Journal articles: 'High Weissenberg number problem'

1

Keunings, Roland. "On the high Weissenberg number problem." Journal of Non-Newtonian Fluid Mechanics 20 (January 1986): 209–26. http://dx.doi.org/10.1016/0377-0257(86)80022-2.

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Trebotich, David. "Toward a solution to the high Weissenberg number problem." PAMM 7, no. 1 (December 2007): 2100073–74. http://dx.doi.org/10.1002/pamm.200700989.

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Evans, J. D. "Re-entrant corner flows of upper convected Maxwell fluids: the small and high Weissenberg number limits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (July 21, 2006): 3749–74. http://dx.doi.org/10.1098/rspa.2006.1737.

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We discuss here the steady planar flow of the upper convected Maxwell fluid at re-entrant corners in the singular limits of small and large Weissenberg number. The Weissenberg number is a parameter representing the dimensionless relaxation time and hence the elasticity of the fluid. Its value determines the strength of the fluid memory and thus the influence of elastic effects over viscosity. The small Weissenberg limit is that in which the elastic effects are small and the fluid's memory is weak. It is an extremely singular limit in which the behaviour of a Newtonian fluid is obtained in a main core region away from the corner and walls. Elastic effects are confined to boundary layers at the walls and core regions nearer to the corner. The actual asymptotic structure comprises a complicated four-region structure. The other limit of interest is the large Weissenberg limit (or high Weissenberg number problem) in which the elastic effects now dominate in the main regions of the flow. We explain how the transition in solution from Weissenberg order 1 flows to high Weissenberg flows is achieved, with the singularity in the stress field at the corner remaining the same but its effects now extending over larger length-scales. Implicit in this analysis is the absence of a lip vortex. We also show (for the main core region) that there is a small reduction in the velocity field at the corner and walls where it becomes smoother. This high Weissenberg number limit has a six-region local asymptotic structure and comment is made on its relevance to the case in which a lip vortex is present.

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Mohamadali, Meysam, and Nariman Ashrafi. "Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet." Journal of Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/9718786.

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High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.

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TANOUE, Shuichi, Jiro KOGA, Toshihisa KAJIWARA, Yoshiyuki IEMOTO, and Kazumori FUNATSU. "High Weissenberg Number Problem and Numerical Simulation of an Annular Extrudate Swell of Viscoelastic Fluids." Seikei-Kakou 9, no. 10 (1997): 817–24. http://dx.doi.org/10.4325/seikeikakou.9.817.

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Bielça Silva, Luciene Aparecida, and Messias Meneguette. "Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term." TEMA (São Carlos) 15, no. 3 (January 27, 2014): 293. http://dx.doi.org/10.5540/tema.2014.015.03.0293.

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<pre>The objective of this work is to study, through a simpler equation, the statement that the numerical instability associated to the high number of Weissenberg in equations with source term can be resolved by the use of the so called logarithmic representation conformation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. We will see that the representation of such equation by log-conformation removes the restriction of stability inherent to the elastic balance pointed out by [3] as the cause of high Weissenberg number problem (HWNP).</pre>

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7

Renardy, Michael. "The initial value problem for creeping flow of the upper convected Maxwell fluid at high Weissenberg number." Mathematical Methods in the Applied Sciences 38, no. 5 (March 17, 2014): 959–65. http://dx.doi.org/10.1002/mma.3121.

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8

Varchanis, S., A. Syrakos, Y. Dimakopoulos, and J. Tsamopoulos. "A new finite element formulation for viscoelastic flows: Circumventing simultaneously the LBB condition and the high-Weissenberg number problem." Journal of Non-Newtonian Fluid Mechanics 267 (May 2019): 78–97. http://dx.doi.org/10.1016/j.jnnfm.2019.04.003.

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Abedijaberi, A., and B. Khomami. "Continuum and multi-scale simulation of mixed kinematics polymeric flows with stagnation points: Closure approximation and the high Weissenberg number problem." Journal of Non-Newtonian Fluid Mechanics 166, no. 11 (June 2011): 533–45. http://dx.doi.org/10.1016/j.jnnfm.2011.03.001.

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AFONSO, A. M., P. J. OLIVEIRA, F. T. PINHO, and M. A. ALVES. "Dynamics of high-Deborah-number entry flows: a numerical study." Journal of Fluid Mechanics 677 (April 13, 2011): 272–304. http://dx.doi.org/10.1017/jfm.2011.84.

