Effects of Wall Roughness-Blog

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Numerical investigation into the effects of wall roughnesson a gasparticle flow in a 90 bend

Z.F. Tian a, K. Inthavong a, J.Y. Tu a,*, G.H. Yeoh b

a School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, P.O. Box 71, Bundoora Vic 3083, Australiab Australian Nuclear Science and Technology Organisation (ANSTO), PMB 1, Menai, NSW 2234, Australia

Received 29 November 2006; received in revised form 26 November 2007Available online 31 January 2008

Abstract

This paper presents a numerical study of a dilute gasparticle flow in a 90 bend by employing a Lagrangian particle-tracking modelcombined with a particlewall collision model and a stochastic wall roughness model. The major objective of this study was to investigatethe effects of wall roughness on the particle flow properties. The numerical simulation revealed that wall roughness significantly reducedthe particle free zone and smoothed the particle number density profiles by altering the particle rebounding behaviours. It was alsofound that wall roughness reduced the particle mean velocities and also increased the particle fluctuating velocities in both streamwiseand transverse directions. 2007 Elsevier Ltd. All rights reserved.

Keywords: Gasparticle flow; 90 bend; CFD; Particlewall collision; Wall roughness

1. Introduction

Gasparticle flows inside of pipe bends are found in manyengineering applications. Aircoal flows in coal combustionequipments, coal liquefactiongasification in pipe systems,gasparticle flows in turbo machinery, and contaminantparticle flows in ventilation ducts are some typical examples.With the significant advancement of computer speed andmemory, computational fluid dynamics (CFD) is becominga viable tool to provide detailed information of both gas andparticle phases in the components composing these systems.

For the CFD approach, the particlewall collisionmodel has an important influence on the prediction ofgasparticle flows, especially for relatively large particles[1]. Nevertheless, despite the experimental and computa-tional investigations reported in [18] and many others,the success in properly modelling the particlewall collisionprocess remains elusive due to its complex nature.

Among the parameters, such as the particle incidentvelocity, incident angle, diameter of particle and its mate-rial properties, the wall surface roughness is one of thephysical parameters that govern the particlewall collisionprocess and the wall collision frequency [5]. Sommerfeldand Huber [5] measured the gasparticle flows in a horizon-tal channel using particle-tracking velocimetry. They foundthat wall roughness considerably alters the particlerebound behaviour and on average causes a re-dispersionof the particle by reducing the gravitational settling.Another contribution to this work was the development

and validation of a stochastic wall roughness distributionmodel that takes into consideration the so-called shadoweffect for small particle incident angles. It was demon-strated that particles may not hit the lee side of a roughnessstructure when the absolute value of the negative inclina-tion angle jc

j becomes larger than the impact angle [5].

This results in a higher probability for the particle to hitthe luff side, effectively shifting the probability distributionfunction of the effective roughness angle towards positivevalues. Later, Kussin and Sommerfeld [6] conducteddetailed measurements of gasparticle horizontal channel

0017-9310/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2007.12.005

* Corresponding author. Tel.: +61 3 99256191; fax: +61 3 99256108.E-mail address: [email protected] (J.Y. Tu).

www.elsevier.com/locate/ijhmt

Available online at www.sciencedirect.com

International Journal of Heat and Mass Transfer 51 (2008) 12381250

Tian, Z. F., Inthavong, K., Tu, J. Y. and Yeoh, G. H. (2008). Numerical investigation into the effectsof wall roughness on a gas-particle flow in a 90-degree bend. International Journal of Heat andMass Transfer 51:1238-1250.
mailto:[email protected]:[email protected]


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flows using glass particles with diameters from 60 lm to1000 lm and two stainless steel walls with different degreesof wall roughness. It was found that irregular particlewallcollision due to the roughness enhances the transverse dis-persion of the particles across the channel and that the wallcollision frequency is increased due to a reduction in the

mean free path. The wall roughness was also found todecrease the particle mean velocity that is associated witha higher momentum loss in the particle phase while increas-ing both the streamwise and transverse fluctuating veloci-ties. The effects of wall roughness on particle velocities ina fully developed downward channel flow in air was exper-imentally investigated by Benson et al. [7], employing alaser Doppler anemometer (LDA) system. Similar to thestudies by Kussin and Sommerfeld [6], the wall roughnesswas found to substantially reduce the streamwise particlevelocities causing the particles to be uniformly distributedacross the channel after wall collision. The wall roughnessalso increases the particle fluctuating velocities by nearly100% near the channel centerplane. Using a stochastic wallroughness model similar to that of Sommerfeld and Huber[5], Squires and Simonin [8] numerically studied the particlephase properties in a gasparticle channel flow with threewall roughness angles, 0 (smooth wall), 2.5 and 5. Themost pronounced effect of wall roughness was found onthe wall-normal component of the particle velocity (thetransverse particle velocity). The streamwise particle veloc-ity variance was increased, while the transverse particlefluctuating velocity was less sensitive to the wall roughness.

