Theoretical Analysis and Experimental Verification on Flow Field of Piezoelectric Pump with Unsymmetrical Slopes Element

Regular valveless piezoelectric pumps have rectifying elements outside their chambers to produce net flow. These rectifying elements outside the chamber will increase the overall volume of the pump and prevent its minimization. Valveless piezoelectric pump with unsymmetrical slopes elements（USE）, proposed in this paper, differs from other valveless pumps in that it is easy to be minimized by developing the chamber bottom as such a rectifying element. In this research, the working principle of the proposed pump was analyzed first. Numerical models were thereby established and numerical simulation was conducted to the chamber flow field with the method of time-dependent velocity. The effects of the USEs on the flow field in the chamber were shown clearly in simulation. And the particular feature of flow field in the chamber was discovered. It behaves a complex flow field, in which strong turbulent occurs companying a lot of vortexes in different directions and different sizes. This feature is just opposite to what regular piezoelectric pumps expect： a moderate flow field. The turbulent flow could be used to have different liquids stirred and well mixed in the chamber to produce homogeneous solution, emulsion or turbid liquid. Meanwhile, numerical simulation also presents the effect of the angles difference of the two slopes upon the flow field, and upon the flow rate of the pump, which fits to the theoretical analysis. Experiments with the proposed pump were also conducted to verify the numerical results. In these experiments, six USEs with different slope angles were used for efficiency tests, which proved the validity and reliability of the numerical analysis. The data obtained from numerical analysis agree well with that from the experiments. The errors ranged from 4.4% to 14.8% with their weighted average error being 9.7%.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

ANISOTROPIC MULTISTAGE FINITE ELEMENT METHOD FOR TWO DIMENSIONAL VISCOUS TRANSONIC FLOW IN TURBOMACHINERY

A new method based on the anisotropic tensor force finite element and Taylor-Galerkin finite element is presented in the present paper.Its application to two-dimensional viscous transonic flow in turbomachinery improves the conver- gence rate and stability of calculation,and the results obtained agree well with the experimental measurements.

GPU-based discrete element simulation on flow stability of flat-bottomed hopper

In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow rate indicates an unstable discharge. The flow regions of the unstable discharge were compared with that of the stable discharge, a key transformation zone, where the voidage showed the largest difference between unstable and stable discharge, was revealed. To identify the relevance of the key transformation zone and the hopper flow stability, the voidage variation of the key transformation zone with material height reducing was studied.A sharp increase in the voidage in the key transformation zone was considered to be the standard for judging the unstable hopper flow, and the ‘Top–Bottom effect' of the hopper was defined, which indicated the hopper flow was unstable when the hopper only had the top area and the bottom area, because the voidage of particles in the top area and the bottom area were both variables.

A PENALTY-HYBRID FINITE ELEMENT ANALYSIS OF STOKES FLOW

A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.

Simulation of Temperature and Flow Field by Three Dimension Finite ElementMethod for Castex Process of AS Wire

Castex of AS wire is a new technology of near net shape. To study the variation of temperature and velocity of liquid (or semisolid) aluminum during dynamic solidification the numerical simulation was carried out with the theory of heat-transfer and hydrodynamics by means of 3-dimensional finite element method. From simulation results, it is found that the variation of temperature and velocityis mainly influenced by the casting temperature of aluminum, rotating speed of Castex wheel and flow of cooling water. Among theseinfluencing factors, the casting temperature distributes most to the length of liquid phase metal. Moreover, the faster the metal solidifies,the higher the metal there moves with the overall trend of descending from the bottom of the wheel to the shoe wall as well as from sidewalls to the center of wheel groove. In comparison with the practical value, the simulation is reliable.

CONSTRUCTION OF MODIFIED TAYLOR－GALERKIN FINITE ELEMENTS AND ITS APPLICATION IN COMPRESSIBLE FLOW COMPUTATION

In this paper we begin with Taylor-Galerkin Finite Elements,then n improve it completely and finally construct Modified Taylor-Galerkin Finite Elements.Computation is done by two methods to study two kinds of subsonic and supersonic flow.field.The results show that the new one is much better than the old one.

INFLUENCE OF SURFACE-ACTIVE ELEMENTS ON FLUID FLOW OF MIG WELDPOOL

A mathematical model describing the behavior of metal inert gas (MIG) welding isformulated in the paper. By means of numerical simulation, the influence of surface-active elements on fluid flow of MIG weldpool is studied. The calculation resultsshow that by adding surface-active elements, the fluid flow behavior is drasticallychanged and the flow fluid flows from lower to upper in vertical direction at the rearof weldpool (w>0). The physical phenomenon is explained from the viewpoint of fluidflow behavior of weldpool that the properties of weld metal is greatly improved andthe content of diffused hydrogen is reduced, thus providing a basis for developing newwelding materials.

Numerical Calculation of Marine Propeller Hydrodynamic Characteristics in Unsteady Flow by Boundary Element Method

In this paper, a low order potential based on surface panel method is used for the analysis of marine propellers in unsteady flow. A linear propeller wake model is employed and its geometry is assumed to be independent of the time. The calculation in time domain is carried out from a moment when the rotation of the propeller becomes steady instead of from the moment when the rotation starts from stationary condition. At every time step a linear algebraic equation established on a key blade is solved numerically combined with the Kutta pressure condition. The calculated results by developed code indicate good convergency and effectiveness of present algorithm for conventional propellers and highly skewed propellers.

FINITE ELEMENT ANALYSIS OF THE FREE EXTRUSION FLOWS OF BOGER FLUIDS

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.

A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.

