To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficu...To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.展开更多
A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for-...A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.展开更多
A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) ...A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.展开更多
The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. T...The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. The solutions converge as the polynomial order of the approximation increases. An upper Deborah number (De) limit attains 30 (p≤5). With De increasing, The boundary layers form and develop in the stress, which match closely with those predicted by asymptotic analysis. The results show that numerical oscillations is caused by the boundary layers of stress and can be reduced by increasing the polynomial order of the approximation.展开更多
A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the ve...A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin(SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.展开更多
基金Project supported by the National Natural Science Foundation of China （Nos. 51005209 and 51375449）
文摘To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.
基金the National Natural Science Foundation of China (Grants 41372301 and 51349011)the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109)
文摘A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.
基金Project supported by the National Natural Science Foundation of China (No.51078230)the Research Fund for the Doctoral Program of Higher Education of China (No.200802480056)the Key Project of Fund of Science and Technology Development of Shanghai (No.10JC1407900),China
文摘A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.
文摘The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. The solutions converge as the polynomial order of the approximation increases. An upper Deborah number (De) limit attains 30 (p≤5). With De increasing, The boundary layers form and develop in the stress, which match closely with those predicted by asymptotic analysis. The results show that numerical oscillations is caused by the boundary layers of stress and can be reduced by increasing the polynomial order of the approximation.
文摘A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin(SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.
