cfd investigation of particle deposition in a horizontal looped turbulent pipe flow
TRANSCRIPT
CFD Investigation of Particle Deposition in a HorizontalLooped Turbulent Pipe Flow
Alamgir Hossain & Jamal Naser & Monzur Alam Imteaz
Received: 2 December 2009 /Accepted: 3 February 2011 /Published online: 19 February 2011# Springer Science+Business Media B.V. 2011
Abstract This paper presents comprehensive 3D numericalinvestigations on depositions of particles flowing through ahorizontal pipe loop consisting of four bends. The multiphasemixture model available in FLUENT 6.2 was used in thisstudy. In this numerical simulation, five different particle sizeshave been used as secondary phases to calculate realmultiphase effect in which inter-particle interaction has beenconsidered. The deposition of particles along the periphery ofthe pipe wall was investigated as a function of particle size andfluid velocity. The simulations showed that near the upstreamof the bends, maximum particle concentration occurred at thebottom of the pipe. However, downstream the bends, themaximum particle concentration occurred at an angle of 60°from the bottom. The larger particles clearly showed deposi-tion near the bottomwall except downstream. As expected, thesmaller particles showed less tendency of deposition and lesserat higher velocity. This numerical investigation showedqualitative agreement with the experiments conducted byCommonwealth Scientific and Industrial Research Organisa-tion, Melbourne team for similar conditions.
Keywords CFD simulation . Numerical investigation .
Particle deposition . Two-phase flow . Turbulence
List of Symbols~a secondary-phase particle’s accelerationC+ concentration of particlesCf friction co-efficientD pipe diameter
Df fluid diffusivityDp particle diffusion coefficientdp diameter of the particles of secondary phase~F body forcefdrag drag functionk proportional constantkD constantkn eigenvaluesL Length scalel particle mean free pathmT mass transfern number of phasesP Peclet numberRD deposition fluxRe entrainment flux of the particlesRe* Reynolds number based on the friction velocityRef fluid Reynolds numberS Stokes numbert0 initial timeTL integral flow time scaleTP particle integral time scaleU Velocity scaleu* the friction velocityu* friction velocityv free-flight velocity~vdr;k drift velocity for secondary phaseVf pipe average fluid velocityvf ′ fluctuating velocityvg Particle free fall velocityvg gravitational settling velocity of the particle~vm mass-averaged velocity of the mixture~vqp relative velocity
v02pD E
particle’s mean square velocitylK Kolmogorov length scaleρm mixture densityρp densities of the particle
A. Hossain : J. Naser :M. A. Imteaz (*)Faculty of Engineering and Industrial Sciences,Swinburne University of Technology,Melbourne, VIC 3122, Australiae-mail: [email protected]: http://www.swinburne.edu.au/feis/civil/staff/monzur_imteaz.html
Environ Model Assess (2011) 16:359–367DOI 10.1007/s10666-011-9252-8
αk volume fraction of phaseε kinetic energy dissipationf angle around the pipe circumferenceγcross crossing trajectories coefficientginert inertial coefficientl free-flight/diffusion ratioμm viscosity of the mixtureνf kinematic viscosityνf kinematic viscosityρf densities of the fluidtp particle relaxation timetqp particulate relaxation timets wall shear stress
1 Introduction
Deposition of particles from flowing suspensions is animportant process in various fields of engineering and innature. Analyzing deposition of small particles suspended influid streams has attracted considerable attention in the pastthree decades [1–4, 8, 10, 12, 20, 22]. This is because particledeposition plays a major role in a number of industrialprocesses such as filtration, separation, particle transport,combustion, air, and water pollution and many others.
Computational models for simulating the hydraulicbehavior of water distribution systems have been availablefor many years [10, 16]. More recently, these models havebeen extended to analyze water quality as well [10]. In thepast Euler–Lagrange approach (particle tracking) was usedbecause it is computationally less demanding. The numberof particles used was fairly small and therefore numericalaccuracy suffered from insufficient statistics. In this study,we have used Euler–Euler approach and introduced wateras primary and five different sediments (spherical particles) assecondary phases. The driving force behind this trend is thetimely challenge to comply with increasingly stringentgovernmental regulations and customer-oriented expecta-tions. Modern management of water distribution systems orwater authorities in general need simulation models that arecapable of predicting the hydrodynamic behavior of particles(cause of dirty water) in the water distribution networks.
