Flow Of Viscoplastic Fluid Research Articles

An Approximate Method for Predicting the Friction Factor of Viscoplastic Shear-Thinning Fluids in Non-Circular Channels of Regular Cross-Sections.

The objective of this study is to provide a straightforward generalized simple and quick method for the prediction of the friction factor for fully developed laminar flow of viscoplastic shear-thinning fluids in non-circular channels of regular cross-sections. The most frequently represented substances processed under these conditions are polymers in the processing and plastics industry. A generalized approximate method was proposed to express the relationship between the friction factor and the Reynolds number for the Herschel-Bulkley rheological model. This method uses the generalized Reynolds number for power-law fluids. Moreover, an additional simplified method for rapid engineering calculations was obtained as well. The suggested method was verified by comparing experimental data for concentric annulus found in the literature and results from simulations for concentric annulus, rectangular, square duct with a central cylindrical core and elliptical cross-sections. The results showed that the suggested methods enable us to estimate the friction factor with high accuracy for the investigated geometries.

Applications of Conic Programming in Non-smooth Mechanics

In the field of nonlinear mechanics, many challenging problems (e.g., plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. In this contribution, we review old and novel formulations of various non-smooth mechanics problems including associated plasticity with nonlinear hardening, nonlinear membranes, minimal crack surfaces, and viscoplastic fluid flows.

Clogged corners

Viscoplastic materials cannot flow if the local stress falls below the yield stress of the material. Such materials tend to ‘clog up’ geometrical features like corners or side branches by forming rigid plugs, because the stress becomes insufficient to yield them. In this volume, Taylor-West and Hogg (J. Fluid Mech., vol. 941, 2022, A64) consider the problem of flow of an idealised viscoplastic fluid in a wedge forced by a disturbance far from the corner; this is the viscoplastic analogue of Moffatt's famous corner eddies. They demonstrate and describe the details of how the fluid clogs up the corner of the wedge with a rigid plug bounded by a viscoplastic eddy. More generally, this study provides a way to explain some of the details of cloggings in different geometries that have previously been observed in viscoplastic materials.

Enhanced electroosmotic flow, conductance and ion selectivity of a viscoplastic fluid in a hydrophobic cylindrical pore

We have studied the electroosmotic flow (EOF) of a non-Newtonian viscoplastic fluid, modeled as a Herschel-Bulkley (H-B) fluid, through a single hydrophobic nanopore in a uniformly charged solid hydrophobic membrane separating two identical reservoirs. An interfacial slip velocity develops when the viscoplastic fluid is strained over a hydrophobic surface. It is well established in the context of Newtonian fluid that the interfacial slip at the charged surface augments the EOF. For the viscoplastic fluid, the EOF depends on the fluid behavioral index and the yield stress. We have illustrated the impact of the interfacial slip on the EOF, conductance and ion selectivity of the cylindrical nanopore at different yield stresses for both the shear thinning and the shear thickening cases of the H-B fluid. The slip velocity, characterized by the slip length, enhances the average flow and conductance of the pore and this impact is pronounced for the shear thinning case. The unyielded zone, which develops along the central line of the pore, contracts as the slip length is increased. The ion concentration polarization enhances for the shear thinning fluid, however, the slip length creates a marginal increment. The counterion selectivity of the pore is found to be significant for the Newtonian case as compared to the non-Newtonian fluid and the velocity slip enhances the ion selectivity further. We have determined an analytic solution for the EOF of a power-law fluid in a long hydrophobic tube. Our computed solution for the case of a long tube effectively coincides with this analytic solution. An increment in the pore length reduces its conductance but enhances the ion selectivity. The increment of the average EOF for the hydrophobic pore as compared to the no-slip case grows as the pore length is increased.

