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

Water ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 19 ◽  
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.

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

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Kofi Freeman K. Adane ◽  
Martin Agelin-Chaab
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Stress Ratio ◽  
Rheological Parameters ◽  
Transition Model ◽  
Flow Conditions ◽  
Wide Range ◽  
Engineering Models ◽  
Wall Shear

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).

scholarly journals Pipe rheology of microfibrillated cellulose suspensions

Cellulose ◽  
2019 ◽  
Vol 27 (1) ◽  
pp. 141-156 ◽  
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.

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

2020 ◽  
Vol 142 (6) ◽  
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.

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

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.

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

2013 ◽  
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.

scholarly journals Increased Inlet Blood Flow Velocity Predicts Low Wall Shear Stress in the Cephalic Arch of Patients with Brachiocephalic Fistula Access

PLoS ONE ◽  
2016 ◽  
Vol 11 (4) ◽  
pp. e0152873 ◽  
Author(s):  
Mary Hammes ◽  
Michael Boghosian ◽  
Kevin Cassel ◽  
Sydeaka Watson ◽  
Brian Funaki ◽  
...  
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Velocity ◽  
Blood Flow Velocity ◽  
Wall Shear ◽  
Brachiocephalic Fistula

scholarly journals Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study

2019 ◽  
Author(s):  
Haifeng Wang ◽  
Timm Krüger ◽  
Fathollah Varnik
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Velocity ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Side Wall ◽  
Aneurysm Rupture ◽  
Immersed Boundary ◽  
Wall Shear

AbstractBlood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture.

scholarly journals Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress.

1983 ◽  
Vol 53 (4) ◽  
pp. 502-514 ◽  
Author(s):  
C K Zarins ◽  
D P Giddens ◽  
B K Bharadvaj ◽  
V S Sottiurai ◽  
R F Mabon ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Velocity ◽  
Carotid Bifurcation ◽  
Velocity Profiles ◽  
Quantitative Correlation ◽  
Wall Shear

Steady motion of Bingham liquid plugs in two-dimensional channels

2011 ◽  
Vol 705 ◽  
pp. 258-279 ◽  
Author(s):  
Parsa Zamankhan ◽  
Brian T. Helenbrook ◽  
Shuichi Takayama ◽  
James B. Grotberg
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Stress Gradient ◽  
Core Region ◽  
Driving Pressure ◽  
Two Dimensional ◽  
Airway Epithelial ◽  
The Core ◽  
Wall Shear

AbstractWe study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channels as a model of mucus behaviour during airway reopening in pulmonary airways. In addition to flow analysis related to propagation of the plug, the stress distribution on the wall is studied for better understanding of potential airway epithelial cell injury mechanisms. The yield stress behaviour of the fluid was implemented through a regularized constitutive equation. The capillary number, $\mathit{Ca}$, and the Bingham number, $\mathit{Bn}$, which is the ratio of the yield stress to a characteristic viscous stress, varied over the ranges 0.025–0.1 and 0–1.5, respectively. For the range of parameters studied, it was found that, while the yield stress reduces the magnitude of the shearing along the wall, it can magnify the amplitude of the wall shear stress gradient significantly, and also it can elevate the magnitude of the wall shear stress and wall pressure gradient up to 30 % and 15 %, respectively. Therefore, the motion of mucus plugs can be more damaging to the airway epithelial cells due to the yield stress properties of mucus. The yield stress also modifies the profile of the plug where the amplitude of the capillary waves at the leading meniscus decreases with increase in $\mathit{Bn}$. Other findings are that: the thickness of the static film increases with increasing $\mathit{Bn}$; the driving pressure difference increases linearly with $\mathit{Bn}$; and increasing $\mathit{Bn}$ extends any wall stagnation point beneath the leading meniscus to an unyielded line segment beneath the leading meniscus. With an increase in $\mathit{Bn}$, the unyielded areas appear and grow in the adjacent wall film as well as the core region of the plug between the two menisci. The plug length, ${L}_{P} $, mostly modifies the topology of the yield surfaces. It was found that the unyielded area in the core region between the two menisci grows as the plug length decreases. The very short Bingham plug behaves like a solid lamella. In all computed liquid plugs moving steadily, the von Mises stress attains its maximum value near the interface of the leading meniscus in the transition region. For Bingham plugs moving very slowly, $\mathit{Ca}\ensuremath{\rightarrow} 0$, the driving pressure is non-zero.

Separations and secondary structures due to unsteady flow in a curved pipe

2017 ◽  
Vol 815 ◽  
pp. 26-59 ◽  
Author(s):  
C. Vamsi Krishna ◽  
Namrata Gundiah ◽  
Jaywant H. Arakeri
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Flow Velocity ◽  
Secondary Flow ◽  
Flow Separation ◽  
Unsteady Flows ◽  
Stress Components ◽  
Wall Shear

Unsteady flows in highly curved geometries are of interest in many engineering applications and also in physiological flows. In this study, we use flow visualization and computational fluid dynamics to study unsteady flows in a highly curved tube ($\unicode[STIX]{x1D6FD}=0.3$) with square cross-section; here, $\unicode[STIX]{x1D6FD}$ is the ratio of the half edge length to the radius of curvature of the tube. To explore the combined effects of curvature and pulsatility, we use a single flow pulse of duration $T$ and peak area averaged axial velocity $U_{p(max)}$, which are independently varied to investigate a range of Dean and Womersley numbers. This range includes cases corresponding to flows in the ascending aorta. We observe radially inward moving secondary flows which have the structure of wall jets on the straight walls; their subsequent collision on the inner wall leads to a re-entrant radially outward moving jet. The wall jet arises due to an imbalance between the centrifugal force and the radial pressure gradient. During the deceleration phase, the low-axial-momentum fluid accumulated in the jet reverses direction and leads to flow separation near the inner wall. We use boundary layer equations to derive scales, which have not been reported earlier, for the secondary flow velocities, the wall shear stress components and the distance ($\hat{P}$) traversed by the secondary flow structures in the transverse plane. We show that $\hat{P}$ predicts the movement of vortical structures until collision. In the limit $\unicode[STIX]{x1D6FD}\rightarrow 0$, the Reynolds number based on this secondary flow velocity scale asymptotes to the secondary streaming Reynolds number proposed by Lyne (J. Fluid Mech., vol. 45 (01), 1971, pp. 13–31) in loosely curved pipes. The magnitude of the secondary flow velocity is high and ${\sim}40\,\%$ of $U_{p(max)}$ for physiological flow conditions. We show that the flow separation on the inner wall has origins in the secondary flow, which was reported in a few earlier studies, and is not due to the axial pressure gradient in the tube as proposed earlier. The wall shear stress components, hypothesized to be important in arterial mechanobiology, may be estimated using our scaling relations for geometries with different curvatures and varying pulsatilities.

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