Laminar-Turbulent Transition Flows of Non-Newtonian Slurries: Models Assessment

In this study, a qualitative assessment of transitional velocity engineering models for predicting non-Newtonian slurry flows in a horizontal pipe was performed using data from a wide range of pipe diameters (25–268 mm). In addition, the gamma theta transition model was used to compute selected flow conditions. These models were used to predict transitional velocities in large pipe diameters (up to 420 mm) for slurries. In general, it was observed that most of the current engineering models predict transitional velocities conservatively. Based on the gamma theta transition model results, for large Hedström numbers (He ≳ 105), other methods should be used to predict transitional velocities if a change in the pipe diameter (scale-up) results in an order of magnitude increase in the He value. It was also found that the gamma theta transition model predicted a laminar flow condition in the fully developed region for flow conditions with a small plug region (low-yield stress-to-wall shear stress ratio), which is contrary to what has been observed in some experiments. This is attributed to the local fluid rheological parameters values, which might be different from those reported. However, the gamma theta transition model results are in good agreement with the experimental data for flow conditions that have a large plug region (high-yield stress-to-wall shear stress ratio).

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Sensitivity Analysis of a Wall Boundary Condition for the Turbulent Pipe Flow of Herschel–Bulkley Fluids

Water ◽

10.3390/w11010019 ◽

2018 ◽

Vol 11 (1) ◽

pp. 19 ◽

Cited By ~ 2

Author(s):

Dhruv Mehta ◽

Adithya Thota Radhakrishnan ◽

Jules van Lier ◽

Francois Clemens

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Flow Velocity ◽

Yield Stress ◽

Pressure Loss ◽

Rheological Parameters ◽

Relative Reduction ◽

Wall Function ◽

Wall Shear ◽

Behaviour Index

This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel–Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel–Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel–Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ 1 hereafter) was developed using Launder and Spalding’s standard wall function as a guide and was validated against a range of experimental test-cases, with positive results. ψ 1 is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ 1 can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier–Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ 1 is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ 1 is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ 1 a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

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Analysis of Laminar Mixed Convective Plumes Along Vertical Adiabatic Surfaces

Journal of Heat Transfer ◽

10.1115/1.3246714 ◽

1984 ◽

Vol 106 (3) ◽

pp. 552-557 ◽

Cited By ~ 22

Author(s):

K. V. Rao ◽

B. F. Armaly ◽

T. S. Chen

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Leading Edge ◽

Vertical Surface ◽

Stream Velocity ◽

Thermal Source ◽

Flow Conditions ◽

Velocity Overshoot ◽

Wall Shear ◽

Prandtl Numbers

Laminar mixed forced and free convection from a line thermal source imbedded at the leading edge of an adiabatic vertical surface is analytically investigated for the cases of buoyancy assisting and buoyancy opposing flow conditions. Temperature and velocity distributions in the boundary layer adjacent to the adiabatic surface are presented for the entire range of the buoyancy parameter ξ (x) = Grx/Rex5/2 from the pure forced (ξ(x) = 0) to the pure free (ξ(x) = ∞) convection regime for fluids having Prandtl numbers of 0.7 and 7.0. For buoyancy-assisting flow, the velocity overshoot, the temperature, and the wall shear stress increase as the plume’s strength increases. On the other hand, the velocity overshoot, the wall shear stress, and the temperature decrease as the free-stream velocity increases. For buoyancy opposing flow, the velocity and wall shear stress decrease but the temperature increases as the plume’s strength increases.

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Analysis of the wall shear stress in a generic aneurysm under pulsating and transitional flow conditions

Experiments in Fluids ◽

10.1007/s00348-020-2901-4 ◽

2020 ◽

Vol 61 (2) ◽

Author(s):

Andreas Bauer ◽

Maximilian Bopp ◽

Suad Jakirlic ◽

Cameron Tropea ◽

Axel Joachim Krafft ◽

...

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Transitional Flow ◽

Flow Conditions ◽

Wall Shear

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Pipe rheology of microfibrillated cellulose suspensions

Cellulose ◽

10.1007/s10570-019-02784-4 ◽

2019 ◽

Vol 27 (1) ◽

pp. 141-156 ◽

Cited By ~ 1

Author(s):

Tuomas Turpeinen ◽

Ari Jäsberg ◽

Sanna Haavisto ◽

Johanna Liukkonen ◽

Juha Salmela ◽

...