The main focus of this paper is to numerically investigatethe effects of wall roughness on the particlewall collision

phenomenon and to extend these ideas to further character-

ize the particle phase flow in a 90 bend. Previously, Tu andFletcher [9] computed a gasparticle flow in a square-sec-tioned 90 bend via an EulerianEulerian model. Thistwo-fluid model, implemented the Re-Normalisation Group(RNG) ke model along with generalised wall boundaryconditions and a particlewall collision model to better rep-

resent the particlewall momentum transfer. Comparisonsof both gas and particle phase velocity computations againstLaser Doppler Anemometry (LDA) measurements ofKliafa and Holt [10] were reasonably good. However, theinherent weakness of the Eulerian formulation is its inabilityto capture the aerodynamic drag force on the particle phasein the vicinity of a wall surface. The incident and reflectedparticles during the process of a particlewall collision inthe Eulerian model is still far from adequate in terms of res-olution [11]. To overcome these difficulties, the Lagrangianparticle-tracking is thereby revisited to fundamentallydescribe the near-wall particle collision process.

The authors [12] used a Lagrangian particle-trackingmodel, which included the stochastic wall roughness modelof Sommerfeld [1], to numerically simulate a gasparticleflow over a tube bank. The predicted mean velocities andfluctuations for both gas and 93 lm particles were vali-dated against experimental data with good agreements.The numerical predictions revealed that the wall roughnesshas a considerable effect by altering the rebounding behav-iours of the large particles, consequently affecting the par-ticle motion downstream and shifting the particle collisionfrequency distribution on the tubes.

This study employed the Lagrangian model, whileincluding a particlewall collision model and a stochastic

wall roughness model [5] to study the effects of wall rough-

Nomenclature

a1, a2, a3 empirical const ants in Eq. (4)CD particle drag coefficientD width of the bend

dp particle diameteren mean normal restitution coefficientg gravitational accelerationri inner wall radiusro outer wall radiusr* non-dimensional wall distanceRe Reynolds numberRep relative Reynolds numberSt Stokes numbertp particle relaxation timets system response timeUb bulk velocityupn; v

pn particle normal incident velocity and normal re-

flected velocityu

pt ; v

pt particle tangential incident velocity and tangen-

tial reflected velocityVs characteristic velocity of the system

Greek symbols

l dynamic viscosityh,h0 the particle incident angle without and with

roughness effectq densityx,X particle annular velocity before and after colli-

sionf normally distributed random number

Subscripts

g gas phasen normal directiont tangential directionp particle phases system

Superscriptg gas phasep particle phase( )0 fluctuation

Z.F. Tian et al. / International Journal of Heat and Mass Transfer 51 (2008) 12381250 1239


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ness on the particle phase flow field in a two-dimensional90 bend. The aforementioned models were implementedinto the FLUENT code via user-defined subroutines.Using user-defined subroutines allows the flexibility inextending the collision model to handle complex engineer-ing flows. To gain confidence in this numerical study, the

predicted mean velocities for both gas phase and 50 lmparticles were validated against experimental data of Kliafaand Holt [10]. The Lagrangian model was used to investi-gate effects of wall roughness on the particle trajectories,particle number density distribution, particle mean veloci-ties and particle fluctuating velocities.

2. Computational method

2.1. Gas phase and particle phase modelling

The generic CFD commercial code, FLUENT [13], wasutilised to predict the continuum gas phase of the velocityprofiles under steady-state conditions. The air phase turbu-lence was handled by the RNG ke model [14].

A Lagrangian-formulated particle equation of motionwas solved with the trajectory of a discrete particle phasedetermined by integrating the force balance on the particle,which is written in a Lagrangian reference frame. Appro-priate forces such as the drag and gravitational forces areincorporated into the equation of motion. The equationcan be written as

dupdt

FDug up gqp qg

qp1

where u is the velocity, q is density, g is the gravitationalacceleration and the subscript g and p denote the gas andparticle phase parameters, respectively. FD(ug up) is thedrag force per unit particle mass, and FD is given by

FD 18lg

qpd2p

CDRep

242

where lg is gas phase dynamic viscosity. Rep is the relativeReynolds number defined as

