scholarly journals Velocity fluctuations generated by the flow through a random array of spheres: a model of bubble-induced agitation

2017 ◽  
Vol 823 ◽  
pp. 592-616 ◽  
Author(s):  
Zouhir Amoura ◽  
Cédric Besnaci ◽  
Frédéric Risso ◽  
Véronique Roig
Keyword(s):  
Reynolds Number ◽  
Volume Fraction ◽  
Experimental Investigations ◽  
Sphere Diameter ◽  
Spatial Fluctuation ◽  
Average Flow Velocity ◽  
Random Array ◽  
Time Fluctuation ◽  
Flow Through ◽  
Non Gaussian

This work reports an experimental investigation of the flow through a random array of fixed solid spheres. The volume fraction of the spheres is 2 %, and the Reynolds number $Re$ based on the sphere diameter and the average flow velocity is varied from 120 to 1040. Using time and spatial averaging, the fluctuations have been decomposed into two contributions of different natures: a spatial fluctuation that accounts for the strong inhomogeneity of the flow around each sphere, and a time fluctuation that comes from the instability of the flow at large enough Reynolds numbers. The evolutions of these two contributions with the Reynolds number are different, so that their relative importance varies. However, when each is normalized by using its own variance and the integral length scales of the fluctuations, their spectra and probability density functions (PDFs) are almost independent of $Re$. The spatial fluctuation mostly comes from the velocity deficit in the wakes of the spheres, and is thus dominated by scales larger than one or two sphere diameters. It is found to be responsible for the asymmetry of the PDFs of the vertical fluctuations and of the major part of the anisotropy level between the vertical and the horizontal components of the fluctuations. The time fluctuation dominates at scales smaller than the integral length scale. It is isotropic and its PDFs, well described by an exponential distribution, are non-Gaussian. The spectra of the spatial and the time fluctuations both show an evolution as the power $-3$ of the wavenumber, but not exactly in the same subrange. All these properties are found in remarkable agreement with the results of both experimental investigations and large eddy simulations (LES) of a homogeneous bubble swarm. This confirms that the main mechanism responsible for the production of bubble-induced fluctuations is the interaction of the velocity disturbances caused by obstacles immersed in a flow and that the structure of this agitation is weakly dependent on the precise nature of the obstacles. The understanding and the modelling of the agitation generated by the motion of a dispersed phase, such as the bubble-induced agitation, therefore require one to distinguish between the roles of these two contributions.

Flow past periodic arrays of spheres at low Reynolds number

1997 ◽  
Vol 335 ◽  
pp. 189-212 ◽  
Author(s):  
HONGWEI CHENG ◽  
GEORGE PAPANICOLAOU
Keyword(s):  
Reynolds Number ◽  
Viscous Flow ◽  
Small Volume ◽  
Volume Fraction ◽  
Periodic Array ◽  
Periodic Arrays ◽  
Flow Past ◽  
Random Array ◽  
Single Sphere ◽  
Small Volume Fraction

We calculate the force on a periodic array of spheres in a viscous flow at small Reynolds number and for small volume fraction. This generalizes the known results for the force on a periodic array due to Stokes flow (zero Reynolds number) and the Oseen correction to the Stokes formula for the force on a single sphere (zero volume fraction). We use a generalization of Hasimoto's approach that is based on an analysis of periodic Green's functions. We compare our results to the phenomenological ones of Kaneda for viscous flow past a random array of spheres.

scholarly journals Wake attenuation in large Reynolds number dispersed two-phase flows

2008 ◽  
Vol 366 (1873) ◽  
pp. 2177-2190 ◽  
Author(s):  
Frédéric Risso ◽  
Véronique Roig ◽  
Zouhir Amoura ◽  
Guillaume Riboux ◽  
Anne-Marie Billet
Keyword(s):  
Reynolds Number ◽  
Volume Fraction ◽  
Bubble Diameter ◽  
Temporal Variations ◽  
The Body ◽  
Experimental Investigations ◽  
Large Reynolds Number ◽  
Two Phase Flows ◽  
Two Phase ◽  
Multi Body

The dynamics of high Reynolds number-dispersed two-phase flow strongly depends on the wakes generated behind the moving bodies that constitute the dispersed phase. The length of these wakes is considerably reduced compared with those developing behind isolated bodies. In this paper, this wake attenuation is studied from several complementary experimental investigations with the aim of determining how it depends on the body Reynolds number and the volume fraction α . It is first shown that the wakes inside a homogeneous swarm of rising bubbles decay exponentially with a characteristic length that scales as the ratio of the bubble diameter d to the drag coefficient C d , and surprisingly does not depend on α for 10 −2 ≤ α ≤10 −1 . The attenuation of the wakes in a fixed array of spheres randomly distributed in space ( α =2×10 −2 ) is observed to be stronger than that of the wake of an isolated sphere in a turbulent incident flow, but similar to that of bubbles within a homogeneous swarm. It thus appears that the wakes in dispersed two-phase flows are controlled by multi-body interactions, which cause a much faster decay than turbulent fluctuations having the same energy and integral length scale. Decomposition of velocity fluctuations into a contribution related to temporal variations and that associated to the random character of the body positions is proposed as a perspective for studying the mechanisms responsible for multi-body interactions.

