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A new exact solution of the two-dimensional Oberbeck-Boussinesq equations has been found in this paper. The solution is found in the case of the nonuniform distribution of velocities and a linear heat source at the upper boundary of an infinite layer of a viscous incompressible fluid. Analysis of polynomial solutions describing the natural fluid convection is presented. The existence of points at which hydrodynamic fields vanish inside the fluid layer is demonstrated. [ABSTRACT FROM AUTHOR]

Exact solutions for three-dimensional nonlinear flows of a viscous incompressible fluid are examined. These solutions belong to Lin’s class of solutions, which are velocities linearly dependent on a part of coordinates. This allows these solutions to be used for the description of large-scale currents of the World Ocean. The obtained exact solution describes the flow of a vertical vortex fluid. A vertical twist in the fluid arises from the consideration of inertia forces and the nonuniform velocity distribution on the free boundary of the fluid layer. This solution allows one to describe counterflows of an incompressible fluid for flows in a thin layer. Thus, the obtained exact solution of the Navier-Stokes equations describes a new mechanism of momentum transfer in a fluid. The obtained solutions are analyzed in this paper. The existence of stagnation points for the flow of a vertical vortex fluid in an infinite layer with permeable boundaries is shown. [ABSTRACT FROM AUTHOR]

This paper focus on the numerical approximation of a fluid-structure-acoustic interaction problem. The two-dimensional non-linear fluid-structure interaction problem is mathematically modelled by the linear elastic problem coupled with the incompressible Navier-Stokes equations. The arbitrary Lagrangian-Eulerian method is used in order to treat the moving domain. The acoustic problem is solved with the perturbed convective wave equation analogy. The finite element discretization is described and the the modified streamline-upwind/Petrov-Galerkin stabilization is used for the flow problem. Numerical results are presented. [ABSTRACT FROM AUTHOR]

The paper proposes a numerical investigation based on RANS computation for solving the viscous flow around a ship podded propulsion unit. A set of computations has been performed to better understand the influences exerted by different configurations on the wake structure in the propeller disk in the pushing type case. The RANS computation method is employed to evaluate the flow field structure around the podded propulsion units and the forces acting on it. Hydrodynamic design podded system has not, so far, been fully established in the propeller-pod-strut system. It is necessary to use a reliable procedure in the design of such propulsion systems to increase the propulsion efficiency. In an attempt to meet these needs, the present paper introduces a numerical procedure to analyze the hydrodynamic performance of the propeller and steering system using a combined lifting line and RANS methods. [ABSTRACT FROM AUTHOR]

This paper presents numerical simulation results of the deformation and breakup of an isolated liquid drop suspended in an ambient, immiscible viscous fluid under shear flow. The model predicting the dynamic behavior of the drop is based on a diffuse interface method. The interface between the two fluids is tracked by an order parameter, namely the mass concentration. The fully transient, three dimensional Navier-Stokes equations for an incompressible fluid are solved by a projection method on a fixed Cartesian grid which the interface moves through to ensure accurate calculation of the surface evolution. Surface tension effects are incorporated into the model through a modified stress. This paper focuses on steady shape analysis and the end pinching mechanism of drop breakup. The numerical results of drop deformation and breakup show very good agreement with theoretical analysis and experimental observations, which indicate that the diffuse interface method can successfully capture the main behavior of the drop deformation and breakup Detailed instructions for typing your article are given in the following. [ABSTRACT FROM AUTHOR]

In this paper, a two phase model to compute liquid-liquid flows is presented. We consider that one phase is a highly viscous thermodependent liquid (polymer phase), whereas the second one is a low viscosity low temperature fluid (water). The first part of this paper concerns capture of the interface between the water and the polymer (or determination of the phase field function). Classical VOF and Level set techniques have been implemented and were ameliorated using mesh adaptation techniques. To accurately determine the velocity field, a two-phase formulation is considered, based in the theory of mixtures, and we introduce a scalar parameter, the phase fraction quantifying the presence of each phase in each point of the computational domain. A friction type coupling between both phases is retained. Using the mixed finite element method within an eulerian framework, we calculate in a single system the whole kinematic variables for both liquids (velocity and pressure of each phase). Results are shown, for 2D and 3D parts. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The article presents a research paper which discusses a unified, computational synthesis of analytical and numerical calculations to study stability of viscous unsteady nonparallel flows. The research paper shows that the stability analysis of the unsteady nonparallel base flows via separation of variables may provide useful testing for the numerical methods used in the hydrodynamic stability studies.

