Newtonian Viscosity Model Research Articles

Sensitivity of TEHL Simulations to the Use of Different Models for the Constitutive Behaviour of Lubricants

This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consists of the Tait equation of state, the Doolittle Newtonian viscosity model, and the Carreau shear thinning model. The second group includes the Dowson equation of state, the Roelands–Houpert Newtonian viscosity model, and the Eyring shear thinning model. The simulations were conducted using a Computational Fluid Dynamic and Fluid-Structure Interaction (CFD-FSI) approach, which employs a homogeneous equilibrium model for the flow simulation along with a linear elastic solver to describe the deformation of the solid materials. The simulations were conducted under a load range of 100 kN/m to 200 kN/m and a slide-to-roll-ratio (SRR) range between 0 and 2 using Squalane lubricant. The results show up to a 10% deviation in central film thickness, a 31% deviation in coefficient of friction (CoF), and a 38% deviation in maximum lubricant temperature when using the different constitutive models. This study highlights the sensitivity of TEHL simulation results to the choice of constitutive models for lubricants and the importance of carefully selecting the appropriate models for specific applications.

Comprehensive Dense Slurry CFD Model for Performance Evaluation of Industrial Hydrocyclones

In most mineral processing industries, hydrocyclone separators are operated at high feed solids content in the comminution circuits. Computational fluid dynamic (CFD) models developed so far are unable to predict the accurate classification behavior at high feed solid loadings. The dense slurry CFD model adopts algebraic slip mixture (ASM) model corrected with shear lift and hindered settling velocity-based drag forces to account for fluid-particle interactions and granular flow options for particle-particle interactions. The slurry rheology is modeled with a fine fraction-corrected Newtonian viscosity model. This model is utilized for running the multiphase simulations in five hydrocyclones (75-381 mm) at different design and operating conditions for the feed solids content varying between 0 and 65% by weight. Turbulence is modeled using the large Eddy simulation (LES) model. The results are analyzed in terms of air core diameter, water split, solid split, cut size, and sharpness of separation. In 75 and 250 mm hydrocyclones, the modified ASM model can predict accurate performance characteristics, including fine and coarse particle misplacement up to 30 wt % feed solids. Slight deviations are observed in the fine fraction recovery for the 50 wt % and higher feed solids content. Further, the same model is tested to predict the roping phenomena in a 381 mm hydrocyclone.

Fiber suspension in 2D nonhomogeneous flow: The effects of flow/fiber coupling for Newtonian and power-law suspending fluids

A numerical study is presented for fiber suspension flows through a parallel plate channel and a planar 4:1 contraction. Besides examining a Newtonian suspending fluid, a non-Newtonian matrix exhibiting a pseudoplastic behavior and describing a power-law model is also investigated. Furthermore, instead of using orientation tensors for the macroscopic constitutive modeling, the proposed approach addresses the macroscopic scale by describing the fiber orientation state with the probability distribution function (PDF). It enables us to eliminate the error introduced due to the closure approximation when using orientation tensor description as our numerical scheme solves the PDF in both the spatial and configurational spaces. This allows us to correctly implement expressions for both the fiber extra stress, especially for the suspending matrix displaying a pseudoplastic behavior, and the fiber orientation state, describing the configuration. Hence, these two constitutive relations for suspensions are used to perform simulations in which flow and fiber orientation are fully coupled. Results are presented in planar geometries involving channel and 4:1 contraction flows. It is found that the coupling effect flattens the velocity profile for both suspending fluids but has a small impact on the fiber orientation distributions at the geometry outlets. However, in the corner region where a vortex is observed, its magnitude increases with the coupling and this enhancement is more pronounced for the Newtonian suspending fluid. The Newtonian viscosity model is replaced with the Carreau model and results are compared to a bi-viscosity model. It gives qualitatively correct results if no rapid fiber orientation change occurs along the streamlines.

Evidence for non-Newtonian behavior of intracranial blood flow from Doppler ultrasonography measurements.

