Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows

The generalized Newtonian fluid, as an important kind of non-Newtonian fluids, has been widely used in both science and engineering. In this paper, we present a multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid, and validate the model through a detailed comparison with analytical solutions and some published results. The accuracy and stability of the present model are also studied, and compared with those of the popular single-relaxation-time lattice Boltzmann model. Finally, the limit and potential of the multiple-relaxation-time lattice Boltzmann model are briefly discussed.     

The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia

The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.     

Transient flow towards a well in an aquifer including the effect of fluid inertia

Transient propagation of weak pressure perturbations in a homogeneous, isotropic, fluid saturated aquifer has been studied. A damped wave equation for the pressure in the aquifer is derived using the macroscopic, volume averaged, mass conservation and momentum equations. The equation is applied to the case of a well in a closed aquifer and analytical solutions are obtained to two different flow cases. It is shown that the radius of influence propagates with a finite velocity. The results show that the effect of fluid inertia could be of importance where transient flow in porous media is studied.List of symbols b Thickness of the aquifer, m - c ₀ Wave velocity, m/s - k Permeability of the porous medium, m² - n Porosity of the porous medium - p( ,t) Pressure, N/m² - Q Volume flux, m³/s - r Radial coordinate, m - r _w Radius of the well, m - s Transform variable - S Storativity of the aquifer - S _d(r, t) Drawdown, m - t Time, s - T Transmissivity of the aquifer, m²/s - ( ,t) Velocity of the fluid, m/s - Coordinate vector, m - z Vertical coordinate, m - Coefficient of compressibility, m²/N - Coefficient of fluid compressibility, m²/N - Relaxation time, s - (r, t) Hydraulic potential, m - Dynamic viscosity of the fluid, Ns/m² - Dimensionless radius - Density of the fluid, Ns²/m⁴ - (, ) Dimensionless drawdown - Dimensionless time - , x Dummy variables - ₀, ₁ Auxilary functions     

Creeping flow of an ellis fluid past a Newtonian fluid sphere

Upper and lower bounds on the drag offered to a Newtonian fluid sphere placed in an Ellis model fluid in creeping flow have been found using variational principles. For a solid sphere, the bounds are in good agreement with those reported by earlier investigators.     

Performance of iterative methods for Newtonian and generalized Newtonian flows

We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.     

An incompressible smoothed particle hydrodynamics scheme for Newtonian/non-Newtonian multiphase flows including semi-analytical solutions for two-phase inelastic Poiseuille flows

An incompressible smoothed particle hydrodynamics (ISPH) method is developed for the modeling of multiphase Newtonian and inelastic non-Newtonian flows at low density ratios. This new method is the multiphase extension of Xenakis et al, J. Non-Newtonian Fluid Mech., 218, 1-15, which has been shown to be stable and accurate, with a virtually noise-free pressure field for single-phase non-Newtonian flows. For the validation of the method a semi-analytical solution of a two-phase Newtonian/non-Newtonian (inelastic) Poiseuille flow is derived. The developed method is also compared with the benchmark multiphase case of the Rayleigh Taylor instability and a submarine landslide, thereby demonstrating capability in both Newtonian/Newtonian and Newtonian/non-Newtonian two-phase applications. Comparisons with analytical solutions, experimental and previously published results are conducted and show that the proposed methodology can accurately predict the free-surface and interface profiles of complex incompressible multi-phase flows at low-density ratios relevant, for example, to geophysical environmental applications.     

A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows

A weakly compressible smoothed particle hydrodynamics (WCSPH) method is used along with a new no-slip boundary condition to simulate movement of rigid bodies in incompressible Newtonian fluid flows. It is shown that the new boundary treatment method helps to efficiently calculate the hydrodynamic interaction forces acting on moving bodies. To compensate the effect of truncated compact support near solid boundaries, the method needs specific consistent renormalized schemes for the first and second-order spatial derivatives. In order to resolve the problem of spurious pressure oscillations in the WCSPH method, a modification to the continuity equation is used which improves the stability of the numerical method. The performance of the proposed method is assessed by solving a number of two-dimensional low-Reynolds fluid flow problems containing circular solid bodies. Wherever possible, the results are compared with the available numerical data.     

