On the drag force closures for multiphase flow modeling

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamid Reza Norouzi ◽  
Shahab Golshan ◽  
Reza Zarghami
Keyword(s):  
Drag Force ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Fluid Volume ◽  
Spherical Particles ◽  
Two Phase ◽  
Dem Simulation ◽  
Data Points ◽  
Drag Models ◽  
Different Sources

Abstract Drag force models are one of the most important factors that can affect TFM and CFD-DEM simulation results of two-phase systems. This article investigates the accuracies, implementation issues and limitations of the majority of the drag models for spherical, non-spherical and systems with size distribution and evaluates their performance in various simulations. Around 1888 data points were collected from 19 different sources to evaluate the drag force closures on mono-dispersed spherical particles. The Reynolds number and fluid volume fraction ranges were between 0.01 and 10,000 and between 0.33 and 1, respectively. In addition, 776 data points were collected from seven different sources to evaluate the drag force closures on poly-dispersed spherical particles. The Reynolds numbers were between 0.01 and 500, fluid volume fractions between 0.33 and 0.9, and diameter ratios up to 10. A comprehensive discussion on the accuracy and application of these models is given in the article.

scholarly journals Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity

2021 ◽  
Vol 932 ◽  
Author(s):  
Christoph Rettinger ◽  
Sebastian Eibl ◽  
Ulrich Rüde ◽  
Bernhard Vowinckel
Keyword(s):  
Friction Coefficient ◽  
Shear Flow ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Rheological Behaviour ◽  
Spherical Particles ◽  
Particle Volume ◽  
Two Phase ◽  
Transport Modelling ◽  
Static State

Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.

scholarly journals Lattice Boltzmann simulations of low-Reynolds-number flows past fluidized spheres: effect of inhomogeneities on the drag force

2017 ◽  
Vol 833 ◽  
pp. 599-630 ◽  
Author(s):  
Gregory J. Rubinstein ◽  
Ali Ozel ◽  
Xiaolong Yin ◽  
J. J. Derksen ◽  
Sankaran Sundaresan
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Low Reynolds Number ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Particle Volume ◽  
Lattice Boltzmann Simulations ◽  
Low Reynolds

The formation of inhomogeneities within fluidized beds, both in terms of the particle configurations and flow structures, have a pronounced effect on the interaction force between the fluid and particles. While recent numerical studies have begun to probe the effects of inhomogeneities on the drag force at the particle scale, the applicability of prior microscale constitutive drag relations is still limited to random, homogeneous distributions of particles. Since an accurate model for the drag force is needed to predict the fluidization behaviour, the current study utilizes the lessons of prior inhomogeneity studies in order to derive a robust drag relation that is both able to account for the effect of inhomogeneities and applicable as a constitutive closure to larger-scale fluidization simulations. Using fully resolved lattice Boltzmann simulations of systems composed of fluid and monodisperse spherical particles in the low-Reynolds-number (Re) regime, the fluid–particle drag force, normalized by the ideal Stokes drag force, is found to significantly decrease, over a range of length scales, as the extent of inhomogeneities increases. The extent of inhomogeneities is found to most effectively be quantified through one of two subgrid-scale quantities: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. Scale-similar models are developed to estimate these two subgrid measures over a wide range of system properties. Two new drag constitutive models are proposed that are not only functions of the particle volume fraction and the Stokes number ($St$), but also dependent on one of these subgrid measures for the extent of inhomogeneities. Based on the observed, appreciable effect of inhomogeneities on drag, these new low-Re drag models represent a significant advancement over prior constitutive relations.

Interaction of Shock and Expansion Wave With Solid Particles in Supersonic Flows

2002 ◽  
Author(s):  
Ali Dolatabadi ◽  
Javad Mostaghimi ◽  
Valerian Pershin
Keyword(s):  
Mach Number ◽  
Flow Regime ◽  
Drag Force ◽  
Gas Flow ◽  
Volume Fraction ◽  
Supersonic Flows ◽  
Operating Conditions ◽  
Solid Particles ◽  
Process Efficiency ◽  
Two Phase

