Showing papers on "Herschel–Bulkley fluid published in 2017"

Progress in numerical simulation of yield stress fluid flows

Abstract: Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant to natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, and combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.

Combined effects of magnetic field and rheological properties on the peristaltic flow of a compressible fluid in a microfluidic channel

Abstract: The MHD peristaltic motion of a compressible and electrically conducting Jeffrey fluid induced by a surface acoustic wave in a confined parallel-plane microchannel through a porous medium is analytically investigated. A proper attention is given to the combined effects of physical parameters and magnetic field on the rheological aspects of the considered flow. The slip velocity is considered and the problem is discussed for free pumping case. The wave amplitude is related to the power output of an acoustic source. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. The critical value of the magnetic parameter M is discussed such that an optimum M is shown where some physical variables are obtained maximum. It is noticed that, for the Jeffrey fluid, oscillations decay rapidly as we move from the hydrodynamic to the hydromagnetic fluid, and the effect of retardation time becomes weak. It is inferred that increasing the magnetic parameter makes the fluid less prone to nonlinear effects. Several results of other fluid models are deduced as the limiting cases of our problem. This work is the most general model of peristalsis created to date with wide-ranging applications in biological microfluidic networks.

Gravity-driven flow of Herschel--Bulkley fluid in a fracture and in a 2D porous medium

Abstract: New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time ; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

Insight into the boundary layer flow of non-Newtonian Eyring-Powell fluid due to catalytic surface reaction on an upper horizontal surface of a paraboloid of revolution

Abstract: Bonnet of a car, the upper surface of a pointed bullet and upper surface of the pointed part of an aircraft are typical examples of an upper horizontal surface of a paraboloid of revolution (uhspr) However, the flow of some fluids past these kinds of objects fit the description of Eyring-Powell fluid flow Theoretical investigation of two-dimensional Eyring-Powell fluid flow over such object which is neither cone/wedge nor horizontal/vertical is investigated It is assumed that the flow of Eyring-Powell fluid is induced by catalytic surface reaction and stretching fluid layers at the free stream The numerical solutions of the governing equation are obtained using classical fourth order Runge-Kutta scheme together with shooting techniques The impacts of the most important parameters on the flow are presented It is concluded that the maximum velocity of the flow is ascertained when the flow is characterized as Newtonian fluid flow On the surface of uhspr, rapid increase and suppress in the temperature distribution and concentration with an increase in the magnitude of one of the Eyring-Powell fluid parameters are guaranteed A significant fall in the local skin friction coefficients is ascertained due to rise in the magnitude of thickness parameter

Optimizing the rheological properties of silica nano-modified bentonite mud using overlaid contour plot and estimation of maximum or upper shear stress limit

Abstract: An optimization based statistical (response surface) approach was used to evaluate the rheological properties of bentonite mud treated with silica nanoparticles. The overlaid contour plot established the feasible region for the various factor settings from multiple regression equations. The steepest method was used to further determine the optimal factor settings for minimum rheological properties and this was established at 6.3 wt.% bentonite content and 0.94 wt.% silica nanoparticles. The rheological properties of the bentonite mud containing and without silica nanoparticles was evaluated using a Hyperbolic (new) model and related with other oil industry based models: Herschel Bulkley, Sisko, Casson. The hyperbolic rheological model estimated the rheological behaviour of the nano-modified mud satisfactorily while also predicting a shear stress limit for the nano-modified mud. The maximum shear stress limit values for 6.3, 13 and 15 wt.% mud were 14.59, 61.74 and 107.4 Pa respectively. Upper shea...

Flow of yield stress and Carreau fluids through rough-walled rock fractures: Prediction and experiments

Abstract: Many natural phenomena in geophysics and hydrogeology involve the flow of non-Newtonian fluids through natural rough-walled fractures. Therefore, there is considerable interest in predicting the pressure drop generated by complex flow in these media under a given set of boundary conditions. However, this task is markedly more challenging than the Newtonian case given the coupling of geometrical and rheological parameters in the flow law. The main contribution of this paper is to propose a simple method to predict the flow of commonly used Carreau and yield stress fluids through fractures. To do so, an expression relating the “in-situ” shear viscosity of the fluid to the bulk shear-viscosity parameters is obtained. Then, this “in-situ” viscosity is entered in the macroscopic laws to predict the flow rate-pressure gradient relations. Experiments with yield stress and Carreau fluids in two replicas of natural fractures covering a wide range of injection flow rates are presented and compared to the predictions of the proposed method. Our results show that the use of a constant shift parameter to relate “in-situ” and bulk shear viscosity is no longer valid in the presence of a yield stress or a plateau viscosity. Consequently, properly representing the dependence of the shift parameter on the flow rate is crucial to obtain accurate predictions. The proposed method predicts the pressure drop in a rough-walled fracture at a given injection flow rate by only using the shear rheology of the fluid, the hydraulic aperture of the fracture and the inertial coefficients as inputs.