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High-elasticity simulations of flows through a two-dimensional (2D) 4 : 1 abrupt contraction and a 4 : 1 three-dimensional square–square abrupt contraction were performed with a finite-volume method implementing the log-conformation formulation, proposed by Fattal & Kupferman (J. Non-Newtonian Fluid Mech., vol. 123, 2004, p. 281) to alleviate the high-Weissenberg-number problem. For the 2D simulations of Boger fluids, modelled by the Oldroyd-B constitutive equation, local flow unsteadiness appears at a relatively low Deborah number (De) of 2.5. Predictions at higher De were possible only with the log-conformation technique and showed that the periodic unsteadiness grows with De leading to an asymmetric flow with alternate back-shedding of vorticity from pulsating upstream recirculating eddies. This is accompanied by a frequency doubling mechanism deteriorating to a chaotic regime at high De. The log-conformation technique provides solutions of accuracy similar to the thoroughly tested standard finite-volume method under steady flow conditions and the onset of a time-dependent solution occurred approximately at the same Deborah number for both formulations. Nevertheless, for Deborah numbers higher than the critical Deborah number, and for which the standard iterative technique diverges, the log-conformation technique continues to provide stable solutions up to quite (impressively) high Deborah numbers, demonstrating its advantages relative to the standard methodology. For the 3D contraction, calculations were restricted to steady flows of Oldroyd-B and Phan-Thien–Tanner (PTT) fluids and very high De were attained (De ≈ 20 for PTT with ϵ = 0.02 and De ≈ 10000 for PTT with ϵ = 0.25), with prediction of strong vortex enhancement. For the Boger fluid calculations, there was inversion of the secondary flow at high De, as observed experimentally by Sousa et al. (J. Non-Newtonian Fluid Mech., vol. 160, 2009, p. 122).

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Shah, Syed Amir Ghazi Ali, Ali Hassan, Najah Alsubaie, Abdullah Alhushaybari, Fahad M. Alharbi, Ahmed M. Galal, Diana-Petronela Burduhos-Nergis, and Costica Bejinariu. "Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity." Nanomaterials 12, no. 22 (November 20, 2022): 4084. http://dx.doi.org/10.3390/nano12224084.

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This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton’s method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction 5≤S≤7.5 effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained.

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12

Wang. "Reynolds Stress Model for Viscoelastic Drag-Reducing Flow Induced by Polymer Solution." Polymers 11, no. 10 (October 11, 2019): 1659. http://dx.doi.org/10.3390/polym11101659.

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Viscoelasticity drag-reducing flow by polymer solution can reduce pumping energy of pipe flow significantly. One of the simulation manners is direct numerical simulation (DNS). However, the computational time is too long to accept in engineering. Turbulent model is a powerful tool to solve engineering problems because of its fast computational ability. However, its precision is usually low. To solve this problem, we introduce DNS to provide accurate data to construct a high-precision turbulent model. A Reynolds stress model for viscoelastic polymer drag-reducing flow is established. The rheological behavior of the drag-reducing flow is described by the Giesekus constitutive Equation. Compared with the DNS data, mean velocity, mean conformation tensor, drag reduction, and stresses are predicted accurately in low Reynolds numbers and Weissenberg numbers but worsen as the two numbers increase. The computational time of the Reynolds stress model (RSM) is only 1/120,960 of DNS, showing the advantage of computational speed.

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Abedijaberi, A., and B. Khomami. "Sedimentation of a sphere in a viscoelastic fluid: a multiscale simulation approach." Journal of Fluid Mechanics 694 (January 18, 2012): 78–99. http://dx.doi.org/10.1017/jfm.2011.504.

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AbstractA long-standing problem in non-Newtonian fluid mechanics, namely the relationship between drag experienced by a sphere settling in a tube filled with a dilute polymeric solution and the sphere sedimentation velocity, is investigated via self-consistent multiscale flow simulations. Comparison with experimental measurements by Arigo et al. (J. Non-Newtonian Fluid Mech., vol. 60, 1995, pp. 225–257) have revealed that the evolution of the drag coefficient as a function of fluid elasticity can be accurately predicted when the macromolecular dynamics is described by realistic micromechanical models that closely capture the transient extensional viscosity of the experimental fluid at high extension rates. Specifically, for the first time we have computed the drag coefficient on the sphere at high Weissenberg number $\mathit{Wi}$ utilizing multi-segment bead–spring chain models with appropriate molecular parameters and have demonstrated that a hi-fidelity multiscale simulation is not only capable of accurately describing the drag on the sphere as a function of $\mathit{Wi}$ at various sphere-to-tube diameter ratios but also it can closely reproduce the experimentally observed velocity and stresses in the wake of the sphere.

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14

Zhurba Eremeeva, I. A., D. Scerrato, C. Cardillo, and A. Tran. "A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS." Problems of strenght and plasticity 81, no. 4 (2019): 500–511. http://dx.doi.org/10.32326/1814-9146-2019-81-4-500-511.