Interaction of solid particles with shock and expansions in supersonic flows is analyzed. In this analysis, a dense cloud of solid particulates is modeled by using a fully Eulerian approach. The dispersed flow and the gas flow were considered in the Eulerian frame whereby most of the physical aspects of the gas-particle flow can be incorporated. In addition to the momentum and energy exchanges in the form of source terms appearing in the governing equations, the two phases were strongly coupled by considering the volume fraction of the particulate phase in the equations. The simulation performed for a High Velocity Oxy-Fuel (HVOF) process under typical operating conditions in which the powder loading is high and the two-phase flow is not dilute near the injection port. The simulations showed large variations in the flow regime in the region that most of the particles exist. Unlike the results corresponding to the Lagrangian approach, the flow becomes subsonic near the centerline and the drag force decreases significantly since the relative Mach number is small. The validation experiments showed that the variation of flow regime by changing the relative Mach number could significantly change the particle drag force, and consequently process efficiency.

Drag coefficient of a sphere in a non-stationary flow: new results

2007 ◽  
Vol 463 (2088) ◽  
pp. 3323-3345 ◽  
Author(s):  
G Jourdan ◽  
L Houas ◽  
O Igra ◽  
J.-L Estivalezes ◽  
C Devals ◽  
...  
Keyword(s):  
Drag Coefficient ◽  
Stationary Flow ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Steady Flows ◽  
Two Phase ◽  
Spider Web ◽  
Wide Range ◽  
The Difference ◽  
Sphere Drag

The drag coefficient of a sphere placed in a non-stationary flow is studied experimentally over a wide range of Reynolds numbers in subsonic and supersonic flows. Experiments were conducted in a shock tube where the investigated balls were suspended, far from all the tube walls, on a very thin wire taken from a spider web. During each experiment, many shadowgraph photos were taken to enable an accurate construction of the sphere's trajectory. Based on the sphere's trajectory, its drag coefficient was evaluated. It was shown that a large difference exists between the sphere drag coefficient in steady and non-steady flows. In the investigated range of Reynolds numbers, the difference exceeds 50%. Based on the obtained results, a correlation for the non-stationary drag coefficient of a sphere is given. This correlation can be used safely in simulating two-phase flows composed of small spherical particles immersed in a gaseous medium.

Effect of Turbulence on Drag Force in Gas-Particle Two-Phase Flow

2002 ◽  
Author(s):  
Changfu You ◽  
Haiying Qi ◽  
Xuchang Xu
Keyword(s):  
Drag Force ◽  
Turbulence Intensity ◽  
Two Phase Flow ◽  
Reynolds Numbers ◽  
Length Scale ◽  
Phase Flow ◽  
Two Phase ◽  
Turbulence Flow ◽  
Turbulence Length ◽  
Turbulence Length Scale

Effect of turbulence on drag force in gas-particle two-phase flow had been investigated using numerical simulation. In order to select an accurate turbulence model, some promising models, such as standard k-ε model, RNG k-ε model and Realizable k-ε model, had been examined through calculating the flow over a backward-facing step. RNG k-ε model performing better than others had been used to simulate the turbulence flow over a spherical particle. In computation, the turbulence intensity was ranged from 10% to 80%, and the turbulence length scale from 10−5m to 4m. Results show that the turbulence length scale had a small effect on the drag force, except at small length scale. Comparing with the drag on a particle in laminar flow, the turbulence intensity enhances it comparatively, especially at small particle Reynolds numbers, which differs from the previous publications.

Intersect distributions of a `dead leaves' model with spherical primary grains

2005 ◽  
Vol 38 (3) ◽  
pp. 520-527 ◽  
Author(s):  
Wilfried Gille
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Length Distribution ◽  
Hard Core ◽  
Spherical Particles ◽  
Characteristic Functions ◽  
Phase System ◽  
Two Phase ◽  
Linear Integration ◽  
Dead Leaves Model

This article analyses a tightly packed random two-phase system possessing spherical particles having the volume fraction of 1/8. For a three-dimensional hard-core `dead leaves' model of spheres of constant diameter, the chord length distribution density of typical chords m i of the connected phase (outside the hard particles) is investigated. The calculation starts from the second derivative of the small-angle scattering correlation function of the model and applies characteristic functions. The result fulfills Rosiwal's linear integration principle.

scholarly journals The rheology of three-phase suspensions at low bubble capillary number

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140557 ◽  
Author(s):  
J. M. Truby ◽  
S. P. Mueller ◽  
E. W. Llewellin ◽  
H. M. Mader
Keyword(s):  
Capillary Number ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Bubbly Liquid ◽  
Particle Suspension ◽  
Suspension Rheology ◽  
Particle Volume ◽  
Two Phase ◽  
Three Phase

We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction ( 0 ≤ ϕ p ≲ 0.5 ) and bubble volume fraction ( 0 ≤ ϕ b ≲ 0.3 ). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.

