The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful ...The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.展开更多
The spinning flow of Boger fluids and the gravity-drawing extrusion flow of a Newtonianas well as a Boger fluid have been simulated by using the stream-line finite element method and thetechnique of matching the finit...The spinning flow of Boger fluids and the gravity-drawing extrusion flow of a Newtonianas well as a Boger fluid have been simulated by using the stream-line finite element method and thetechnique of matching the finite element solutions with those of one-dimensional spinning equations.The recoverable shear strain is proved not to be a basic parameter in characterising thespinning flow of Boger fluids.For Newtonian fluids this technique predicts the experimental jetshape accurately.For Boger fluids,the numerical simulation agrees with the experimental data of spin-ning flow reported by Sridhar et al.,but seems to give an insufficient swelling and over contractionof the jets when drawn by its own weight,compared with the experimental results of Trang andYeow.It implies that the Oldroyd-B model fitting the viscometric-flow data fails to describeaccurately the elasticity and extensional viscosity in the extrusion flow of Boger fluids with gravi-ty-drawing.展开更多
In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an al...In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.展开更多
The mathematical model and the numerical simulation for the transfer of coal bed methane were established based on the combination of the porous flow theory and elastic plastic mechanics theory and the numerical solut...The mathematical model and the numerical simulation for the transfer of coal bed methane were established based on the combination of the porous flow theory and elastic plastic mechanics theory and the numerical solution was given, together with the consideration of the fluid solid interaction between the coal bed gas and coal framework. Then the dispersion for the equation of gas porous flow and coal seam distortion was carried out and the functional analysis equation was obtained. Finally, the coupling solution was educed and calculated by finite element method(FEM) on a model example.展开更多
A simulation was carried out on an unsteady flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate. A generic computer program using the Galerkin finite element meth...A simulation was carried out on an unsteady flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate. A generic computer program using the Galerkin finite element method is employed to solve the coupled non-linear differential equations for velocity and temperature fields. The diffusion equation, the energy equation, the momentum equations and other relevant parameters are transformed into interpretable postfix codes. Numerical calculations are carried out on the flow fields both in the presence of cooling and heating of the plate by free convection currents. The effects of the dimensionless parameters, namely, the Prandtl number, the Eckert number, the modified Grashof number, the Schmidt number and the time on the temperature and velocity distributions are discussed.展开更多
This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based ...This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.展开更多
While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boun...While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.展开更多
The lateral vibration differential equation for a marine riser conveying fluid is derived by use of the small deflection theory, and the effect of internal flow velocity and top tension on the natural frequency of the...The lateral vibration differential equation for a marine riser conveying fluid is derived by use of the small deflection theory, and the effect of internal flow velocity and top tension on the natural frequency of the riser is studied by use of FEM. At the same time, the preliminary relationship between the natural Frequency and riser span under different internal flow velocities is obtained, the effect of riser supports on the vibration frequency is computed. It is found that the natural frequency of the marine riser increases with the increase of top tension, however decreases with the increase of internal flow velocity. In addition, the Frequency decreases drastically with the increase of riser span.展开更多
In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation ...In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined.The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method(GFEM)is used to solve the proposed problem.The effect of local Deborah numbers 0,and ft.local buoyancy parameter z,Prandtl number Pr,Deborah number y,and heat generation/absorption parameter<5 on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms.The result shows the enlargement in the local buoyancy parameter A will improve the velocity field and the heat transfer rate of the boundary layer flow.Moreover,our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect.The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.展开更多
To study the airflow distribution in human nasal cavity during respiration and the characteristic parameters for nasal structure, thirty three-dimensional, anatomically accurate representations of adult nasal cavity m...To study the airflow distribution in human nasal cavity during respiration and the characteristic parameters for nasal structure, thirty three-dimensional, anatomically accurate representations of adult nasal cavity models were reconstructed based on processed tomography images collected from normal people. The airflow fields in nasal cavities were simulated using the fluid dynamics with the finite element software ANSYS. The results showed that the difference of human nasal cavity structure led to varying airflow distribution in the nasal cavities and the main airflow passed through the common nasal meatus. The nasal resistance in the regions of nasal valve and nasal vestibule accounted for more than a half of overall resistance. The characteristic model of nasal cavity was extracted based on the characteristic points and dimensions deducted from the original models. It showed that either the geometric structure or the air-flow field of the two kinds of model was similar. The characteristic dimensions were the characteristic parameters of nasal cavity that properly represented the original model in research for nasal cavity.展开更多
The complex flow has been simulated with finite element method for Navier-Stokes equations. Both two and three dimensional, laminar and turbulent problems were included. The velocity-pressure decoupling method was ado...The complex flow has been simulated with finite element method for Navier-Stokes equations. Both two and three dimensional, laminar and turbulent problems were included. The velocity-pressure decoupling method was adopted and related algorithm was discussed. Effects of turbulence were accounted by large eddy simulation.展开更多
The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media.Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes...The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media.Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results.To avoid this,a multiscale finite element method is developed using bubble functions.It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements.In this paper the performances of different types of bubble functions are evaluated.These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.展开更多
基金Project supported by the National Natural Science Foundation of China and the Natural Science Foundationof Zhejiang Province
文摘The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.