The paper concerns the design of kinetic models on finite grids for the numerical simulation of flows close to the fluid dynamic limit. Taking into account numerical efficiency, we restrict to small grids. We discuss the limitations of such an approach, derive a suitable mathematical framework and address questions of the design of appropriate grids and corresponding two-particle collision models. [ABSTRACT FROM AUTHOR]

Boundary-layer combustion, a major characteristic of a hybrid rocket engine, is a complex phenomenon of fluid dynamics and combustion. Its rate-limiting process is diffusion, whereas combustion reactions are generally very fast. One of numerical approaches for this is to solve simultaneously the Navier-Stokes equations with the transport equation for the mixture fraction. Chemical composition of the combustion gas can be determined by solving local chemical equilibrium for a given flow and mixture fraction fields. The governing equations for a diffusion-combustion flow with fast chemistry are characterized by the convective term, the diffusion term, and the chemical equilibrium calculation. As seen from the numerical methods for these, the convective-flux Jacobian and the numerical flux schemes, upwind higher precision approximation and limiter design, and chemical equilibrium calculation method. This study is focused especially on upwind higher precision approximation method. In this paper, by solving test problems such as quasi-one-dimensional hybrid rocket flow, assessment is made on a variety of numerical methods with respect to precision and convergence. [ABSTRACT FROM AUTHOR]

This paper presents a potential flow numerical solution for the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible fluid in a stratified shear flow. As a problem: the two-fluid model becomes illposed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the potential equation method for the time derivatives in conjunction with the two-fluid model is analyzed. The normal stress balance (with the normal viscous stress) at the interface for the two-fluid model is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis shows that: stability condition for two-fluid with equal kinematic viscosity ratio and inviscid flow, supply numerical stability. Excellent agreement has obtained according to analytical result that existing of imaginary part in solution which specialized this method. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density and viscosity ratios in rectangular channel. Simulation of this model has implemented by writing a code in FORTRAN programming. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation on heat transfer in power-law fluids aligned with a semi-infinite plate in the presence of viscous dissipation and radiation. The effects of power-law viscosity on temperature field are taken into account by assuming that the thermal diffusivity varies as a function of velocity gradient. Since the problem is very complex to solve analytically, a similarity transformation based on the least square approximation principle and shooting technique may be a considerable approach. The effects of generalized Prandtl number, viscous dissipation and radiation on the heat transfer are tabulated. [ABSTRACT FROM AUTHOR]

This paper describes the formulation of fluid equation in application of Smoothed Particle Hydrodynamics (SPH) and ability of meshfree SPH method to model lid driven cavity problem. Although the lid driven cavity problem are usually successfully solved using traditional Finite Difference Method (FDM), they are all depends on the mesh ability. This SPH method is relatively new approach in solving fluid flow problem. The SPH method can be used to discretize the Navier-Stokes equation that governs fluid flows. In the present study, the ability of the meshless SPH method are investigate in simulating the fluid flow which is in 2D lid driven cavity problem. The result of this problem using meshfree SPH method is compare to the solution done using meshing software Fluent with Reynold Number 1 and it shows that the SPH method give good comparison to the FDM method. [ABSTRACT FROM AUTHOR]

This paper presents a numerical research on the solid particle behavior in a shear driven cavity using an Eulerian-Lagrangian approach. The dynamics of a solid particle in a lid-driven cavity was investigated at a wide range of particle-fluid density ratio. The results show that the particle trajectories are critically dependence on the magnitude of density ratio and the vortex behavior in the cavity. [ABSTRACT FROM AUTHOR]

A Finite Volume Method is employed for solving the coupled fluid/structure problem encountered in porous deformable media, namely the flow in the porous rock of a petroleum reservoir coupled with the stress field in the porous matrix. As oil is produced, the porous pressure diminishes changing the porosity of the structure, requiring careful monitoring of the structure of the matrix to avoid rock collapse. This coupled problem is normally solved using two different methodologies, finite volume, or finite-differences, for the flow in the porous media, and finite element for the rock mechanics. The reason for this approach is the belief that finite volume methods are suitable only for fluid flow problems. In fact, the momentum conservation equation is, obviously, the same for both problems, allowing the proposition of a single method, using a single grid for solving the coupled problem. As a consequence, it is not required grid interpolation to transfer results from one problem to another and, even more attractive, the approximate equations are conservative for both problems. This paper presents such a solution, whereby the mechanical behavior of the rock is modeled using the Biot's Linear Poroelasticity Theory [1], and the Principle of Effective Stresses [2], while the flow is modeled by the Darcy's equation. The numerical solutions are obtained for 2D domains for a plane strain condition. The method is evaluated by solving the classical problem of porous media compaction with comparison with available analytical solutions. The advantage of having a conservative scheme for the rock mechanics problem, only attainable using a finite-volume method, is clearly demonstrated. The unified numerical approach presented herein is an encouraging alternative for solving coupled problems of engineering interest. [ABSTRACT FROM AUTHOR]

