Annular Shear-Thinning Flow Over an Axisymmetric Sudden Expansion

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Shear Thinning ◽  
Sudden Expansion ◽  
Rheological Parameters ◽  
Recirculation Region ◽  
Flow Recirculation ◽  
Flow Stagnation ◽  
Power Law Index ◽  
Annular Pipe ◽  
Steady Laminar

Suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid were numerically investigated within the steady laminar flow regime. The power-law constitutive equation is used to model the rheology of interest. A parametric study is performed to reveal the influence of annular diameter ratio, k, and power-law index, n, over the following range of parameters: k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates two recirculation regions. The first is a central recirculation region between the expansion plane and the flow stagnation point along the centerline. A second, corner recirculation region forms between the expansion plane and the flow reattachment point along the wall. The results demonstrate impact of the investigated geometrical and rheological parameters on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane.

Flow Inertia and Heat Transfer in Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Heat Transfer Augmentation ◽  
Flow And Heat Transfer ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
Annular Pipe ◽  
Flow Inertia ◽  
The Impact

The impact of flow inertia on flow and heat transfer in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. The equations governing conservation of mass, momentum, and energy, along with the power-law constitutive model are numerically solved using a finite-difference numerical scheme. The influence of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer augmentation, downstream the plane of expansion, is only observed for Pr = 10 and 100. The extent and intensity of recirculation in the corner region, increases with inflow inertia. Higher Reynolds and Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane.

Inflow Conditions and Suddenly Expanding Annular Shear-Thinning Flows

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Power Law ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Inflow Velocity ◽  
Flow Recirculation ◽  
Shear Thinning Fluids ◽  
Power Law Index ◽  
The Impact ◽  
Inflow Conditions

The impact of inflow conditions on the flow structure and evolution characteristics of annular flows of Newtonian and shear-thinning fluids through a sudden pipe expansion are studied. Numerical solutions to the elliptic form of the governing equations along with the power-law constitutive equation were obtained using a finite-difference scheme. A parametric study is performed to reveal the influence of inflow velocity profiles, annular diameter ratio, k, and power-law index, n, over the following range of parameters: inflow velocity profile = {fully-developed, uniform}, k = {0, 0.5, 0.7} and n = {1, 0.8, 0.6}. Flow separation and entrainment, downstream of the expansion plane, creates central and a much larger outer recirculation regions. The results demonstrate the influence of inflow conditions, annular diameter ratio, and rheology on the extent and intensity of both flow recirculation regions, the wall shear stress distribution, and the evolution and redevelopment characteristics of the flow downstream the expansion plane. Fully-developed inflows result in larger reattachment and redevelopment lengths as well as more intense recirculation, within the central and corner regions, in comparison with uniform inflow conditions.

Influence of a Yield-Shear-Thinning Rheology on the Flow Behavior of Submerged Annular Jets

2020 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Momentum Conservation ◽  
Recirculation Region ◽  
Substantial Impact ◽  
Laminar Jet ◽  
Power Law Index

Abstract The flow structure and decay characteristics of submerged annular yield-pseudoplastic jets are investigated. Numerical solutions to the governing mass and momentum conservation equations, along with the Herschel-Bulkley rheological model, are obtained using a finite-difference scheme. A parametric study is implemented to investigate the effects of annular nozzle diameter ratio, κ, the power-law index, n, and yield number, Y, over the following range: κ = {0, 0.5}; n = {1, 0.6}; and Y = {0, 1, 5}. The Reynolds number was fixed at Re = 100, which ensured steady and laminar jet flow conditions throughout the whole flow field. The selected yield number and power-law index values allowed for the investigation of the presence of yield stress and shear-thinning effects on the resulting structure and evolution of the flow field. The results demonstrate the substantial impact of the inflow conditions and rheology on the annular jet evolution, and on the extent of the outer recirculation region and recirculation strength of both the outer and central regions.

Thermorheological Characterization of Elastoviscoplastic Carbopol Ultrez 20 Gel

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Experimental Investigation ◽  
Yield Stress ◽  
Elastic Properties ◽  
Viscous Dissipation ◽  
Power Law ◽  
Effect Of Temperature ◽  
Rheological Parameters ◽  
Frequency Range ◽  
Power Law Index

The temperature and concentration play an important role on rheological parameters of the gel. In this work, an experimental investigation of thermorheological properties of aqueous gel Carbopol Ultrez 20 for various concentrations and temperatures has been presented. Both controlled stress ramps and controlled stress oscillatory sweeps were performed for obtaining the rheological data to find out the effect of temperature and concentration. The hysteresis or thixotropic seemed to have negligible effect. Yield stress, consistency factor, and power law index were found to vary with temperature as well as concentration. With gel concentration, the elastic effect was found to increase whereas viscous dissipation effect was found to decrease. Further, the change in elastic properties was insignificant with temperature in higher frequency range of oscillatory stress sweeps.

Heat Transfer Enhancement in Annular Shear-Thinning Flows Over a Sudden Pipe Expansion

2017 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Diameter Ratio ◽  
Transfer Enhancement ◽  
Heat Transfer Augmentation ◽  
Prandtl Numbers ◽  
Power Law Index ◽  
The Impact

Heat transfer enhancement in suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported for: Re = {50, 100}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers, Nu, higher than the fully developed value, in the downstream pipe, is observed only for Pr = 10 and 100. Higher Prandtl numbers, power-law index values, and annular diameter ratios, in general, reflect a more dramatic heat transfer augmentation downstream of the expansion plane. Heat transfer augmentation for Pr = 10 and 100, is more dramatic for suddenly expanding annular flows, in comparison with suddenly expanding pipe flow. For a given annular diameter ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, for both Newtonian and shear-thinning non-Newtonian flows.