Squeeze film flow of viscoplastic Bingham fluid between non-parallel plates

Squeeze film flow of a viscoplastic Bingham fluid between non-parallel plates has been analysed. It is assumed that the force applied to the plates is known, therefore, their velocity must be found, and the film thickness decreases then as time proceeds. Moreover, for non-parallel plates, the position along the plates at which flow reverses direction is found as part of the solution. In the Newtonian limit, the thickness of the gap between the plates in the parallel system never quite reaches zero at any finite time, while for the non-parallel case a finite time can be obtained when the plates touch one another at a point. In squeeze flow of a viscoplastic Bingham fluid between parallel and non-parallel plates, under a fixed applied force, a final steady film thickness can sometimes be reached. This final thickness turns out to be sensitive not just to the plate tilt angle but also to the so called Oldroyd number which is defined as the ratio between yield stress and imposed stress. Nevertheless for squeeze film flow of Bingham viscoplastic fluid between non-parallel plates, the results show that other cases exist in which the lubrication force cannot always balance the applied force, leading to the plates approaching and touching at the narrowest end of the gap. Moreover torques that develop within the system have been analysed. • Squeeze flow of fluid between non-parallel plates is considered. • Fluid is considered as Bingham viscoplastic. • In some cases, plates stop at finite height; in other cases, plates touch. • Which case is realised depends on tilt angle and Oldroyd number. • Torque in Bingham fluid is lower than in Newtonian.

Large-eddy simulation of turbulent pipe flow of Herschel-Bulkley fluids - Assessing subgrid-scale models

This paper investigates the turbulent pipe flow of viscoplastic fluids using large-eddy simulation (LES) and the OpenFOAM package. The Herschel-Bulkley model is employed to describe the viscosity function with shear-thinning and viscoplastic behavior. Many LES studies evaluating different subgrid-scale (SGS) models for Newtonian fluids are available in the literature. However, studies regarding LES and SGS models involving non-Newtonian fluids are scarce, despite the importance of the subject. The present paper focuses on evaluating the performance of the Dynamic Smagorinsky and Wall Adapting Local Eddy-viscosity (WALE) models, and the under-resolved direct numerical simulation (UDNS) with viscoplastic fluids. The first- and second-order turbulence statistics and flow features, such as mean wall shear stress, mean wall viscosity, friction factor, mean shear rate, and mean viscosity profiles are used to assess the different models. Simulations are carried out at two different generalized Reynolds numbers (ReG) of 5000 and 7500. The numerical results computed with LES are compared with direct numerical simulation (DNS) results and experimental data for turbulent pipe flow of a Newtonian fluid to validate the numerical method. LES results for the Herschel-Bulkley fluid show a good agreement for the first- and second-order turbulence statistics compared with DNS data. Moreover, mean flow quantities obtained with LES follow the trend of DNS data.

Turbulent displacement flows of viscoplastic fluids in obstructed eccentric annuli: Experiments

We present an experimental study of turbulent displacement flows in eccentric annuli, where the displacing fluids are water, 0.1% and 0.2% xanthan gum solutions, and the in situ fluid is a viscoplastic, 0.15% Carbopol solution. We focus on the effect of a solid obstruction on the narrow side of the annular gap, analogous to a consolidated cuttings bed in well cementing operations. For comparison we include experiments with an unobstructed test section with eccentricity e set at ∼0.5. While the displacement flow is successful without the obstruction regardless of the displacing fluid, we find that the obstruction at e∼0.5 is mostly detrimental to removal of the yield stress fluid stuck downstream of it, and a decrease in Reynolds numbers via formulation of xanthan gum solutions contribute to a less effective displacement in all situations due to the decrease in fluctuating stresses. Upstream of the obstruction, we observe complete removal of the Carbopol, likely due to enhanced vorticity effects. However, at high eccentricity values of e∼0.7, the effect of the obstruction on the displacement of Carbopol appears to be negligible, especially in the less turbulent situations with the xanthan gum solutions where the stationary Carbopol layer covers the entirety of the solid blockage, both upstream and downstream. Thus, in a highly eccentric obstructed annulus, the eccentricity remains the dominant factor to hinder the displacement.