The first effects of fluid inertia on flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 213-241 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Drag Force ◽  
Stokes Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Random Arrays ◽  
Long Time

Theory and lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at small Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is determined at small but finite Reynolds numbers, at solid volume fractions up to the close-packed limits of the arrays. For small solid volume fraction, the simulations are compared to theory, showing that the first inertial contribution to the drag force, when scaled with the Stokes drag force on a single sphere in an unbounded fluid, is proportional to the square of the Reynolds number. The simulations show that this scaling persists at solid volume fractions up to the close-packed limits of the arrays, and that the first inertial contribution to the drag force relative to the Stokes-flow drag force decreases with increasing solid volume fraction. The temporal evolution of the spatially averaged velocity and the drag force is examined when the fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. Theory for the short- and long-time behaviour is in good agreement with simulations, showing that the unsteady force is dominated by quasi-steady drag and added-mass forces. The short- and long-time added-mass coefficients are obtained from potential-flow and quasi-steady viscous-flow approximations, respectively.

scholarly journals Inertial Migration of Neutrally Buoyant Spherical Particles in Square Channels at Moderate and High Reynolds Numbers

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 198
Author(s):  
Yanfeng Gao ◽  
Pascale Magaud ◽  
Lucien Baldas ◽  
Yanping Wang
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Particle Volume ◽  
Inertial Focusing ◽  
Inertial Migration ◽  
High Reynolds Numbers ◽  
Micro Channels ◽  
High Reynolds

The inertial migration of particles in microchannel flows has been deeply investigated in the last two decades. In spite of numerous reports on the inertial focusing patterns in a square channel, the particle inertial focusing and longitudinal ordering processes remain unclear at high Reynolds numbers (>200) in square microchannels smaller than 100 µm in width. Thus, in this work, in situ visualization of particles flowing in square micro-channels at Reynolds numbers Re ranging from 5 to 280 has been conducted and their migration behaviors have been analyzed. The obtained results confirm that new equilibrium positions appear above a critical Re depending on the particle to channel size ratio and the particle volume fraction. It is also shown that, for a given channel length, an optimal Reynolds number can be identified, for which the ratio of particles located on equilibrium positions is maximal. Moreover, the longitudinal ordering process, i.e., the formation of trains of particles on equilibrium positions and the characterization of their length, has also been analyzed for the different flow conditions investigated in this study.

scholarly journals Numerical analysis for thermal–hydraulic characteristics and the laminar two-phase nanofluid flow inside a tube equipped with helically twisted tapes as swirl and turbulence promoters

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Iman Kalani ◽  
Davood Toghraie
Keyword(s):  
Nusselt Number ◽  
Friction Factor ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Hydraulic Characteristics ◽  
Nanofluid Flow ◽  
Two Phase ◽  
Twisted Tapes ◽  
Different Types

AbstractIn this study, the numerical simulation of heat transfer of Al2O3-water nanofluid in a pipe equipped with helically twisted tapes is investigated. The volume fraction of nanoparticles in this study is equal to 0, 1, 2, and 3%, and a two-phase mixture method has been used to simulate the nanofluids. The flow regime is laminar in the present study, and Reynolds numbers are Re = 250, 500, 750, and 1000. The helical twisted tapes are in three different types, single, double, and triple. The same heat flux 5000Wm-2 is applied to the walls. The simulation results showed that increasing the Re increases the Nusselt number and decreasing the friction factor. Nusselt number in case 1 and volume fraction of nanoparticles 0% for Re = 250, 500, 750 and 1000 are equal to 95.8, 57.11, 56.13 and 22.15, respectively. The average friction factor is equal to 0.18, 0.09, 0.07, and 0.05. The presence of helical twisted tapes increases the $${\text{Nu}}_{ave}$$ Nu ave . The friction factor due to secondary flows and increases the contact of the fluid and the solid surface, so that the Nusselt number in volume fraction of nanoparticles 0%, Re = 250 for case 1, case 2, case 3, and case 4 are 95.8, 46.10, 58.11, and 51.12, respectively, and the friction factor are 18.0, 29.0, 0.38 and 0.48, respectively.

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