scholarly journals Computational fluid simulation of non-Newtonian two-phase fluid flow through a channel with a cavity

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1045-1054 ◽  
Author(s):  
Mehdi Ahmadi ◽  
Farsani Khosravi
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Newtonian Fluid ◽  
Volume Fraction ◽  
Staggered Grid ◽  
Mixed Solution ◽  
Two Phase ◽  
Flow Through ◽  
Velocity Pressure ◽  
Phase Fluid

In this paper, the numerical solution of non-Newtonian two-phase fluid-flow through a channel with a cavity was studied. Carreau-Yasuda non-Newtonian model which represents well the dependence of stress on shear rate was used and the effect of n index of the model and the effect of input Reynolds on the attribution of flow were considered. Governing equations were discretized using the finite volume method on staggered grid and the form of allocating flow parameters on staggered grid is based on marker and cell method. The QUICK scheme is employed for the convection terms in the momentum equations, also the convection term is discretized by using the hybrid upwind-central scheme. In order to increase the accuracy of making discrete, second order Van Leer accuracy method was used. For mixed solution of velocity-pressure field SIMPLEC algorithm was used and for pressure correction equation iteratively line-by-line TDMA solution procedure and the strongly implicit procedure was used. As the results show, by increasing Reynolds number, the time of sweeping the non-Newtonian fluid inside the cavity decreases, the velocity of Newtonian fluid increases and the pressure decreases. In the second section, by increasing n index, the velocity increases and the volume fraction of non-Newtonian fluid after cavity increases and by increasing velocity, the pressure decreases. Also changes in the velocity, pressure and volume fraction of fluids inside the channel and cavity are more sensible to changing the Reynolds number instead of changing n index.

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.

Characteristics of Porescale Vortical Structures in Random and Arranged Packed Beds of Spheres

2012 ◽  
Author(s):  
Justin R. Finn ◽  
Sourabh V. Apte ◽  
Brian D. Wood
Keyword(s):  
Reynolds Number ◽  
Unsteady Flow ◽  
Reynolds Numbers ◽  
Random Packing ◽  
Packed Beds ◽  
Sphere Diameter ◽  
Vortical Structures ◽  
Simple Cubic ◽  
Principal Axes ◽  
Flow Through

The characteristics of pore scale vortical structures observed in moderate Reynolds number flow through mono-disperse packed beds of spheres are examined. Our results come from direct numerical simulations of flow through (i) a periodic, simple cubic arrangement of 54 spheres, (ii) a wall bounded, close packed arrangement of 216 spheres, and (iii) a realistic randomly packed tube containing 326 spheres with a tube diameter to sphere diameter ratio of 5.96. Pore Reynolds numbers in the steady inertial (10 ≲ Re ≲ 200) and unsteady inertial (Re ≈ 600) regimes are considered. Even at similar Reynolds numbers, the vortical structures observed in flows through these three packings are remarkably different. The interior of the arranged packings are dominated by multi-lobed vortex ring structures which align with the principal axes of the packing. The random packing and the near wall region of the close packed arrangement are dominated by helical vortices, elongated in the mean flow direction. In the simple cubic packing, unsteady flow is marked by periodic vortex shedding which occurs at a single frequency. Conversely, at a similar Reynolds number, the vortical structures in unsteady flow through the random packing oscillate with many characteristic frequencies.

The Influence of Surface Roughness on Resistance to Flow Through Packed Beds

1986 ◽  
Vol 108 (3) ◽  
pp. 343-347 ◽  
Author(s):  
C. W. Crawford ◽  
O. A. Plumb
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Entire Range ◽  
Reynolds Numbers ◽  
Packed Beds ◽  
Sphere Diameter ◽  
Relative Roughness ◽  
Roughness Elements ◽  
Flow Through ◽  
High Reynolds

Experiments were performed to determine the effect of roughness on flow through randomly packed beds of spheres. Three different packings were investigated, one of smooth spheres, and two others composed of spheres with roughness elements added to the surface. The relative roughness, defined as the height of the added elements divided by the diameter of the smooth spheres, was .012 and .026 for these two cases. The experiments covered a range of Reynolds numbers based on the sphere diameter from near unity where the flow is dominated by viscosity to 1600 where the flow is dominated by inertia. It was found that the pressure drop is substantially increased by the presence of surface roughness over the entire range of Reynolds numbers studied. The observed behavior is quite different from that which has been proposed previously by drawing analogy with flow in rough pipes, since the flow at low Reynolds number as well as high Reynolds number was affected by roughness.