Rep qpdpjup ugj

lg3

dp is the particle diameter. The drag coefficient CD is givenas

CD a1 a2

Rep

a3

Re2p4

where the as are empirical constants for smooth sphericalparticles over several ranges of particle Reynolds number[15]. By using stochastic tracking method as part of theEulerianLagrangian approach, FLUENT predicts the tur-bulent dispersion of particles by integrating the trajectoryequations for individual particles, using the instantaneousfluid velocity, ugi u

0it along the particle path during the

integration process. With this method, discrete random

walk or eddy lifetime model, is applied where the fluctu-ating velocity components, u0i that prevail during the life-time of the turbulent eddy are sampled by assuming thatthey obey a Gaussian probability distribution, so that

u0i n ffiffiffiffiffiffiu02iq 5

where n is a normally distributed random number, and theremaining right-hand side is the local root mean square(rms) velocity fluctuations that can be obtained (assumingisotropy) byffiffiffiffiffiffi

u02i

q

ffiffiffiffiffiffiffiffiffiffiffiffi2kg=3

q6

The interaction time between the particles and eddies is thesmaller of the eddy lifetime, se and the particle eddy cross-ing time, tcross. The characteristic lifetime of the eddy is de-fined as

se TL logr 7

where TL is the fluid Lagrangian integral time, TL % 0.15/x. The variable r is a uniform random number between 0and 1. The particle eddy crossing time is given by

tcross tp ln 1 Le

tp ugi u

pi

!" #

8

where tp is the particle relaxation time qsd2p=18qgvg, Le

is the eddy length scale, and jugi upi j is the magnitude of

the relative velocity. The particle interacts with the fluideddy over the interaction time. When the eddy lifetime isreached, a new value of the instantaneous velocity is ob-tained by applying a new value of n in Eq. (5).

The main focus of this paper is the effects of wall rough-ness on the particle phase flow field therefore, the volumefraction of particle phase was assumed to be very low(6106). According to Elghobashi [16], the particles donot influence the carrier phase when the particle phase vol-ume fraction is less than 106 and the flow is in the limit ofone-way coupling.

2.2. The particlewall collision model and wall roughness

model

The particlewall collision model of Sommerfeld and

Huber [5] was employed to account for the particlewallinteraction process. Fig. 1 illustrates the impact of a spher-

p

p

inu

p

nu

ptu

p

nvptv

p

rev n

p

Fig. 1. Particlewall collision configuration.

1240 Z.F. Tian et al. / International Journal of Heat and Mass Transfer 51 (2008) 12381250


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ical particle on a plane wall in two-dimensional form. Atthe end of contact with a wall, a particle is considered roll-ing when the following conditioned is satisfied:

upt dp

2xp

6

7

2ld1 enu

pn 9

The subscript n and t represents the normal and tangentialvelocity components, respectively. ld is the particle dy-namic friction coefficient, xp denotes the particle incidentangular velocity and en is the kinematic restitution coeffi-cient that can be expressed as

en vpn=u

pn 10

where upn is the normal incident velocity and vpn is the nor-

mal reflected velocity.Under conditions of rolling collision, the rebounding

velocity components are as follows:

vpt 1

75upt dpxp

vpn enupn

Xp 2v

pt

dp11

where Xp is particle rebound angular velocity.If Eq. (9) is not satisfied, the particle is then considered

to be sliding and the rebound velocity components aredefined as

vpt upt ld1 ene0u

pn

vpn enupn

Xp xp 5ld1 ene0 up

n

dp12

here e0 is the direction of the relative velocity between par-ticle surface and wall, obtained by

e0 sign upt

dp

2xp

13

The values for the restitution coefficient en and the dynamicfriction coefficient ld are obtained from experiments. Inthis study, en and ld were calculated based on the constantsof 100 lm glass particles impacting on a plexiglass surface[5]. The measured restitution coefficient en was measured

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

Incident Angle (degree)

Restitutio

nCoefficient

100 m glass particles/plexiglass wall

Fig. 2. Restitution coefficient of 100 lm glass particles collision onplexiglass wall [5].

1m

Line A(y=0.276m)

1.2m

Line B(x=1.1m)

(0m, 0m)

=0

Outlet

=90(Bend exit)

=30

0.1m

ro=0.226m

ri=0.126mio

i

rr

rrr

=*

=60

Inlet

(1.426m, 1.226m)

Fig. 3. Computational domain and grids of a two-dimensional 90 bend.



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for incident angles up to 40, thus values of en above 40were assumed to have the same value as en at 40. Fig. 2gives the restitution coefficient en of 100 lm glass particlescollision on plexiglass wall used in this study. The dynamicfriction coefficient ld was 0.15.

