Flow Of Viscoelastic Fluid Research Articles

Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes

Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force $$\langle F \rangle$$ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow ( $$Re\ll 1$$ ) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of $$N=150$$ different systems, in which the normalized average fluid–particle force $$\langle F \rangle$$ is obtained as a function of the volume fraction $$\phi$$ $$(0 < \phi \le 0.2)$$ of the dispersed solid phase and the Weissenberg number Wi $$(0 \le Wi \le 4)$$ . From these predictions a closure law $$\langle F(\phi,Wi) \rangle$$ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio $$\beta = 0.5$$ ) which is, on average, within $$5.7\%$$ of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with $$O(10^5-10^6)$$ rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers $$0\le El \le 30$$ (where $$El=Wi/Re$$ ) and for different suspension particle volume fractions.

Free convection flow of second grade dusty fluid between two parallel plates using Fick\u2019s and Fourier\u2019s laws: a fractional model

The paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The phenomenon has been modelled in terms of PDEs. The constitutive equations are fractionalized by using the definition of the Caputo fractional operator with Fick’s and Fourier’s Laws. The system of fractional PDEs is non-dimensionalized by using appropriate dimensionless variables. The closed-form solutions of thermal and concentration boundary layers are obtained by using the Laplace and finite Fourier-Sine transforms, while the momentum equation is solved by a numerical approach by Zakian using textit{PYTHON}. Furthermore, the parametric influence of various embedded physical parameters on momentum, temperature, and concentration distributions is depicted through various graphs. It is observed that the fractional approach is more convenient and realistic as compared to the classical approach. It is worth noting that the increasing values of M, Sc and Re retard the boundary layer profile. For instance, this behaviour of M is significant where boundary control is necessary. That is, in the case of resonance, the physical solution may be obtained by adding the effect of MHD. The Reynolds number is useful in characterising the transport properties of a fluid or a particle travelling through a fluid. The Reynolds number is one of the main controlling parameters in all viscous flow. It determines whether the fluid flow is laminar or turbulent. The evolution of the rate of heat, mass transfer, and skin friction on the left plate with various physical parameters are presented in tables. These quantities are of high interest for engineers. Keeping in mind the effect of various parameters on these engineering quantities, they make their feasibility reports.

Data-driven closure model for the drag coefficient of the creeping flow past a translating sphere in a shear-thinning viscoelastic fluid

A drag force closure model for particle-laden viscoelastic fluid flows is the key to describing the ensemble-averaged behavior of the mixture. The effects of fluid rheological properties on the flow dynamics of a spherical particle in viscoelastic fluids in the creeping flow regime are parameterized using the Giesekus rheological model. Direct numerical simulations are performed within a large range of Deborah number(0−10).The drag force of a sphere in unbounded Giesekus fluids decreases monotonically with the increase of Deborah number. The negative wake may occur when the viscosity ratio is larger than 0.6 in Giesekus fluids but is absent in Oldroyd-B fluids in all conditions. An explicit closure model for the drag coefficient of a sphere in Giesekus fluids is established using the backpropagation artificial neural network. The drag closure model provides a method for explicitly formulating the momentum exchange model for dilute suspensions of solid particles in shear-thinning viscoelastic fluids.

On the some issues of particle motion in the flow of viscoelastic fluids

On the some issues of particle motion in the flow of viscoelastic fluids

Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

In this work, we study the unsteady electro‐osmotic flow of fractional viscoelastic fluids in micro‐parallel channels, where the velocity slip effect on the walls is also considered. The analytical solution is obtained through solving the Cauchy momentum equation, together with the linearized Poisson–Boltzmann equation and the fractional Maxwell constitutive equation. The influences of the normalized electrokinetic width K, Deborah number De, slip length L and fractional derivative α on the velocity and volume flow rate are discussed. The results demonstrate that the dimensionless parameters L, De and K all have a promoting effect on the electro‐osmotic flow and resonance behavior of fractional Maxwell fluids. In addition, compared with the classical Maxwell fluid, the microstructure of the fractional Maxwell fluid weakens the resonance behavior.

Heat transport in entropy-optimized flow of viscoelastic fluid due to Riga plate: analysis of artificial neural network

In this paper, we focus to design intelligence numerical computing through artificial neural networks (ANNs) which are backpropagated with Levenberg–Marquard technique (NN-BLMT) for the theoretical approach of physical aspects of heat generation in second-grade fluid (PA-HG-SGF) due to Riga plate. The Riga plate (RP) is known as the physical interaction stimulus, which consists of electrodes and enduring electromagnets that are located on plane surface. The purpose of NN-BLMT is to learn the weight of neural networks on the basis of optimization of the fitness value based on mean-square error between the proposed result and reference numerical solution. The innovation and reliability of NN-BLMT used will be greatly better as compared to traditional numerical techniques that are used to solve commercial and industrial problems. NN-BLMT is fast and easy to apply on nonlinear problems and get best results. The original model PA-HG-SGF in term of PDEs is first converted into system of nonlinear ODEs through suitable transformation and then numerically solved. Through Adam numerical technique (AMT) in Mathematica software, a dataset for PA-HG-SGF is attained for different scenarios of PA-HG-SGF by variation of second-grade parameter, heat-generation parameter, Hartman number, thermal lamination parameter, thermal composure parameter and Prandtl number. Expected solutions are described for PA-HG-SGF through the NN-BLMT testing, training, and validation process. In addition, NN-BLMT relative studies and performance analysis are validated by histogram studies, regression analysis and MSE and then analyzed PA-HG-SGF.

