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.

Moderate-Reynolds-number flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 243-278 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Hydrodynamic Dispersion ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Arrays Of Spheres

Lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at moderate 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 calculated as a function of the Reynolds number at solid volume fractions up to the close-packed limits of the arrays. At Reynolds numbers up to O(102), the non-dimensional drag force has a more complex dependence on the Reynolds number and the solid volume fraction than suggested by the well-known Ergun correlation, particularly at solid volume fractions smaller than those that can be achieved in physical experiments. However, good agreement is found between the simulations and Ergun's correlation at solid volume fractions approaching the close-packed limit. For ordered arrays, the drag force is further complicated by its dependence on the direction of the flow relative to the axes of the arrays, even though in the absence of fluid inertia the permeability is isotropic. Visualizations of the flows are used to help interpret the numerical results. For random arrays, the transition to unsteady flow and the effect of moderate Reynolds numbers on hydrodynamic dispersion are discussed.

Dense, bounded shear flows of agitated solid spheres in a gas at intermediate Stokes and finite Reynolds numbers

2009 ◽  
Vol 618 ◽  
pp. 181-208 ◽  
Author(s):  
HAITAO XU ◽  
ROLF VERBERG ◽  
DONALD L. KOCH ◽  
MICHEL Y. LOUGE
Keyword(s):  
Shear Flows ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Solid Volume Fraction ◽  
Reynolds Numbers ◽  
Fluid Inertia ◽  
Particle Inertia ◽  
Dissipation Term ◽  
Solid Spheres ◽  
Fluctuation Energy

We consider moderately dense bounded shear flows of agitated homogeneous inelastic frictionless solid spheres colliding in a gas between two parallel bumpy walls at finite particle Reynolds numbers, volume fractions between 0.1 and 0.4, and Stokes numbers large enough for collisions to determine the velocity distribution of the spheres. We adopt a continuum model in which constitutive relations and boundary conditions for the granular phase are derived from kinetic theory, and in which the gas contributes a viscous dissipation term to the fluctuation energy of the grains. We compare its predictions to recent lattice-Boltzmann (LB) simulations. The theory underscores the role played by the walls in the balances of momentum and fluctuation energy. When particle inertia is large, the solid volume fraction is nearly uniform, thus allowing us to treat the rheology using unbounded flow theory with an effective shear rate, while predicting slip velocities at the walls. When particle inertia decreases or fluid inertia increases, the solid volume fraction becomes increasingly heterogeneous. In this case, the theory captures the profiles of volume fraction, mean and fluctuation velocities between the walls. Comparisons with LB simulations allow us to delimit the range of parameters within which the theory is applicable.

scholarly journals Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

2018 ◽  
Vol 852 ◽  
pp. 329-357 ◽  
Author(s):  
Dhiya Alghalibi ◽  
Iman Lashgari ◽  
Luca Brandt ◽  
Sarah Hormozi
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Shear Thickening ◽  
Fluid Phase ◽  
Local Strain ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Strain Rates ◽  
Local Shear ◽  
The Mean

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$) and particle Reynolds numbers ($0.1\leqslant Re_{p}\leqslant 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$. The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$.

Computational Study of Slurry Flow in Pipes to Determine Profiles Sensed in Near Infrared Slurry Measurements

2011 ◽  
Author(s):  
V. Pasangulapati ◽  
N. R. Kesana ◽  
G. Sharma ◽  
F. W. Chambers ◽  
M. E. McNally ◽  
...  
Keyword(s):  
Near Infrared ◽  
Volume Fraction ◽  
Solid Phase ◽  
Computational Study ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Optical Measurements ◽  
Concentration Profiles ◽  
Horizontal Pipe ◽  
Volume Fractions

It is desired to perform accurate Near Infrared sensor measurements of slurries flowing in pipes leaving large batch reactors. A concern with these measurements is the degree to which the slurry sensed is representative of the material in the reactor and flowing through the pipe. Computational Fluid Dynamics (CFD) has been applied to the flow in the pipe to determine the flow fields and the concentration profiles seen by the sensors. The slurry was comprised of a xylene liquid phase and an ADP (2-amino-4, 6-dimethylpyrimidine) solid phase with a density ratio of 1.7. Computations were performed for a horizontal pipe with diameter 50.8 mm, length 2.032 m, and 1.76 m/s and 3.26 m/s mixture velocities. The corresponding pipe Reynolds numbers were 1.19E+05 and 2.21E+05. The flow through a slotted cylindrical probe inserted radially in the pipe also was considered. Spherical slurry particles with diameters from 10 μm to 1000 μm were considered with solid volume fractions of 12%, 24%, and 35%. Computations were performed with ANSYS FLUENT 12 software using the Realizable k-ε turbulence model and the enhanced wall treatment function. Comparisons of computed vertical profiles of solid volume fraction to results in the literature showed good agreement. Symmetric, nearly flat solid volume fraction profiles were observed for 38 μm particles for all three initial solid volume fractions. Asymmetric solid volume fraction profiles with greater values toward the bottom were observed for the larger particles. Changes in the profiles of turbulent kinetic energy also were observed. These changes are important for optical measurements which depend upon the mean concentration profiles as well as the turbulent motion of the slurry particles.