A stochastic approach has been developed by Sommer-

feld [1] to take into consideration the wall roughness effect.Here, the incident angle a01 comprises of the particle inci-dent angle a1 and a stochastic contribution due to the wallroughness, viz.

a01 a1 Dcn 14

From the above, n is a Gaussian random variable withmean of 0 and a standard deviation of 1. The value of Dcis determined through experiments.

When the absolute value of the negative Dcn is largerthan the incident angle, particles may not impact on thelee side of a roughness structure. This phenomenon is

known as the shadow which leads to a higher probabilityof particles colliding on the luff side, causing a shift ofthe probability distribution function ofDcn towards posi-

tive values. The method proposed by Sommerfeld andHuber [5] is implemented in this study to handle the sha-dow effect. This procedure allows for the positive shift ofthe distribution function ofDcn thus avoiding the unphys-ical situation where particles hit the roughness structurewith a negative angle. In this study, the wall roughness

angles of 0, 2.5 and 5 was used. More details aboutthe wall roughness model can be found in Sommerfeldand Huber [5].

2.3. Numerical procedure

The non-equilibrium wall function was employed for thegas phase flow because of its capability to better handlecomplex flows where the mean flow and turbulence are sub-jected to severe pressure gradients and rapid change, such asseparation, reattachment and impingement. The governingtransport equations were discretised using the finite-volume

approach and the QUICK scheme was used to approximatethe convective terms while the second-order accurate centraldifference scheme is adopted for the diffusion terms. The

0

0.2

0.4

0.6

0.8

1

r

*

0 1.5

=0 =15 =300 0 0

ug/ub

0

0.2

0.4

0.6

0.8

1

r*

0 1.5up/ub

=0 =15 =300 0 0

a

b

Fig. 4. Comparison between the experimental data and numerical simulation: (a) gas phase streamwise velocity, (b) particle phase streamwise velocity

(Ub = 52.19 m/s, 50 lm particle). Circles: experimental data, line: prediction.



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Fig. 5. Computed trajectories for 100 lm particles released at (1.376,0.16) with different wall roughness angle: (a) 0, (b) 2.5 and (c) 5.M represents thelength of the second collision region (Ub = 10 m/s, Re = 6.65 10

4).



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pressurevelocity coupling was realized through the SIM-PLE method and the convergence criteria for the gas phase

properties were assumed to have been met when the itera-tion residuals had reduced by five orders of magnitude.

Fig. 6. Computed trajectories for particles released at 1D before the bend with different wall roughness angle: (a) 0, (b) 2.5 and (c) 5 (Ub = 10 m/s,

Re = 6.65 104).



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The governing equations for the gas phase were initiallysolved towards steady state. The Lagrangian solution forthe particle phase was thereafter achieved by the injectionof particles into the bulk gas flow where the trajectoriesof each particle were determined from the steady-stategas phase results. For gasparticle flows in bends, the sec-

ondary flow and side walls may impose significant influenceon particle phase properties such as the particle numberdensity (particle concentration) distribution, particle meanvelocities and particle fluctuating velocity. In order to ana-lyze the effect of the wall roughness on particle phase fieldindependent of the effects from the secondary flow and sidewall, the current study was simulated in a two-dimensionalbend. For the same reason of simplicity, particles wereassumed to be spherical and mono-sized.

3. Results and discussion

Fig. 3 shows the computational domain where the inletbegins 1 m upstream from the bend entrance and extends1.2 m downstream from the bend exit. The bend has aninner radius (ri) of 0. 126 m and an outer radius (ro) of0.226 m for the outer wall. The results were plotted againsta non-dimensional wall distance r rri

rori. Within the 1 m

long channel before the bend, 380 (in the streamwise direc-tion) 58 (in the transverse direction) grid points havebeen allocated. In the bend, the mesh is with 168 gridpoints in the streamwise direction and 58 grid points in

the transverse direction. The 1.2 m long channel after thebend has a 450 (in the streamwise direction) 58 (in thelateral direction) grid mesh. Grid independence waschecked by refining the mesh system by a mesh density of1122 (in the streamwise direction) 68 (in the transversedirection) grid points. Simulations of 10 m/s case revealed

that the difference of the velocity profile between the twomesh schemes at h = 0 is less than 3%. The coarser meshwas therefore applied in order to embrace the increase ofcomputational efficiency towards achieving the finalresults. Part of the mesh of 998 58 grid mesh is illustratedin Fig. 3.

