A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficien...A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficient removal of gas bubbles. The electromagnetic fields were described by solving Maxwell＇s equations. The bubble movement was studied with two-way coupling Euler-Lagrange approach. The interplay of current density and bubble nucleation rate was included. The collision and coalescence of bubbles were considered. Random walk module was invoked for involving the chaotic effect of the turbulence. The numerical results were validated by experimental measurements. The results indicate that the current distribution and the bubble nucleation periodically change. Due to the slot, the bubble elimination heavily increases. The contribution of the slot to the bubble removal exceeds 50% in the case of three currents, and the promotion of the slot decays with increasing the current.展开更多
The passenger side airbags(PAB)are usually larger than the driver airbags.Therefore,the inflator of PAB is more powerful with high mass rate.In this paper,an Arbitrary Lagrangian-Eulerian(ALE)method based computationa...The passenger side airbags(PAB)are usually larger than the driver airbags.Therefore,the inflator of PAB is more powerful with high mass rate.In this paper,an Arbitrary Lagrangian-Eulerian(ALE)method based computational method is developed to simulate the deployment of a PAB.The tank test is used to test the property of the inflator.Through comparison of numerical and experimental results,the ALE method is validated.Based on a failed airbag test,a smaller sub-airbag is placed inside PAB to disperse the gas flow to directions which are less damaging.By applying dynamic relaxation,the initial mesh corresponding to the experimental terms is obtained.The results indicate that the interior pressure and impact force coincide with the test data,and the method in this paper is capable of capturing airbag deploying process of the PAB module accurately.展开更多
Numerical simulation of gas-solid flow behaviors in a rectangular fluidized bed is carried out three dimensionally by the discrete element method (DEM).Euler method and Lagrange method are employed to deal with the ga...Numerical simulation of gas-solid flow behaviors in a rectangular fluidized bed is carried out three dimensionally by the discrete element method (DEM).Euler method and Lagrange method are employed to deal with the gas phase and solid phase respectively.The collided force among particles,striking force between particle and wall,drag force,gravity,Magnus lift force and Saffman lift force are considered when establishing the mathematic models.Soft-sphere model is used to describe the collision of particles.In addition,the Euler method is also used for modeling the solid phase to compare with the results of DEM.The flow patterns,particle mean velocities,particles' diffusion and pressure drop of the bed under typical operating conditions are obtained.The results show that the DEM method can describe the detailed information among particles,while the Euler-Euler method cannot capture the micro-scale character.No matter which method is used,the diffusion of particles increases with the increase of gas velocity.But the gathering and crushing of particles cannot be simulated,so the energy loss of particles' collision cannot be calculated and the diffusion by using the Euler-Euler method is larger.In addition,it is shown by DEM method,with strengthening of the carrying capacity,more and more particles can be schlepped upward and the dense suspension upflow pattern can be formed.However,the results given by the Euler-Euler method are not consistent with the real situation.展开更多
Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simul...Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simulation is used to simulate the fluid phase for high accuracy in both two approaches.The mean and fluctuating PM concentrations,as well as instantaneous PM distributions at different downstream and height positions,are presented.Higher mean and fluctuating particle concentrations are predicted by the Eulerian approach than the Lagrangian one.For the Lagrangian method,PM distributions cluster near the ground-wall because of the preferential dispersion of inertial particles by turbulence structures in the ABL,while it cannot be obtained by the Eulerian single fluid method,because the two-phase velocity differences are neglected in the Eulerian method.展开更多
In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic ...In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.展开更多
In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus （HIV-1） infection is presented. Numerical solutions are obtained using a generalized Euler method （GEM） to handle the...In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus （HIV-1） infection is presented. Numerical solutions are obtained using a generalized Euler method （GEM） to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These compar- isons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.展开更多
基金Project(51434005) supported by the National Natural Science Foundation of China
文摘A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficient removal of gas bubbles. The electromagnetic fields were described by solving Maxwell＇s equations. The bubble movement was studied with two-way coupling Euler-Lagrange approach. The interplay of current density and bubble nucleation rate was included. The collision and coalescence of bubbles were considered. Random walk module was invoked for involving the chaotic effect of the turbulence. The numerical results were validated by experimental measurements. The results indicate that the current distribution and the bubble nucleation periodically change. Due to the slot, the bubble elimination heavily increases. The contribution of the slot to the bubble removal exceeds 50% in the case of three currents, and the promotion of the slot decays with increasing the current.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2013CB036101 and 2010CB832704)the National Natural Science Foundation of China(Grant Nos.51221961,51279030 and 51309040)
文摘The passenger side airbags(PAB)are usually larger than the driver airbags.Therefore,the inflator of PAB is more powerful with high mass rate.In this paper,an Arbitrary Lagrangian-Eulerian(ALE)method based computational method is developed to simulate the deployment of a PAB.The tank test is used to test the property of the inflator.Through comparison of numerical and experimental results,the ALE method is validated.Based on a failed airbag test,a smaller sub-airbag is placed inside PAB to disperse the gas flow to directions which are less damaging.By applying dynamic relaxation,the initial mesh corresponding to the experimental terms is obtained.The results indicate that the interior pressure and impact force coincide with the test data,and the method in this paper is capable of capturing airbag deploying process of the PAB module accurately.
基金Supported by National Natural Science Foundation of China(51006106)National High Technology Research and Development of China 863 Program(2006AA05A103)
文摘Numerical simulation of gas-solid flow behaviors in a rectangular fluidized bed is carried out three dimensionally by the discrete element method (DEM).Euler method and Lagrange method are employed to deal with the gas phase and solid phase respectively.The collided force among particles,striking force between particle and wall,drag force,gravity,Magnus lift force and Saffman lift force are considered when establishing the mathematic models.Soft-sphere model is used to describe the collision of particles.In addition,the Euler method is also used for modeling the solid phase to compare with the results of DEM.The flow patterns,particle mean velocities,particles' diffusion and pressure drop of the bed under typical operating conditions are obtained.The results show that the DEM method can describe the detailed information among particles,while the Euler-Euler method cannot capture the micro-scale character.No matter which method is used,the diffusion of particles increases with the increase of gas velocity.But the gathering and crushing of particles cannot be simulated,so the energy loss of particles' collision cannot be calculated and the diffusion by using the Euler-Euler method is larger.In addition,it is shown by DEM method,with strengthening of the carrying capacity,more and more particles can be schlepped upward and the dense suspension upflow pattern can be formed.However,the results given by the Euler-Euler method are not consistent with the real situation.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50876053 and 11132005)Opening fund of State of Key Laboratory of Nonlinear Mechanics
文摘Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simulation is used to simulate the fluid phase for high accuracy in both two approaches.The mean and fluctuating PM concentrations,as well as instantaneous PM distributions at different downstream and height positions,are presented.Higher mean and fluctuating particle concentrations are predicted by the Eulerian approach than the Lagrangian one.For the Lagrangian method,PM distributions cluster near the ground-wall because of the preferential dispersion of inertial particles by turbulence structures in the ABL,while it cannot be obtained by the Eulerian single fluid method,because the two-phase velocity differences are neglected in the Eulerian method.
基金supported by the National Science Foundation(No.DMS-0913982)
文摘In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.
文摘In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus （HIV-1） infection is presented. Numerical solutions are obtained using a generalized Euler method （GEM） to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These compar- isons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.
