermally non-reflecting boundary condition in
nanomechanical computation.
In ABL methods, two major mapping formulations are proposed and the corresponding
performances are discussed analytically as well as verified numerically. Starting from the
ω -mapping formulation, a series of extensive ABL methods are developed and investigated
to improve the performance of wave absorption, and one ABL method is recommended due
to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting
boundary condition is addressed.
Based on a rigorous definition of Verlet radius with respect to temperature and
list-updating interval, this study gives an estimation formula of computation time, with which
the best algorithm can be chosen according to different total number of atoms, system
average density and system average temperature in the nanomechanical system. It has been
shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a
system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm
optimized with a list-updating interval and cell-dividing number is analyzed and shows the
reduction of the computation time by 30% ~ 60%, which is verified by the
molecular-dynamics simulation for a two-dimensional system.
Finally, the molecular dynamics simulation accompanied with the isothermally
non-reflecting boundary condition is performed to analyze the related material physics in
laser-assisted nano-imprinting. Results show that the implemented boundary condition relax
the lattice well, and eventually absorb the wave propagation of momentum/energy during
heating and imprinting process. Besides, the temperature/force evolution in substrate, effect
of the molding-demolding interval, and surface situation of mold are discussed
633-018 airfoil at Re ranging from 1.32×10E4 ~ 1.09×10E5. For theoretical approach, the catastrophe theory was applied to model the aerodynamic transition problem and to predict
some aerodynamic characteristics undiscovered before. The so-called catastrophe theory describes the discontinuous phenomena with continuous functions based on the study of
singularities of nonlinear functions. Results of aerodynamic loading measurement well verified the validity of the catastrophe theory on the aerodynamically transitional problems and flow visualization provided some physical essences of the flow field about the theory employed here. Finally, the aerodynamic transition of the airfoil was redefined and reexamined through the cusp catastrophe model.
Combining the mathematical model and the experimental results, it can be deduced that the transition and sudden change of aerodynamic coefficients, in essence, is a
phase-changing process of the topological structure of the flow field. The predicted sudden-changing points of the aerodynamic coefficients match very well with the experimental results within the error margin of α less than 0.5 degree and Re less than two thousand. It indicates that the lift or drag and Re as well as α actually constitutes a cubic hypersurface relationship during the transitional process, which is believed to be a new direction of related aerodynamic researches.
efficiency in nanomechanical simulation, this dissertation performs a series of
theoretical/numerical studies on the crystalline solid material, including nanomechanics of
monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor
list, and the application/simulation in laser-assisted nano-imprinting.
Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are
introduced, which is the foundation for the development of non-reflecting boundary condition
and the simulation of corresponding nano materials. Based on the assumptions and the
harmonic approximation for the utilized inter-atomic potential, the equation of motion as well
as dispersive relation will be given. Furthermore, from the statistical properties of phonon
and lattice energy, the thermal amplitude can be calculated and lattice temperature can be
defined, which covers the result previously derived by other researchers at high temperatures.
Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL)
are two main philosophies to derive the generalized Langevin equation, which is a general
form of non-reflecting boundary conditions. The general concepts of THK method, including
the formulation, kernel generation, time convolution, application assessments and numerical
verification, are given. Based on the Crump’s method to express the THK function in the
exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from O(N 2 ) down to O(N). By applying the THK method
in lattice relaxation and the system under external forcing or heating, it is demonstrated that
the THK method indeed provides an isothermally non-reflecting boundary condition in
nanomechanical computation.
In ABL methods, two major mapping formulations are proposed and the corresponding
performances are discussed analytically as well as verified numerically. Starting from the
ω -mapping formulation, a series of extensive ABL methods are developed and investigated
to improve the performance of wave absorption, and one ABL method is recommended due
to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting
boundary condition is addressed.
Based on a rigorous definition of Verlet radius with respect to temperature and
list-updating interval, this study gives an estimation formula of computation time, with which
the best algorithm can be chosen according to different total number of atoms, system
average density and system average temperature in the nanomechanical system. It has been
shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a
system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm
optimized with a list-updating interval and cell-dividing number is analyzed and shows the
reduction of the computation time by 30% ~ 60%, which is verified by the
molecular-dynamics simulation for a two-dimensional system.
Finally, the molecular dynamics simulation accompanied with the isothermally
non-reflecting boundary condition is performed to analyze the related material physics in
laser-assisted nano-imprinting. Results show that the implemented boundary condition relax
the lattice well, and eventually absorb the wave propagation of momentum/energy during
heating and imprinting process. Besides, the temperature/force evolution in substrate, effect
of the molding-demolding interval, and surface situation of mold are discussed