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Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

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15

Zhurba Eremeeva, I. A., D. Scerrato, C. Cardillo, and A. Tran. "A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS." Problems of strenght and plasticity 81, no. 4 (2019): 501–12. http://dx.doi.org/10.32326/1814-9146-2019-81-4-501-512.

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Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

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Mavi, Anele, and Tiri Chinyoka. "Finite Volume Computational Analysis of the Heat Transfer Characteristic in a Double-Cylinder Counter-Flow Heat Exchanger with Viscoelastic Fluids." Defect and Diffusion Forum 424 (May 8, 2023): 19–43. http://dx.doi.org/10.4028/p-j482zy.

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This work presents a computational analysis of the heat-exchange characteristics in a double-cylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement.The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheological behaviour of the core fluid is governed by the Giesekus viscoelastic constitutive model. The governing system of coupled nonlinear PDEs is intractable to analytic treatment and hence is solved numerically using Finite Volume Methods (FVM). The FVM numerical methodology is implemented via the open-source software package OpenFOAM. The numerical methods are stabilized, specifically to address numerical instabilities arising from the High Weissenberg Number Problem (HWNP), via a combination of the Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-Conformation Reformulation (LCR) methodology. The DEVSS and LCR stabilization techniques are integrated into the relevant viscoelastic fluid solvers. The novelties of the study center around the simulation and analysis of the optimal heat-exchange characteristics between the heated Giesekus fluid and the coolant Newtonian fluid within a double-pipe counter-flow arrangement. Existing studies in the literature have either focused exclusively on Newtonian fluids and/or on rectangular geometries. The existing OpenFOAM solvers have also largely focused on non-isothermal viscoelastic flows. The relevant OpenFOAM solvers are modified for the present purposes by incorporating the energy equation for viscoelastic fluid flow. The flow characteristics are presented qualitatively (graphically) via the fluid pressure, temperature, velocity, and the polymer-stress components as well as the related normal stress differences. The results illustrate the required decrease in the core fluid temperature in the longitudinal direction due to the cooling effects of the shell fluid, whose temperature predictably increases in the counter-flow direction.

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Pogrebnyak, Volodymyr G., Volodymyr Y. Shimanskii, Andriy V. Pogrebnyak, and Iryna V. Perkun. "Viscoelastic effects under water-polymer flooding conditions of the fractured-porous reservoir." Nafta-Gaz 79, no. 7 (July 2023): 455–63. http://dx.doi.org/10.18668/ng.2023.07.02.

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The work is devoted to the numerical simulation of the flow of simple and viscoelastic (polymer solution) fluids through a fracture by using polymer solutions for enhanced oil recovery from a reservoir. Polymer solutions have viscoelastic properties. Therefore, when polymer solution flows through the slot, we use the well-known Maxwell’s fluid model with the Jaumann derivative to evaluate deformation characteristics of the flow (stream functions, distributions of the longitudinal velocity gradient and normal stress) resulting in the manifestation of abnormal (compared with the behaviour of the ordinary fluid) effects. The case of slow flow is considered. In this case, the inertial terms can be neglected, the velocities, stresses, and stream functions can be written as the decomposition by Weisenberg number, and we can assume that the Weissenberg number is less than one. The determined regularities of viscoelastic (polymer solution) liquid behaviour with longitudinal velocity gradient and the elastic deformations effects manifested in this case have a decisive meaning in understanding the mechanism of anomalously high oil recovery capacity of a reservoir by using water-polymer flooding of the fractured-porous reservoir. Understanding the nature of the effects of elastic deformations under the conditions of water-polymer flooding of the fractured-porous reservoir enables hydrodynamic calculations of the optimal flow of the polymer solution. One of the main issues that need to be solved when developing the technology for increasing oil recovery from formations using polymer solutions is to determine the optimal flow regime in the fractured-porous reservoir. The calculation results verify the ideas obtained from the experimental solution of this problem concerning the strain-stress state of polymer macromolecules (liquid elements) during polymer flow in the inlet area of the fracture in the oil reservoir and confirm the possibility of using numerical analysis of convergent polymer flow for calculating longitudinal velocity gradients in the inlet area of the fracture and can also serve as additional substantiation of the proposed earlier mechanism for increasing oil recovery from reservoirs by using polymer solutions.

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18

Hao, Jian, and Tsorng-Whay Pan. "Simulation for high Weissenberg number." Applied Mathematics Letters 20, no. 9 (September 2007): 988–93. http://dx.doi.org/10.1016/j.aml.2006.12.003.

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19

Xi, Li, and Michael D. Graham. "Intermittent dynamics of turbulence hibernation in Newtonian and viscoelastic minimal channel flows." Journal of Fluid Mechanics 693 (January 17, 2012): 433–72. http://dx.doi.org/10.1017/jfm.2011.541.