Tangential annular (Couette) flow of a viscoplastic microgel with wall slip

Abstract: The tangential annular or Couette flow of a viscoplastic microgel, i.e., 0.12 wt. % aqueous solution of poly(acrylic acid), Carbopol® 940, under isothermal and creeping flow conditions was investigated by simultaneous particle image velocimetry and rheometrical measurements (Rheo-PIV). A wide range of ratios of the inner over the outer radii of the annuli, i.e., κ = 0.329, 0.749, and 0.933, were used. The PIV measurements revealed the viscoplasticity of the microgel in Couette flow via the formation of plug flow (rigid body motion) and slip at the two walls. A procedure that relied on the characterization of the wall slip behavior was developed for the determination of the yield stress of the microgel, in turn leading to other parameters of the shear viscosity of the viscoplastic fluid. The wall slip velocity versus wall shear stress behavior of the microgel was overall consistent with the mechanism of apparent slip for all three gaps. However, the apparent slip layer thicknesses were dependent on the wal...

Effects of lubricated surface in the oblique stagnation point flow of a micro-polar fluid

Abstract: In this investigation, we have considered steady, two-dimensional, oblique flow of a micro-polar fluid towards a stagnation point over a lubricated plate. A power-law fluid is utilized for the purpose of lubrication. To derive the slip condition in the present flow situation, continuity of shear stress and velocity has been imposed at the fluid lubricant interface. The set of non-linear coupled ordinary differential equations subject to boundary conditions is solved by a powerful numerical technique called the Keller-box method. Some important flow features have been analyzed and discussed under the influence of slip parameter $\lambda$ , the material parameter K, a free parameter $\beta$ and ratio of micro-rotation to the skin friction parameter n . The main purpose of the present article is to analyze the reduction in the shear stress and shift of stagnation point in the presence of lubrication as compared to the viscous fluid that may be beneficial during polymeric processing.

The effect of yield stress on pipe flow turbulence for generalised newtonian fluids

Abstract: The effect of modifying yield stress on turbulent pipe flow of generalised Newtonian fluids at a friction Reynolds number of 323 is investigated using direct numerical simulations. Simulations are carried out for Bingham and Herschel–Bulkley fluids with the yield stress varying from 0% to 20% of the mean wall shear stress. Results show that the effect of increasing yield stress is mostly similar to shear thinning in power-law fluids. The turbulent viscous stress which arises due to viscosity fluctuations is negative for a yield stress fluid and is higher in magnitude for higher yield stress. An analysis of the turbulent kinetic energy budget showed that the effect of yield stress is mainly significant near the wall for y + ≲ 60 which was also seen for shear-thinning power-law fluids at similar Re τ . Additional shear thinning enhances the yield stress effect. The main difference between shear thinning and yield stress is that the effect of yield stress is maximum outside the viscous sublayer whereas shear thinning has a more significant effect inside the viscous sublayer.

Flow of Reiner–Philippoff fluid over a stretching sheet with variable thickness

Abstract: The characteristics of flow of Reiner–Philippoff fluid over a nonlinearly stretching sheet with variable thickness are investigated in this article. The similarity solution of associated boundary layer equation is obtained to examine the effects of non-uniform surface on the flow of Reiner–Philippoff fluid. It is worth mentioning that the skin friction is decreasing with non-uniform surface parameter. Furthermore, skin friction is an increasing function of Bingham number for dilatant fluid, a decreasing function for pseudo-plastic, and a constant function for viscous fluid.

A deformable plate interacting with a non-Newtonian fluid in three dimensions

Abstract: We consider a deformable plate interacting with a non-Newtonian fluid flow in three dimensions as a simple model problem for fluid-structure-interaction phenomena in life sciences (e.g., red blood cell interacting with blood flow). A power-law function is used for the constitutive equation of the non-Newtonian fluid. The lattice Boltzmann equation (the D3Q19 model) is used for modeling the fluid flow. The immersed boundary (IB) method is used for modeling the flexible plate and handling the fluid-plate interaction. The plate drag and its scaling are studied; the influences of three dimensionless parameters (power-law exponent, bending modulus, and generalized Reynolds number) are investigated.

Free convection flows over a vertical plate that applies shear stress to a fractional viscous fluid

Abstract: Free convection flow of a fractional viscous fluid over an infinite vertical plate with exponential heating is studied using a fractional derivative with non-singular kernel. Fluid motion is induced by the plate that applies an arbitrary time-dependent shear stress to the fluid. Closed-form solutions for the dimensionless velocity and temperature fields and Nusselt number are established under the usual Boussinesq approximation. The obtained results can generate exact solutions for any motion with technical relevance of this type. Moreover, fluid’s velocity is presented as a sum of its mechanical and thermal components. A semi analytical solution based on the Stehfest’s formula for the inverse Laplace transform is also obtained. Finally, the influence of fractional parameter on the fluid motion as well as the contributions of mechanical and thermal components of velocity are graphically underlined and discussed.