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Yield Stress ◽

Power Law ◽

Slip Flow ◽

Microfibrillated Cellulose ◽

Flow Index ◽

Shear Rheology ◽

Power Law Fluids ◽

Wall Shear

Abstract The shear rheology of two mechanically manufactured microfibrillated cellulose (MFC) suspensions was studied in a consistency range of 0.2–2.0% with a pipe rheometer combined with ultrasound velocity profiling. The MFC suspensions behaved at all consistencies as shear thinning power law fluids. Despite their significantly different particle size, the viscous behavior of the suspensions was quantitatively similar. For both suspensions, the dependence of yield stress and the consistency index on consistency was a power law with an exponent of 2.4, similar to some pulp suspensions. The dependence of flow index on consistency was also a power law, with an exponent of − 0.36. The slip flow was very strong for both MFCs and contributed up to 95% to the flow rate. When wall shear stress exceeded two times the yield stress, slip flow caused drag reduction with consistencies higher than 0.8%. When inspecting the slip velocities of both suspensions as a function of wall shear stress scaled with the yield stress, a good data collapse was obtained. The observed similarities in the shear rheology of both the MFC suspensions and the similar behavior of some pulp fiber suspensions suggests that the shear rheology of MFC suspensions might be more universal than has previously been realized.

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Time-dependent rheological behavior of blood at low shear in narrow vertical tubes

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1993.265.2.h553 ◽

1993 ◽

Vol 265 (2) ◽

pp. H553-H561 ◽

Cited By ~ 15

Author(s):

C. Alonso ◽

A. R. Pries ◽

P. Gaehtgens

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Shear Flow ◽

Apparent Viscosity ◽

Flow Behavior ◽

Time Dependent ◽

Flow Conditions ◽

Wall Shear ◽

Vertical Tubes ◽

Low Shear

The time-dependent flow behavior of normal human blood after a sudden reduction of wall shear stress from 5,000 mPa to a low level (2-100 mPa) was studied during perfusion of vertical tubes (internal diam 28-101 microns) at constant driving pressures. Immediately after the implementation of low-shear flow conditions the concentration of red blood cells (RBCs) near the tube wall started to decrease, and marginal plasma spaces developed as a result of the assembly of RBC aggregates. This was associated with a time-dependent increase of flow velocity by up to 200% within 300 s, reflecting a reduction of apparent viscosity. These time-dependent changes of flow behavior increased strongly with decreasing wall shear stress and with increasing tube diameter. A correlation between the width of the marginal plasma layer and relative apparent viscosity was obtained for every condition of tube diameter, wall shear stress, and time. Time-dependent changes of blood rheological properties could be relevant in the circulation, where the blood is exposed to rapid and repeated transitions from high-shear flow conditions in the arterial and capillary system to low-shear conditions in the venous system.

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Effects of Surface Tension and Yield Stress on Mucus Plug Rupture: A Numerical Study

Journal of Biomechanical Engineering ◽

10.1115/1.4045596 ◽

2020 ◽

Vol 142 (6) ◽

Cited By ~ 3

Author(s):

Yingying Hu ◽

Francesco Romanò ◽

James B. Grotberg

Keyword(s):

Surface Tension ◽

Shear Stress ◽

Wall Shear Stress ◽

Yield Stress ◽

Pressure Difference ◽

Rupture Process ◽

Viscoplastic Fluid ◽

Air Interface ◽

Mucus Plug ◽

Wall Shear

Abstract We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimensional simplified configuration is employed to simulate mucus plug rupture in a collapsed lung airway of the tenth generation. The Herschel–Bulkley model is used to take into account the non-Newtonian viscoplastic fluid properties of mucus. Results show that the maximum wall shear stress greatly changes right prior to the rupture of the mucus plug. The surface tension influences mainly the late stage of the rupture process when the plug deforms greatly and the curvature of the mucus–air interface becomes significant. High surface tension increases the wall shear stress and the time needed to rupture since it produces a resistance to the rupture, as well as strong stress and velocity gradients across the mucus–air interface. The yield stress effects are pronounced mainly at the beginning. High yield stress makes the plug take a long time to yield and slows down the whole rupture process. When the effects induced by the surface tension and yield forces are comparable, dynamical quantities strongly depend on the ratio of the two forces. The pressure difference (the only driving in the study) contributes to wall shear stress much more than yield stress and surface tension per unit length. Wall shear stress is less sensitive to the variation in yield stress than that in surface tension. In general, wall shear stress can be effectively reduced by the smaller pressure difference and surface tension.

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Hemodynamic impacts of hematocrit level by two-way coupled FSI in the left coronary bifurcation

Clinical Hemorheology and Microcirculation ◽

10.3233/ch-200854 ◽

2020 ◽

Vol 76 (1) ◽

pp. 9-26

Author(s):