During material forming process (metal, glass, polymer), one stage is the solidification of the material, from a bulk melt part. Occurrence of solid particles in the melt material may alter the properties of the final product, as aggregation of particles potentially induces a local weakness (bad shape, mechanical or thermal properties, for example). Considering one particle, a wide range of thermal and dynamic phenomena can be observed: a particle settling is mainly due to Archimedes forces. Free convection due to gravity effects can increase the fluid flow (which is defined as an assisting flow) or may limit it (defined as an opposing flow). A high fluid-particle relative velocity also implies forced convection. The competition between the two thermal phenomena (so-called mixed convection) widely influences the particle transport. Many works have studied the fluid velocity field induced by a cylinder or a spherical particle in a isothermal medium, and have highlighted transitions of flow regime (a laminar flow at low velocity, a deviation in the particle transport at a moderate velocity and various flow structures at a high velocity). Some studies have taken into account heat transfer between the particle and the fluid, and focused on the thermal effects upon the particle fluid velocity. Experiments are difficult (or impossible) to lead, since some materials (like metals for example) do not allow visualizing the particle in the melt fluid. We propose in the present study to carry out the numerical 3D-simulation of a cold particle submitted to a fluid flow, in order to link the fluid-particle thermal transfer and the fluid flow properties. A volume of fluid method is used, on a fixed Cartesian grid to determine the particle transport, the fluid flow and heat transfers in both the fluid and the particle. The domain must be large enough to avoid wall effects. The mixed convection is quantified by the Richardson number (Ri). The aim of this paper will consist in studying the influence of Ri (by modifying the particle temperature) and to link this parameter to the flow regime and heat transfer. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the class of high order compact schemes in the context of numerical simulation of stratified flow. The numerical schemes presented here are based on the approach outlined in Lele [1]. The numerical model presented in this contribution is based on the solution of the Boussinesq approximation by a finite-difference scheme. The numerical scheme itself follows the principle of semi-discretization, with high order compact discretization in space, while the time integration is carried out by suitable Runge-Kutta time-stepping scheme. In the case presented here the steady flow was considered and thus the artificial compressibility method was used to resolve the pressure from the modified continuity equation. The test case used to demonstrate the capabilities of the selected model consists of the flow of stably stratified fluid over low, smooth hill. [ABSTRACT FROM AUTHOR]

In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented. [ABSTRACT FROM AUTHOR]

This paper continues a previous work (ICNAAM 2009; AIP Conference Proceedings, 1168, 601–604) on solving a hyperbolic conservative model for compressible gas—solid mixture flow using upwind Godunov methods. The numerical resolution of the model from Godunov first—order upwind and MUSCL—Hancock methods are reported. Both methods are based on the HLL Riemann solver in the framework of finite volume techniques. Calculation results are presented for a series of one—dimensional test problems. The results show that upwind Godunov methods are accurate and robust enough for two—phase mixture conservation laws. [ABSTRACT FROM AUTHOR]

We make use of the formulation developed by Lovalenti and Brady [1] for the hydrodynamic force acting upon a spherical particle undergoing arbitrary time dependent motion in an arbitrary time dependent uniform flow field at low Reynolds numbers, to derive an expression for the effects of a constant bias force acting on a periodically forced rigid spherical particle in a Newtonian fluid. We use Newton’s second law to relate the total force acting on the particle to the motion of the particle. The total force is given by: Total force = Fext+FH, where, Fext is the external force inclusive of both the periodic force and the constant bias force. FH is the hydrodynamic force derived by Lovalenti and Brady [1] including both unsteady and convective inertia. The equation derived contains a nonlinear history term and is nonlinear. This equation is solved numerically using an adaptive step size Runge—Kutta scheme. We obtain several phase plots (plots between particle displacement and particle velocity), which show the effects of low Reynolds numbers, the periodic force and the effects of the constant bias force on the particle motion. It is observed that at low magnitudes of the periodic forcing the external constant force dominates and the particle moves along the direction of the external constant force. As we increase the magnitude of the periodic forcing, the periodic force is seen to dominate and the particle is seen to oscillate along a mean position with a slight drift along the direction of the periodic force and the external constant force, when they are imposed in the same direction. However the motion of the particle becomes more complicated when the directions of the periodic forcing and external constant force are opposite to each other. We also observe a reflection in phase space when the directions of both the forces are reversed. The phase plots typically are of a half sinusoidal, sinusoidal and a coiled (solenoidal) pattern. These plots include the effects of both periodic force and the constant bias force. As the Reynolds numbers increases the drift of the particle reduces, which indicates the effects of inertia. We present a preliminary analysis of the dynamics in this paper. [ABSTRACT FROM AUTHOR]