Temporal Artificial Stress Diffusion for Numerical Simulations of Oldroyd-B Fluid Flow

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution.

Slippery electrokinetic flow of viscoelastic fluids with pressure-dependent viscosity and relaxation time

In this paper, the pressure-driven electrokinetic flow of incompressible viscoelastic fluids with exponential type pressure-dependent viscosity and relaxation time is investigated in a slippery nanochannel. Based on the exponential type pressure-dependent viscosity and relaxation time, the 2D momentum equation has been solved. By regular perturbation expansion method, asymptotic analytical solutions of flow velocity and pressure are obtained up to second order. The results show the magnitude of streaming potential decreases and fluid viscosity increases with an increase of pressure relaxation coefficient ω. When slip length increases, the viscosity of viscoelastic fluids becomes gradually weak. The increase in ω can cause a decrease in electrokinetic energy conversion (EKEC) efficiency. In addition, slip length can enhance EKEC efficiency of viscoelastic fluids with pressure-dependent viscosity and relaxation time.

Turbulent entrainment in viscoelastic fluids

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation.

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

AbstractThis article discusses the numerical simulation of viscoelastic fluid flows using the edge‐based smoothed finite element method (ESFEM). The incompressible Navier–Stokes equations coupled with the Oldroyd‐B constitutive relation are decoupled via the characteristic‐based split scheme that enables the use of equal‐order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three‐node triangular elements which work very well with the ESFEM. Edge‐based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak‐form integral. The discrete viscoelastic system is entirely formulated in the edge‐based notion such that all gradient‐related terms are readily smoothed cell‐by‐cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.

Influential study of novel microorganism and nanoparticles during heat and mass transport in Homann flow of visco-elastic materials

A novel analysis in terms of unsteady flow of viscoelastic fluid with combination of nanofluid particles is reported in this particular work. Additional physical influences are introduced by incorporating the impact of microorganism, bio convection, mixed convection, magnetic field, and heat absorption/generation. However, the physical boundary conditions according to geometric configuration are illustrated in the form of convective conditions. The converted ODE's from PDE's are not well posed, for which a perturbation approach through (MATHEMATICA) is used to make the new problem well posed accordingly. Moreover, the novel effects are exercised on the form of velocity, temperature, concentration, microorganism and displacement thickness graphs. Velocity components determined with reduction order by uplifting the bio convection and buoyancy ratio parameters respectively. The transient parameters declined the temperature, concentration and microorganism which reverse effect is noticed for velocity components. Reduction in microorganism is observed while leaping Lewis number and Peclet number with increases order.

Thermal boundary layer of laminar flow of dilute polymer solution

The thermal boundary layer flow is a canonical flow with characteristics that are present in most natural and industrial convection flows. An approximate self-similar solution is proposed for the first time for the thermal boundary layer of steady laminar flow of viscoelastic fluids, described by the finitely extensible nonlinear elastic constitutive equation with Peterlin's closure (FENE-P model). This semi-analytical thermal solution is obtained by performing an order of magnitude analysis and ensuing simplifications of the governing equations by assuming that the fluid properties are independent of temperature therefore decoupling the flow governing equations from the energy equation. The effects of viscoelasticity quantified with the Weissenberg number based on the streamwise coordinate (x) (Wix) up to Wix=1 and viscous dissipation (results are presented for Brinkman numbers between -40 and +40) on thermal boundary layer characteristics are investigated comprehensively for both constant wall temperature and constant wall heat flux. At low elasticity levels (Wix<0.01) the solution exhibits a global self-similar behavior in which flow and thermal quantities collapse on the corresponding Newtonian curves, and the polymer characteristics show a unique behavior if adequately normalized. However, by increasing flow elasticity the unique self-similar behavior of the approximate solution is lost, with the elasticity dependent results exhibiting local variations. In addition, the effects of elasticity are intensified by viscous dissipation. For the present study cases, it is observed that elasticity may change Nusselt numbers by more than 8%, and the thermal boundary layer thickens by up to 10%.