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AbstractMaximum drag reduction (MDR), the asymptotic upper limit of reduction in turbulent friction drag by polymer additives, is the most important unsolved problem in viscoelastic turbulence. Recent studies of turbulence in minimal flow units have identified time intervals showing key features of MDR. These intervals, denoted ‘hibernating turbulence’ are found in both Newtonian and viscoelastic flows. The present study provides a comprehensive examination of this turbulence hibernation phenomenon in the minimal channel geometry, and discusses its impact on the turbulent dynamics and drag reduction. Similarities between hibernating turbulence and MDR are established in terms of both flow statistics (an intermittency factor, mean and fluctuating components of velocity) and flow structure (weak vortices and nearly streamwise-invariant kinematics). Hibernation occurs more frequently at high levels of viscoelasticity, leading to flows that increasingly resemble MDR. Viscoelasticity facilitates the occurrence of hibernation by suppressing the conventional ‘active’ turbulence, but has little influence on hibernation itself. At low Weissenberg number $\mathit{Wi}$, the average duration of active turbulence intervals is constant, but above a critical value of $\mathit{Wi}$, the duration decreases dramatically, and accordingly, the fraction of time spent in hibernation increases. This observation can be explained with a simple mathematical model that posits that the lifetime of an active turbulence interval is the time that it takes for the turbulence to stretch polymer molecules to a certain threshold value; once the molecules exceed this threshold, they exert a large enough stress on the flow to suppress the active turbulence. This model predicts an explicit form for the duration as a function of $\mathit{Wi}$ and the simulation results match this prediction very closely. The critical point where hibernation frequency becomes substantially increased coincides with the point where qualitative changes are observed in overall flow statistics – the transition between ‘low-drag-reduction’ and ‘high-drag-reduction’ regimes. Probability density functions of important variables reveal a much higher level of intermittency in the turbulent dynamics after this transition. It is further confirmed that hibernating turbulence is a Newtonian structure during which polymer extension is small. Based on these results, a framework is proposed that explains key transitions in viscoelastic turbulence, especially the convergence toward MDR.

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Davoodi, Mahdi, Allysson F. Domingues, and Robert J. Poole. "Control of a purely elastic symmetry-breaking flow instability in cross-slot geometries." Journal of Fluid Mechanics 881 (October 28, 2019): 1123–57. http://dx.doi.org/10.1017/jfm.2019.781.

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The cross-slot stagnation point flow is one of the benchmark problems in non-Newtonian fluid mechanics as it allows large strains to develop and can therefore be used for extensional rheometry measurements or, once instability arises, as a mixing device. In such a flow, beyond a critical value for which the ratio of elastic force to viscous force is high enough, elasticity can break symmetry even in the absence of significant inertial forces (i.e. creeping flow), which is an unwanted phenomenon if the device is to be used as a rheometer but beneficial from a mixing perspective. In this work, a passive control mechanism is introduced to the cross-slot by adding a cylinder at the geometric centre to replace the ‘free’ stagnation point with ‘pinned’ stagnation points at the surface of the cylinder. In the current modified geometry, effects of the blockage ratio (the ratio of the diameter of the cylinder to the width of the channel), the Weissenberg number (the ratio of elastic forces to viscous forces) and extensibility parameters ($\unicode[STIX]{x1D6FC}$ and $L^{2}$) are investigated in two-dimensional numerical simulations using both the simplified Phan-Thien and Tanner and finitely extensible nonlinear elastic models. It is shown that the blockage ratio for fixed solvent-to-total-viscosity ratio has a stabilizing effect on the associated symmetry-breaking instability. The resulting data show that the suggested modification, although significantly changing the flow distribution in the region near the stagnation point, does not change the nature of the symmetry-breaking instability or, for low blockage ratio, the critical condition for onset. Using both numerical and physical experiments coupled with a supporting theoretical analysis, we conclude that this instability cannot therefore be solely related to the extensional flow near the stagnation point but it is more likely related to streamline curvature and the high deformation rates towards the corners, i.e. a classic ‘curved streamlines’ purely elastic instability. Our work also suggests that the proposed geometric modification can be an effective approach for enabling higher flow rates to be achieved whilst retaining steady symmetric flow.

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GOTO, Ikuhisa, Hikaru WAKI, Shuichi IWATA, Hideki MORI, and Tsutomu ARAGAKI. "Numerical analysis of viscoelastic flow at high Weissenberg number." Proceedings of the Fluids engineering conference 2000 (2000): 155. http://dx.doi.org/10.1299/jsmefed.2000.155.

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Miller, Joel C., and J. M. Rallison. "Instability of coextruded elastic liquids at high Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 143, no. 2-3 (May 2007): 88–106. http://dx.doi.org/10.1016/j.jnnfm.2007.01.008.

