Defect correction method for time-dependent viscoelastic fluid flow

A defect correction method for solving the time-dependent viscoelastic fluid flow, aiming at high Weissenberg numbers, is presented. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the residual is considered in the correction step. We show the convergence of the method and derive an error estimate. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.     

Approximation algorithms for time-dependent orienteering

The time-dependent orienteering problem is dual to the time-dependent traveling salesman problem. It consists of visiting a maximum number of sites within a given deadline. The traveling time between two sites is in general dependent on the starting time.For any ε>0, we provide a (2+ε)-approximation algorithm for the time-dependent orienteering problem which runs in polynomial time if the ratio between the maximum and minimum traveling time between any two sites is constant. No prior upper approximation bounds were known for this time-dependent problem.     

Finite-element approximation of viscoelastic fluid flow with slip boundary condition

We present a theoretical study of a creeping, steady-state, isothermal flow of a viscoelastic fluid obeying an Oldroyd-type constitutive law with slip boundary condition. The slip boundary condition is appropriate for problems that involve free boundaries and other examples where the usual no-slip condition u = 0 is not valid, such as fiber spinning and microfluidics.First, we study the Newtonian problem with slip boundary condition where the viscoelastic stress is added into the list of unknowns. In addition, the normal viscoelastic stress component associated with the slip boundary condition is introduced. In order to balance its effects, a second inf-sup condition is proven.To treat the discrete case, we assume that the continuous solution of the non-Newtonian problem exists and is small and smooth. Approximating the extra stress, velocity, pressure, and normal viscoelastic stress component via P₁ discontinuous, P₂ continuous, P₁ continuous, and P₀ discontinuous elements, respectively, yields a stable finite-element scheme. Finally, via a fixed point argument, we establish the existence of an approximate solution and derive error estimates.     

Mixed finite element method for analysis of viscoelastic fluid flow

In the present paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method. Because Maxwellian viscoelasticity is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system. Because of this, mixed finite element method is utilized to discretize the basic equations. For the solution procedures to solve discretized equation system, Newton-Raphson method for steady flow and perturbation method for unsteady flow is employed. As the numerical examples, comparison was made on the finite element computational results between by direct method and by mixed method. Effects of the viscoelasticity is analyzed for the flows at Reynold's numbers 30, 50 and 70.     

An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow

In this paper we present a simple, general methodology for the generation of high-order operator decomposition (splitting) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described.     

Rotating flow of viscoelastic fluid with nonlinear thermal radiation: a numerical study

This work is concerned with the numerical solution for rotating viscoelastic flow developed by an exponentially stretching impermeable surface. Temperature at the sheet is also assumed to vary exponentially. Energy equation involves the novel nonlinear radiation heat flux term. Suitable transformations are utilized to nondimensionalize the relevant boundary layer equations. Numerical solutions are developed by means of standard shooting approach. The results demonstrate that both rotation and viscoelasticity serve to reduce the hydrodynamic boundary layer thickness. Temperature function has a special S-shaped profile when the difference between wall and ambient temperatures is sufficiently large. Heat transfer coefficient at the surface diminishes when rotation parameter is increased. Current numerical computations are consistent with those of the existing studies in the literature.

     

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

In this work we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow. A Giesekus model is chosen as constitutive equation of the suspending liquid. In order to study the sole effect of the fluid viscoelasticity, both fluid and particle inertia are neglected.The governing equations are solved through the finite element method with proper stabilization techniques to get convergent solutions at relatively large flow rates. An Arbitrary Lagrangian–Eulerian (ALE) formulation is adopted to manage the particle motion. The mesh grid is moved along the flow so as to limit particle motion only in the gradient direction to substantially reduce mesh distortion and remeshing.Viscoelasticity of the suspending fluid induces particle cross-streamline migration. Both large Deborah number and shear thinning speed up the migration velocity. When the particle is small compared to the gap (small confinement), the particle migrates towards the channel centerline or the wall depending on its initial position. Above a critical confinement (large particles), the channel centerline is no longer attracting, and the particle is predicted to migrate towards the closest wall when its initial position is not on the channel centerline. As the particle approaches the wall, the translational velocity in the flow direction is found to become equal to the linear velocity corresponding to the rolling motion over the wall without slip.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow

Particle migration is a relevant transport mechanism whenever suspensions flow in channels with gap size comparable to particle dimensions (e.g. microfluidic devices). Several theoretical as well as experimental studies have been performed on this topic, showing that the occurring of this phenomenon and the migration direction are related to particle size, flow rate, and the nature of the suspending liquid.In this work we perform a systematic analysis on the migration of a single particle in a sheared viscoelastic fluid through 2D finite element simulations in a Couette planar geometry. To focus on the effects of viscoelasticity alone, inertia is neglected. The suspending medium is modeled as a Giesekus fluid.An ALE particle mover is combined with a DEVSS/SUPG formulation with a log-representation of the conformation tensor giving stable and convergent results up to high flow rates. To optimize the computational effort and reduce the remeshing and projection steps, needed as soon as the mesh becomes too distorted, a ‘backprojection’ of the flow fields is performed, through which the particle in fact moves along the cross-streamline direction only, and the mesh distortion is hence drastically reduced.Our results, in agreement with recent experimental data, show a migration towards the closest walls, regardless of the fluid and geometrical parameters. The phenomenon is enhanced by the fluid elasticity, the shear thinning and strong confinements. The migration velocity trends show the existence of a master curve governing the particle dynamics in the whole channel. Three different regimes experienced by the particle are recognized, related to the particle-wall distance. The existence of a unique migration behavior and its qualitative aspects do not change by varying the fluid parameters or the particle size.     

Thermophoresis and MHD mixed convection three-dimensional flow of viscoelastic fluid with Soret and Dufour effects

Heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface with convective boundary conditions are investigated. The fluid is electrically conducting in the presence of constant applied magnetic field. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. First order chemical reaction effects are also taken into account. By using the similarity transformations, the governing boundary layer equations are reduced into the ordinary differential equations. The transformed boundary layer equations are computed for the series solutions. Dimensionless velocity, temperature, and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. It is found that the behaviors of viscoelastic, mixed convection, and concentration buoyancy parameters on the Nusselt and Sherwood numbers are similar. However, the Nusselt and Sherwood numbers have qualitative opposite effects for Biot number, thermophoretic parameter, and Soret-Dufour parameters.

     

Pulsatile vibrations of viscoelastic microtubes conveying fluid

In this paper, the pulsatile coupled vibrations of a viscoelastic microtube conveying pulsatile fluid is examined for the first time. The problem is grouped into the class of parametrically excited, internally damped, gyroscopic where both Coriolis and parametric forces are present in the presence of viscosity. The Kelvin–Voigt approach of the viscosity, the Euler–Bernoulli for the deformation, the modified couple stress theory for the small size, and Hamilton’s principle for deriving differential equations are used. Parametric frequency–response curves are obtained in the vicinity of the parametric resonance near the critical speed for both subcritical and supercritical regimes. The effect of the flow pulsation on the oscillations is investigated.

     

Visualizing transport structures of time-dependent flow fields

This article focuses on the transport characteristics of physical properties in fluids-in particular, visualizing the finite-time transport structure of property advection. Applied to a well-chosen set of property fields, the proposed approach yields structures giving insights into the underlying flow's dynamic processes.     

Chaotic oscillations of viscoelastic microtubes conveying pulsatile fluid

As the first endeavour, the influence of a pulsatile flow on the large-amplitude bifurcation behaviour of viscoelastic microtubes subject to longitudinal pretention is studied with special consideration to chaos. The viscoelastic microtube is surrounded by a nonlinear spring bed. A modified size-dependent nonlinear tube model is developed based on a combination of the couple stress theory and the Euler–Bernoulli theory. Hamilton’s principle, as an equation derivation technique, and Galerkin’s procedure, as a discretisation technique, are used. Finally, the discretised differential equations of the pulsatile fluid-conveying viscoelastic microscale tube are solved using a time-integration approach. It is investigated that how the bifurcation response for both motions along the axial and transverse axes is highly dependent of the mean value and the amplitude of the speed of the pulsatile flow.     

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

The dynamic behavior of a droplet on a solid surface is simulated by the lattice Boltzmann method (LBM) for two-phase fluids with large density differences; the wetting boundary condition on solid walls is incorporated in this simulation. By using the method, the dynamic behavior of a droplet impinging on a horizontal wall is investigated in terms of various Weber numbers. The dynamic contact angle, the contact line velocity, and the wet length are calculated, and found to be in good agreement with available experimental data. In addition, the method is applied to simulations of the collision of a falling droplet with a stationary droplet on a solid surface. The behavior of the droplets and the mixing process during their collision are simulated in terms of various impact velocities and several static contact angles on the solid surface. It is seen that mixing occurs around the rim of the coalescent droplet due to the circular flows. Also, the relationship between the mixing rate of the primary coalescent droplet and Weber number is investigated.     