Deposition of small particles in turbulent flows hadattracted the interest of many researchers, due to itsrelevance with flows in water supply pipes. Using thestopping distance of a particle near a wall, Friendlander andJohnstone [7] developed the free-flight model for particledeposition process. Davies [5] among others offered animproved theoretical model for particle deposition rate. Liuand Agarwal [14] analyzed the deposition of aerosolparticles in turbulent pipe flows. Simplified simulationprocedures for deposition of particles in turbulent flowswere described by Abuzeid et al. [1], and Li and Ahmadi
[13]. Ta et al. [21] developed a multiphase (Eulerian–Eulerian) computational fluid dynamics (CFD) model topredict flow dynamic, particle removal and settlement in adissolved air floatation tank. Stovin and Saul [19] usedparticle tracking routine contained in FLUENT [6] compu-tational fluid dynamics software for the prediction ofsediment deposition in storage chambers.
Hossain [9] proposed an analytical model for thecircumferential particle deposition in a straight pipe forturbulent flow and verified the analytical model with CFDsimulations. Mols and Oliemans [16] developed a mathe-matical model for particle deposition and resuspension, inwhich researchers explained the circumferential depositionin straight pipes. But this model is not applicable forpredicting circumferential deposition in a general pipelayout including bends. Particle deposition in bends of acircular pipes were studied by a number of investigators[4, 23], however, the validity of the theoretical models inrelation with the different flow regimes is still unclear. Inthe experimental study by David et al. [4], it was revealedthat discrepancies still exist between the experimental dataand the available theories. These discrepancies are believedto be mainly caused by various flow field assumptionsmade by different investigators. Even though the problemhas been studied both theoretically and experimentally by anumber of investigators, it is still unclear in regards to theapplicability of theories under different flow regimes. Thecomplexity of the flow field (three dimensional with strongsecondary motion) makes it very difficult to calculate theparticle trajectories and deposition in the bend. There is nodetailed experiment on two-phase (solid–liquid) flow,which can be compared with this numerical study, exceptexperiments on aerosol particles deposition in the bend[7, 11]. This paper shows partial comparison of CFD resultswith the experimental results of Grainger et al. [8].
The motivation for this study is twofold; (1) toinvestigate the deposition of solid spherical particles witha specific gravity of 1.64, since these are commonlyencountered in water supply networks and (2) to investigatethe segregation of solid particles along the circumference ofthe pipe wall at upstream and downstream of bends. Theparticle size ranges typically between 2 and 20 μ fordifferent Reynolds numbers. The Eulerian description ofturbulence parameters used in this study will give us abetter understanding of the segregation
2 Description of the Experimental Setup and ModelGeometry
In order to study the hydrodynamics of particles behavior ina turbulent flow field numerically, a geometry shown inFig. 1 comprising 41 m long and 100 mm diameter pipe,
360 A. Hossain et al.
close-loop with four 90° bends has been considered with anaxial flow pump near a bend same as Grainger et al. [8]used in their experiment (Table 1). The boundary con-ditions used in the present study is described
3 Governing Equation
The multiphase mixture model of FLUENT 6.2 used in thisstudy solves the continuity and the momentum equation forthe mixture. Mixture model is suitable for this study and iscomputationally less expensive than the full multi-componentmultiphase model. The continuity equation was used to obtainthe pressure and the momentum equations for velocities.Volume fraction equations were also solved for the secondaryphases. The model also solves for the well-known algebraicexpressions for the relative velocities for secondary phases(FLUENT 6.2). The turbulence parameters were obtainedwith the eddy viscosity turbulence model proposed by Spalartand Allmaras [18].
3.1 Continuity Equation for the Mixture
The continuity equation for the mixture is,
@
@trmð Þ þ r � rm~vmð Þ ¼ 0 ð1Þ
where,~vm is the mass-averaged velocity:
~vm ¼Pn
k¼1 akrk~vkrm
ð2Þ
and ρm is the mixture density:
rm ¼Xnk¼1
akrk ð3Þ
αk is the volume fraction of phase k.