The micromechanical nature of stresses in triphasic granular media with interfaces

Abstract: The total stress tensor as the average stress within a triphasic granular medium is formally derived from micromechanics where internal forces associated with the solid phase, the two immiscible fluid phases and the associated three interfaces are explicitly accounted for. It is demonstrated that for rigid solid particles, the contributions of all local solid-fluid surface tensions to the total stress are eventually zero. The present work gives the total stress expression as a function of a solid-phase specific stress tensor and a fluid mixture stress contribution that is related to the material's microstructure. A generally non-spherical fluid mixture stress is obtained in contrast to an averaged hydrostatic fluid pressure usually associated with standard thermodynamics. The tensorial nature of this fluid mixture stress contribution is highlighted through numerical experiments pertaining to an idealized granular material in the pendular regime at low wetting saturations. Numerical simulations providing full access to microstructural information are conducted using the Discrete Element Method (DEM), which describes internal forces using resultant forces that clearly deviate from the distributed nature of internal forces in triphasic granular media, e.g., fluid pressures. Nevertheless, this micro-scale representation is demonstrated to be indeed valid for macro-scale stress description in the pendular regime.

Numerical study of non-Newtonian fluid flow over an exponentially stretching surface: an optimal HAM validation

Abstract: Present study is devoted to investigate the Casson fluid flow phenomena over an exponentially stretching surface at the heated wall. The stresses defined for Casson fluid model are reduced in the form of partial differential equations via boundary layer approximation and then converted into the system of nonlinear ODEs by means of similarity transformation. Present Casson fluid model is tackled via three different techniques: in which the numerical results are obtained through Runge–Kutta Felburge method and verified these results with the help of homotopy analysis method and modified technique known as optimal homotopy analysis method. Graphical comparisons and numerical tables are constructed to validate the results for three different techniques. The effects of each emerging parameters on velocity and temperature profiles are demonstrated through graphs. Moreover, skin friction and Nusselt number are also calculated and also provide the comparison between Newtonian fluid and non-Newtonian fluid. It is concluded that non-Newtonian fluid shows the higher skin friction coefficient as compared to Newtonian fluid, while the Nusselt number is more dominant for Newtonian case as compared to non-Newtonian case for different values of temperature exponent. Temperature exponent also play a significant role in heat transfer within the boundary layer domain.

An exact solution for the calendering analysis of a third-order fluid

Abstract: This paper presents the exact solution for calendering a third-order fluid under lubrication approximation. The solution obtained is valid for all values of the third-order fluid parameter. This ex...

Micromechanical modeling of discontinuous shear thickening in granular media-fluid suspension

Abstract: Shear thickening in a fluid occurs when the viscosity of the fluid increases with the increasing applied strain rate. When the rise in viscosity occurs by orders of magnitude, the fluid undergoes discontinuous shear thickening, which can be devastating in industrial applications. We present a particle-scale numerical technique that can simulate these phenomena. By coupling the discrete element method (DEM) and lattice Boltzmann method (LBM), we developed a micromechanical model that can simulate the interparticle stresses for particles that are immersed in a fluid. A comparison of the simulation results against the experimental results reported in the literature demonstrates the potential of the method as a research tool. The comparison included parametric studies to investigate the effects of solid fraction, particle-particle, and particle-wall contact stiffness. With a systematic variation of the wall stiffness, the DEM-LBM model demonstrates that increasing boundary stiffness directly increases the max...

Stability of plane Couette flow of a power-law fluid past a neo-Hookean solid at arbitrary Reynolds number

Abstract: The linear stability of plane Couette flow of a power-law fluid past a deformable solid is analyzed at arbitrary Reynolds number (Re). For flow of a Newtonian fluid past a deformable solid, at high Re, there are two different modes of instability: (i) “wall modes” (Γ∝Re−1∕3) and (ii) “inviscid modes” (Γ∝Re−1) where Γ=VμfGR is the non-dimensional shear-rate in the fluid (V, μf, G, and R denote the top-plate velocity, fluid viscosity, shear modulus of the solid, and fluid thickness, respectively). In this work, we consider the power-law model for the fluid to elucidate the effect of shear-thickening/shear-thinning behaviour on the modes of instability present in the flow, especially at moderate and high Re. At high Re, our numerical results show that wall modes exhibit different scalings in Γ (VηfGR, where ηf is Newtonian-like constant viscosity) vs Re for different values of the power-law index (n), and the scaling exponents are different from that for a Newtonian fluid. This drastic modification in the sc...