To gain confidence in this computational study, experi-mental measurements for a gasparticle flow with the samebend configuration as this study but three-dimensional [10]was used to validate the simulations. In this validationcase, the gas phase bulk velocity was 52.19 m/s correspond-ing to the Reynolds number of 3.47 105 (based on thebend width of 0.1 m). A total of 100,000 glass particles

(material density 2990 kg/m3) with a diameter of 50 lmwere released from 100 uniformly distributed points acrossthe inlet surface, were individually tracked within the com-putational domain. The particle inlet velocity for this vali-dation case was 52.19 m/s. The restitution coefficient en ofthe glass particle collision on the plexiglass surface [5] wasused and the wall roughness degree was 3.8.

Fig. 4a shows the comparison between the measuredand predicted streamwise gas velocities normalised by the

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3

Normalised particle number density

r*

a

= 30

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3


r*

b

= 60

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3


r*

c

= 90

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3


r*

d

Line B

Fig. 7. Computed particle number concentration with different wall roughness angles: (a) at h = 30, (b) at h = 60, (c) at h = 90, (d) at Line B. Circles: 0

roughness, line: 2.5 roughness, solid triangle: 5 roughness (Ub = 10 m/s, Re = 6.65 104).



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bulk velocity at h = 0, 15 and 30 angles within the bendsection. The numerical simulation successfully predictedthe flow acceleration of the gas phase near the inner wallregion (r* $ 0). In the region near the outer wall (r* $ 1),the fluid deceleration caused by the unfavorable pressuregradient was also captured. The predicted gas phase veloc-

ity is in good agreement with the measurement (within10%) except for an under prediction of up to (35%)observed in the outer wall region at h = 30. Fig. 4b pre-sents the normalised velocity profile of 50 lm particles ath = 0, 15 and 30 stations. The predictions and measure-ments showed good agreement (within 10 %) while there isan under-prediction of up to 20% in the outer wall regionat h = 30.

To investigate the effects of wall roughness on the parti-cle phase flow field in the bend, glass particles with corre-sponding diameters of 100 lm were simulated under theflow condition of 10 m/s. The corresponding Reynoldsnumber based on the bend width of 0.1 m was 6.65

104. Note that the flow condition now uses an inlet velocity

of 10 m/s which is more likely to be found in real engineer-ing applications.

3.1. Effects of wall roughness on particle trajectories

The influence of wall roughness on the particle trajecto-

ries was firstly investigated by tracking 25 particles releasedfrom a point location at (1.376,0.13). For qualitative pur-poses only a small number of particles are used as thisallows particle-tracking to be performed graphically with-out smearing of the results due to the overloading of linesassociated with a large number of particles being graphi-cally tracked. Fig. 5a illustrates the particle trajectorieswith 0 wall roughness angle. All the particles reboundingfrom the first collision followed very similar trajectorieswhich consequently produced a narrow secondary collisionzone. The center of this secondary collision zone is locatedabout 0.3D after the bend (x = 1.17 m). When the wallroughness angle was increased, the behaviours of particleswere markedly different. The particles were observed to

0.0

0.2

0.4

0.6

0.8

1.0

r*

0 1up/ub

=30 =450 0 0 =60

5

2.5

0

0.0

0.2

0.4

0.6

0.8

1.0

r*

0 1up/ub

=75 =900 0 0 Line B

a

b

Fig. 8. Comparison of particle streamwise mean velocity profiles with different roughness angles at different locations.M The length of the particle free

zone. Circles: 0 roughness, line: 2.5 roughness, solid triangle: 5 roughness (Ub = 10 m/s, Re = 6.65 104).



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rebound in many directions caused by an increase in therandomness from the rebounding of a rougher wall surface.A wider dispersion of particles was observed, leading to asignificant increase in the second collision zone length.An increase of almost 4 times for the case of a 2.5 rough-ness angle was found in Fig. 5b, while an increase of 10

times was found for 5 roughness angle in Fig. 5c. A closerinvestigation for the 5 roughness angle, revealed that thesecondary collision zone contained more particles impact-ing to the left of x = 1.17 m, which is the secondary colli-sion zone location for 0 roughness. It should be notedthat there exists a significant contribution from the parti-cles inertia on the particle trajectory after the first collision.The increase in wall roughness causes a wider re-dispersionof particles, and thus this new trajectory, coupled with ahigh inertia results in the negligible influences from thebulk fluid. This allows the particles to travel further tothe left, causing a wider secondary collision zone.

