The Role of Elasticity in the Vortex Formation in Polymeric Flow around a Sharp Bend

Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works.

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Electroosmotic Flow Behavior of Viscoelastic LPTT Fluid in a Microchannel

Micromachines ◽

10.3390/mi10120881 ◽

2019 ◽

Vol 10 (12) ◽

pp. 881 ◽

Cited By ~ 1

Author(s):

Dilin Chen ◽

Jie Li ◽

Haiwen Chen ◽

Lai Zhang ◽

Hongna Zhang ◽

...

Keyword(s):

Newtonian Fluid ◽

Electroosmotic Flow ◽

Fluid Shear Stress ◽

Viscosity Ratio ◽

Biological Fluids ◽

Flow Behavior ◽

Fluid Velocity ◽

Viscoelastic Fluids ◽

Weissenberg Number ◽

Fluid Medium

In many research works, the fluid medium in electroosmosis is considered to be a Newtonian fluid, while the polymer solutions and biological fluids used in biomedical fields mostly belong to the non-Newtonian category. Based on the finite volume method (FVM), the electroosmotic flow (EOF) of viscoelastic fluids in near-neutral (pH = 7.5) solution considering four ions (K+, Cl−, H+, OH−) is numerically studied, as well as the viscoelastic fluids’ flow characteristics in a microchannel described by the Linear Phan-Thien–Tanner (LPTT) constitutive model under different conditions, including the electrical double layer (EDL) thickness, the Weissenberg number (Wi), the viscosity ratio and the polymer extensibility parameters. When the EDL does not overlap, the velocity profiles for both Newtonian and viscoelastic fluids are plug-like and increase sharply near the charged wall. Compared with Newtonian fluid at Wi = 3, the viscoelastic fluid velocity increases by 5 times and 9 times, respectively, under the EDL conditions of kH = 15 and kH = 250, indicating the shear thinning behavior of LPTT fluid. Shear stress obviously depends on the viscosity ratio and different Wi number conditions. The EOF is also enhanced by the increase (decrease) in polymer extensibility parameters (viscosity ratio). When the extensibility parameters are large, the contribution to velocity is gradually weakened.

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Two-phase flow in Hele-Shaw cells: numberical studies of sweep efficiency in a five-spot pattern

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000005890 ◽

1988 ◽

Vol 29 (4) ◽

pp. 375-400 ◽

Cited By ~ 4

Author(s):

Leonard W. Sahwartiz ◽

Anthony J. Degregoria

Keyword(s):

Dimensionless Parameter ◽

Viscosity Ratio ◽

Nonlinear Behavior ◽

Boundary Integral ◽

Porous Media Flow ◽

Sweep Efficiency ◽

Two Phase ◽

Production Wells ◽

Range Of Values

AbstractThe unsteady Hele-Shaw problem is a model nonlinear system that, for a certain parameter ranger, exhibits the phenomenon known as viscous fingering. While not directly applicable to multiphase porous-media flow, it does prove to be an adequate mathematical model for unstable dieplacement in laboratory parallel-plate devices. We seek here to determine, by use of an accurate boundary-integral frount-tracking scheme, the extent to which the simplified system captures the canonical nonlinear behavior of displacement flows and, in particular, to ascertain the role of noise in such systems. We choose to study a particular pattern of injection and production “wells.” The pattern chosen is the isolated “five-spot,” that is a single source surrounded by four symmetrically-placed sinks in an infinite two-dimensional “reservoir.” In cases where the “pusher” fluid has negligible viscosity, sweep efficiency is calculated for a range of values of the single dimensionless parameter τ, an inverse capillary number. As this parameter is reduced, corresponding to increased flow rate or reduced interfacial tension, this efficiency decreases continuously. For small values of τ, these stable displacements change abruptly to a regime characterized by unstable competing fingers and a significant reduction in sweep efficiency. A simple stability argument appears to correctly predict the noise level required to transit from the stable to the competing-finger regimes. Published compilations of experimental results for sweep efficiency as a function of viscosity ratio showed an unexplained divergence when the pusher fluid is less viscous. Our simulations produce a similar divergence when, for a given viscosity ratio, the parameter τ is varied.

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Core–annular flow in a periodically constricted circular tube. Part 1. Steady-state, linear stability and energy analysis

Journal of Fluid Mechanics ◽

10.1017/s0022112000003153 ◽

2001 ◽

Vol 432 ◽

pp. 31-68 ◽

Cited By ~ 11

Author(s):

CHARALAMPOS KOURIS ◽

JOHN TSAMOPOULOS

Keyword(s):