From breakup to coiling and buckling regimes in buoyant viscoplastic injections

We study the injection flow of a heavy viscoplastic fluid into a light Newtonian fluid, via modelling and experiments. The injection is carried out downward, via an eccentric inner pipe inside a vertical closed-end outer pipe. This configuration results in a core viscoplastic fluid surrounded by an annular Newtonian fluid. The flow is structured and mixing is negligible. As the injection rate increases in a typical experiment, we observe three distinct flow regimes, associated with the core fluid behaviour, namely the breakup, coiling and buckling (bulging) regimes. In the breakup regime, the core fluid is yielded due to the extension caused by buoyancy, while in the buckling regime the yielding occurs due to the compression promoted by the pressure and the interfacial shear stress applied by the upward flow of the annular fluid. For the coiling regime, the core fluid remains largely unyielded until it exhibits a coiling behaviour. We develop a lubrication approximation model, using the Herschel–Bulkley constitutive equation, with dimensionless flow parameters including the Bingham number, the power-law index, the buoyancy number, the viscosity ratio, the diameter ratio, the eccentricity and the aspect ratio. Based on a reasonable prediction to the yielding onset, the model allows us to classify the flow regimes versus an elegant combination of the dimensionless numbers.

Effects of the Rotation on the Mixed Convection Heat Transfer Analysis for the Peristaltic Transport of Viscoplastic Fluid in Asymmetric Channel

In this paper, we study the impact of the variable rotation and different variable on mixed convection peristaltic flow of incompressible viscoplastic fluid. This is investigated in two dimensional asymmetric channel, such as the density, viscosity, rate flow, Grashof number, Bingham number, Brinkman number and tapered, on the mixed convection heat transfer analysis for the peristaltic transport of viscoplastic fluid with consideration small Reynolds number and long wavelength, peristaltic transport in asymmetric channel tapered horizontal channel and non-uniform boundary walls to possess different amplitude wave and phases. Perturbation technique is used to get series solutions. The effects of different values of these parameters for the axial velocity, stream function, stress, temperature and pressure gradient have been obtained. The impact of these parameters is discussed and illustrated graphically through the set of figures. Numerical results have been computed by using MATHEMATICA software.

An eddy-viscosity model for turbulent flows of Herschel–Bulkley fluids

This article presents a new turbulence closure based on the k-ω SST model for predicting turbulent flows of Herschel–Bulkley fluids, including Bingham and power-law fluids. The model has been calibrated with direct numerical simulations (DNS) data for fully-developed pipe flow of shear-thinning and viscoplastic fluids. The new model shows good agreement in the mean velocity, average viscosity, mean shear stress budget and friction factor. The latter compares well also against correlations from the literature for a wide range of Reynolds numbers. With the new model, improvements are also observed in the iterative convergence, which is often difficult for calculations with yield-stress fluids. Additionally, three eddy-viscosity models for Newtonian fluids, namely the k-ω SST, k-kL and Spalart–Allmaras model, have been tested on turbulent Herschel–Bulkley flows. Results show that (i) the new model produces the best prediction; (ii) the standard SST model may be considered for simulations of weakly shear-thinning/viscoplastic fluids at high Reynolds numbers; (iii) the k-kL and the Spalart–Allmaras models appear to be unsuitable for turbulent Herschel–Bulkley flows. The new model is simple and appealing for engineering applications concerned with turbulent wall-bounded flows and is presented in a formulation that can be easily adapted to other generalised Newtonian fluids.

Stagnation Zone Near A Corner In Viscoplastic Fluid Flow

Abstract The shape, size and location of the stagnation zone between flat non-parallel walls that make up the corner of a tube with non-circular cross section through which a phase change material of the Bingham plastic type flows is investigated. We show that the stagnant area is bounded by a convex meniscus whose size depends on the degree of plasticity and the vertex angle. The maximum and minimum energy dissipation occurs at the wall and at the bisectrix, respectively. The stagnant zone can be altogether avoided by modifying the shape of the wall in the corner area. A new design of the cross section of the tube that allows reducing or eliminating this area to optimize the mass transport is developed. Two optimal solutions, a vertex with a straight cut and a concavely curved vertex, are proposed.

