Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Izadpanah Ehsan ◽  
Sefid Mohammad ◽  
Nazari Mohammad Reza ◽  
Jafarizade Ali ◽  
Ebrahim Sharifi Tashnizi
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Power Law Fluid ◽  
Tandem Arrangement ◽  
Square Cylinders ◽  
Shear Thickening Fluids ◽  
Power Law Index

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

Two Dimensional Unsteady Laminar Flow of Power Law Fluids Past a Square Cylinder: A Numerical Study

2008 ◽  
Author(s):  
Akhilesh K. Sahu ◽  
Raj P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
Edge Separation

The two-dimensional and unsteady flow of power-law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time for Newtonian fluids. However, no such information is available for power law fluids. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The macroscopic quantities such as drag coefficients, Strouhal number, lift coefficient as well as the detailed kinematic variables like stream function, vorticity and so on, have been calculated as functions of the pertinent dimension-less groups. In particular, the effects of Reynolds number and of the power-law index have been investigated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening behaviour delays the leading edge separation. So, the drag coefficient in the above-mentioned range of Reynolds number, Re, in shear-thinning fluids (n &lt; 1) initially decreases but at high values of the Reynolds number, it increases. As expected, on the other hand, in case of shear-thickening fluids (n &gt; 1) drag coefficient reduces with Reynolds number, Re. Furthermore, the present results also suggest the transition from steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thickening fluids than that in Newtonian fluids. Also, the spectra of lift signal for shear-thickening fluids show that the flow is truly periodic in nature with a single dominant frequency in the above range of Reynolds number. In shear-thinning fluids at higher Re, quasi-periodicity sets in with additional frequencies, which indicate the transition from the 2-D to 3-D flows.

Non-Newtonian Fluids Mixing Behavior Behind a Grid

2012 ◽  
Author(s):  
T. D. Nguyen ◽  
M. Elhajem ◽  
Q. Nguyen ◽  
S. Simoëns ◽  
A. Delache ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Chemical Engineering ◽  
Vertical Plane ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Point Of View ◽  
Newtonian Fluids ◽  
Shear Thickening Fluids ◽  
Set Up

Numerous biological, biomedical or chemical engineering processes involve non-Newtonian fluids as shear-thinning or shear-thickening fluids. As early as 1969, Lumley [1] investigated the influence of the non-Newtonian characteristics on the Kolmogorov cascade. In 1986, De Gennes [2] revisited such point of view by considering more precisely elasticity and shear thinning properties. As of today, the correlation between elasticity and other flow properties is still unclear, recent numerical simulations attempted to clarify the issue with the use of FENE-P or other linear viscoelastic models. The goal of this experimental work is to further clarify these assumptions by using new optical tools (PIV, PLIF) to study non-Newtonian decaying isotropic homogeneous turbulence (IHT), using the approach and analysis of the 1971 work of Comte-Bellot and Corrsin [3] for Newtonian fluids, and more recently (2010, 2011) by Lenoir et al. [4]. The experimental set-up consists of a small, 1m long liquid channel, with a cross-section of 6.6 × 6.6 cm2, as in Simoëns and Ayrault [5]. In order to obtain best possible quasi-isotropic flow for sufficient large Reynolds numbers (see Comte-Bellot and Corrsin [6]), the grid was installed transversally upstream the flow, at the outlet of a contraction chamber; the grid squared mesh was 8mm wide. A PIV Lavision System with two synchronized pulsed YAG Lasers was used to obtain Instantaneous velocity maps on selected vertical plane crossing longitudinally the channel at its center. The flow was seeded with 10μm diameter fluorescent particles for PIV measurements. IHT experiments were done on a 1% carboxymethyl cellulose (CMC) aqueous solution (such dilute CMC solution is non-Newtonian as shown in the 2008 work of Benchabane and Bekkour [7]) and then compared to measurements in water at the same flow rate. To prevent molecular modification of the CMC fluid structure out of its natural shear stress, the flow was driven by gravity, not by a pump. For this study, the water flow Reynolds number was 1600; the flow regime was too low to reach a turbulent state. Frequent rheometer checks were performed during the CMC experiments to verify the preservation of the integral shear thinning properties of the fluids. For the CMC flow, the Reynolds number was determined locally, based on the local viscosity after a Carreau-Yasuda model of order 2, in which γ̇ is the rate of shear strain, η is the viscosity at iteration n, η0 is the viscosity at zero shear rate; λ is a constant with units of time, where 1/λ is the critical shear rate at which viscosity begins to decrease (see Nguyen et al. (2010, 2012) [8], [9]).

scholarly journals Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1959
Author(s):  
Adrian S. Halifi ◽  
Sharidan Shafie ◽  
Norsarahaida S. Amin
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Power Law ◽  
Vortex Formation ◽  
Shear Thickening ◽  
Power Law Model ◽  
Governing Equations ◽  
Power Law Fluid ◽  
Transfer Parameters ◽  
Power Law Index