3.1.1 Momentum Equation for the Mixture
The momentum equation for the mixture can be obtainedby summing the individual momentum equations for allphases. It can be expressed as:
@
@trm~vmð Þ þ r � rm~vm~vmð Þ ¼ �rpþr � mm r~vmþð½ þr~vTm
��þ rm~g þ~F þr �
Xnk¼1
akrk~vdr;k~vdr;k
! ð4Þ
where, n is the number of phases, ~F is a body force, and μm
is the viscosity of the mixture:
mm ¼Xnk¼1
akmk ð5Þ
~vdr;k is the drift velocity for secondary phase k:
~vdr;k ¼~vk �~vm ð6Þ
3.1.2 Relative (Slip) Velocity and the Drift Velocity
The relative velocity (also referred to as the slip velocity) isdefined as the velocity of a secondary phase (p) relative tothe velocity of the primary phase (q):
~vqp ¼~vp �~vq ð7Þ
The drift velocity and the relative velocity (~vqp) areconnected by the following expression:
~vdr;p ¼~vqp �Xnk¼1
akrkrm
~vqk ð8Þ
dneBdr3dneBdn2
Measuring Point
dneBht4dneBts1
Fig. 1 Schematic diagram of the pipe loop with four 900 bends
Physical Characteristics Description
Pipe loop length (m) 41.0
Diameter of the pipe D (m) 0.1
Total volume of water (m3) 0.322
No. of phases 6
VF of each secondary phases (ppm) 310×10−6
Pump True axial flow
Average water velocities (m/s) 0.05, 0.1, 0.2, 0.3, and 0.4
Particle density (kg/m3) 1,640
Particles sizes (μm) 2, 5, 10, 15, and 20
No of computational cells 129,654
Table 1 Physical and hydrauliccharacteristics of the systemused for CFD simulation
CFD Investigation of Particle Deposition 361
The basic assumption of the algebraic slip mixture modelis that, to prescribe an algebraic relation for the relativevelocity, a local equilibrium between the phases should bereached over short spatial length scales. The form of therelative velocity is given by
~vqp ¼ tqp~a ð9Þwhere ~a is the secondary phase particle’s acceleration andτqp is the particulate relaxation time. Following Manninenet al. [15], τqp is of the form:
tqp ¼rm � rp� �
d2p
18mqfdragð10Þ
where, dp is the diameter of the particles of secondary phasep, and the drag function (fdrag) is taken from Schiller andNaumann [17]:
fdrag ¼ 1þ 0:15Re0:687 Re � 10000:0183Re Re > 1000
�ð11Þ
The secondary phase particle’s acceleration,~a is given by,
~a ¼~g � ~vm � rð Þ~vm � @~vm@t
ð12Þ
The simplest algebraic slip formulation is the so-calleddrift flux model, in which the acceleration of the particle isgiven by gravity and/or a centrifugal force and theparticulate relaxation time is modified to take into accountthe presence of other particles.
3.1.3 Volume Fraction Equation for the Secondary Phases
From the continuity equation for secondary phase p, thevolume fraction equation for secondary phase p can beobtained as:
@
@taprp� �
þr � aprp~vm� �
¼ �r � aprp~vdr;p� �
ð13Þ
The volume fraction of phase “p” can be defined as:αp=volume of phase “p” in a cell/volume of all the
phase in a cell
3.1.4 Computational Cells, Model Boundary, and InitialConditions Used
The geometry and boundary conditions used in thepresent study are same as that of experimental study byGrainger et al. [8] detailed in Fig. 1, Table 1. Gridindependency tests were carried out and 129,654 un-structured cells (mostly hexahedral) were found toprovide grid independency result. The pump was mod-eled as a group of cells with fixed axial velocities equalto average water velocities given in Table 1. The standardlog-law-of-the-wall was employed at the solid walls. Thesolution domain was initialized with the volume fractionof 310 (ppm; Table 1) for each of the secondary phases.The transient simulations were carried out for five differentaverage water velocities (Table 1) until the normalizedresiduals of every equation solved were reduced to 1.0×10−4 or below.
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Fig. 2 Comparison of CFD results and experimental data [8] for thevelocity 0.4 m/s at center of the pipe
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at 0.05 mat 0.10 mat 0.20 mat 0.30 mat 0.40 mat 0.50 mat 0.60 mat 0.70 mat 0.80 mat 0.90 mat 0.95 m
y
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Fig. 4 Particle volume fraction as function of velocity at differentheights across the pipe at the measuring plane