Shear flow of a Newtonian fluid over a quiescent generalized Newtonian fluid

The flow of an upper shear-driven Newtonian fluid above an otherwise still non-Newtonian fluid is considered. The lower fluid is modelled as a generalized Newtonian fluid and set into motion by interfacial shear. By means of similarity transformations, the governing partial differential equations for the two-fluid problem transform exactly into two sets of ordinary differential equations coupled only at the interface. The successful transformation of the two-fluid problem is applied to the particular case when the lower fluid obeys power-law rheology. The resulting three-parameter problem is solved numerically for some different parameter combinations by means of a direct integration approach with the density ratio fixed to unity. We observed that the interfacial velocities decreased with increasing values of the power-law index n in the range from 0.6 to 1.4 whereas the shear-induced motion of the lower fluid penetrates far deeper into a shear-thinning (n < 1) than into a shear-thickening (n > 1) fluid. This phenomenon is ascribed to a corresponding increase of the non-linear viscosity function with lower n-values.     

Fractal analysis of atomizing liquid flows

The work reported in this paper questions the relevance of using fractal concept to study liquid primary atomization process by characterizing the shape of the continuous liquid flow from the nozzle exit to the end of the atomization process. First, three fractal methods were tested on synthetic images in order to define the best adapted protocol to the objective of the study. It appeared that the Euclidean distance mapping was the best appropriate method. Second, this technique was applied to analyze series of images of atomizing liquid flows obtained for several working conditions. This application demonstrates that atomizing liquid flows are fractal objects and that primary atomization can be reasonably seen as fractal processes. The appropriateness of fractal concept was also demonstrated by the fact that fractal characteristics such as textural or structural fractal dimension and inner cutoff scale are physically representative of the process investigated here.     

Transient finite element analysis of generalized Newtonian coextrusion flows in complex geometries

A two-dimensional transient finite element model capable of simulating problems related to two-layer polymer flows has been developed. This technique represents an effective tool which can be used to study the possibility of the onset of interfacial instability in coextrusion flows, considering melt rheology as well as the fluid–geometry interaction. A code has been developed to solve the transient problem of the flow of bi-component systems of Newtonian and generalized Newtonian fluids through parallel plates and complex geometries, such as: 2:1 abrupt expansion, 2:1 (30°) expansion, 4:1 abrupt contraction and 4:1 tapered (30°) contraction. Solutions are compared with experimental data from the literature and results provided by linear stability analysis (LSA) for the case of parallel plate flows. Numerical results are in agreement with LSA results for the parallel plate geometry cases studied. The expansion geometries tend to stabilize flows in the parallel plate section downstream of the expansion. Contractions may give rise to break-up of the interface depending on the flow conditions. © 1998 John Wiley & Sons, Ltd.     

Unsteady flows of an inhomogeneous incompressible viscous fluid

This paper deals with a theoretical analysis of the transfer of reactive impurities by open and filtration flows of an incompressible viscous fluid. The first section of the paper studies the model of an inhomogeneous incompressible viscous fluid, which is widely used in meteorology and oceanology, with additional allowance for the drag of the magnetic field or porous medium. Another object of research in this paper is the model of filtration of an inhomogeneous incompressible fluid in porous media proposed by V. N. Monakhov (1977) (Section 2). In both models, hydrodynamic flows determine the motion of the mixture as a whole and the temperature and concentration distributions of the components of an inhomogeneous fluid are described by a common nonlinear system of equations of diffusive heat and mass transfer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 44–51, March–April, 2005.     

Squeezing a viscoelastic liquid from a wedge: an exact solution

The paper reports an exact solution for the squeezing flow from a wedge of a general viscoelastic liquid. To obtain numerical values for the field variables, a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow is adopted. It is found that both these features are important in this transient flow; stress overshoot is responsible for a stiffer response of the fluid (compared to the inelastic case) at moderate time —at large time, shear-thinning dominates and the fluid behaves like an inelastic fluid. On the other hand, the Oldroyd-B fluid always predicts a softer response than the Newtonian one. Furthermore, there is a limiting Weissenberg number above which one component of the stresses of the Oldroyd-B fluid increases unboundedly with time. This limiting Weissenberg number is approximately $\text{sol2}\text{3}$.     

Squeezing of an Oldroyd-B fluid from a tube: Limiting Weissenberg number

It is shown that the squeezing flow of an Oldroyd-B fluid from a tube with a prescribed time-dependent radius has an exact separable solution. In the special case where the tube radius varies exponentially with time a similarity solution exists. However, in this case there is a critical Weissenberg number above which a component of the stress tensor increases without bound in time.     

Twisted films of Newtonian and viscoelastic liquids

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–178, May–June, 1988.