Computational fluid dynamics (CFD) studies of intracranial hemodynamics often use Newtonian viscosity model to close the shear rate term in the Navier-Stokes equation. This is based on a commonly accepted hypothesis which state that non-Newtonian effects can be neglected in intracranial blood flow. This study aims to examine the validity of such hypothesis to guide future CFD studies of intracranial hemodynamics. Doppler ultrasonography (DUS) measurements of systolic and diastolic vessel diameter and blood velocity were conducted on 16 subjects (mean age 50.6). The measurements were conducted on the internal carotid (ICA), middle cerebral (MCA), and anterior communicating (AComA) arteries. Systolic and diastolic wall shear stress (WSS) values were calculated via the Hagen-Poiseuille exact solution using Newtonian and three different non-Newtonian models: namely Carreau, power-law and Herschel-Bulkley models. The Weissenberg-Rabinowitsch correction for blood shear-thinning viscosity was applied to the non-Newtonian models. The error percentage between the two sets of models was calculated and discussed. The Newtonian hypothesis was tested statistically and discussed using paired t tests. Significant differences (P < 0.0001) were found between the Newtonian and non-Newtonian WSS in ICA. In MCA and AComA, similar differences were found except in the systole and diastole for the Herschel-Bulkley and power-law models (P = 0.0669, P = 0.7298), respectively. The error between the Newtonian and non-Newtonian models ranged from -27 to 30% (0.2 to 2.2Pa). These values could affect the physical interpretation of IA CFD studies. Evidence suggests that the Newtonian assumption may be inappropriate to investigate intracranial hemodynamics. Graphical abstract The WSS estimation error resulting from using the Newtonian assumption compared to three non-Newtonian models for ICA, MCA, and AComA in systole and diastole conditions, based on TCCD measurements of 16 subjects. The error due to the Newtonian assumption ranged from 0.2 to 2.2Pa (- 27 to 30%). These values could affect the physical interpretation of IA CFD studies.

An experimental investigation and modeling of micro array replication with Zr-based bulk metallic glass using a hot embossing process

Zirconium-based bulk metallic glass (Zr-based BMG) is a potential material for micro/nano molds. In this study, we investigated the flow characteristics of Zr-based BMG in the supercooled liquid region (SLR) with a series of uniaxial compression tests. The Newtonian viscosity model of Zr-based BMG is constructed by fitting with the experimental results based on the Arrhenius equation. The hot embossing process which can be seen as a combination of two kinds of simultaneous flows is theoretically analyzed based on Navier-Stokes (N-S) equations. The velocity and pressure fields in a BMG sample have been evaluated. Two kinds of filling modes are proposed considering the interfacial tension and oxide layer that forms on the BMG surface. The exact solutions are obtained when the cavities of the micro arrays are circular, triangular and rectangular in shape based on N-S equations. The theoretical solutions, considered surface resistance, are in good agreement with our experimental results. These models can be used to describe the fillings of metallic glass in micro hot embossing process. Finally, we studied the effects of micro cavity size and shape on BMG filling, and found that the cavities of micro rectangular array are easier filling in same feature size, however, the cavities of micro circular array are easier filling in same area. The exact models developed in this paper can be used to calculate the BMG filling heights in the cavities of micro arrays and verify the reliability of simulation results in future mold designs.

Simulations of Magnetohemodynamics in Stenosed Arteries in Diabetic or Anemic Models.

Pulsatile flow simulations of non-Newtonian blood flow in an axisymmetric multistenosed artery, subjected to a static magnetic field, are performed using FLUENT. The influence of artery size and magnetic field intensity on transient wall shear stress, mean shear stress, and pressure drop is investigated. Three different types of blood, namely, healthy, diabetic, and anemic are considered. It is found that using Newtonian viscosity model of blood in contrast to Carreau model underestimates the pressure drop and wall shear stress by nearly 34% and 40%, respectively. In addition, it is found that using a magnetic field increases the pressure drop by 15%. Generally, doubling the artery diameter reduces the wall shear stress approximately by 1.6 times. Also increasing the stenosis level from moderate to severe results in reduction of the shear stress by 1.6 times. Furthermore, doubling the diameter of moderately stenosed artery results in nearly 3-fold decrease in pressure drop. It is also found that diabetic blood results in higher shear stress and greater pressure drop in comparison to healthy blood, whereas anemic blood has a decreasing effect on both wall shear stress and pressure drop in comparison to healthy blood.

Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone

In this work, an improved multiphase computational fluid dynamics (CFD) model is developed for simulating medium segregation in a dense medium cyclone. This model approach uses the modified mixture model with the granular option and Reynolds stress model (RSM) to resolve the turbulent mixing of the particles. Rheological behavior of the medium is considered through various forms of viscosity models such as granular viscosity, Newtonian and non-Newtonian model corrected with particle loading and fraction of ultra-fines. Multiphase simulations using the granular viscosity option although predict the overall slurry volume split, product medium densities better than Newtonian models, but the mixture viscosity values are restricted to substantially lower values close to water viscosity levels. Simulations using the Newtonian viscosity model corrected with particle loading and fine fraction below 53μm size are predicted the overall medium viscosity levels well above water viscosity levels but underpredicted the cyclone underflow medium density to the experimental data. Multiphase simulations with the non-Newtonian Herschel–Bulkley viscosity model are able to predict the medium segregation close to the gamma ray tomography data, and the predicted medium viscosity levels are increased up to 18 cp. Overall predicted product medium densities, underflow volume split and radial medium segregation levels are compared to the experimental data. Lagrangian particle tracking (LPT) is super imposed on converged medium simulations used for coal partitioning predictions. This model can be further used in developing new designs in the future.

A 3D swallowing simulation using smoothed particle hydrodynamics

A three-dimensional (3D) computer simulation of swallowing is presented. The soft structures (i.e. pharyngeal wall, soft palate and tongue) are simulated using finite element models. Bony structures (e.g. mandible, hard palate and hyoid) are simulated as rigid bodies. A fluid bolus is simulated using smoothed particle hydrodynamics (SPH). A Newtonian viscosity model is validated by comparing a 3D SPH simulation of Hagen–Poiseuille flow with theoretical results. A previously unreported source of error is reported and discussed. In the swallowing simulation, fluid boundaries are determined by the rigid and deformable surfaces, and the coupling is in one direction only. Movement of solid boundaries was determined in previous work for a deformable solid bolus. Two swallowing simulations are presented with different bolus viscosities in order to demonstrate that SPH can be used to simulate and track the liquid phase of a bolus during swallow. We find that SPH robustly handles moving boundary conditions as well as changes in viscosity. SPH simulations of the bolus are therefore potentially a useful visual aid to understand the effects of solid boundary motion on swallowing.

Virtual Treatment of Basilar Aneurysms Using Shape Memory Polymer Foam

Numerical simulations are performed on patient-specific basilar aneurysms that are treated with shape memory polymer (SMP) foam. In order to assess the post-treatment hemodynamics, two modeling approaches are employed. In the first, the foam geometry is obtained from a micro-CT scan and the pulsatile blood flow within the foam is simulated for both Newtonian and non-Newtonian viscosity models. In the second, the foam is represented as a porous media continuum, which has permeability properties that are determined by computing the pressure gradient through the foam geometry over a range of flow speeds comparable to those of in vivo conditions. Virtual angiography and additional post-processing demonstrate that the SMP foam significantly reduces the blood flow speed within the treated aneurysms, while eliminating the high-frequency velocity fluctuations that are present within the pre-treatment aneurysms. An estimation of the initial locations of thrombus formation throughout the SMP foam is obtained by means of a low fidelity thrombosis model that is based upon the residence time and shear rate of blood. The Newtonian viscosity model and the porous media model capture similar qualitative trends, though both yield a smaller volume of thrombus within the SMP foam.

Newtonian viscosity model could overestimate wall shear stress in intracranial aneurysm domes and underestimate rupture risk

ObjectiveComputational fluid dynamics (CFD) simulations of intracranial aneurysm hemodynamics usually adopt the simplification of the Newtonian blood rheology model. A study was undertaken to examine whether such a model affects...