基金Subject supported by the National Natural Science Foundation of China and Natural Science Foundation of Zhejiang Province
文摘The spinning flow of Boger fluids and the gravity-drawing extrusion flow of a Newtonianas well as a Boger fluid have been simulated by using the stream-line finite element method and thetechnique of matching the finite element solutions with those of one-dimensional spinning equations.The recoverable shear strain is proved not to be a basic parameter in characterising thespinning flow of Boger fluids.For Newtonian fluids this technique predicts the experimental jetshape accurately.For Boger fluids,the numerical simulation agrees with the experimental data of spin-ning flow reported by Sridhar et al.,but seems to give an insufficient swelling and over contractionof the jets when drawn by its own weight,compared with the experimental results of Trang andYeow.It implies that the Oldroyd-B model fitting the viscometric-flow data fails to describeaccurately the elasticity and extensional viscosity in the extrusion flow of Boger fluids with gravi-ty-drawing.
文摘In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.
文摘The mathematical model and the numerical simulation for the transfer of coal bed methane were established based on the combination of the porous flow theory and elastic plastic mechanics theory and the numerical solution was given, together with the consideration of the fluid solid interaction between the coal bed gas and coal framework. Then the dispersion for the equation of gas porous flow and coal seam distortion was carried out and the functional analysis equation was obtained. Finally, the coupling solution was educed and calculated by finite element method(FEM) on a model example.
文摘A simulation was carried out on an unsteady flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate. A generic computer program using the Galerkin finite element method is employed to solve the coupled non-linear differential equations for velocity and temperature fields. The diffusion equation, the energy equation, the momentum equations and other relevant parameters are transformed into interpretable postfix codes. Numerical calculations are carried out on the flow fields both in the presence of cooling and heating of the plate by free convection currents. The effects of the dimensionless parameters, namely, the Prandtl number, the Eckert number, the modified Grashof number, the Schmidt number and the time on the temperature and velocity distributions are discussed.
文摘This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.
文摘While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.
基金National 95 Science an Technology Project(96-922-03-03)
文摘The lateral vibration differential equation for a marine riser conveying fluid is derived by use of the small deflection theory, and the effect of internal flow velocity and top tension on the natural frequency of the riser is studied by use of FEM. At the same time, the preliminary relationship between the natural Frequency and riser span under different internal flow velocities is obtained, the effect of riser supports on the vibration frequency is computed. It is found that the natural frequency of the marine riser increases with the increase of top tension, however decreases with the increase of internal flow velocity. In addition, the Frequency decreases drastically with the increase of riser span.
文摘In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined.The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method(GFEM)is used to solve the proposed problem.The effect of local Deborah numbers 0,and ft.local buoyancy parameter z,Prandtl number Pr,Deborah number y,and heat generation/absorption parameter<5 on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms.The result shows the enlargement in the local buoyancy parameter A will improve the velocity field and the heat transfer rate of the boundary layer flow.Moreover,our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect.The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.
文摘To study the airflow distribution in human nasal cavity during respiration and the characteristic parameters for nasal structure, thirty three-dimensional, anatomically accurate representations of adult nasal cavity models were reconstructed based on processed tomography images collected from normal people. The airflow fields in nasal cavities were simulated using the fluid dynamics with the finite element software ANSYS. The results showed that the difference of human nasal cavity structure led to varying airflow distribution in the nasal cavities and the main airflow passed through the common nasal meatus. The nasal resistance in the regions of nasal valve and nasal vestibule accounted for more than a half of overall resistance. The characteristic model of nasal cavity was extracted based on the characteristic points and dimensions deducted from the original models. It showed that either the geometric structure or the air-flow field of the two kinds of model was similar. The characteristic dimensions were the characteristic parameters of nasal cavity that properly represented the original model in research for nasal cavity.
文摘The complex flow has been simulated with finite element method for Navier-Stokes equations. Both two and three dimensional, laminar and turbulent problems were included. The velocity-pressure decoupling method was adopted and related algorithm was discussed. Effects of turbulence were accounted by large eddy simulation.
文摘The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media.Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results.To avoid this,a multiscale finite element method is developed using bubble functions.It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements.In this paper the performances of different types of bubble functions are evaluated.These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.