Non-Newtonian slender drops in a nonlinear extensional flow

2019 ◽  
Vol 877 ◽  
pp. 561-581 ◽  
Author(s):  
Moshe Favelukis
Keyword(s):  
Stability Analysis ◽  
Power Law ◽  
Analytical Solutions ◽  
Viscosity Ratio ◽  
Extensional Flow ◽  
Shear Thinning ◽  
Newtonian Liquid ◽  
Creeping Flow ◽  
Stationary States ◽  
Power Law Index

In this theoretical report we explore the deformation and stability of a power-law non-Newtonian slender drop embedded in a Newtonian liquid undergoing a nonlinear extensional creeping flow. The dimensionless parameters describing this problem are: the capillary number $(Ca\gg 1)$, the viscosity ratio $(\unicode[STIX]{x1D706}\ll 1)$, the power-law index $(n)$ and the nonlinear intensity of the flow $(|E|\ll 1)$. Asymptotic analytical solutions were obtained near the centre and close to the end of the drop suggesting that only Newtonian and shear thinning drops $(n\leqslant 1)$ with pointed ends are possible. We described the shape of the drop as a series expansion about the centre of the drop, and performed a stability analysis in order to distinguish between stable and unstable stationary states and to establish the breakup point. Our findings suggest: (i) shear thinning drops are less elongated than Newtonian drops, (ii) as non-Newtonian effects increase or as $n$ decreases, breakup becomes more difficult, and (iii) as the flow becomes more nonlinear, breakup is facilitated.

Flow and Decay Characteristics of Submerged Yield-Pseudoplastic Jets

2014 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Flow Structure ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Critical Value ◽  
Momentum Conservation ◽  
Recirculation Region ◽  
Centerline Velocity ◽  
General Increase ◽  
Flow Recirculation ◽  
The Impact

The flow structure and decay characteristics of submerged yield-pseudoplastic jets are investigated. Numerical solutions to the governing mass and momentum conservation equations, along with the Herschel-Bulkley rheological model, are obtained using a finite-difference scheme. A large recirculation region exists for Newtonian and pseudoplastic non-Newtonian jets. However, the extent and strength of the recirculation region substantially diminish with the yield number and, to a much lesser extent, when the shear-thinning index is decreased from 1 to 0.6. Increasing the yield number beyond a critical value eliminates flow recirculation. The centerline velocity and momentum decay of yield-pseudoplastic jets, in general, increase with the yield number. The impact of shear-thinning on the flow structure and decay characteristics of the jet is more pronounced at low yield numbers.

Heat Transfer in Annular Shear-Thinning Non-Newtonian Flows Over a Sudden Pipe Expansion

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Power Law ◽  
Shear Thinning ◽  
Wall Heat Transfer ◽  
Transfer Enhancement ◽  
Transfer Rates ◽  
Newtonian Flows ◽  
Prandtl Numbers ◽  
Annular Pipe

Non-isothermal suddenly expanding annular pipe flows of a shear-thinning non-Newtonian fluid are numerically studied within the steady laminar flow regime. The power-law constitutive equation is used to model the shear-thinning rheology of interest. A parametric study is performed to reveal the influence of annular-nozzle-diameter-ratio, k, power-law index, n, and Prandtl numbers over the following range of parameters: k = {0, 0.5}; n = {1, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement, i.e., wall heat transfer rates higher than the fully developed ones downstream of the expansion plane, is observed only for Pr = 10 and 100. In the case of Pr = 1, wall heat transfer rates monotonically increase to the fully developed value. Higher Pr, k, and n values, in general, result in more significant heat transfer enhancement downstream of the expansion plane. Further, shear-thinning non-Newtonian flows display two local peak wall heat transfer rates, in comparison with only one peak value in the case of Newtonian flows.

Shear thinning of the bulk metallic glass forming alloy Zr41.2 Ti13.8 Cu12.5 Ni10.0 Be22.5 close to the liquidus temperature.

2003 ◽  
Vol 806 ◽  
Author(s):  
Tyler Shaw ◽  
Christopher Way ◽  
Ralf Busch
Keyword(s):  
Metallic Glass ◽  
Bulk Metallic Glass ◽  
Power Law ◽  
Liquidus Temperature ◽  
Flow Behavior ◽  
Shear Thinning ◽  
Shear Rates ◽  
Glass Forming ◽  
Power Law Index ◽  
Type Response

ABSTRACTThe viscous properties of the multi component Zr41.2 Ti13.8 Cu12.5 Ni10.0 Be22.5 bulk metallic glass forming alloy was studied above the liquidus temperature. A shear thinning behavior for the molten alloy has been discovered. The shear thinning behavior can be characterized as a power law fluid with a power-law index of -0.5. Additionally, at low shear rates and temperatures near the liquidus temperature a visco-elastic type response in the flow behavior is observed.

scholarly journals Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

2017 ◽  
Vol 826 ◽  
pp. 918-941 ◽  
Author(s):  
A. Bougouin ◽  
L. Lacaze ◽  
T. Bonometti
Keyword(s):  
Power Law ◽  
Temporal Evolution ◽  
Volume Fraction ◽  
Fluid Model ◽  
Particle Diameter ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Rheological Parameters ◽  
Power Law Fluids ◽  
Neutrally Buoyant

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

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