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Evans, J. D. "High Weissenberg number boundary layer structures for UCM fluids." Applied Mathematics and Computation 387 (December 2020): 124952. http://dx.doi.org/10.1016/j.amc.2019.124952.

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Sobh, Ayman Mahmoud. "Slip flow in peristaltic transport of a Carreau fluid in an asymmetric channel." Canadian Journal of Physics 87, no. 8 (August 2009): 957–65. http://dx.doi.org/10.1139/p09-027.

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In this paper, peristaltic transport of a Carreau fluid in an asymmetric channel is studied theoretically under zero Reynolds number and long-wavelength approximation for both slip and no-slip flow (Kn = 0). The problem is analyzed using a perturbation expansion in terms of the Weissenberg number as a parameter. Analytic forms for the axial velocity component and the pressure gradient are obtained to second order. The pressure rise is computed numerically and explained graphically. Moreover, the effects of the slip parameter, Weissenberg number, power-law index, and phase difference on the pressure gradient, the axial velocity, and the trapping phenomena have been discussed.

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Lin, Che-Yu, and Chao-An Lin. "Direct Numerical Simulations of Turbulent Channel Flow With Polymer Additives." Journal of Mechanics 36, no. 5 (August 6, 2020): 691–98. http://dx.doi.org/10.1017/jmech.2020.34.

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ABSTRACTDirect numerical simulations have been applied to simulate flows with polymer additives. FENE-P (finite-extensible-nonlinear-elastic-Peterlin) dumbbell model solving for the conformation tensor is adopted to investigate the influence of the polymer on the flowfield. Boundary treatments of the conformation tensor on the flowfield are examined first, where boundary condition based on the linear extrapolation scheme provides more accurate results with second-order accurate error norms. Further simulations of the turbulent channel flow at different Weissenberg numbers are also conducted to investigate the influence on drag reduction. Drag reduction increases in tandem with the increase of Weissenberg number and the increase saturates at Weτ~200, where the drag reduction is close to the maximum drag reduction (MDR) limit. At the regime of y+ > 5, the viscous layer thickens with the increase of the Weissenberg number showing a departure from the traditional log-law profile, and the velocity profiles approach the MDR line at high Weissenberg number. The Reynolds stress decreases in tandem with the increase of Weτ, whereas the levels of laminar stress and polymer stress act adversely. However, as the Weissenberg number increases, the proportion of the laminar stress in the total stress increases, and this contributes to the drag reduction of the polymer flow.

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Guo, Shihan, and Xinhui Si. "Parametric study of the Giesekus fluid flow in a curved duct with square cross section." Physics of Fluids 34, no. 10 (October 2022): 103107. http://dx.doi.org/10.1063/5.0119071.

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In this paper, the log-conformation representation method (LCR) is applied in an orthogonal curvilinear coordinate system to study the Giesekus fluid flow in a curved duct. Derivations for evolution equations of LCR in this curvilinear coordinate system are presented. Secondary flow patterns and oscillation solutions are computed by using the collocation spectral method. The influence of a wide range of Dean number, Weissenberg number, and dimensionless mobility parameter α on fluid behaviors is studied. A six-cell secondary flow pattern is found under very low Dean number and relatively high Weissenberg number and α. Moreover, both Weissenberg number and α are able to facilitate the development of the secondary flow. In addition, simulations under critical Reynolds number for oscillation imply that Giesekus fluid flow with [Formula: see text] is not able to retain a four-cell secondary flow pattern in a steady state, which is different from Newtonian fluids.

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27

Henry, Christopher K., Giuseppe R. Palmese, and Nicolas J. Alvarez. "The evolution of crystalline structures during gel spinning of ultra-high molecular weight polyethylene fibers." Soft Matter 14, no. 44 (2018): 8974–85. http://dx.doi.org/10.1039/c8sm01597j.

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The Weissenberg number during gel spinning controls the crystalline morphology of the as spun UHMWPE fiber. The final drawn crystalline morphology strongly depends on the starting as-spun crystalline structure.

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Renardy, Michael. "High weissenberg number boundary layers for the upper convected Maxwell fluid." Journal of Non-Newtonian Fluid Mechanics 68, no. 1 (January 1997): 125–32. http://dx.doi.org/10.1016/s0377-0257(96)01491-7.

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29

Tsai, Tai-Ping, and David S. Malkus. "Numerical breakdown at high Weissenberg number in non-Newtonian contraction flows." Rheologica Acta 39, no. 1 (January 14, 2000): 62–70. http://dx.doi.org/10.1007/s003970050007.

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30

Ervin, Vincent J., and Hyesuk Lee. "Defect correction method for viscoelastic fluid flows at high Weissenberg number." Numerical Methods for Partial Differential Equations 22, no. 1 (2005): 145–64. http://dx.doi.org/10.1002/num.20090.