362 A. Hossain et al.
4 Result and Discussion
Model Validation The results of CFD simulations havebeen validated against the experimental investigationsconducted by Grainger et al. [8]. At CommonwealthScientific and Industrial Research Organisation (CSIRO)Grainger et al. [8] demonstrated an experiment for particledistribution and deposition in a test loop. To compare withthe aforementioned experimental results, we have used thesame geometry and boundary conditions (Table 1). Figure 2represents the summation of volume fractions of allparticles as a function of height across the pipe at certainlocation in the loop. Figure 2 does not show a greatagreement between experimental and CFD results. Never-theless, the trend is similar, the experimental results showlower volume fraction. This may be due to the short-comings of the measuring instruments which were used forthe experiment. Grainger et al. [8] reported that particlelarger than 20 μm could not be detected by the instrumentsalthough particle distribution showed that some particleslarger than 20 μm were introduced. These larger particles
which tend to settle quickly at the bottom were not countedfor during the experiment. This may be the cause of muchlower volume fraction at the very bottom. However, inother depths (other than bottom) experimental results showsmarginally lower volume fraction than that of CFD resultsas shown in Fig. 2. As explained below, this discrepancymay be attributed to the assumptions of constant densityand spherical shape of the particles and also one of theshortcomings of the numerical model used in this studylike: particle resuspension is not accurately captured.
Figure 3 shows the particle volume fraction for bothCFD and experimental results as a function of velocity atthe center of vertical cross-section plane at measuring point(Fig. 1). The experimental results show lower particlevolume fraction than that of CFD. This difference is morepronounced for lower velocity. This happens because ofparticle introduced into the experimental system were notspherical nor had uniform size and density. In the CFDmodel, a particle density of 1.64 g/cc was considered;however, during experiment, it was not possible to strictlymaintain it at that value [8]. Due to diversity of particle
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(a)Fig. 5 a Relative volumefraction of particles for differentdepths along the pipe at0.05 m/s. b Relative volumefraction of particles for differentdepths along the pipe at 0.4 m/s
CFD Investigation of Particle Deposition 363
diameters, particle deposition is not linear with fluid flowfor experimental results. At lower velocity, only lighterparticles (sometimes even lighter than water, [8]) werefound suspended in the central region. However, for thehigher velocity the larger and heavier (than water) particlesget resuspended and can be found in the central region,which causes particle concentration closer to the CFDresults.
Spatial Distribution of Particle Volume Fraction as aFunction of Velocity Figure 4 shows the particle volumefraction variation at different depths of the pipe as a
function of velocity. Above y=0.4D (D, diameter of thepipe) the volume fraction increases as the velocity increaseswhereas volume fraction below y=0.4D decreases forhigher velocity. This is because higher velocity is associ-ated with higher turbulence causing particle resuspensionand more uniform distribution leading to increased volumefraction near the top and decreased volume fraction belowy=0.4D. As obvious, this difference in concentrationsbetween top and bottom regions is more pronounced atlower velocity.
Figure 5a,b show the relative volume fraction plottedalong the pipe for different height of 0.25D, 0.5D, 0.75D,
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Fig. 6 a Total particle deposition as a function of circumferential pipeangles at up- and downstream of bends at 0.05 m/s. b Total particledeposition as a function of circumferential pipe angles at up- anddownstream of bends at 0.1 m/s. c Total particle deposition as afunction of circumferential pipe angles at up- and downstream of
bends at 0.2 m/s. d Total particle deposition as a function ofcircumferential pipe angles at up- and downstream of bends at0.3 m/s. e Total particle deposition as a function of circumferentialpipe angles at up- and downstream of bends at 0.4 m/s
364 A. Hossain et al.
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up- and downstream of bend for different particle sizes at 0.2 m/s. dParticle deposition as a function of circumferential pipe angles at the up-and downstream of bend for different particle sizes at 0.3 m/s/. eParticle deposition as a function of circumferential pipe angles at the up-and downstream of bend for different particle sizes at 0.4 m/s
CFD Investigation of Particle Deposition 365
and 1D from the bottom wall of the pipe. Relative volumefraction is a dimensionless parameter, which represents theratio of local particle volume fraction to that at the bottom(y=0) of the pipe wall. Figure 5a,b show more homoge-neous distribution of particles at different depths in thebend region. This is due to high steam line curvature andassociated centrifugal force. The fluid at different depthsgets well mixed resulting in homogeneous distribution ofparticles. Downstream of the bend, the streamline curvatureand associated centrifugal force disappears and particlesstart to segregate to different concentration at differentdepths. This segregation or stratification is more pro-nounced at lower velocity. At higher velocity, the particlesdo not get enough time to segregate before they reach thenext bend. Higher turbulence at higher velocity alsocontributes to homogeneity of the particles.