Analysis of Hydro Magnetic Flow of Visco Elastic Fluid in a Vertical Channel

In the present paper we have Analysis of hydro magnetic flow of visco elastic fluid. Hydro magnetic visco elastic fluid flow between two horizontal infinite parallel porous plates with time varying sinusoidal pressure gradient and magnetic field has been discussed in the present study. The visco elasticity in an effective approach to modeling the dissipative mechanism. Some interesting observations are low-frequency oscillating pressure gradient Prevents back flow, significant reduction in skin frictions is observed by embedding the channel in porous medium and magnetic field and elasticity decelerate the fluid flow and also in this paper a Theoretical Analysis is carried out of study the visco elastic effects on hydro magnetic heat &amp; mass transfer in a vertical channel. The two vertical plates are in porous medium and non-uniform wall temperatures. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The visco elastic fluid flow is characterized by second order fluid. The effects of different flow parameters on skin friction are analyzed and illustrated graphically.

On MHD Flow of Non-newtonian Viscoelastic Fluid over a Stretched Magnetized Surface

The purpose of this research is to investigate heat and mass transport in a magnetohydrodynamic (MHD) flow of a non-Newtonian viscoelastic fluid on a stretched magnetized surface. The investigations involve modelling the governing partial differential equations with respect to the Cartesian coordinate system. The models are then transformed into a set of coupled ordinary differential equations. Numerical and graphical solutions were obtained using similarity analysis. The effect of the magnetized sheet on the flow behavior; local skin friction, Nusselt, and Sherwood numbers, are presented in tables. It was observed that an enhanced thickening of the thermal boundary layer was due to the induced magnetization of the sheet. This leads to a significant decline in the heat transfer rate. Certain significant discoveries reported in this research discloses that the effect of viscous dissipation and the non-uniform heat transmission have momentous impact in controlling the rate of heat transfer in the boundary layer region. Again, from the outcome of the analysis it is seen that, the effect of appreciating the Soret number or lessening the Dufour number tends to decrease the velocity and temperature profiles while enhancing the concentration dissemination. Magnetizing the surface shows similar effects on the local skin friction, Nusselt number, and Sherwood number. It is concluded that magnetized surfaces significantly influence the rate of cooling and hence the quality of the penultimate product.

Drag of circular cylinders in viscoelastic fluid flow

Drag forces on a circular cylinder placed in a rotating cylindrical annulus filled with a viscoelastic wormlike micellar fluid are measured using a load cell. The flow patterns are extracted from the PIV (particle image velocimetry) measurements of the flow fields around the circular cylinder. In viscoelastic fluids, shear waves can be propagated, and the viscoelastic Mach number M is defined as the ratio of the speed of an object in a fluid to the speed of shear waves in the fluid. In this study, the effect of viscoelastic Mach number on the drag characteristics of the circular cylinder is investigated. The results show that when the viscoelastic Mach number M > 1, an increase of drag over that expected from the growth rate at viscoelastic Mach numbers M < 1 is observed. From the results of PIV measurements, a dead water region is observed, which is formed symmetrically around the circular cylinder when M < 1 and behind the circular cylinder when M > 1. It plays an important role in the drag increase on a circular cylinder.

UNSTEADY STAGNATION FLOW OF VISCOELASTIC FLUID THROUGH POROUS MEDIUM OVER STRETCHING/SHRINKING SURFACE USING UCM MODEL

In the present paper, Upper-Convected Maxwell model is used for formulation of the problem of two-dimensional unsteady stagnation point flow of viscoelastic fluid which passes through a porous medium over a stretching/shrinking surface. The effect of magnetic field on flow is also considered in the presence of time dependent heat source/sink. Using similarity parameters, we convert the governing non-linear system of partial differential equations into non dimensional system of ordinary differential equations. This system of equations is solved by using Runge-Kutta fourth order method with shooting technique. Effect of different physical parameters e.g. Maxwell parameter(β), permeability parameter(K), unsteadiness parameter(γ), velocity ratio parameter(λ) etc. on flow and heat transfer characteristics are analyzed and discussed graphically. It is observed that for some values of λ, dual solution also exists for both velocity and temperature, and existence and uniqueness of solution also depends upon unsteadiness parameter. For the validation of present study, the results are compared to previous investigations and found in good agreement.

DNS of turbulent boundary layer flow of viscoelastic fluids with concentration and temperature variations

We performed direct numerical simulations (DNS) of turbulent boundary layer flows of viscoelastic fluids with variations of solution concentration and temperature in order to investigate the effects on the turbulent statistics and structures. In this study, we proposed a new constitutive equation model, c-T-FENE-P model, in which the relaxation time varies with temperature. DNS date for 6 cases of increasing and decreasing relaxation times with temperature were investigated. It was found that the dependence of the increasing and decreasing relaxation times on the drag reduction ratio was opposite to each other.

Numerical Method for Solving the Inverse Problem of Non-Stationary Flow of Viscoelastic Fluid in the Pipe

Numerical Method for Solving the Inverse Problem of Non-Stationary Flow of Viscoelastic Fluid in the Pipe