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.

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.

scholarly journals High mixing performances of shear-thinning fluids in two-layer crossing channels micromixer at very low Reynolds numbers

2019 ◽  
Vol 13 (4) ◽  
pp. 5938-5960
Author(s):  
A. Kouadri ◽  
Y. Lasbet ◽  
M. Makhlouf
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Transport Model ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Species Transport ◽  
Industrial Sectors ◽  
Power Law Fluids ◽  
Power Law Index

In a recent study, the Two-Layer Crossing Channels Micromixer (TLCCM) exhibited good mixing capacities in the case of the Newtonian fluids (close to 100%) for all considered Reynolds number values. However, since the majority of the used fluids in the industrial sectors are non-Newtonians, this work details the mixing evolution of power-law fluids in the considered geometry. In this paper, the power-law index ranges from 0.73 to 1 and the generalized Reynolds number is bounded between 0.1 and 50. The conservation equations of momentum, mass and species transport are numerically solved using a CFD code, considering the species transport model. The flow structure at the cross-sectional planes of our micromixer was studied using the dynamic systems theory. The evolutions of the intensity, also the axial, radial and tangential velocity profiles were examined for different values of the Reynolds number and the power-law index. Besides, the pressure drop of the power-law fluids under different Reynolds number was calculated and represented. Furthermore, the mixing efficiency is evaluated by the computation of the mixing index (MI), based on the standard deviation of the mass fraction in different cross-sections. In such geometry, a perfect mixing is achieved with MI closed to 99.47 %, at very small Reynolds number (from the value 0.1) whatever the power-law index and generalized Reynolds numbers taken in this investigation. Consequently, the targeted channel presents a useful tool for pertinent mass transfer improvements, it is highly recommended to include it in various microfluidic systems.

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.

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.

A Numerical Model for Edge Effect Correction of the Mooney Rheometer

2009 ◽  
Vol 82 (4) ◽  
pp. 401-417
Author(s):  
Sergio A. Montes
Keyword(s):  
Experimental Data ◽  
Edge Effect ◽  
Power Law ◽  
Power Law Fluid ◽  
One Dimensional ◽  
Complex Shear ◽  
Theoretical Predictions ◽  
Power Law Index ◽  
Significant Concentration ◽  
Finite Difference Techniques

Abstract The flow of a power law fluid within the cavity of a multi-speed Mooney rheometer is studied by means of finite difference techniques with the aim of quantifying the edge effects that occur in the vicinity of the rotor corner. As expected, a significant concentration of shear stress occurs near the rotor edge. As the power law index varies, significant stagnation zones are found within the cavity, which combined with thin-shearing behavior near the moving surfaces, yield complex shear rate distributions. However, when torque is calculated, the edge effect can be described by a factor which is numerically very similar to a factor obtained from one-dimensional models described in the literature. Comparison of theoretical predictions and experimental data was found to be satisfactory.

Developing and Fully Developed Non-Newtonian Fluid Flow and Heat Transfer Through Concentric Annuli

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Mohammad Sefid ◽  
Ehsan Izadpanah
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Convection Heat Transfer ◽  
Channel Length ◽  
Laminar Flows ◽  
Rheological Parameter ◽  
Power Law Fluid ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Power Law Index

Developing and fully developed laminar flows of power law fluid with forced convection heat transfer through a concentric annular duct are numerically analyzed. The results are presented for the following ranges: 0.2 ≤ n ≤ 1.8 (power law index), 10 ≤ Re ≤ 1000 (Reynolds number), and r* = 0.2, 0.5, 0.8 (aspect ratio). In addition, the influences of different thermal boundary conditions on the thermal performance are delineated. The effects of rheological parameter on the developing length, friction factor, temperature distribution, velocity profile, and Nusselt number along the channel length are investigated. The results are compared with earlier research and excellent agreement was observed.

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