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

2014 ◽  
Vol 30 (5) ◽  
pp. 505-513 ◽  
Author(s):  
C.-I. Chen ◽  
M.-C. Lin ◽  
C.-K. Chen
Keyword(s):  
Power Law ◽  
Spin Coating ◽  
Film Flow ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Landau Equation ◽  
Shear Thickening ◽  
Vital Role ◽  
Power Law Fluid ◽  
Power Law Index

AbstractThe phenomena of surface instabilities in a thin power-law fluid during spin coating are investigated. The set of Navier-Stokes equations with non-Newtonian behavior in the region of low Reynolds number serves as a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolution equation of the Ostwald de-Waele type fluid to govern the propagation of surface waves. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The amplitude of instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of power-law index plays a vital role in stabilizing the film flow. The shear-thinning fluid is more unstable than the shear-thickening fluid in the stability analysis. Further, the nonlinear wave speed in the supercritical stability region decreases with increasing values of power-law index.

scholarly journals Deformation of a Capsule in a Power-Law Shear Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Fang-Bao Tian
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lattice Boltzmann Method ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method

2014 ◽  
Vol 15 (1) ◽  
pp. 265-284 ◽  
Author(s):  
Qiuxiang Li ◽  
Ning Hong ◽  
Baochang Shi ◽  
Zhenhua Chai
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Two Dimensional ◽  
Square Cavity ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

AbstractIn this paper, the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the vortex strength, vortex position and velocity distribution are extensively studied. In our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to 1.75, covering both cases of shear-thinning and shear-thickening. Compared with the Newtonian fluid, numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number, but also related to power-law index.

Flow of Power-Law Fluids Past a Rotating Cylinder At High Reynolds Numbers

2021 ◽  
Author(s):  
Pooja Thakur ◽  
Naveen Tiwari ◽  
Raj P. Chhabra
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Rotational Velocity ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Rotating Cylinder ◽  
Critical Values ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Power Law Index

Abstract In this study, a rotating cylinder is placed in a stream of shear-thinning fluids, flowing with an uniform velocity. Detailed investigations are performed for the following range of conditions: Reynolds number 100 ? Re ? 500, power-law index 0.2 ? n ? 1 and rotational velocity 0 ? ? ? 5. Flow transitions are observed from steady to unsteady at critical values of the Reynolds number, the rotational velocity, and the power-law index. Critical values of the Reynolds number Re^c have been obtained for varying levels of the rotational velocity, and the power-law index. Re^c varies non-monotonically with the rotational velocity. At a particular Reynolds number, an increase of the rotational velocity acts as a vortex suppression technique. For shear-thinning ?uids considered here, the vortex suppression occurs at a larger value of the critical rotational velocity ?^c, relative to Newtonian ?uids. For the unsteady ?ow, lift coef?cient versus time curve exhibits oscillatory behavior, and this has been used to delineate the ?ow regime as steady or unsteady ?ow. For unsteady ?ow regimes, both the amplitude of the lift coef?cient and the Strouhal number increase with increasing Reynolds numbers. The results presented in this work for such high Reynolds numbers elucidate the possible complex interplay between the kinematic and rheological parameters of non-Newtonian ?uids. This investigation also complements the currently available low Reynolds number results up to ? Re = 140.

Experimental Determination of the Virtual Mass Coefficient for Two Spheres Accelerating in a Power Law Fluid

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Abbas H. Sulaymon ◽  
Catherine A. M. E. Wilson ◽  
Abeer I. Alwared
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Reynolds Numbers ◽  
Separation Distance ◽  
Virtual Mass ◽  
Power Law Fluid ◽  
Mass Coefficient ◽  
Single Sphere ◽  
Power Law Index

The virtual mass coefficient is determined experimentally for the motion of two spheres side by side and in line in a power law fluid. The velocities of the two accelerating spheres and their separation distance was measured as they accelerated under the action of driving weights through a cylindrical column filled with different concentrations of polyacryamaide solution (0.01%, 0.03%, 0.05%, and 0.07% by weight). For comparison purposes, the experiments were repeated with water. Various densities of spheres and separation distances were examined. Within the range of power law indices (0.61–0.834) and Reynolds numbers (1.1–75) examined, the virtual mass coefficient was found to decrease with an increasing Reynolds number for the two spheres moving side by side, and found to be greater than 0.5 when the spheres were touching each other. As the distance between the spheres increased, the virtual mass coefficient was found to decrease and approached the single sphere value of 0.5 when the distance between the spheres was more than ten radii. When the spheres were in line and touching each other, the virtual mass coefficient was found to be less than 0.5, however, when the distance between the spheres increased, the virtual mass coefficient increased and approached the value of 0.5. The virtual mass coefficient was found to be consistent with the shear thinning behavior; for a given Reynolds number, it increased with an increasing power law index.

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