Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetr...Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.展开更多
The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic press...The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.展开更多
The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The ca...The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.展开更多
A numerical simulation model based on an open source Computational Fluid Dynamics （CFD） package-Open Field Operation and Manipulation （OpenFOAM） has been developed to study highly nonlinear steady and unsteady fre...A numerical simulation model based on an open source Computational Fluid Dynamics （CFD） package-Open Field Operation and Manipulation （OpenFOAM） has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid （VOF） method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include： （1） a submerged NACA0012 2-D hydrofoil moving at a constant speed, （2） the Wigley hull moving at a constant speed, （3） numerical wave tank, （4） green water overtopping a fixed 2-D deck, （5） green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.展开更多
This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model...This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model. In order to treat the non-rectangular boundary (or curvilinear boundary), orthogonal boundary-fitted grid is used and the Navier-Stokes Eqs. and k-ε turbulence model are rewritten and discreted in orthogonal curvilinear coordinates. Meanwhile, gas-liquid two-field model theory is introduced to treat the free-surface problem.展开更多
基金The project supported by The National Education Commission of China and NASA under cooperative grant agreement # NCC5-34
文摘Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.
文摘The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No.51009038/E091002）.
文摘The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50739004, 11072154)the Foundation of State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University (Grant No. GKZD 010053-11)
文摘A numerical simulation model based on an open source Computational Fluid Dynamics （CFD） package-Open Field Operation and Manipulation （OpenFOAM） has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid （VOF） method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include： （1） a submerged NACA0012 2-D hydrofoil moving at a constant speed, （2） the Wigley hull moving at a constant speed, （3） numerical wave tank, （4） green water overtopping a fixed 2-D deck, （5） green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.
文摘This paper presents a new numerical method to simulate the high velocity turbulent flow with free surface by solving two-dimensional incompressible unsteady Navier-Stokes Eqs. , together with the k-ε turbulence model. In order to treat the non-rectangular boundary (or curvilinear boundary), orthogonal boundary-fitted grid is used and the Navier-Stokes Eqs. and k-ε turbulence model are rewritten and discreted in orthogonal curvilinear coordinates. Meanwhile, gas-liquid two-field model theory is introduced to treat the free-surface problem.