In Fig. 5a, the small deviation of particle trajectories after

the first collision is attributed to the gas phase turbulence.For gasparticle flows, the dimensionless Stokes number,St = tp/ts, represents an important criteria towards betterunderstanding the state of the particles in determiningwhether they are in kinetic equilibrium with the surroundinggas or not. The system relaxation time ts in the Stokes num-ber is determined from the characteristic length (Ls = D =0.1 m) and the characteristic velocity (Ub = 10 m/s) for thesystem under investigation, i.e. ts = Ls/Ub. For the case of100 lm particle, the Stokes number is equal to 9, muchgreater than unity. Therefore, the influence from the gas

phase turbulence on the 100 lm particle trajectories is neg-ligible in comparison with the influence from the wall rough-ness as shown in Fig. 5b and c.

To further investigate the effects of wall roughness onthe particle trajectories, 58 particles with streamwise veloc-ity of 10 m/s were released from Line A as shown in Fig. 3

(y = 0.276 m), which is located 1D upstream from the bendentrance. Fig. 6ac shows the particle trajectories in thebend for different wall roughness angles, i.e., 0, 2.5 and5, respectively. With the increase of the wall roughnessangle, the particle free zone occurring at the inner wallregion is reduced as the wall roughness increases. For the5 case, particles were found to disperse further intothe upper region of the channel after the bend, followingthe first collision. This same region is observed to be aparticle free zone for the 0 case.

3.2. Effects of wall roughness on particle number density

To investigate the influence of wall roughness on theparticle dispersion, the particle number density distributiontaken along different sections around the bend is used. Toobtain statistically meaningful results a larger number ofparticles is now used where 100,000 mono-sized particles(100 lm) with streamwise velocity of 10 m/s were releasedfrom 100 uniformly distributed points across Line A. Theindependence of statistical particle phase prediction fromthe increase of the number of particles used was tested byimplementing 50,000, 100,000 and 200,000 particles. Thedifference of the particle phase velocities at h = 0 of

0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8

Vp/Ub (at 30-degree)

r*

a

0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8


r*

b

0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8


r*

c

0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8


r*

d

Fig. 9. Comparison of particle transverse mean velocity profiles with different roughness angles at different locations. Circles: 0 roughness, line: 2.5

roughness, solid triangle: 5 roughness (Ub = 10 m/s, Re = 6.65 104).



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50,000 and 100,000 particles was less than 3% and for100,000200,000 was less than 1%, thus in terms of compu-tational efficiency 100,000 particles was used hereafter.

The particle number density normalised by the numberof inlet particles, 100,000 at h = 30 with different wallroughness angles, are presented in Fig. 7a. The particle dis-

tribution profiles in this case for the three wall roughnessangles are very similar. A much higher particle numberdensity for all roughness angles is found near the outer wallregion and this phenomenon is consistent with the observa-tions from the experimental study of [10] and the EulerianEulerian simulation of [9]. With the turning of the bendfrom h = 30 to h = 60 the trend for particle number den-sity sees an increase in the outer region from r* = 0.65 tor* = 0.9 for all wall roughness angles and a decrease inthe region from r* = 0.4 to r* = 0.45 for roughness angleof 5. No particles are found in the inner wall region (fromr* = 0 to r* = 0.4). This is due to the high inertia of 100 lmparticles, which causes particles to respond slowly to the

local gas phase changes. At h = 60, an interesting phe-nomenon is found for the 0 wall roughness case where

two local maximus for particle number density areobserved at the region at r* = 0.75 and in the outer wallregion. The prediction of high particle number density inthe middle bend region was not found either in the exper-imental study of [10] or in the EulerianEulerian simula-tion of [9]. This non-physical phenomenon is remedied

when the wall roughness is taken into consideration. Thehigh particle number density at r* = 0.75 is reduced dra-matically when the wall roughness was increased to 2.5.A further increase to 5, showed a smoother particle num-ber density profile, suggesting a greater dispersion of parti-cles being distributed over a greater area within the bend.This leads to a significant decrease in the particle freezone. However, the total number of particles in the regionfrom r* = 0.4 to r* = 0.55 is about 2000 which accounts for2% of the total particles tracked whereas high particle num-ber densities are found in the region next to the outer wallfor all roughness angles. A similar phenomenon is found ath = 90, the high particle number density at r* = 0.6 is

found in the 0 wall roughness case. With the increase ofwall roughness angles, the high particle density at this

0.0

0.2

0.4

0.6

0.8

1.0

r*

0 0.25u'p/ub

=30 =450 0 0 =60

0.0

0.2

0.4

0.6

0.8

1.0

r*

0 0.25u'p/ub

=75 =900 0 0 Line B

a

b

Fig. 10. Comparison of particle streamwise rms fluctuation velocity profiles with different roughness angles at different locations. Circles: 0 roughness,

line: 2.5 roughness, solid triangle: 5 roughness (Ub = 10 m/s, Re = 6.65 104).