A comparison between non-Newtonian and Newtonian blood viscosity models

In this study the effects of some non-Newtonian viscosity and Newtonian viscosity models on the Wall Shear Stress and velocity distributions in carotid artery are investigated. Three distinct non-Newtonian viscosity models named Carreua, Casson and Generalised Power Method and Newtonian model are employed in the simulations. 3D Navier–Stokes equations is solved numerically on anatomically realistic geometry which is obtained from CT data. At the inlet of the numerical model experimental flow data which is measured at a real common carotid artery is imposed. The WSS and velocity distributions which are calculated using different viscosity models are compared. Results show that the differences between non-Newtonian models and Newtonian model are important at the regions having low velocity.

Finite element and sensitivity analysis of thermally induced flow instabilities

AbstractThis paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Compression moulding simulations of SMC using a multiobjective surrogate-based inverse modeling approach

A multiobjective surrogate-based inverse modeling technique to predict the spatial and temporal pressure distribution numerically during the fabrication of sheet moulding compounds (SMCs) is introduced. Specifically, an isotropic temperature-dependent Newtonian viscosity model of a SMC charge is fitted to experimental measurements via numerical simulations in order to mimic the temporal pressure distribution at two spatial locations simultaneously. The simulations are performed by using the commercial computational fluid dynamics (CFD) code ANSYS CFX-10.0, and the multiobjective surrogate-based fitting procedure proposed is carried out with a hybrid formulation of the NSGA-IIa evolutionary algorithm and the response surface methodology in Matlab. The outcome of the analysis shows the ability of the optimization framework to efficiently reduce the total computational load of the problem. Furthermore, the viscosity model assumed seems to be able to re solve the temporal pressure distribution and the advancing flow front accurately, which can not be said of the spatial pressure distribution. Hence, it is recommended to improve the CFD model proposed in order to better capture the true behaviour of the mould flow.

Particle migration and free-surface topography in inclined plane flow of a suspension

Gravity-driven free-surface flow of a suspension of neutrally buoyant particles down an inclined plane channel of constant width has been studied experimentally and by flow modelling. A uniform suspension of spheres, sieved to radii of a = 53-125 μm or 125-150 μm, was introduced to create films of initial depth h o . The flow was always at small film-depth-based Reynolds numbers. The film depth and the mixture flow profile were measured at the initial and two locations at least 200h o and 400h o downstream. The bulk particle volume fraction, Φ B , was varied in the range 0.01 ≤Φ B ≤0.5; h o 1.8-3.2 mm and the inclination angle relative to horizontal, 0.1° < α ≤ 90°, were also varied. Analysis of the particle velocity was performed by stereoscopic imaging to determine particle location followed by particle correlation velocimetry. A two-layer Newtonian viscosity model was applied to the velocimetry results in order to infer particle concentration information

Laminar Converging Flow of Dilute Polymer Solutions in Conical Sections. II

The test fluids were three aqueous solutions of Natrosol 250 H hydroxyethyl cellulose. Their nominal concentrations were 0.3, 0.5, and 0.7%. Viscosity data for each solution wee filled with a generalized Newtonian viscosity model which properly describes the zero-shear viscosity. The test geometries were two conical sections. Their vertex angles were approximately 14 and 21°. Laminar flow rate vs. pressure drop data were taken for each Natrosol solution in each conical section. Approximate expressions relating flow rate and pressure drop were derived for the limiting cases of very low and very high flow rates. The low flow rate (non-Newtonian flow) expression was of form: pressure drop=function of (flow rate, geometry, viscosity model parameters). The high flow rate (inviscid flow) expression was of form: pressure drop=function of (flow rate, geometry, fluid density). These two expressions were in excellent agreement with data at low and high flow rates. The sum of these two expressions was in good agreement with data over the entire range of flow rates. This superposition expression in no way accounts for normal stresses, time-dependent elastic effects, or the effect of the third invariant on viscosity. Its success in describing the data implies that these phenomena were not important. For engineering purposes generalized Newtonian viscosity models will probably be adequate for characterizing the flow of dilute polymer solutions in conical sections.