In attempting to capture the non-linearity of the fire turbulent flow structures, a fully-coupled Large Eddy Simulation (LES) model which incorporates all essential subgrid scale (SGS) turbulence, combustion, radiation and soot chemistry considerations has been developed. This paper presents a thorough validation study comparing predictions of the present model with a one-meter diameter methane pool fire experimental data [1] as well as numerical results from other well-known LES models [2–3]. The predicted time-averaged velocities and turbulent quantities have been found to be in good agreement with the experimental data and other model predictions. In term of transient flow structures, for the very first time, the predicted instantaneous velocity field show satisfactory agreement with the Particle Image Velocimetry (PIV) measurements demonstrating the success of capturing the temporal vortical structure by the present model. Quantitative comparisons of velocity time history and pulsation frequency also show close agreement against experimentally evaluated quantities. Nonetheless, turbulent kinetic energy was slightly over-predicted by the present model. Possible sources of errors are discussed leading to the potential direction for future model. [ABSTRACT FROM AUTHOR]

We study the inclined oil-water two-phase flow using complex networks and construct flow pattern complex network with the conductance fluctuating signals measured from oil-water two-phase flow experiments. A new method, based on Time-Delay Embedding and modularity, is proposed to construct network from nonlinear time series. Through detecting the community structure of the resulting network using the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used to identify three inclined oil-water flow patterns. In this paper, from a new perspective, we not only introduce complex network theory to the study of oil-water two-phase flow, but also demonstrate that complex network may be a powerful tool for exploring nonlinear time series in practice. [ABSTRACT FROM AUTHOR]

A comparison study of algorithm on a rectangular collocated mesh is conducted for variable density Navier-Stokes equations with continuous surface forces. The algorithms include the original projection method (AI-TI) with the surface force calculated only in the predictor steps, the named balanced-force projection method (AII-TIV) with the surface force and the pressure gradient calculated together, and a consistent projection method (AIII-TVII) developed in this paper. Detailed comparisons are also conducted among the techniques for calculation of the pressure gradient and surface force at a cell center. A consistent projection method updates the velocity at a cell center in a very difference way with the balanced-force projection formula. A conservative interpolation is used to update the velocity a cell center, which is further used to obtain the sum of the pressure gradient and the surface force. [ABSTRACT FROM AUTHOR]

In this paper the analysis of incompressible three-phase flow systems is studied. A stable numerical method for the model equations based on the flux splitting approach is developed. A useable methodology for reducing the number of numerical flux computations in the multiphase equations is proposed. The multiresolution is based on the analysis of the solutions regularity according to various levels of resolution. Numerical predictions of transient flow problems in pipelines are compared to available experimental data. [ABSTRACT FROM AUTHOR]

The paper deals with shear localization in dry cohesionless sand during confined granular flow in a silo. The calculations were carried out with the finite element method using an explicit dynamic approach. The behaviour of sand was described with a non-local hypoplastic constitutive model taking into account the effect of pressure, density, direction of deformation rate and mean grain diameter on shear localization. The numerical analyses were performed with the help of an uncoupled Arbitrary Lagrangian-Eulerian (ALE) approach to simulate the entire discharge process and avoid large mesh distortions. The effect of a different silo size, silo shape, wall roughness, characteristic length of micro-structure and initial sand density was studied. The FE-results were compared with corresponding laboratory tests. [ABSTRACT FROM AUTHOR]

Due to the implementation of numerical solution algorithms for the nonstationary Navier-Stokes equations of an incompressible fluid on massively parallel computers iterative methods are of special interest. A red-black pressure-velocity-iteration which allows an efficient parallelization based on a domain decomposition [1] will be analyzed in this paper. We prove the equivalence of the pressure-velocity-iteration (PUI) by Chorin/Hirt/Cook [2][3] with a SOR-iteration to solve a poisson equation for the pressure. We show this on a 2D rectangle with some special outflow boundary conditions and Dirichlet data for the velocity elsewhere. This equivalence allows us to prove the convergence of that iteration scheme. [ABSTRACT FROM AUTHOR]