An immersed boundary-lattice Boltzmann method with hybrid multiple relaxation times for viscoplastic fluid-structure interaction problems

Existing studies of fluid-structure interaction (FSI) in ocean engineering mainly focus on the interaction between Newtonian fluids and structure. The FSI problems involving non-Newtonian fluids, especially viscoplastic fluids, have rarely been studied while the inherent dynamic behavior is not clear. In this paper, an immersed boundary-lattice Boltzmann method (IB-LBM) is developed for numerical investigations on FSI problems involving viscoplastic fluids. The present IB-LBM is integrated with a hybrid multiple relaxation times (MRT) scheme where different diagonal relaxation matrices are used for modeling Newtonian and non-Newtonian fluids, and are combined in a hybrid manner using a step function to achieve smooth transition for Newtonian to non-Newtonian fluid behavior at the FSI area. Four benchmark problems are used to validate the IB-LBM with hybrid MRT scheme. It is demonstrated that the numerical model can avoid numerical instability when modeling viscoplastic fluid flow and reduce the numerical boundary slip in the IB-LBM. The numerical model is further used to study the viscoplastic fluid flow around a fixed and moving cylinder (or particle). We show that the present IB-LBM with the hybrid MRT scheme is effective in modeling FSI involving viscoplastic fluids while the obtained phenomena are quite different from those with Newtonian fluids.

A PIV investigation of laminar and turbulent viscoplastic fluid flow on axisymmetric abrupt contraction

The current work is devoted to analyzing viscoplastic fluid flow in a circular axisymmetric abrupt contraction with ratio . The velocity fields and static pressure along a hydraulic loop were measured employing Particle Image Velocimetry technique and a pressure transducers system, respectively. Four aqueous solutions of Carbopol 940 with different rheological parameters were used as viscoplastic fluids. Laminar and turbulent flow conditions are evaluated and compared with the generalized Hagen–Poiseuille law and the Malin friction factor correlations supported by turbulent fluctuations measurements. The formation of a plug core region is observed around the centerline of the pipe. The relationships between the velocity profiles and the shear stress distribution with the plug core were investigated supported via shear rate calculations. The results show that the yield stress highly influences the shape of the velocity profiles and the appearance of unyielded regions at the contraction edges. The shear stress maps show a layered distribution across the pipe diameter with higher values located at the contraction entrance. Instead, a constant shear stress distribution is found in the unyielded regions. The size of these unyielded regions increases with the yield stress but is reduced at regions with high shear rates due to increased inertial forces. Pressure drop measurements contrasted with the shear stress and velocity gradients maps illustrated that the pressure losses along the pipe are affected by the yield stress and the Reynolds number. However, a non-dependence of the pressure loss coefficient at the contraction plane with the rheological parameters is evidenced, as presented in earlier experimental results. This differs from many numerical studies since the contraction’s pressure loss coefficient for viscoplastic fluids is directly affected by the increase of inertial forces at this region.

RANS modeling of turbulent flow and heat transfer of non-Newtonian viscoplastic fluid in a pipe

A mathematical model of the movement and heat transfer of a turbulent non-isothermal non-Newtonian fluid through a pipe wall with a cold surrounding space has been developed and simulated numerically. Fluid turbulence is described in the framework of the isotropic two-parameter k– ε˜ model. The Newtonian properties of the fluid in the initial cross-sections of the pipe transformed gradually into a viscoplastic non-Newtonian Bingham-Schwedoff fluid state due to heat transfer through the pipe wall between the heated fluid and a cold environment. The value of its streamwise velocity in the axial zone increased significantly when the fluid moved along the pipe. On the contrary, it decreased in the near-wall zone and the height of the region with a zero fluid velocity increased. This occurred due to the viscoplastic properties of a non-Newtonian fluid. The height of the region with a zero fluid velocity in the pipe increased gradually as the non-Newtonian fluid (waxy crude oil) moved through the pipe. A noticeable increase in the level of turbulent kinetic energy in the axial zone of the pipe and its noticeable decrease in its near-wall region were observed. A significant increase in the average dynamic viscosity and yield stress in the near-wall part of the pipe was shown. The boundary of the area of existence of Newtonian properties of fluid was determined. The height of the region with a zero fluid velocity in the pipe increased gradually as waxy crude oil moved through the pipe and reached y/R ≈ 0.1 at x/D = 15.

