A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

The SPH approach to the process of container filling based on non-linear constitutive models

In this work,the transient free surface of container filling with non-linear constitutive equation’s fluids is numerically investigated by the smoothed particle hydrodynamics(SPH) method.Specifically,the filling process of a square container is considered for non-linear polymer fluids based on the Cross model.The validity of the presented SPH is first verified by solving the Newtonian fluid and OldroydB fluid jet.Various phenomena in the filling process are shown,including the jet buckling,jet thinning,splashing or spluttering,steady filling.Moreover,a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.     

Stability of aneurysm solutions in a fluid-filled elastic membrane tube

When a hyperelastic membrane tube is inflatedby an internal pressure, a localized bulge will form when thepressure reaches a critical value. As inflation continues thebulge will grow until it reaches a maximum size after whichit will then propagate in both directions to form a hat-likeprofile. The stability of such bulging solutions has recentlybeen studied by neglecting the inertia of the inflating fluidand it was shown that such bulging solutions are unstableunder pressure control. In this paper we extend this recentstudy by assuming that the inflation is by an inviscid fluidwhose inertia we take into account in the stability analysis.This reflects more closely the situation of aneurysm forma-tion in human arteries which motivates the current series ofstudies. It is shown that fluid inertia would significantly re-duce the growth rate of the unstable mode and thus it has astrong stabilizing effect.     

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.     

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4 π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.     

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling (HC) algorithm for modeling of fluid-structure interaction (FSI) in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled (LC) and tightly coupled (TC) algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible structures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incompressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen’s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical instability issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.     

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.     

Stabilization control of a hovering model insect: lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability (passive stability),because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables (i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect) to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.     

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dynamic fracture toughness(DFT) of high strength steel,using the split Hopkinson tension bar(SHTB) apparatus,combined with a hybrid experimental-numerical method.The center-cracked tension specimen is connected between the bars with a specially designed fixture device.The fracture initiation time is measured by the strain gage method,and dynamic stress intensity factors(DSIF) are obtained with the aid of 3D finite element analysis(FEA).In this approach,the dimensions of the specimen are not restricted by the connection strength or the stress-state equilibrium conditions,and hence plane strain state can be attained conveniently at the crack tip.Through comparison between the obtained results and those in open publication,it is concluded that the experimental data are valid,and the method proposed here is reliable.The validity of the obtained DFT is checked with the ASTM criteria,and fracture surfaces are examined at the end of paper.     

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions(symmetric and non-symmetric)are studied in this work.Reliability of the obtained results is verified by the finite difference method(FDM)and the finite element method(FEM)with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes(regular and non-regular).The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.     

Study on fluid-structure interaction in liquid oxygen feeding pipe systems using finite volume method

The fluid-structure interaction may occur in space launch vehicles,which would lead to bad performance of vehicles,damage equipments on vehicles,or even affect astronauts’ health.In this paper,analysis on dynamic behavior of liquid oxygen (LOX) feeding pipe system in a large scale launch vehicle is performed,with the effect of fluid-structure interaction (FSI) taken into consideration.The pipe system is simplified as a planar FSI model with Poisson coupling and junction coupling.Numerical tests on pipes between the tank and the pump are solved by the finite volume method.Results show that restrictions weaken the interaction between axial and lateral vibrations.The reasonable results regarding frequencies and modes indicate that the FSI affects substantially the dynamic analysis,and thus highlight the usefulness of the proposed model.This study would provide a reference to the pipe test,as well as facilitate further studies on oscillation suppression.     

Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.     

Research of air-cushion isolation effects on high arch dam reservoir

A three-dimensional (3D) finite element model of air-cushion isolated arch dam is presented with the nonlinear gas-liquid-solid multi-field dynamic coupling effect taken into account.In this model,the displacement formulation in Lagrange method,pressure formulation in Euler method,nonlinear contact model based on Coulomb friction law are applied to the air-cushion,reservoir and contraction joint domain,respectively.The dynamic response of Jinping I arch dam with a height of 305 m is analyzed using the seismic records of the Wenchuan Earthquake in 2008.Numerical results show that the air-cushion isolation reduces significantly the hydrodynamic pressure as well as the opening width for the contraction joints of high arch dam.     

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet-to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acous- tic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.     

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effiectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.     

An immersed boundary method for incompressible flows using volume of body function

A simple and effective immersed boundary method using volume of body (VOB) function is implemented on unstructured Cartesian meshes. The flow solver is a second‐order accurate implicit pressure‐correction method for the incompressible Navier–Stokes equations. The domain inside the immersed body is viewed as being occupied by the same fluid as outside with a prescribed divergence‐free velocity field. Under this view a fluid–body interface is similar to a fluid–fluid interface encountered in the volume of fluid (VOF) method for the two‐fluid flow problems. The body can thus be identified by the VOB function similar to the VOF function. In fluid–body interface cells the velocity is obtained by a volume‐averaged mixture of body and fluid velocities. The pressure inside the immersed body satisfies the same pressure Poisson equation as outside. To enhance stability and convergence, multigrid methods are developed to solve the difference equations for both pressure and velocity. Various steady and unsteady flows with stationary and moving bodies are computed to validate and to demonstrate the capability of the current method. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method(NSM) is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,η. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient(a function of Knudsen number),thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.     

考虑固体域几何非线性的固液耦合系统瞬态有限元分析

本文基于理想可压缩流体压力传输方程及增量型ＴｏｔａＩＬａｇｒａｎｇｉａｎ列式，建立了考虑固体域几何非线性的固液耦合系统有限元方程，并开展了非线性分析工作。本文的方法可用于流体域远大于固体域，从而可仅仅研究固体域非线性响应的情况。由于流体域每个节点仅有一个未知量（压力），故流体域的计算规模得以大大减缩。同时，因为本文方法仅需对固体域进行非线性分析，故显著地简化了固液耦合非线性问题的求解工作。本文的方法亦可用于三维分析。     

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation.The model is inspired by the distribution of the measured in-plane and out-of-plane deformation.The inplane displacement of crack-tip fields under both Mode I and mixed-mode(Mode I-II) fracture conditions is measured by using the digital Moire’ method.The deformation characteristics and experimental sector division mode are investigated by comparing the measured displacement fields under different fracture modes.The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.