In the paper a numerical analysis of coupled processes within three phase dry-type and cast-resin transformers involving heat and fluid flow, electromagnetic and mechanical phenomena was presented. The main CFD analysis was coupled with the electromagnetic model to examine the specific power losses within coils and a core. The mechanical model determined the thermal stresses within the encapsulated device based on the final temperature field obtained from the CFD-electromagnetic coupling. The thermal boundary conditions, i.e. local and temperature-dependent heat fluxes, were computed by considering a numerical model of the surrounding air. Moreover, separate numerical and analytical models were considered to obtain the anisotropic thermal conductivities for different types of the coils and also for the laminated cores. To validate the numerical model, experimental transformer temperature tests under different loading according to the current European Standards were performed. During the tests, temperatures were measured at selected points on transformer elements using thermocouples, while on the external tank walls an infrared thermography was employed. The obtained numerical results showed that the prediction of the temperature field within the analyzed transformers and their surroundings was very accurate. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of the flow interactions with a stented artery during a cardiac cycle. Both the artery and the stent were modeled as hyperelastic, isotropic and homogeneous material. The stent thickness was selected such that the area was reduced by 27.8% in the undisturbed artery/stent system. The spatial and temporal distributions of pressure, wall displacement and wall shear stress were evaluated for stent modulus of elasticity Es that varied from 1 to 100 times that of the main artery, Ea. The simulations suggested that increasing the elasticity ratio Es/Ea from 1 to 100 had only minor effects on the pressure axial variations, and the abrupt changes in the pressure and consequently the wall shear stress at the compliance transition zone were mainly due the stent geometry. Increasing the stent elasticity seemed to have a more pronounced affect on the wall displacement in that, the simulations suggested that drastic wall deformation occurred at the compliance transition zones when Es/Ea increased from 1 to 5 but increasing Es/Ea further did not result in further significant changes of the wall shape. [ABSTRACT FROM AUTHOR]

In this paper we have studied the acoustic behavior of a sandwich non metallic panel for roofs by the finite element method (FEM). This new field of analysis is the fully coupled solution of fluid flows with structural interactions, commonly referred to as fluid-structure interaction (FSI). It is the natural next step to take in the simulation of mechanical systems. The finite element analysis of acoustic-fluid/structure interactions using potential-based or displacement-based Lagrangian formulations is now well established. The non-linearity is due to the ‘fluid-structure interaction’ (FSI) that governs the problem. In a very considerable range of problems the fluid displacement remains small while interaction is substantial. In this category falls our problem, in which the structural motion influence and react with the generation of pressures in two reverberation rooms. The characteristic of acoustic insulation of the panel is calculated basing on the pressures for different frequencies and points in the transmission rooms. Finally the conclusions reached are shown. [ABSTRACT FROM AUTHOR]

Drop impact has various applications like supercooled drops freezing when hitting air-crafts or electrical power lines, spray cooling, soldering, ink jet printing. When a drop hits a solid surface, a circular wall jet appears, which may spread and/or splash afterwards. The modeling of this jet is still an open problem. In the present paper we propose an axisymmetric dynamic model of the jet appearance, as an inviscid fluid, and its evolution in time towards a thin viscous film, as a boundary layer develops from the wall. Typical values of the drop diameter considered here are O(1 mm) and typical values of the impact velocity are O(1 m/s). Numerical results for the jet thickness and lateral velocity are shown for some typical process parameters and are compared with experimental data obtained with a rapid shutter video camera. [ABSTRACT FROM AUTHOR]

This work introduces new functions based on the spherical harmonic and the solid harmonic which be used to construct a multipole development for the 3D Stokes problem, in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serves to calculate the multipole moments and the transfer functions that are necessar for the schemes of order O(NlogN). Moreover, new translations formulas were introduced to obtain O(N) scheme. The error truncation of the resulting scheme is discussed. [ABSTRACT FROM AUTHOR]

Current numerical calculation of acoustic streaming can involve major computing time and resources. To develop a quicker model, the vorticity transport equation (VTE) is used. In this paper Rayleigh streaming in a cylindrical tube is simulated using the VTE. The goal of using the VTE is to obtain a relatively fast solution with minimal computational resources, which in this case is a single PC. A clustered grid is utilized to capture the boundary layer effect on the acoustic streaming. The governing equations used are the VTE, Poisson’s equation, and an equation that relates the stream function with the velocity. It is demonstrated that the VTE method to calculate Rayleigh streaming works well. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]