Numerical simulations of the vortex-shedding in flows around rectangular cylinders

Flows around rectangular cylinders with a series of width-to-height ratios are calculated by means of the Improved Finite Analytic Method (IFAM) and the formation, development and shedding of vortices from the cylinders are simulated successfully. According to these results of time-dependent processes the physical phenomena in the flows are investigated in detail, and the discontinuity of Strouhal number is explained in the case of the width-to-height ratio equal to 3.0. The numerical solutions here show good agreement with the experimental results. In addition, based on several hundreds of the calculated flow patterns a moving picture is made by the computer image processing technology and recorded on a video tape, and then the vivid pictures of the physical process of vortex-shedding can be replayed later and analysed in detail. The project supported by the National Natural Science Foundation of China     

Numerical investigation of particle lateral migration in straight channel flows using a direct-forcing immersed boundary method

Inertia-induced cross-stream migration has been recently exploited for precise position of particles in confined channel flows. In this work, a three-dimensional finite volume based immersed boundary method has been developed to study the lateral migration and hydrodynamic self-assembly of neutrally-buoyant particles in pressure-driven flows. Simulation results show that, in 2D channel flows, the equilibrium position for a circular particle is closer to the centreline for larger particle Reynolds number due to the increasing flow rate, while in 3D square duct flow, the equilibrium position for a spherical particle is near a face centre and is closer to the wall for larger particle Reynolds number. Self-assembly of a pair of particles is observed in 3D square duct flows but not in 2D channel flows. Mechanisms for the self-assembly are discussed.     

Numerical simulations of viscous flows using a meshless method

This paper uses the element‐free Galerkin (EFG) method to simulate 2D, viscous, incompressible flows. The control equations are discretized with the standard Galerkin method in space and a fractional step finite element scheme in time. Regular background cells are used for the quadrature. Several classical fluid mechanics problems were analyzed including flow in a pipe, flow past a step and flow in a driven cavity. The flow field computed with the EFG method compared well with those calculated using the finite element method (FEM) and finite difference method. The simulations show that although EFG is more expensive computationally than FEM, it is capable of dealing with cases where the nodes are poorly distributed or even overlap with each other; hence, it may be used to resolve remeshing problems in direct numerical simulations. Flows around a cylinder for different Reynolds numbers are also simulated to study the flow patterns for various conditions and the drag and lift forces exerted by the fluid on the cylinder. These forces are calculated by integrating the pressure and shear forces over the cylinder surface. The results show how the drag and lift forces oscillate for high Reynolds numbers. The calculated Strouhal number agrees well with previous results. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct measurements of shear-induced particle migration in suspensions of bimodal spheres

A variety of studies reported in the literature have established that initially well mixed suspensions subjected to non-homogeneous shear flows attain an anisotropic particulate structure. It has also been shown that non-homogeneous shearing causes suspensions of unimodal spheres to demix, i.e., gradients in solids concentration are formed. The objective of this study was to determine the effect of non-homogeneous shear flows on suspensions of bimodal particles, and specifically, to determine if the solids concentration gradients which develop are accompanied by size segregation of the coarse with respect to the fine fraction. We used the simplest and most direct methods to determine the relative solids concentrations: visual observation of tracer particles in transparent suspensions and physical separation of the coarse and fine solid fractions. Three different types of non-homogeneous shear flows were examined, and in each case the data support two main conclusions: 1) suspended particles migrate from regions of high shear rate to regions of low shear rate, and 2) the coarse fraction of particles migrates much faster than the fine fraction, leading to size segregation of initially well-mixed suspensions. While the former conclusion is consistent with other studies reported in the literature, to our knowledge this paper provides the first data supporting and, to a limited extent, quantifying the latter conclusion.     

A particle suspension model: an unstructured finite-volume implementation

In this paper, a modified particle temperature model for concentrated suspensions is proposed, which allows for the shear-induced migration of particles. The migration is modelled by a convection–diffusion equation, derived from the particle mass and momentum conservation. The model is implemented in an unstructured finite volume method and is utilized to investigate the shear-induced particle migration in channel flow. The profiles and the evolution of the velocity, concentration and particle temperature along the channel are presented. The entrance lengths needed to reach a fully developed profile of the corresponding field variables are also checked against different averaged concentrations and different relative particle radii. Comparison with available experimental data is made whenever possible.     

Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics

This paper presents a two-dimensional SPH model designed to simulate free-surface flows of dense granular materials. Smoothed particle hydrodynamics (SPH) is a mesh-free numerical method based on a Lagrangian discretization of the continuum mass and momentum conservation equations. The rheology of dense granular materials is modelled using a new local constitutive law recently proposed by Jop et al. (Nature, 2006). Of the viscoplastic class, this law is characterized by an apparent viscosity depending both on the local strain rate and local pressure. Validation test cases of the model in steady and unsteady configurations are presented. For steady cases (vertical chute flow and uniform free-surface layers on inclines), excellent agreement with analytical predictions is obtained. In the unsteady case, the simulations satisfactorily capture the dynamics of gravity-driven surges observed in experiments, including behaviours that are very specific to granular materials. Among the various parameters involved in the computations, the influence of SPH particle configuration within the flow and of the threshold viscosity used in the regularization of the constitutive yield criterion are particularly discussed.     

Numerical simulation of lateral migration of red blood cells in Poiseuille flows

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology in two‐dimensional Poiseuille flows using an immersed boundary method. The lateral migration properties of the cells in Poiseuille flows have been investigated. The simulation results show that the rate of migration toward the center of the channel depends on the swelling ratio and the deformability of the cells. We have also combined the above methodology with a fictitious domain method to study the motion of RBCs in a two‐dimensional micro‐channel with a constriction with an application to blood plasma separation. Copyright © 2010 John Wiley & Sons, Ltd.     

Methodology for numerical simulations of ellipsoidal particle-laden flows

Despite being relevant in many natural and industrial processes, suspensions of nonspherical particles have been largely underinvestigated compared with the extensive analyses made on the gravity-driven motions of spherical particles. One of the main reasons for this disparity is the difficulty of accurately correcting the short-range hydrodynamic forces and torques acting on complex particles. These effects, also known as lubrication, are essential to the suspension of the particles and are usually poorly captured by direct numerical simulation of particle-laden flows. In this article, we propose a partitioned volume penalization-discrete element method solver, which estimates the unresolved hydrodynamic forces and torques. Corrections are made locally on the surface of the interacting particles without any assumption on the particle global geometry. Numerical validations have been made using ellipsoidal particles immersed in an incompressible Navier-Stokes flow.     

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.     

明渠条件下单丁坝绕流特征的数值模拟Numerical simulations of flows around a single spur dike in an open channel

丁坝结构广泛应用于水利工程中,用以调整水流和护滩固堤,维护优良的水道通航条件。针对单丁坝局部水流,基于非结构网格,采用有限体积法（FVM ）,建立了三维自由表面水流模型,湍流模型采用S‐A一方程模型。针对非淹没、正挑单丁坝,开展了系列 Fr数条件下的水流模拟。重点分析丁坝局部流动结构,探讨丁坝坝根处局部涡系演化等特征,研究了丁坝下游回流区长度和宽度的变化,总结了丁坝引起的剪切流的沿程变化特征。     

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

In the present work a finite‐difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49 (2):112–115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross‐flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross‐flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in‐depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulation of contraction and expansion flows of Langmuir monolayers

Langmuir monolayers consist of amphiphilic molecules at the air–water interface and can be modeled as two-dimensional fluids. Earlier experiments [D.J. Olson, G.G. Fuller, J. Non-Newtonian Fluid Mech. 89 (2000) 187–207] on 4:1 contraction and 4:1 expansion flows have been simulated using an integral constitutive equation of the K-BKZ type, suitably modified to account for strain-thickening in the planar extensional viscosity. The model has been used to fit linear viscoelastic data (G′ and G″) and the shear viscosity (η_S), while the amount of strain-hardening is assumed, due to lack of experimental data. The simulations are in good agreement with the experiments on Newtonian monolayers, which show no vortices in the contraction but large inertial vortices in the expansion. For the viscoelastic monolayer (a poly-octadecyl methacrylate or PODMA), the opposite is true. The contraction flow shows vortices, while in the expansion flow the vortex activity is substantially reduced compared with the Newtonian one. The viscoelastic behavior is well captured by the model, provided that substantial strain-thickening is exhibited by the monolayer in planar extension. The latter behavior is very much like that for a branched LDPE melt, which also shows big vortices due to strain-hardening in planar as well as in uniaxial extension.     