Weber Number ◽

Annular Flow ◽

Viscosity Ratio ◽

Solid Wall ◽

Immiscible Fluids ◽

Straight Tube ◽

Neutral Stability ◽

Ohnesorge Number ◽

Dimensionless Numbers ◽

Two Phase

The concentric, two-phase flow of two immiscible fluids in a tube of sinusoidally varying cross-section is studied. This geometry is often used as a model to study the onset of different flow regimes in packed beds. Neglecting gravitational effects, the model equations depend on five dimensionless parameters: the Reynolds and Weber numbers, and the ratios of density, viscosity and volume of the two fluids. Two more dimensionless numbers describe the shape of the solid wall: the constriction ratio and the ratio of its maximum radius to its period. In addition to the effect of the Weber number, which depends on both the fluid and the flow, the effect of the Ohnesorge number J has been examined as it characterizes the fluid alone. The governing equations are approximated using the pseudo-spectral methodology while the Arnoldi algorithm has been implemented for computing the most critical eigenvalues that correspond to axisymmetric disturbances. Stationary solutions are obtained for a wide parameter range, which may exhibit flow recirculation at the expanding portion of the tube. Extensive calculations are made for the dependence of the neutral stability boundaries on the various parameters. In most cases where the steady solution becomes unstable it does so through a Hopf bifurcation. Exceptions to this are cases where the viscosity ratio is O(10−3) and, then, the most unstable eigenvalue remains real. Generally, steady core–annular flow in this geometry is more susceptible to instability than in a straight tube and, in similar ranges of the parameters, it may be generated by different mechanisms. Decreasing the thickness of the annular fluid, inverse Weber number or the Ohnesorge number or the density of the core fluid stabilizes the flow. For stability reasons, the viscosity ratio must remain strictly below unity and it has an optimum value that maximizes the range of allowed Reynolds numbers.

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Overview of a Theory for Planning Similar Experiments with Different Fluids at Supercritical Pressure

Energies ◽

10.3390/en14123695 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3695

Author(s):

Andrea Pucciarelli ◽

Sara Kassem ◽

Walter Ambrosini

Keyword(s):

Heat Transfer ◽

Similarity Theory ◽

Fluid Dynamic ◽

Supercritical Pressure ◽

Dimensionless Numbers ◽

Body Of Knowledge ◽

Definition Of ◽

Complex Phenomena ◽

Semi Empirical

The recent advancements achieved in the development of a fluid-to-fluid similarity theory for heat transfer with fluids at supercritical pressures are summarised. The prime mover for the development of the theory was the interest in the development of Supercritical Water nuclear Reactors (SCWRs) in the frame of research being developed worldwide; however, the theory is general and can be applied to any system involving fluids at a supercritical pressure. The steps involved in the development of the rationale at the basis of the theory are discussed and presented in a synthetic form, highlighting the relevance of the results achieved so far and separately published elsewhere, with the aim to provide a complete overview of the potential involved in the application of the theory. The adopted rationale, completely different from the ones in the previous literature on the subject, was based on a specific definition of similarity, aiming to achieve, as much as possible, similar distributions of enthalpies and fluid densities in a duct containing fluids at a supercritical pressure. This provides sufficient assurance that the complex phenomena governing heat transfer in the addressed conditions, which heavily depend on the changes in fluid density and in other thermophysical properties along and across the flow duct, are represented in sufficient similarity. The developed rationale can be used for planning possible counterpart experiments, with the aid of supporting computational fluid-dynamic (CFD) calculations, and it also clarifies the role of relevant dimensionless numbers in setting up semi-empirical correlations for heat transfer in these difficult conditions, experiencing normal, enhanced and deteriorated regimes. This paper is intended as a contribution to a common reflection on the results achieved so far in view of the assessment of a sufficient body of knowledge and understanding to base successful predictive capabilities for heat transfer with fluids at supercritical pressures.

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Effects of hoop stress, initial shear stress, and shear viscosity ratio on the steady two-phase fiber spinning

International Journal of Multiphase Flow ◽

10.1016/s0301-9322(97)88384-x ◽

1996 ◽

Vol 22 ◽

pp. 124

Author(s):

W Lee

Keyword(s):

Shear Stress ◽

Shear Viscosity ◽

Hoop Stress ◽

Viscosity Ratio ◽

Fiber Spinning ◽

Two Phase

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Peristaltic Carreau-Yasuda nanofluid flow and mixed heat transfer analysis in an asymmetric vertical and tapered wavy wall channel

Reports in Mechanical Engineering ◽

10.31181/rme200101128h ◽

2020 ◽

Vol 1 (1) ◽

pp. 128-140 ◽

Cited By ~ 1

Author(s):

Mohammad Hatami ◽

◽

D Jing ◽

Keyword(s):

Heat Transfer ◽

Least Square Method ◽

Weissenberg Number ◽

Least Square ◽

Heat Transfer Analysis ◽

Phase Method ◽

Nanofluid Flow ◽

Two Phase ◽

Nanoparticles Concentration ◽

The Right

In this study, two-phase asymmetric peristaltic Carreau-Yasuda nanofluid flow in a vertical and tapered wavy channel is demonstrated and the mixed heat transfer analysis is considered for it. For the modeling, two-phase method is considered to be able to study the nanoparticles concentration as a separate phase. Also it is assumed that peristaltic waves travel along X-axis at a constant speed, c. Furthermore, constant temperatures and constant nanoparticle concentrations are considered for both, left and right walls. This study aims at an analytical solution of the problem by means of least square method (LSM) using the Maple 15.0 mathematical software. Numerical outcomes will be compared. Finally, the effects of most important parameters (Weissenberg number, Prandtl number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof numbers) on the velocities, temperature and nanoparticles concentration functions are presented. As an important outcome, on the left side of the channel, increasing the Grashof numbers leads to a reduction in velocity profiles, while on the right side, it is the other way around.