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31

Elshehawey, Elsayed F., and Ayman M. F. Sobh. "Peristaltic viscoelastic fluid motion in a tube." International Journal of Mathematics and Mathematical Sciences 26, no. 1 (2001): 21–34. http://dx.doi.org/10.1155/s0161171201003556.

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Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model the chyme movement in the small intestine by considering the chyme as an Oldroyd fluid. We found out that the pumping rate of Oldroyd fluid is less than that for a Newtonian fluid. Further, the effects of Reynolds number, Weissenberg number, amplitude ratio and wave number on the pressure rise and friction force have been discussed. It is found that the pressure rise does not depend on Weissenberg number at a certain value of flow rate. The results are studied for various values of the physical parameters of interest.

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Renardy, Michael. "On the high Weissenberg number limit of the upper convected Maxwell fluid." Journal of Non-Newtonian Fluid Mechanics 165, no. 1-2 (January 2010): 70–74. http://dx.doi.org/10.1016/j.jnnfm.2009.10.001.

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STOKES, JASON R., LACHLAN J. W. GRAHAM, NICK J. LAWSON, and DAVID V. BOGER. "Swirling flow of viscoelastic fluids. Part 2. Elastic effects." Journal of Fluid Mechanics 429 (February 25, 2001): 117–53. http://dx.doi.org/10.1017/s0022112000002901.

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A torsionally driven cavity has been used to examine the influence of elasticity on the swirling flow of constant-viscosity elastic liquids (Boger fluids). A wealth of phenomena is observed as the degree of inertia, elasticity and viscous forces are varied by using a range of low- to high-viscosity flexible polyacrylamide Boger fluids and a semi-rigid xanthan gum Boger fluid. As the inertia is decreased and elasticity increased by using polyacrylamide Boger fluids, the circulation rates for a ‘Newtonian-like’ secondary flow decreases until flow reversal occurs owing to the increasing magnitude of the primary normal stress difference. For each polyacrylamide fluid, the flow becomes highly unstable at a critical combination of Reynolds number and Weissenberg number resulting in a new time-dependent elastic instability. Each fluid is characterized by a dimensionless elasticity number and a correlation with Reynolds number is found for the occurrence of the instability. In the elasticity dominated flow of the polyacrylamide Boger fluids, the instability disrupts the flow dramatically and causes an increase in the peak axial velocity along the central axis by as much as 400%. In this case, the core vortex spirals with the primary motion of fluid and is observed in some cases at Reynolds numbers much less than unity. Elastic ‘reverse’ flow is observed for the xanthan gum Boger fluid at high Weissenberg number. As the Weissenberg number decreases, and Reynolds number increases, counter-rotating vortices flowing in the inertial direction form on the rotating lid. The peak axial velocity decreases for the xanthan gum Boger fluid with decreasing Weissenberg number. In addition, several constitutive models are used to describe accurately the rheological properties of the fluids used in this work in shear and extensional flow. This experimental investigation of a complex three-dimensional flow using well-characterized fluids provides the information necessary for the validation of non-Newtonian constitutive models through numerical analysis of the torsionally driven cavity flow.

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Zaman, Akbar, M. Sajid, and Nabeela Kousar. "Biomedical study of effects nanoparticles on unsteady blood (non-Newtonian) flow through a catheterized stenotic vessel." Canadian Journal of Physics 97, no. 5 (May 2019): 487–97. http://dx.doi.org/10.1139/cjp-2018-0376.

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The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.

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Renardy, Michael. "The high Weissenberg number limit of the UCM model and the Euler equations." Journal of Non-Newtonian Fluid Mechanics 69, no. 2-3 (April 1997): 293–301. http://dx.doi.org/10.1016/s0377-0257(96)01544-3.

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36

Kadyirov, A. I., and E. K. Vachagina. "Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe." Journal of Physics: Conference Series 2057, no. 1 (October 1, 2021): 012007. http://dx.doi.org/10.1088/1742-6596/2057/1/012007.

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Abstract A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

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Ali, Hashim, and Masood Khan. "Impact of heat transfer analysis on Carreau fluid-flow past a static/moving wedge." Thermal Science 22, no. 2 (2018): 809–20. http://dx.doi.org/10.2298/tsci160115169a.