Pseudospectral simulation of turbulent viscoelastic channel flow

The methodology and validation of direct numerical simulations of viscoelastic turbulent channel flow are presented here. Using differential constitutive models derived from kinetic and network theories, numerical simulations have demonstrated drag reduction for various values of the parameters, under conditions where there is a substantial increase in the extensional viscosity compared to the shear viscosity (Sureshkumar, Beris, Handler, Direct numerical simulation of turbulent channel flow of a polymer solution, Phys. Fluids 9 (1997) 743–755 and Dimitropoulos, Sureshkumar, Beris, Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters, J. Non-Newtonian Fluid Mech. 79 (1998) 433–468). In this work, new results pertaining to the Reynolds stress and the pressure are presented, and the convergence of the pseudospectral algorithm utilized in the simulations, as well as its parallel implementation, are discussed in detail. It is shown that the lack of mesh refinement, or the use of a larger value for the artificial stress diffusivity used to stabilize the conformation tensor evolution equations, introduce small quantitative errors which qualitatively have the effect of lowering the drag reduction capability of the simulated fluid. However, an insufficient size of the periodic computational domain can also introduce errors in certain cases, which albeit usually small, can qualitatively alter various features of the solution.     

Scheduling of multi-component products in a two-stage flexible flow shop

In this research, the problem of scheduling and sequencing of two-stage assembly-type flexible flow shop with dedicated assembly lines, which produce different products according to requested demand during the planning horizon with the aim of minimizing maximum completion time of products is investigated. The first stage consists of several parallel machines in site I with different speeds in processing components and one machine in site II, and the second stage consists of two dedicated assembly lines. Each product requires several kinds of components with different sizes. Each component has its own structure which leading to difference processing times to assemble. Products composed of only single-process components are assigned to the first assembly line and products composed of at least a two-process component are assigned to the second assembly line. Components are placed on the related dedicated assembly line in the second phase after being completed on the assigned machines in the first phase and final products will be produced by assembling the components. The main contribution of our work is development of a new mathematical model in flexible flow shop scheduling problem and presentation of a new methodology for solving the proposed model. Flexible flow shop problems being an NP-hard problem, therefore we proposed a hybrid meta-heuristic method as a combination of simulated annealing (SA) and imperialist competitive algorithms (ICA). We implement our obtained algorithm and the ones obtained by the LINGO9 software package. Various parameters and operators of the proposed Meta-heuristic algorithm are discussed and calibrated by means of Taguchi statistical technique.     

On a time-dependent grade-two fluid model in two dimensions

We prove the existence of a weak solution of a time-dependent grade-two fluid model in a plane Lipschitz domain and uniqueness of the solution in a convex polygon. The method of proof is constructive and can be adapted to the numerical analysis of finite-element schemes for solving this problem numerically.     

Thermal convection of viscoelastic fluid with Biot boundary conduction

Two-dimensional unsteady natural convection of a non-linear fluid represented by Criminale–Erickson–Filbey (CEF) fluid model in a square cavity is studied in the fluid for Rayleigh–Benard convection case. The governing vorticity and energy transport equations are solved numerically either simple explicit and ADI methods, respectively. The two-dimensional convective motion is generated by buoyancy forces on the fluid in a square cavity, when the vertical walls are either perfectly insulated or conducted with Biot boundary conduction condition. The contributions of the elastic and shear dependent characteristics of the liquid to the non-Newtonian behaviour are investigated on the temperature distribution and heat transfer. The effect of the Weissenberg (which is a measure of the elasticity of the fluid), Rayleigh and Biot numbers on the temperature and streamline profiles are delineated and this has been documented first time for the viscoelastic fluid.     

Discontinuous Galerkin solution of compressible flow in time-dependent domains

This work is concerned with the simulation of inviscid compressible flow in time-dependent domains. We present an arbitrary Lagrangian–Eulerian (ALE) formulation of the Euler equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. Special attention is paid to the treatment of boundary conditions and the limiting procedure avoiding the Gibbs phenomenon in the vicinity of discontinuities. The presented computational results show the applicability of the developed method.