Finite element modeling to study flow induced deformation of biofilm

Fluid flow past the biofilm surface can bring external force to biofilm which could result in biofilm deformation and detachment. The flow velocity have significant effect on determining biofilm deformation and detachment. In this work, finite element method was adapted to study the flow induced deformation of biofilm in varied flow conditions.

FINITE ELEMENT ANALYSES OF THE EXTRUSION FLOWS OF BOGER FLUIDS WITH END-DRAWING AND GRAVITY-DRAWING

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.

Finite Element Numerical Simulation and PIV Measurement of Flow Field inside Metering-in Spool Valve

The finite element method （FEM） and particle image velocimetry （PIV） technique are utilized to get the flow field along the inlet passage, the chamber, the metering port and the outlet passage of spool valve at three different valve openings. For FEM numerical simulation, the stream function ψ-vorticity ω forms of continuity and Navier-Stokes equations are employed and FEM is applied to discrete the equations. Homemade simulation codes are executed to compute the values of stream function and vorticity at each node in the flow domain, then according to the correlation between stream function and velocity components, the velocity vectors of the whole field are calculated. For PIV experiment, pulse Nd： YAG laser is exploited to generate laser beam, cylindrical and spherical lenses are combined each other to produce 1.0 mm thickness laser sheet to illuminate the object plane, Polystyrene spherical particle with diameter of 30-50 μm is seeded in the fluid as a tracing particles, Kodak ES 1.0 CCD camera is employed to capture the images of interested, the images are processed with fast Fourier transform （FFT） cross-correlation algorithm and the processing results is displayed. Both results of numerical simulation and PIV experimental show that there are three main areas in the spool valve where vortex is formed. Numerical results also indicate that the valve opening have some effects on the flow structure of the valve. The investigation is helpful for qualitatively analyzing the energy loss, noise generating, steady state flow forces and even designing the geometry structure and flow passage.

要素流动对城乡融合发展的影响机理与空间分异研究

城乡要素双向自由流动有利于提高要素配置效率和优化城乡关系,促进城乡融合发展。现有关于要素流动对城乡融合发展的研究主要围绕传统生产要素对城乡融合发展的研究展开讨论,鲜有文献将数据这一新型生产要素纳入城乡要素流动范围并探索其对城乡融合发展的影响机理。基于2010—2021年中国31个省份的面板数据,在测算要素流动、城乡融合发展水平的基础上,构建双向固定效应模型、地理加权回归模型和中介效应模型实证检验要素流动对城乡融合发展的影响效应及作用机制。研究发现:第一,全国要素流动总指数呈现出小幅度增长的态势,位于均值之上的地区中64%是城乡融合发展试验区,说明城乡融合发展政策实施具有重要的引导作用;第二,要素流动显著促进城乡融合发展,这一结论在引入城乡之间距离作为工具变量进行内生性检验、采用删除4个直辖市和缩短时间窗口的方法进行稳健性检验之后仍然成立;第三,空间异质性分析中,劳动力、土地和数据要素始终表现出促进城乡融合发展的作用,随着时间的推移,土地要素对不同地区城乡融合发展影响程度逐渐增强、影响范围逐步扩大,技术要素对城乡融合发展的促进逐渐凸现,由华东和华南地区向东北和西南地区转移;第四,在要素流动影响城乡融合发展的过程中,电商销售是要素流动影响城乡融合发展的重要途径,农业机械化和产业结构变迁并未发挥出中介变量的作用,不同于已有的研究结果。因此,今后持续深化城乡融合发展的内涵与外延、拓展深度与广度;始终以习近平新时代中国特色社会主义思想为指导,运用科学的世界观和方法论,坚持整体推进与试点示范相统一的指导原则,推广实践中形成的典型经验。研究结论为城乡要素双向合理流动的机制建立、城乡融合发展体制机制的健全提供了理论和经验上的参考。

Variable-Domain Variational Finite Element Solution of I_A Inverse Problem of 2-D Unsteady Compressible Flow around Oscillating Airfoils

In this paper, on the basis of the variational principles developed the finite element method (FEM) is employed for numerical solution of the inverse pro blem of 2 D unsteady compressible flow around oscillating airfoils by incorporating the non reflecting far field boundary conditions and a new unsteady Kutta condition. All unknown boundary (airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are determined via the functional variation with variable domain and artificial density concept. For the numerical realization of the variable domain variation, a special finite element with self adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.

COUPLED SIMULATION OF 3D ELECTRO-MAGNETO-FLOW FIELD IN HALL-HEROULT CELLS USING FINITE ELEMENT METHOD

Two full 3D steady mathematical models are developed by finite element method （FEM） to calcalate coupled physics fields. the electro-magnetic model is built and solved first and so is the fluid motion model with the acquired electromagnetic force as source body forces in Navier-Stokes equations. Effects caused by the ferromagnetic shell, busbar system around, and open boundary problem as well as inside induced current were considered in terms of the magnetic field. Furthermore, a new modeling method is found to set up solid models and then mesh them entirely with so-called structuralized grids, namely hex-mesh. Examples of 75kA prebaked cell with two kinds of busbar arrangements are presented. Results agree with those disclosed in the literature and confirm that the coupled simulation is valid. It is also concluded that the usage of these models facilitates the consistent analysis of the electric field to magnetic field and then flow motion to the greater extent, local distributions of current density and magnetic flux density are very much dependent on the cell structure, the steel shell is a shield to reduce the magnetic field and flow pattern is two dimensional in the main body of the metal pad.

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from 100 to 1000. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

SUPG finite element method based on penalty function for lid-driven cavity flow up to Re = 27500

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.