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Rheological Characterization of a Concentrated Phosphate Slurry

Fluids ◽

10.3390/fluids6050178 ◽

2021 ◽

Vol 6 (5) ◽

pp. 178

Author(s):

Souhail Maazioui ◽

Abderrahim Maazouz ◽

Fayssal Benkhaldoun ◽

Driss Ouazar ◽

Khalid Lamnawar

Keyword(s):

Flow Behavior ◽

Continuous Phase ◽

Raw Material ◽

Rheological Characterization ◽

Phosphate Ore ◽

Insoluble Particles ◽

Experimental Protocols ◽

Solid Liquid

Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends toward zero. The suspended particles in the present study were assumed to be noncolloidal. Various grades and phosphate ore concentrations were chosen for this rheological investigation. We created some experimental protocols to determine the main characteristics of these complex fluids and established relevant rheological models with a view to simulate the numerical flow in a cylindrical pipeline. Rheograms of these slurries were obtained using a rotational rheometer and were accurately modeled with commonly used yield-pseudoplastic models. The results show that the concentration of solids in a solid–liquid mixture could be increased while maintaining a desired apparent viscosity. Finally, the design equations for the laminar pipe flow of yield pseudoplastics were investigated to highlight the role of rheological studies in this context.

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Machine Learning Model of Dimensionless Numbers to Predict Flow Patterns and Droplet Characteristics for Two-Phase Digital Flows

Applied Sciences ◽

10.3390/app11094251 ◽

2021 ◽

Vol 11 (9) ◽

pp. 4251

Author(s):

Jinsong Zhang ◽

Shuai Zhang ◽

Jianhua Zhang ◽

Zhiliang Wang

Keyword(s):

Machine Learning ◽

Learning Algorithms ◽

Digital Microfluidics ◽

Flow Patterns ◽

Machine Learning Algorithms ◽

Dimensionless Numbers ◽

Two Phase ◽

The Difference ◽

Input Variables ◽

Digital Microfluidic

In the digital microfluidic experiments, the droplet characteristics and flow patterns are generally identified and predicted by the empirical methods, which are difficult to process a large amount of data mining. In addition, due to the existence of inevitable human invention, the inconsistent judgment standards make the comparison between different experiments cumbersome and almost impossible. In this paper, we tried to use machine learning to build algorithms that could automatically identify, judge, and predict flow patterns and droplet characteristics, so that the empirical judgment was transferred to be an intelligent process. The difference on the usual machine learning algorithms, a generalized variable system was introduced to describe the different geometry configurations of the digital microfluidics. Specifically, Buckingham’s theorem had been adopted to obtain multiple groups of dimensionless numbers as the input variables of machine learning algorithms. Through the verification of the algorithms, the SVM and BPNN algorithms had classified and predicted the different flow patterns and droplet characteristics (the length and frequency) successfully. By comparing with the primitive parameters system, the dimensionless numbers system was superior in the predictive capability. The traditional dimensionless numbers selected for the machine learning algorithms should have physical meanings strongly rather than mathematical meanings. The machine learning algorithms applying the dimensionless numbers had declined the dimensionality of the system and the amount of computation and not lose the information of primitive parameters.

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Upward Vertical Two-Phase Flow Through an Annulus—Part II: Modeling Bubble, Slug, and Annular Flow

Journal of Energy Resources Technology ◽

10.1115/1.2905916 ◽

1992 ◽

Vol 114 (1) ◽

pp. 14-30 ◽

Cited By ~ 26

Author(s):

E. F. Caetano ◽

O. Shoham ◽

J. P. Brill

Keyword(s):

Flow Pattern ◽

Annular Flow ◽

Two Phase Flow ◽

Flow Behavior ◽

Bubble Flow ◽

Phase Flow ◽

Two Phase ◽

Flow Through ◽

Physical Phenomena ◽

Good Agreement

Mechanistic models have been developed for each of the existing two-phase flow patterns in an annulus, namely bubble flow, dispersed bubble flow, slug flow, and annular flow. These models are based on two-phase flow physical phenomena and incorporate annulus characteristics such as casing and tubing diameters and degree of eccentricity. The models also apply the new predictive means for friction factor and Taylor bubble rise velocity presented in Part I. Given a set of flow conditions, the existing flow pattern in the system can be predicted. The developed models are applied next for predicting the flow behavior, including the average volumetric liquid holdup and the average total pressure gradient for the existing flow pattern. In general, good agreement was observed between the experimental data and model predictions.

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