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region is dramatically reduced. Fig. 7d shows the particledistribution profiles at Line B, 1D after the exit. It is seenthat the wall roughness structure enhances the re-disper-sion of particles after the first collision leading to thesmoother particle number density profile. Additionally,the particle free zone was reduced with an increase in

the wall roughness and relatively low particle number den-sities were observed in the region from r* = 0.25 tor* = 0.32.

3.3. Effects of wall roughness on particle mean velocities

The effects of wall roughness on particle mean velocitiesat different locations in the bend are shown in Fig. 8. Ath = 30, the streamwise velocity of 5 roughness is slightlysmaller than the 0 case at the outer wall region fromr* = 0.85 to r* = 0.92. This is the consequence of particleshaving collided on the outer wall before 30 and the lossof momentum which is greater for walls with a higher

roughness. However, the particle streamwise velocity pro-files for the rest of the region is almost identical for all wallroughness, since this region is still in the early stages of thebend and particle collision has not occurred. After h = 60,however, the bend curvature is much greater and most par-ticles have experienced the first wall collision resulting in areduction in the mean streamwise velocities due to the aver-age increase in momentum loss. This can be seen in the com-parison of velocity profiles for at h = 0 to at h = 60 whichhas shifted to the left. For bend angles, h > 60 the meanvelocity profiles for 0 wall roughness exhibit larger magni-tudes than for 2.5 and 5 wall roughness. The higher wall

roughness causes the particles to lose more of its momen-

tum whilst dispersing the particles in greater directions,hence the wider velocity profile, reaching to r* = 0.2 (fromthe outer wall r* = 1) for 5 roughness, compared withr* = 0.4 for 0 roughness at Line B.

Fig. 9 shows the particle mean transverse velocities atdifferent locations. At h = 30, the velocity profiles for dif-

ferent wall roughness angles are almost identical except forthe region from r* = 0.85 to r* = 0.92. At h = 45, thevelocity profile for 5 roughness is much smaller than the0 roughness profile at the region from r* = 0.62 tor* = 0.79. At h = 75, the mean transverse velocities of2.5 and 5 roughness are identical and slightly smallerthan the smooth wall case. This can be attributed to theearly collision occurring before h = 45. The reduction ofthis particle mean velocity is consistent with observationsthat wall roughness reduces the mean particle velocitiesas obtained by Kussin and Sommerfeld [6] and Bensonet al. [7].

3.4. Effects of wall roughness on particle rms fluctuation

velocities

Fig. 10 illustrates the distribution of the particle stream-wise rms fluctuating velocities for 0, 2.5 and 5 roughnessangles at various locations. As shown in Fig. 10a, the par-ticle rms fluctuation velocity at h = 30 for all three rough-ness angles yielded almost zero turbulence intensities fromr* = 0.2 to r* = 0.62. This is attributed to the fact that par-ticle rms fluctuating velocity is zero at the inlet (Line A)and most particles flowing through this region have notcollided with the bend yet. Considerably higher particle

velocity fluctuations were found in the region near the

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

V'p/Ub (at 60-degree)

r*

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5


r*

ba

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5


r*

c

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

V'p/Ub (at Line B)

r*

d

Fig. 11. Comparison of particle transverse rms fluctuation velocity profiles with different roughness angles at different locations. Circles: 0 roughness,

line: 2.5 roughness, solid triangle: 5 roughness (Ub = 10 m/s, Re = 6.65 104).



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outer wall to r* = 0.62 which is a result of the particle col-lisions at outer wall. Also, the particle streamwise rms fluc-tuation velocities of 2.5 and 5 roughness angles are higherthan the 0 case, since the wall roughness model enhancesthe randomness for particle velocities and trajectories aftercollision. At h = 45, the particle streamwise rms fluctua-

tion velocities of 2.5 and 5 roughness angles are higherthan the 0 case from r* = 0.5 to r* = 0.9.The particle transverse rms fluctuation velocities with

different wall roughness angles are shown in Fig. 11. Aninteresting phenomenon can be seen at h = 60 where thetransverse rms fluctuation velocities for all wall roughnesscases are high. This is due to the dominant particle collisionwhich produces a particle rebound velocity that is slightlysmaller than the incident velocity due to the momentumlost during the collision process. At h = 90, the particletransverse rms fluctuation velocities of 2.5 and 5 rough-ness angles are higher than the smooth wall case. Figs. 10and 11 clearly indicate that the wall roughness has a signif-

icant influence on the particle velocity fluctuations.