Pairwise interaction extended point-particle model for a random array of monodisperse spheres

2017 ◽  
Vol 813 ◽  
pp. 882-928 ◽  
Author(s):  
G. Akiki ◽  
T. L. Jackson ◽  
S. Balachandar
Keyword(s):  
Reynolds Number ◽  
Model Prediction ◽  
Volume Fraction ◽  
Point Particle ◽  
Pairwise Interaction ◽  
Force Model ◽  
Random Array ◽  
The Mean ◽  
Particle Force ◽  
Extended Point

This study introduces a new point-particle force model that attempts to account for the hydrodynamic influence of the neighbouring particles in an Eulerian–Lagrangian simulation. In previous point-particle models the force on a particle depends only on Reynolds number and mean volume fraction. Thus, as long as the mean local volume fraction is the same, the force on different particles will be estimated to be the same, even though the precise arrangement of neighbours can be vastly different. From direct numerical simulation (DNS) it has been observed that in a random arrangement of spheres that were distributed with uniform probability, the particle-to-particle variation in force can be as large as the mean drag. Since the Reynolds number and mean volume fraction of all the particles within the array are the same, the standard models fail to account for the significant particle-to-particle force variation within the random array. Here, we develop a model which can compute the drag and lateral forces on each particle by accounting for the precise location of a few surrounding neighbours. A pairwise interaction is assumed where the perturbation flow induced by each neighbour is considered separately, then the effects of all neighbours are linearly superposed to obtain the total perturbation. Faxén correction is used to quantify the force perturbation due to the presence of the neighbours. The single neighbour perturbations are mapped in the vicinity of a reference sphere and stored as libraries. We test the pairwise interaction extended point-particle (PIEP) model for random arrays at two different volume fractions of $\unicode[STIX]{x1D719}=0.1$ and 0.21 and Reynolds numbers in the range $16.5\leqslant Re\leqslant 170$. The PIEP model predictions are compared against drag and lift forces obtained from the fully resolved DNS simulations performed using the immersed boundary method. Although not perfect, we observe the PIEP model prediction to correlate much better with the DNS results than the classical mean drag model prediction.

scholarly journals Experimental Investigations on Leakages in Positive Displacement Machines

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hitesh H. Patel ◽  
Vikas J. Lakhera
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Ratio ◽  
Flow Coefficient ◽  
Experimental Investigations ◽  
Mean Deviation ◽  
Leakage Flow ◽  
Positive Displacement ◽  
Flow Through ◽  
The Mean

The clearance gaps in positive displacement machines such as compressors, pumps, expanders, and turbines are critical for their performance and reliability. The leakage flow through these clearances influences the volumetric and adiabatic efficiencies of the machines. The extent of the leakage flow depends on the size and shape of clearance paths and pressure differences across these paths. Usually, the mass flow through the gaps is estimated using the isentropic nozzle equation with the flow coefficients applied to correct for the real flow conditions. However, the flow coefficients applied generally do not take into account the shape and size of these leakage paths. For that reason, a proper understanding of the relationship between flow coefficients and shape parameters is crucial for an accurate prediction of leakage flows. The present study investigates the influence of the various dimensionless parameters such as Reynolds number, Mach number, and pressure ratio on the flow coefficients for circular and rectangular clearance shapes. The flow coefficients are determined by comparing the experimental values obtained in an experimental test rig and the flow rates obtained from the isentropic nozzle equation. It is observed that in the case of circular clearances, the mean deviation of the experimental leakage results (in comparison to the analytical results using isotropic nozzle equations) is +9.1%, which is significantly lower than the mean deviation (+20.5%) in the case of rectangular clearance leakages. The study indicates that the isentropic nozzle equation method is more suitable for predicting the leakages through the circular clearances and needs modifications for consideration of the rectangular clearances. Using regression analysis, empirical correlations are developed to predict the flow coefficient in terms of Reynolds number, Mach number, pressure ratio, aspect ratio, and β ratio, which are found to match within ±6.4 percent of the numerical results for the rectangular clearance and within the range of -3.6 percent to +5.1 percent of the numerical result for the circular clearance. The empirical relationships presented in this study can be extended to evaluate the flow coefficients in a positive displacement machine.

Study of pumping effect in flow-through electrolysers

1983 ◽  
Vol 48 (8) ◽  
pp. 2232-2248 ◽  
Author(s):  
Ivo Roušar ◽  
Michal Provazník ◽  
Pavel Stuhl
Keyword(s):  
Natural Convection ◽  
Balance Equation ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Pumping Effect ◽  
Flow Through ◽  
The Mean ◽  
The Difference

In electrolysers with recirculation, where a gas is evolved, the pumping of electrolyte from a lower to a higher level can be effected by natural convection due to the difference between the densities of the inlet electrolyte and the gaseous emulsion at the outlet. An accurate balance equation for calculation of the rate of flow of the pumped liquid is derived. An equation for the calculation of the mean volume fraction of bubbles in the space between the electrodes is proposed and verified experimentally on a pilot electrolyser. Two examples of industrial applications are presented.

Sign in / Sign up

Export Citation Format

Share Document