Stability of flow of viscoelastic fluids between arbitrarily spaced cylinders

Résumé On a étudié le problème de la stabilité d'un fluide viscoélastique du troisième ordre contenu entre deux cylindres concentriques. L'approximation habituelle que l'écart entre les cylindres est petit n'est pas faite. On a démontré que pour un fluide viscoélastique le nombre de Taylor critique dépend considerablement de l'écart entre les cylindres.     

Rheological and flow modelling of viscoelastic fluids between eccentric cylinders

Viscoelastic fluid flows within eccentric rotating cylinders are simulated using a finite element based commercial software POLYFLOW, and an approach based on the stream-tube method (STM) and domain decomposition.     

Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels

Transient electro-osmotic flow of viscoelastic fluids in rectangular micro-channels is investigated. The general twofold series solution for the velocity distribution of electro-osmotic flow of viscoelastic fluids with generalized fractional Oldroyd-B constitutive model is obtained by using finite Fourier and Laplace transforms. Under three limiting cases, the generalized Oldroyd-B model simplifies to Newtonian model, fractional Maxwell model and generalized second grade model, where all the explicit exact solutions for velocity distribution are found through the discrete Laplace transform of the sequential fractional derivatives. These exact solutions may be able to predict the flow behavior of viscoelastic biological fluids in BioMEMS and Lab-on-a-chip devices and thus could benefit the design of these devices.     

On hydrodynamics of viscoelastic fluids

In this paper, we study a hydrodynamic system describing fluids with viscoelastic properties. After a brief examination of the relations between several models, we shall concentrate on a few analytical issues concerning them. In particular, we establish local existence and global existence (with small initial data) of classical solutions for an Oldroyd system without an artificially postulated damping mechanism. © 2005 Wiley Periodicals, Inc.     

Numerical solution of laminar incompressible generalized Newtonian fluids flow

This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian fluids in the branching channel. The generalized Newtonian fluids contain Newtonian fluids, shear thickening and shear thinning non-Newtonian fluids. The mathematical model is the generalized system of Navier-Stokes equations. The finite volume method combined with an artificial compressibility method is used for spatial discretization. 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. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.     

Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus

This paper deals with the unsteady axial Couette flow of fractional second grade fluid (FSGF) and fractional Maxwell fluid (FMF) between two infinitely long concentric circular cylinders. With the help of integral transforms (Laplace transform and Weber transform), generalized Mittag–Leffler function and H-Fox function, we get the analytical solutions of the models. Then we discuss the exact solutions and find some results which have been known as special cases of our solutions. Finally, we analyze the effects of the fractional derivative on the models by using the numerical results and find that the oscillation exists in the velocity field of FMF.     

Numerical simulation of free-surface thermally influenced flows for nonhomogeneous fluids

A finite-difference technique is presented to simulate the behavior of natural water bodies under the influence of pollutants and temperature differences. The mathematical model, which has been discretized, is the closed system obtained by combining the Navier-Stokes equations, the heat transfer equation, the diffusion equations, and an equation relating the fluid density to both the chemical concentration and the temperature. The numerical method is based on the marker-and-cell method, which has been extended to consider the volume expansion due to heat transfer and the density variations.     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect

This paper presents a numerical analysis of the flow and heat transfer characteristics of natural convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. The nonlinear formulation governing equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study investigates the effects of the conjugate heat transfer parameter, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The conjugate heat transfer parameter reduces the solid–liquid interfacial temperature, the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater Prandtl number. Moreover, the current results are comparing with Newtonian fluid to obtain the important results of the heat transfer and flow characteristics on micropolar fluids. It shows that an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Two-dimensional flow of chemically reactive viscoelastic fluids with or without the influence of thermal convection

Shear and temperature induced dynamics of a viscoelastic liquid is investigated with direct numerical simulations. A numerical algorithm based on the finite difference method is implemented in time and space with the Oldroyd-B constitutive model for the viscoelastic liquids. The temperature effects are modeled by a combination of Arrhenius kinetics and thermal convection. The standard approach which applies periodic boundary conditions is replaced by one in which the unprescribed boundary values are regenerated from the main flow. The algorithm is validated against well-known Newtonian natural convection flow results. The results show that progressive viscoelasticity leads to lower temperature increases within the fluid system, and that the highest temperature increases are recorded for corresponding Newtonian fluids.     

A least-squares finite-element method for viscoelastic fluids

We present a least-squares finite element method for the steady Oldroyd type viscoelastic fluids. The nonlinear iteration is coupled with global mesh refinement, and locally weighted norms are used to mitigate effects of boundary singularities. Discretization accuracy in a meaningful normis shown to be optimal when using conforming piecewise polynomial elements for the velocity, pressure and extra stress, and Raviart-Thomas finite elements for the total stress. Numerical results are given for an Oldroyd-B fluid in a 4-1 planar contraction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of airfoil vibrations induced by turbulent flow

The subject of this paper is the numerical simulation of the interaction between two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element solution of the Reynolds averaged Navier–Stokes equations with algebraic models of turbulence, coupled with the system of ordinary differential equations describing the airfoil motion. Since the computational domain is time dependent and the grid is moving, the Arbitrary Lagrangian–Eulerian (ALE) method is used. The developed method was applied to the simulation of flow-induced airfoil vibrations.     

Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.     

Numerical simulation of non-Newtonian blood flow in bypass models

The article presents the numerical investigation of non–Newtonian effects of steady blood flow in complete idealized 3–D bypass models, whose native artery is either coronary or femoral with average physiological parameters. Considering the blood to be a generalized Newtonian fluid, the shear–dependent viscosity is described by two well–known macroscopic non–Newtonian models (the Carreau–Yasuda model and the modified Cross model). The results were obtained by own developed computational software based on the pseudo–compressibility approach and on the cell–centred finite volume method defined on unstructured hexahedral grids. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of glottal flow in surgically changed larynx

According to clinical experience the shape of the larynx seems to have a significant impact on the airflow degree and breathing pattern. In this study we perform a set of numerical experiments simulating the glottal flow in surgically changed larynx, where the vocal folds or false vocal are modified. We are aiming to find an optimal geometry of the larynx in terms of easiness for breathing. To this goal we numerically solve the system for weakly compressible Navier–Stokes equations using the finite element method and we compare the airflow resistance and the volumetric flow rate for the set of geometries for inspiration as well as expiration. We discuss the optimal geometry with respect to the quality of breathing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of cross-flow heat exchangers with viscoelastic fluids

The conduction–convection heat loss from a viscoelastic liquid, subjected to two-dimensional flow within the core of a cross-flow heat exchanger arrangement with a mixed or unmixed external fluid, is investigated with direct numerical simulations. A numerical algorithm based on the finite difference method is implemented in time and space with the Giesekus constitutive model for the viscoelastic liquids. The core-fluid is subjected to an initial Poiseuille flow, driven by an adverse pressure gradient and its temperature varies in both the longitudinal and transverse directions. The results show that a viscoelastic core-fluid choice leads to slightly higher temperature losses within the core-fluid stream as compared to a corresponding Newtonian fluid. As is expected, we also observe significantly higher temperature drops within the core-fluid for the case of unmixed ambient fluids as opposed to the mixed external fluid.