4. Conclusion and future work

The physical behaviours of a dilute gasparticle flow in a90 bend were numerically investigated via a Lagrangianparticle-tracking model. A particlewall collision modeland a stochastic model [5] were adopted to take into con-sideration the particlewall collision and wall roughnesseffect. Good agreements were achieved between the predic-tions of mean velocity for gas phase and 50 lm particlesand experimental data of [10].

A substantial amount of work was taken in this study toelucidate further the understanding of the effect of wallroughness on the flow field of large particles (100 lm). Itwas found that the wall roughness considerably alteredthe rebounding behaviours of particles by significantlyreducing the particle free zone and smoothing the particlenumber density profiles. The effects of wall roughness onthe particle mean and fluctuating velocities were also inves-tigated. The numerical results confirmed that the particlemean velocities for 2.5 and 5 roughness angles werereduced due to the wall roughness which, on averageincreases the momentum loss for the particle phase. Also,the particle fluctuating velocities were increased when tak-ing into consideration the wall roughness, since the wallroughness produced greater randomness in the particlerebound velocities and trajectories.

These numerical results suggest that the effect of wallroughness is not negligible for large particles in confinedflow geometries such as a 90 bend. Moreover, the parti-clewall collision model should account for the effect ofwall roughness in order to provide a more realistic descrip-

tion of the particlewall collision phenomenon. This workwill also be beneficial to the understanding and the accu-rate prediction of gasparticle flows as well as furtheringthe understanding of the erosion distribution in 90 bends.

Work is in progress to investigate the effects of wallroughness on the particle flow field in three-dimensional

bend flows. Additionally, the gasparticle flows investi-gated in this study were very dilute and particles were uni-model in size (monodisperse). Therefore, future work is stillrequired to assess the effects of wall roughness for denseparticle flows and polydisperse particles.

Acknowledgement

The financial support provided by the Australian Re-search Council (project ID LP0347399) is gratefullyacknowledged.

References

[1] M. Sommerfeld, Modelling of particlewall collisions in confined gasparticle flows, Int. J. Multiphase Flow 18 (6) (1992) 905926.

[2] S. Matsumoto, S. Saito, Monte Carlo simulation of horizontalpneumatic conveying based on the rough wall model, J. Chem. Eng.Jpn. 3 (1970) 223230.

[3] G. Grant, W. Tabakoff, Erosion prediction in turbomachineryresulting from environmental solid particles, J. Aircraft 12 (5)(1975) 471478.

[4] R.M. Brach, P.F. Dunn, Models of rebound and capture for obliquemicroparticle impact, Aerosol Sci. Technol. 29 (1998) 379388.

[5] M. Sommerfeld, N. Huber, Experimental analysis and modelling ofparticlewall collisions, Int. J. Multiphase Flow 25 (1999) 14571489.

[6] J. Kussin, M. Sommerfeld, Experimental studies on particle behav-iour and turbulence modification in horizontal channel flow withdifferent wall roughness, Exp. Fluids 33 (2002) 143159.

[7] M. Benson, T. Tanaka, J.K. Eaton, Effects of wall roughness onparticle velocities in a turbulent channel flow, J. Fluids Eng. 127(2005) 250256.

[8] K.D. Squires, O. Simonin, LES-DPS of the effect of wall roughnesson dispersed phase transport in particle-laden turbulent channel flow,Int. J. Heat Fluid Flow 27 (2006) 619629.

[9] J.Y. Tu, C.A.J. Fletcher, Numerical computation of turbulent gassolid particle flow in a 90 bend, AICHE J. 41 (1995) 21872197.

[10] Y. Kliafa, M. Holt, LDV measurements of a turbulent airsolid two-phase flow in a 90 bend, Exp. Fluids 5 (1987) 7385.

[11] Z.F. Tian, J.Y. Tu, G.H. Yeoh, Numerical simulation and validationof dilute gasparticle flow over a backward-facing step, Aerosol Sci.Technol. 39 (2005) 319332.

[12] Z.F. Tian, J.Y. Tu, G.H. Yeoh, Numerical modelling and validationof gasparticle flow in an in-line tube bank, Comput. Chem. Eng. 31(2007) 10641072.

[13] Fluent Users Guide, Version 6.2., 2005 (Chapters 11 and 23).[14] V. Yakhot, S.A. Orszag, Renormalization group analysis of turbu-

lence: I. Basic theory, J. Sci. Comput. 1 (1986) 351.[15] S.A. Morsi, A.J. Alexander, Investigation of particle trajectories in

2-phase flow systems, J. Fluid Mech. 55 (1975) 193208.[16] S. Elghobashi, On the predicting particle-laden turbulent flows, Appl.

Sci. Res. 52 (1994) 309329.


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