Saeed Bahrami ◽

Mahmood Norouzi

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Yield Stress ◽

Blood Circulation ◽

Arbitrary Lagrangian Eulerian ◽

Coronary Bifurcation ◽

Shear Rates ◽

3D Geometry ◽

Wall Shear ◽

Rigid Walls

Cardiovascular disease is now under the influence of several factors that encourage researchers to investigate the flow of these vessels. Oscillation influences the blood circulation in the volume of red blood cells (RBC) strongly. Therefore, in this study, its effects have been considered on hemodynamic parameters in the elastic wall and coronary bifurcation. In this study, a 3D geometry of non-Newtonian and pulsatile blood circulation is considered in the left coronary artery bifurcation. The Casson model with various hematocrits is analyzed in elastic and rigid walls. The wall shear stress (WSS) cannot show the stenosis artery alone, therefore, the oscillatory shear index (OSI) is represented as a hemodynamic parameter of WSS individually of time. The results are determined using two-way fluid-structure interaction (FSI) coupling method using an arbitrary Lagrangian-Eulerian method. The most prominent difference in velocity happened in the bifurcation and at hematocrit 30 with yield stress 6.59E-04 Pa. The backflow and vortex flow in the LCx branch grown with increasing shear rates. The likelihood of plaque generation at the ending of the LM branch is observed in hematocrits 10 and 20, while the WSS magnitude is normal in the hematocrit 60 with the greatest yield stress in the bifurcation. The shear stress among the rigid and elastic models is the highest at the ending of the LM branch. The wall shear stress magnitude among the models decreased at most of 24.49% by dividing the flow. Time-independent results for models showed that there is the highest value of OSI at the bifurcation, which then quickly dropped.

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Endothelial cells express a unique transcriptional profile under very high wall shear stress known to induce expansive arterial remodeling

AJP Cell Physiology ◽

10.1152/ajpcell.00369.2011 ◽

2012 ◽

Vol 302 (8) ◽

pp. C1109-C1118 ◽

Cited By ~ 27

Author(s):

Jennifer M. Dolan ◽

Fraser J. Sim ◽

Hui Meng ◽

John Kolega

Keyword(s):

Gene Expression ◽

Endothelial Cells ◽

Shear Stress ◽

Wall Shear Stress ◽

Plasminogen Activator ◽

Transcriptional Profile ◽

Arterial Remodeling ◽

Flow Conditions ◽

Wall Shear ◽

Very High

Chronic high flow can induce arterial remodeling, and this effect is mediated by endothelial cells (ECs) responding to wall shear stress (WSS). To assess how WSS above physiological normal levels affects ECs, we used DNA microarrays to profile EC gene expression under various flow conditions. Cultured bovine aortic ECs were exposed to no-flow (0 Pa), normal WSS (2 Pa), and very high WSS (10 Pa) for 24 h. Very high WSS induced a distinct expression profile compared with both no-flow and normal WSS. Gene ontology and biological pathway analysis revealed that high WSS modulated gene expression in ways that promote an anti-coagulant, anti-inflammatory, proliferative, and promatrix remodeling phenotype. A subset of characteristic genes was validated using quantitative polymerase chain reaction: very high WSS upregulated ADAMTS1 (a disintegrin and metalloproteinase with thrombospondin motif-1), PLAU (urokinase plasminogen activator), PLAT (tissue plasminogen activator), and TIMP3, all of which are involved in extracellular matrix processing, with PLAT and PLAU also contributing to fibrinolysis. Downregulated genes included CXCL5 and IL-8 and the adhesive glycoprotein THBS1 (thrombospondin-1). Expressions of ADAMTS1 and uPA proteins were assessed by immunhistochemistry in rabbit basilar arteries experiencing increased flow after bilateral carotid artery ligation. Both proteins were significantly increased when WSS was elevated compared with sham control animals. Our results indicate that very high WSS elicits a unique transcriptional profile in ECs that favors particular cell functions and pathways that are important in vessel homeostasis under increased flow. In addition, we identify specific molecular targets that are likely to contribute to adaptive remodeling under elevated flow conditions.

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The Impact of Hemorheology on Wall Shear Stress in a Separated and Reattached Flow Region

Volume 3B: Biomedical and Biotechnology Engineering ◽

10.1115/imece2013-62549 ◽

2013 ◽

Cited By ~ 1

Author(s):

Khaled J. Hammad

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Yield Stress ◽

Flow Region ◽

Shear Thinning ◽

Progression Rate ◽

Vortex Center ◽

Wall Shear ◽

Separated And Reattached Flow ◽

The Impact

Wall-bounded separating and reattaching flows are encountered in biological applications dealing with blood flows through arteries and prosthetic devices. Separated and reattached flow regions have been associated in the past with the most common arterial disease, atherosclerosis. Previous studies suggest that local wall shear stress (WSS) patterns affect the location and progression rate of atherosclerotic lesions. A parametric study is performed to investigate the influence of hemorheology on the wall shear stress distribution in a separated and reattached flow region. Recent hemorheological studies quantified and emphasized the yield stress and shear-thinning non-Newtonian characteristics of unadulterated human blood. Numerical solutions to the governing equations that account for yield stress and shear-thinning rheological effects are obtained. A low WSS region is observed around the flow reattachment point while a peak WSS always exists close to the vortex center. The yield shear-thinning hemorheological model always results in the highest observed peak WSS. The yield stress impact on WSS distribution is most pronounced in the case of severe restrictions to the flow.

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