An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

Abstract This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

Fully turbulent flows of viscoplastic fluids in a rectangular duct

Turbulent flows of viscoplastic fluids at high Reynolds numbers have been investigated recently with direct numerical simulations (DNS) but experimental results have been limited. For this reason, we carry out an experimental study of fully turbulent flows of a yield stress fluid in a rectangular aspect ratio channel with a high-resolution laser doppler velocimetry (LDA) setup. We employ aqueous Carbopol solutions, often considered to be a simple yield stress fluid. We formulate different concentrations to address the effect of the rheology of the fluid on the turbulence statistics at an approximately constant Reynolds number. Additionally, we also perform experiments with a single Carbopol formulation at different Reynolds numbers to study its effect. The flow analysis is performed via rheology measurements, turbulence statistics and power spectral densities of velocity fluctuations. The addition of Carbopol to the flow increases turbulence anisotropy, with an enhancement of streamwise velocity fluctuations and a decrease in wall normal velocity fluctuations in comparison to water at the same mean velocity. This change is reflected on the power spectral densities of streamwise velocity fluctuations, where we observe a large increase in energy of large scale turbulent structures. Conversely, the energy of smaller scales is decreased in comparison to water, where the energy drops with a steeper scale than the Newtonian power law of $k_x^{-5/3}$. As we increase the Reynolds number with a Carbopol solution, the streamwise Reynolds stresses approach Newtonian values in the core, which suggests diminishing effects of shear-thinning. The power spectral densities reveal that the energy content at larger scales decreases slightly with the Reynolds number. However, the shear thinning effects do not disappear even as the Reynolds number approaches 50000.

Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosity concept of the Navier-Stokes theory and representation of the solid state as an infinitely rigid non-deformable solid, the solid state in our theory is deformable and the fluid state is considered rather as a “melted” solid via a certain procedure of relaxation of tangential stresses similar to Maxwell’s visco-elasticity theory. The model is formulated as a system of first-order hyperbolic partial differential equations with possibly stiff non-linear relaxation source terms. The computational strategy is based on a staggered semi-implicit scheme which can be applied in particular to low-Mach number flows as usually required for flows of non-Newtonian fluids. The applicability of the model and numerical scheme is demonstrated on a few standard benchmark test cases such as Couette, Hagen-Poiseuille, and lid-driven cavity flows. The numerical solution is compared with analytical or numerical solutions of the Navier-Stokes theory with the Herschel-Bulkley constitutive model for nonlinear viscosity.

The converging flow of viscoplastic fluid in a wedge or cone

Abstract

Electroosmotically driven flow of micropolar bingham viscoplastic fluid in a wavy microchannel: application of computational biology stomach anatomy

A comprehensive mathematical model is presented to study the peristaltic flow of Bingham viscoplastic micropolar fluid flow inside a microlength channel with electro-osmotic effects. The electro-osmotic effects are produced due to an axially applied electric field. The circulation of this electric potential is calculated by utilizing Poisson Boltzmann equation. The dimensionless form of mathematical equations is obtained by using lubrication theory and Debye-Huckel approximation. We have obtained analytical solutions for the final dimensionless governing equations. Finally, the graphical results are added to further discuss the physical aspects of the problem. Electro-osmotic is mainly helping to control the flow and axial velocity decreases with an increase in the electric field but micro-angular velocity increases with an increase in electric field.

Second law analysis of heat transfer in swirling flow of Bingham fluid by a rotating disk subjected to suction effect

This framework presents heat transfer analysis for swirling flow of viscoplastic fluid bounded by a permeable rotating disk. Problem formulation is made through constitutive relations of Bingham fluid model. Viscous dissipation effects are pre-served in the mathematical model. Entropy production analysis is made which is yet to be explored for the von-Karman flow of non-Newtonian fluids. Having found the similarity equations, these have been dealt numerically for broad parameter values. The solutions are remarkably influenced by wall suction parameter and Bingham number which measures the fluid yield stress. Akin to earlier numerical results, thermal boundary-layer suppresses upon increasing wall suction velocity. Thermal penetration depth is much enhanced when fluid yield stress becomes large. Higher heat transfer rate can be accomplished by employing higher suction velocity at the disk. However, deterioration in heat transfer is anticipated as fluid yield stress enlarges. Current numerical results are in perfect line with those of an existing article in limiting sense.