scholarly journals Effects of Surface Rotation on the Phase Change Process in a 3D Complex-Shaped Cylindrical Cavity with Ventilation Ports and Installed PCM Packed Bed System during Hybrid Nanofluid Convection

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2566
Author(s):  
Lioua Kolsi ◽  
Fatih Selimefendigil ◽  
Mohamed Omri
Keyword(s):  
Phase Transition ◽  
Phase Change ◽  
Change Process ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Hybrid Nanofluid ◽  
Surface Rotation ◽  
Phase Change Process

The combined effects of surface rotation and using binary nanoparticles on the phase change process in a 3D complex-shaped vented cavity with ventilation ports were studied during nanofluid convection. The geometry was a double T-shaped rotating vented cavity, while hybrid nanofluid contained binary Ag–MgO nano-sized particles. One of the novelties of the study wasthat a vented cavity was first used with the phase change–packed bed (PC–PB) system during nanofluid convection. The PC–PB system contained a spherical-shaped, encapsulated PCM paraffin wax. The Galerkin weighted residual finite element method was used as the solution method. The computations were carried out for varying values of the Reynolds numbers (100 ≤ Re ≤ 500),rotational Reynolds numbers (100 ≤ Rew ≤ 500), size of the ports (0.1L1 ≤ di ≤ 0.5L1), length of the PC–PB system (0.4L1 ≤ L0 ≤ L1), and location of the PC–PB (0 ≤ yp ≤ 0.25H). In the heat transfer fluid, the nanoparticle solid volume fraction amount was taken between 0 and 0.02%. When the fluid stream (Re) and surface rotational speed increased, the phase change process became fast. Effects of surface rotation became effective for lower values of Re while at Re = 100 and Re = 500; full phase transition time (tp) was reduced by about 39.8% and 24.5%. The port size and nanoparticle addition in the base fluid had positive impacts on the phase transition, while 34.8% reduction in tp was obtained at the largest port size, though this amount was only 9.5%, with the highest nanoparticle volume fraction. The length and vertical location of the PC–PB system have impacts on the phase transition dynamics. The reduction and increment amount in the value of tp with varying location and length of the PC–PB zone became 20% and 58%. As convection in cavities with ventilation ports are relevant in many thermal energy systems, the outcomes of this study will be helpful for the initial design and optimization of many PCM-embedded systems encountered in solar power, thermal management, refrigeration, and many other systems.

Three-Dimensional Printed Dielectric Substrates for Radio Frequency Applications

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Vana Snigdha Tummala ◽  
Ahsan Mian ◽  
Nowrin H. Chamok ◽  
Dhruva Poduval ◽  
Mohammod Ali ◽  
...  
Keyword(s):  
Radio Frequency ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Volume Fractions ◽  
The Core ◽  
Sandwich Construction ◽  
3D Printed ◽  
Rf Antenna

Engineered porous structures are being used in many applications including aerospace, electronics, biomedical, and others. The objective of this paper is to study the effect of three-dimensional (3D)-printed porous microstructure on the dielectric characteristics for radio frequency (RF) antenna applications. In this study, a sandwich construction made of a porous acrylonitrile butadiene styrene (ABS) thermoplastic core between two solid face sheets has been investigated. The porosity of the core structure has been varied by changing the fill densities or percent solid volume fractions in the 3D printer. Three separate sets of samples with dimensions of 50 mm × 50 mm × 5 mm are created at three different machine preset fill densities each using LulzBot and Stratasys dimension 3D printers. The printed samples are examined using a 3D X-ray microscope to understand pore distribution within the core region and uniformity of solid volumes. The nondestructively acquired 3D microscopy images are then postprocessed to measure actual solid volume fractions within the samples. This measurement is important specifically for dimension-printed samples as the printer cannot be set for any specific fill density. The experimentally measured solid volume fractions are found to be different from the factory preset values for samples prepared using LulzBot printer. It is also observed that the resonant frequency for samples created using both the printers decreases with an increase in solid volume fraction, which is intuitively correct. The results clearly demonstrate the ability to control the dielectric properties of 3D-printed structures based on prescribed fill density.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