Circumferential Distribution of Particle Volume Fraction asa Function of Velocity Local deposition along the pipecircumference was also obtained from the simulations.Figure 6a–e show circumferential distributions of summa-tion of near-wall volume fractions of all particles for thevelocities range of 0.05–0.40 m/s. The angle 0° starts atthe top wall and angle 1800 is the bottom wall of the pipe.The location upstream of the bend is defined as the cross-section of the pipe where the bend curvature starts. Thelocation downstream of the bend is defined as the cross-
section of the pipe where the bend curvature ends. Theprofiles, upstream of the bend, exhibit a smooth variationwith the maximum deposition at the bottom of the pipe.Similar trends were observed near the upstream of thebends in the experimental data of Anderson and Russell[2] and the analytical results of Mols and Oliemans [16]and Laurinat et al. [12]. The peak deposition at the bottomwall is high when the velocity is low. This can be easilyexplained, particles disperse at higher velocity and hencecan be found with higher concentration across the cross-section of the pipe due to high turbulence [12, 16].However, the circumferential profiles of the particlevolume fraction downstream the bends (Fig. 6a–e) arenot symmetric with respect to the pipe vertical symmetryplane. This is due to particle dispersion imposed by thepipe bends, and this phenomena is absent in straight pipeflows [10, 12, 16]. Figure 6a–e show that the maximumparticles deposit at downstream of the bends, at 60°skewed locations from the bottom and towards inner sideof the bends. This skewness angle has a maximum value ata certain distance downstream the bend, and will decreaseto 0° further downstream. At downstream locations of thebend the maximum deposition does not occur at thebottom (180°) rather it occurs on the inner wall of thebend. The location of the peak deposition is situated atan angular displacement of 60° with respect to thebottom of the wall. The fluid is under centrifugal forceas it flows around the bend. Particles having higherspecific gravity get segregation and deposit in the bendregion. This deposition will be pronounced near the outerwall at the bend entry and near the inner wall at the bendexit. The higher particle concentration at the inner wallof the bend exit will contribute to relatively higherparticle concentration at the inner wall of the subsequentdownstream bend entry.
In Fig. 7a–e the near-wall volume fractions of differentsize particles are plotted as a function of circumferentialangles for upstream and downstream of third bend fordifferent velocities. For higher velocities, the particleresuspension increases; this results in less particles deposi-tion at the bottom wall. However, this resuspensiondepends on Reynold’s number; after a certain thresholdvalue, particle depositions are independent of velocity/Reynold’s number (Fig. 7d, e). The deposition which is stillobserved is due to centrifugal force at the bends. Thedeposition patterns (Fig. 7a–e) for different particle sizesinvestigated are similar to that shown in Fig. 6a–e, whichindicates that instead of particle sizes, fluid flow governsthe deposition and reentrainment of particles for the particlesizes investigated in this study. As expected, 20 μm particleshows relatively pronounced deposition at the bend entryand exit. This deposition trend of 20 μm particle reduceswith increasing velocity.
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4.00E-03
Vo
lum
e fr
acti
on
20 micron
15 micron
10 micron
5 micron
2 micron
00
180 0
2nd 3rd
1st 4th
Circumferencial pipe angle0 360330300270240210180150120906030
Circumferencial pipe angle0 360330300270240210180150120906030
(e)
Fig. 7 (continued)
366 A. Hossain et al.
5 Conclusion
In this paper, the influence of particle size and flow rate on theparticle-size distribution and deposition in a turbulent pipe(including bends) was investigated by means of CFDsimulations. The results of CFD simulations have beencompared with experimental data from CSIRO. A reasonablequalitative agreement between numerical simulation andexperimental results was found (Figs. 2 and 3). Relativevolume fractions at various velocities indicate that particlesare not evenly distributed around bends. The upstream anddownstream circumferential depositions at different bendswere presented. Near the bends, the maximum deposition ofparticles was not found at the bottom, rather it was skewedtowards the inner wall. This skewness angle depends on thedistance from the bend; it will be maximum at a certaindistance downstream the bend, and will decrease to 0° furtherdownstream. In absence of better experimental data, thedetailed comparison of CFD results was not possible. Furtherexperimental study is required to validate the differences incircumferential depositions around the downstream of bends.
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