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The foremost aspiration of the present endeavor is to investigate the boundary-layer flow of a generalized Newtonian Carreau fluid model past a static/moving wedge. In addition, the effects of heat transfer on the flow field are also taken into account. The governing equations of the problem based on the boundary-layer approximation are changed into a non-dimensional structure by introducing the local similarity transformations. The subsequent system of ODE has been numerically integrated with fifth-order Runge-Kutta method. Influence of the velocity ratio parameter, the wedge angle parameter, the Weissenberg number, the power law index, and the Prandtl number on the skin friction and Nusselt number are analyzed. The variation of the skin friction as well as other flow characteristics has been presented graphically to capture the influence of these parameters. The results indicate that the increasing value of the wedge angle substantially accelerates the fluid velocity while an opposite behavior is noticed in the temperature field. Moreover, the skin friction coefficient for the growing Weissenberg number significantly enhances for the shear thickening fluid and show the opposite behavior of shear thinning fluid. However, the local Nusselt number has greater values in the case of moving wedge. An excellent comparison with previously published works in various special cases has been made.

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Sasmal, C. "Effect of micelle breaking rate and wall slip on unsteady motion past a sphere translating steadily in wormlike micellar solutions." Physics of Fluids 34, no. 7 (July 2022): 073110. http://dx.doi.org/10.1063/5.0096602.

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Many prior experimental studies have found the existence of an unsteady or fluctuating flow field around a solid sphere when falling in wormlike micellar solutions. Based on the two-species Vasquez–Cook–McKinley constitutive model for micelles, a recent numerical study shows that the breakage of long micelles downstream of the translating sphere causes this unsteady motion [C. Sasmal, “Unsteady motion past a sphere translating steadily in wormlike micellar solutions: A numerical analysis,” J. Fluid Mech. 912, A52, (2021)]. This numerical study further shows that the micelle breakage rate and wall slip can strongly influence this phenomenon. In particular, we find that the onset of this unsteady motion is delayed to higher values of the Weissenberg number as the micelle breakage rate decreases, or in other words, micelles become hard to break. Additionally, we observe that at some values of the micelle breakage rate, again, a transition in the flow field from unsteady to steady occurs at high Weissenberg numbers. Therefore, there is a window of the Weissenberg number present to observe this unsteady motion past the translating sphere. On the other hand, we show that the presence of wall slip on the sphere surface suppresses this unsteady motion past the translating sphere, and a probable explanation is also provided for the same.

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Feng, J. Feng, D. D. Joseph, R. Glowinski, and T. W. Pan. "A three-dimensional computation of the force and torque on an ellipsoid settling slowly through a viscoelastic fluid." Journal of Fluid Mechanics 283 (January 25, 1995): 1–16. http://dx.doi.org/10.1017/s0022112095002217.

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The orientation of an ellipsoid falling in a viscoelastic fluid is studied by methods of perturbation theory. For small fall velocity, the fluid's rheology is described by a second-order fluid model. The solution of the problem can be expressed by a dual expansion in two small parameters: the Reynolds number representing the inertial effect and the Weissenberg number representing the effect of the non-Newtonian stress. Then the original problem is split into three canonical problems: the zeroth-order Stokes problem for a translating ellipsoid and two first-order problems, one for inertia and one for second-order rheology. A Stokes operator is inverted in each of the three cases. The problems are solved numerically on a three-dimensional domain by a finite element method with fictitious domains, and the force and torque on the body are evaluated. The results show that the signs of the perturbation pressure and velocity around the particle for inertia are reversed by viscoelasticity. The torques are also of opposite sign: inertia turns the major axis of the ellipsoid perpendicular to the fall direction; normal stresses turn the major axis parallel to the fall. The competition of these two effects gives rise to an equilibrium tilt angle between 0° and 90° which the settling ellipsoid would eventually assume. The equilibrium tilt angle is a function of the elasticity number, which is the ratio of the Weissenberg number and the Reynolds number. Since this ratio is independent of the fall velocity, the perturbation results do not explain the sudden turning of a long body which occurs when a critical fall velocity is exceeded. This is not surprising because the theory is valid only for slow sedimentation. However, the results do seem to agree qualitatively with ‘shape tilting’ observed at low fall velocities.

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King, J. R. C., and S. J. Lind. "High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation." Journal of Non-Newtonian Fluid Mechanics 293 (July 2021): 104556. http://dx.doi.org/10.1016/j.jnnfm.2021.104556.

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Mahdy, A., and Ali J. Chamkha. "Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 11 (November 5, 2018): 2567–80. http://dx.doi.org/10.1108/hff-12-2017-0499.

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Purpose The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish. Design/methodology/approach The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique. Findings Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number. Originality/value A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

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Nimura, Tomohiro, and Takahiro Tsukahara. "Viscoelasticity-Induced Instability in Plane Couette Flow at Very Low Reynolds Number." Fluids 7, no. 7 (July 13, 2022): 241. http://dx.doi.org/10.3390/fluids7070241.