Numerical modelling of detonation structure in two-phase flows

A one-dimensional physical model and a numerical method for the simulation of heterogeneous detonation were proposed based on an Eulerian approach for heterogeneous flows. The combination of modern shock-capturing schemes in combination with a dynamically moving, adaptive grid ensure the properresolution of both reaction zones and flow discontinuities. Numerical examples illustrate the effect of the heat release due to heterogeneous combustion. Received August 4, 1995 / Accepted December 12, 1995     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical scheme for accurately capturing gas migration described by 1D multiphase drift flux model

A numerical scheme is designed and implemented to solve a simplified set of equations modeling 1-D multi-phase flow based on drift flux model in an isothermal setup with phase dissolution. The difficulty in obtaining the analytical Jacobian of the fluxes leads to the difficulty in obtaining an efficient linearized Riemann solver which in turn affects the accuracy in capturing the contact wavefront/gas migration. To address this issue a fully explicit second order finite volume solver based on flux corrected transport (FCT) is implemented. The choice of variables used for limiting the fluxes affects the amount of numerical diffusion and an appropriate choice of the gradient in volume fraction is used. Practical test cases while drilling in the oil and gas industry, of gas injection inside a well annulus and shut-in of the vertical well are presented. The results conclude that the FCT solver is better and efficient for accurately capturing gas migration for multi-phase models with phase behaviour involving slip velocities given by algebraic relations.     

Numerical simulation of the vertical structure of discontinuous flows

A numerical method to solve the Reynolds‐averaged Navier–Stokes equations with the presence of discontinuities is outlined and discussed. The pressure is decomposed into the sum of a hydrostatic component and a hydrodynamic component. The numerical technique is based upon the classical staggered grids and semi‐implicit finite difference methods applied for quasi‐ and non‐hydrostatic flows. The advection terms in the momentum equations are approximated in order to conserve mass and momentum following the principles recently developed for the numerical simulation of shallow water flows with large gradients. Conservation of these properties is the most important aspect to represent near local discontinuities in the solution, following from sharp bottom gradients or hydraulic jumps. The model is applied to reproduce the flow over a step where a hydraulic jump forms downstream. The hydrostatic pressure assumption fails to represent this type of flow mainly because of the pressure deviation from the hydrostatic values downstream the step. Fairly accurate results are obtained from the numerical model compared with experimental data. Deviation from the data is found to be inherent to the standard k–ε model implemented. Copyright © 2001 John Wiley & Sons, Ltd.     

Accounting for finite-size effects in simulations of disperse particle-laden flows

A numerical formulation for Eulerian–Lagrangian simulations of particle-laden flows in complex geometries is developed. The formulation accounts for the finite-size of the dispersed phase. Similar to the commonly used point-particle formulation, the dispersed particles are treated as point-sources, and the forces acting on the particles are modeled through drag and lift correlations. In addition to the inter-phase momentum exchange, the presence of particles affects the fluid phase continuity and momentum equations through the displaced fluid volume. Three flow configurations are considered in order to study the effect of finite particle size on the overall flowfield: (a) gravitational settling, (b) fluidization by a gaseous jet, and (c) fluidization by lift in a channel. The finite-size formulation is compared to point-particle representations, which do not account for the effect of finite-size. It is shown that the fluid displaced by the particles plays an important role in predicting the correct behavior of particle motion. The results suggest that the standard point-particle approach should be modified to account for finite particle size, in simulations of particle-laden flows.     

Dynamics and rheology of a dilute suspension of dipolar nonspherical particles in an external field: Part 1. Steady shear flows

Suspensions of small nonspherical particles having dipolar moments exhibit non-Newtonian behavior under the influence of shear and external fields. Numerical methods are presented for calculating the rheological and rheo-optical properties of dilute suspensions of Brownian particles having permanent dipoles subject to time-dependent shear and external fields. The numerical methods employ the Galerkin method of weighted residuals to solve the differential equation for the particle orientation distribution function. The steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations. These numerical results provide valuable insight into the coupling which occurs between the effects of rotary Brownian motion, the hydrodynamic resistance of nonspherical particles, and the external torque exerted on dipolar particles. The results are applicable to both suspensions of magnetic particles and electrically dipolar particles.