Grouting diffusion of chemical fluid flow in soil with fractal characteristics

Abstract: The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity ϕ >0.4, while there is a linear and slow decrease in pressure difference for high porosity.

Modeling of steady Herschel–Bulkley fluid flow over a sphere

Abstract: Characteristics of the incompressible flow of Herschel–Bulkley fluid over a sphere were studied via systematic numerical modeling. A steady isothermal laminar flow mode was considered within a wide range of flow parameters: the Reynolds number 0 < Re ≤ 200, the Bingham number 0 ≤ Bn ≤ 100, and the power index 0.3 ≤ n ≤ 1. The numerical solution to the hydrodynamic equations was obtained using the finite volume method in the axisymmetric case. The changes in flow structures, pressure and viscous friction distribution, and integral drag as a function of the flow rate and fluid rheology are shown. Depending on whether plastic or inertial effects dominate in the flow, the limiting cases were identified. The power law and Bingham fluid flows were studied in detail as particular cases of the Herschel–Bulkley rheological model. Based on the modeling results, a new correlation was developed that approximates the calculated data with an accuracy of about 5% across the entire range of the input parameters. This correlation is also applicable in the particular cases of the power law and Bingham fluids.

Rotating flow of Oldroyd-B fluid over stretchable surface with Cattaneo – Christov heat flux: Analytic solutions

Abstract: Purpose The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is considered, which accounts for the influence of thermal relaxation time. Design/methodology/approach Based on scale analysis, the usual boundary layer approximations are used to simplify the governing equations. The equations so formed have been reduced to self-similar forms by similarity transformations. A powerful analytic approach, namely, homotopy analysis method (HAM), has been applied to present uniformly convergent solutions for velocity and temperature profiles. Findings Suitable values of the so-called auxiliary parameter in HAM are obtained by plotting h-curves. The results show that boundary layer thickness has an inverse relation with fluid relaxation time. The rotation parameter gives resistance to the momentum transport and enhances fluid temperature. Thermal boundary layer becomes thinner when larger values of thermal relaxation time are chosen. Originality/value To the authors’ knowledge, this is the first attempt to study the three-dimensional rotating flow and heat transfer of Oldroyd-B fluid.

Numerical study of a thermally stratified flow of a tangent hyperbolic fluid induced by a stretching cylindrical surface

Abstract: The effects of temperature stratification on a tangent hyperbolic fluid flow over a stretching cylindrical surface are studied. The fluid flow is achieved by taking the no-slip condition into account. The mathematical modelling of the physical problem yields a nonlinear set of partial differential equations. These obtained partial differential equations are converted in terms of ordinary differential equations. Numerical investigation is done to identify the effects of the involved physical parameters on the dimensionless velocity and temperature profiles. In the presence of temperature stratification it is noticed that the curvature parameter makes both the fluid velocity and fluid temperature increase. In addition, positive variations in the thermal stratification parameter produce retardation with respect to the fluid flow, as a result the fluid temperature drops. The skin friction coefficient shows a decreasing nature for increasing value of both power law index and Weissenberg number, whereas the local Nusselt number is an increasing function of the Prandtl number, but opposite trends are found with respect to the thermal stratification parameter. The obtained results are validated by making a comparison with the existing literature which brings support to the presently developed model.

Effect of yield stress on the behavior of rigid zones during the laminar flow of Herschel-Bulkley fluid

Abstract: The paper is devoted to study numerically the evolution of rigid zones that appear during the flow of Herschel-Bulkley fluids. For this aim, we consider a laminar flow of two fluids of this type in a bounded domain. The effect of yield stress on the behavior of rigid zones is examined, and the location of these solid regions is shown. This numerical study allows us to plot and to propose a model that describes the relationship between the area of rigid zones and the yield stress, as well as to clarify the influence of yield stress on the location of solid cores.

On the influence of the wall shear stress vector form on hemodynamic indicators

Abstract: Hemodynamic indicators such as the averaged wall shear stress (AWSS) and the oscillatory shear index (OSI) are well established to characterize areas of arterial walls with respect to the formation and progression of aneurysms. Here, we study two different forms for the wall shear stress vector from which AWSS and OSI are computed. One is commonly used as a generalization from the two-dimensional setting, the latter is derived from the full decomposition of the wall traction force given by the Cauchy stress tensor. We compare the influence of both approaches on hemodynamic indicators by numerical simulations under different computational settings. Namely, different (real and artificial) vessel geometries, and the influence of a physiological periodic inflow profile. The blood is modeled either as a Newtonian fluid or as a generalized Newtonian fluid with a shear rate dependent viscosity. Numerical results are obtained by using a stabilized finite element method. We observe profound differences in hemodynamic indicators computed by these two approaches, mainly at critical areas of the arterial wall.