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Elasto-inertial turbulence (EIT), a new turbulent state found in polymer solutions with viscoelastic properties, is associated with drag-reduced turbulence. However, the relationship between EIT and drag-reduced turbulence is not currently well-understood, and it is important to elucidate the mechanism of the transition to EIT. The instability of viscoelastic fluids has been studied in a canonical wall-bounded shear flow to investigate the transition process of EIT. In this study, we numerically deduced that an instability occurs in the linearly stable viscoelastic plane Couette flow for lower Reynolds numbers, at which a non-linear unstable solution exists. Under instability, the flow structure is elongated in the spanwise direction and regularly arranged in the streamwise direction, which is a characteristic structure of EIT. The regularity of the flow structure depends on the Weissenberg number, which represents the strength of elasticity; the structure becomes disordered under high Weissenberg numbers. In the energy spectrum of velocity fluctuations, a steep decay law of the structure’s scale towards a small scale is observed, and this can be recognized as a ubiquitous feature of EIT. The existence of instability in viscoelastic plane Couette flow supports the idea that the transitional path toward EIT may be mediated by subcritical instability.

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Khan, Muhammad Rehan, Khuram Javid, and Muhammad Muddassar Javed. "Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel." Siazga Research Journal 1, no. 1 (September 30, 2022): 28–42. http://dx.doi.org/10.58341/srj.v1i1.2.

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The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

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Khan, Muhammad Rehan, Khuram Javid, and Muhammad Muddassar Javed. "Asymptotic Analysis of Peristaltic Hydromagnetic Flow of Carreau Fluid in a Curved Channel." Siazga Research Journal 1, no. 1 (September 30, 2022): 28–42. http://dx.doi.org/10.58341/srj.v1i1.9.

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The boundary layer peristaltic hydromagnetic flow of Carreau fluid in a curved type has been investigated in this article. Carreau fluid model is a generalized Newtonian fluid model having four parameters namely, infinite-shear-rate viscosity (μ∞), zero-shear-rate viscosity (μ0), relaxation time constant (Γ) and power-law index (n). The governing equations of the flow is obtained under long wavelength and low Reynolds number assumptions. An asymptotic solution to this problem is obtained when the strength of the applied magnetic field is large. It is observed the that asymptotic solution is independent of Weissenberg number. The asymptotic solution is also validated against numerical solution obtained via finite difference method.

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Renardy, Michael. "Asymptotic structure of the stress field in flow past a cylinder at high Weissenberg number." Journal of Non-Newtonian Fluid Mechanics 90, no. 1 (April 2000): 13–23. http://dx.doi.org/10.1016/s0377-0257(99)00050-6.

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GOTO, Ikuhisa, Tomomi HAYAKAWA, Hikaru WAKI, Shuichi IWATA, Hideki MORI, and Tsutomu ARAGAKI. "K-1210 Numerical Techniques Improving Convergence Behavior of Viscoelastic Flow Analysis at High Weissenberg Number." Proceedings of the JSME annual meeting II.01.1 (2001): 83–84. http://dx.doi.org/10.1299/jsmemecjo.ii.01.1.0_83.

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Fattal, Raanan, and Raz Kupferman. "Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation." Journal of Non-Newtonian Fluid Mechanics 126, no. 1 (February 2005): 23–37. http://dx.doi.org/10.1016/j.jnnfm.2004.12.003.

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Tanoue, Shuichi, Toshihisa Kajiwara, Yoshiyuki Iemoto, and Kazumori Funatsu. "High weissenberg number simulation of an annular extrudate swell using the differential type constitutive equation." Polymer Engineering & Science 38, no. 3 (March 1998): 409–19. http://dx.doi.org/10.1002/pen.10202.

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Nadeem, Sohail, and Noreen Sher Akbar. "Series Solutions for the Peristaltic Flow of a Tangent Hyperbolic Fluid in a Uniform Inclined Tube." Zeitschrift für Naturforschung A 65, no. 11 (November 1, 2010): 887–95. http://dx.doi.org/10.1515/zna-2010-1101.

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In the present investigation we have studied a tangent hyperbolic fluid in a uniform inclined tube. The governing equations are simplified using long wavelength and low Reynold number approximations. The solutions of the problem in simplified form are calculated with two methods namely (i) the perturbation method and (ii) the homotopy analysis method. The comparison of the solutions show a very good agreement between the two results. At the end of the article the expressions of the pressure rise and the frictional force are calculated with the help of numerical integration. The graphical results are presented to show the physical behaviour of Weissenberg number We, amplitude ratio φ , and tangent hyperbolic power law index n.

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Rusak, Zvi, Nguyen Ly, John A. Tichy, and Shixiao Wang. "Near-critical swirling flow of a viscoelastic fluid in a circular pipe." Journal of Fluid Mechanics 814 (February 6, 2017): 325–60. http://dx.doi.org/10.1017/jfm.2017.16.

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The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.

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Journal articles on the topic 'High Weissenberg number problem'

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