1997 ◽  
Vol 349 ◽  
pp. 31-66 ◽  
Author(s):  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Unit Length ◽  
Reynolds Numbers ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Flow Through ◽  
The Mean ◽  
Square Array

The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

Diffusion of swimming model micro-organisms in a semi-dilute suspension

2007 ◽  
Vol 588 ◽  
pp. 437-462 ◽  
Author(s):  
TAKUJI ISHIKAWA ◽  
T. J. PEDLEY
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Reynolds Numbers ◽  
Surface Velocity ◽  
Biased Random Walk ◽  
Long Time ◽  
Upward Velocity ◽  
Micro Organisms ◽  
Diffusive Behaviour

The diffusive behaviour of swimming micro-organisms should be clarified in order to obtain a better continuum model for cell suspensions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 or 27 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. In the case of (non-bottom-heavy) squirmers, both the translational and the orientational spreading of squirmers is correctly described as a diffusive process over a sufficiently long time scale, even though all the movements of the squirmers were deterministically calculated. Scaling of the results on the assumption that the squirmer trajectories are unbiased random walks is shown to capture some but not all of the main features of the results. In the case of (bottom-heavy) squirmers, the diffusive behaviour in squirmers' orientations can be described by a biased random walk model, but only when the effect of hydrodynamic interaction dominates that of the bottom-heaviness. The spreading of bottom-heavy squirmers in the horizontal directions show diffusive behaviour, and that in the vertical direction also does when the average upward velocity is subtracted. The rotational diffusivity in this case, at a volume fractionc=0.1, is shown to be at least as large as that previously measured in very dilute populations of swimming algal cells (Chlamydomonas nivalis).

scholarly journals Three-dimensional computational fluid dynamics modeling of TiO2/R134a nanorefrigerant

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 175-186 ◽  
Author(s):  
Kamil Arslan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Nanoparticle Volume Fraction ◽  
Steady State Condition ◽  
Volume Fractions

In this study, numerical investigations were carried out for R134a based TiO2 nanorefrigerants. Forced laminar flow and heat transfer of nanorefrigerants in a horizontal smooth circular cross-sectioned duct were investigated under steady-state condition. The nanorefrigerants consist of TiO2 nanoparticles suspended in R134a as a base fluid with four particle volume fractions of 0.8, 2.0 and 4.0%. Numerical studies were performed under laminar flow conditions where Reynolds numbers range from 8?102 to 2.2?103. Flow is flowing in the duct with hydrodynamically and thermally developing (simultaneously developing flow) condition. The uniform surface heat flux with uniform peripheral wall heat flux (H2) boundary condition was applied on the duct wall. Commercial CFD software, Ansys Fluent 14.5, was used to carry out the numerical study. Effect of nanoparticle volume fraction on the average convective heat transfer coefficient and average Darcy friction factor were analyzed. It is obtained in this study that increasing nanoparticle volume fraction of nanorefrigerant increases the convective heat transfer in the duct; however, increasing nanoparticle volume fraction does not influence the pressure drop in the duct. The velocity and temperature distribution in the duct for different Reynolds numbers and nanoparticle volume fractions were presented.

Energy Transfer Enhancement Inside an Annulus Using Gradient Porous Ribs and Nanofluids

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Hamid Reza Talesh Bahrami ◽  
Ehsan Aminian ◽  
Hamid Saffari
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Pressure Drop ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Relative Height ◽  
Transfer Enhancement ◽  
Volume Fractions ◽  
Flow Reynolds Number ◽  
Maximum Volume Fraction

Abstract Porous media and nanofluid utilization are two passive heat transfer improvement tools, which have been employed extensively in recent years. Porous media with gradient properties result in both a higher effective thermal conductivity and better local convective heat transfer because of conducting the flow to the desired regions. In this study, distinct porous ribs are located on the internal border of an annulus. Four different conditions are considered for permeability change of ribs, including the minimum and maximum Darcy numbers and linearly increasing or decreasing variation in the radial direction, called LIV and LVD, respectively. In the first step, effects of porous rib relative height, porous rib porosity, and flow Reynolds number on the thermal efficiency and pressure drop are investigated. The results show that the configuration with Da = LVD and W/Rh = 0.25 has the maximum performance number PN = 2, that is the Nusselt improvement over pressure drop increment. Porous ribs arrangement with W/Rh = 0.25 and the minimum porosity (ɛ = 0.9) give the best PN. In the next step, the effects of nanoparticle addition with different volume fractions to the base fluid in different Reynolds numbers are investigated. In this step, porous rib relative height is set to W/Rh = 0.25. The results show that the maximum volume fraction has the highest heat transfer enhancement (about 2–2.5 times) but the lower volume fractions have higher PNs (PN ≈ 2.5 at ϕ = 1% and Re = 500).

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