investigation of particle deposition and dispersion...

Scientia Iranica B (2018) 25(6), 3173{3182

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringhttp://scientiairanica.sharif.edu

Investigation of particle deposition and dispersion usinghybrid LES/RANS model based on lattice Boltzmannmethod

H. Sajjadia;�, M. Salmanzadehb, G. Ahmadic, and S. Jafarid

a. Department of Mechanical Engineering, Faculty of Engineering, University of Bojnord, Bojnord, P.O. Box 94531-55111, Iran.b. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.c. Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, USA.d. Department of Petroleum Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.

Received 17 February 2018; received in revised form 10 March 2018; accepted 21 July 2018

KEYWORDSHybrid RANS/LES;LBM;Particle deposition;Particle dispersion.

Abstract. In this study, a new hybrid RANS/LES turbulence model within the frameworkof the Multi Relaxation Time (MRT) Lattice Boltzmann Method (LBM) was used to studyparticle dispersion and deposition in a room. For the hybrid RANS/LES method, the near-wall region was simulated by the RANS model, while the rest of the domain was analyzedusing the LES model within the framework of the LBM. In the near-wall layer where RANSwas used, the k � " turbulence model was employed. To simulate the particle dispersionand deposition in the room, particles with diameters of 10 nm to 10 �m were investigated.The simulated results for particle dispersion and deposition showed that the predictionsof the present hybrid method were quite similar to those of earlier LES-LBM. In addition,the predictions of the hybrid model for the particle deposition and dispersion were closerto LES simulation results, as compared to those of the k � " model.

© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

It is well known that people spend more than 85% oftheir time indoors, and most of their exposure to en-vironmental pollutants occurs by breathing the indoorair. Therefore, Indoor Air Quality (IAQ) has receivedincreasing attention in recent years as an importantpublic health issue. In the last decade, ComputationalFluid Dynamics (CFD) has become a powerful tool forstudying IAQ under various conditions [1-4].

*. Corresponding author. Fax: +98 5832410700E-mail addresses: [email protected] (H. Sajjadi);[email protected] (M. Salmanzadeh);[email protected] (G. Ahmadi);[email protected] (S. Ja�ari)

doi: 10.24200/sci.2018.20723

The Lattice Boltzmann Method (LBM) is a rel-atively new, e�cient, and convenient computationalmodel that has increasingly attracted the attention ofresearchers in di�erent areas. The LBM has been usedto simulate turbulent ows, multi-phase ows, singleand multiphase ows in porous media, and particulatesuspensions in the past two decades [5,6]. The mostwidely used method for simulating indoor air ows isto solve the Reynolds-Averaged Navier-Stokes (RANS)equation in conjunction with the use of a turbulencemodel. Among various RANS turbulence models, thetwo-equation k � " model is the most popular one.The RANS model, however, simulates the mean owvelocity and mean-square uctuation �elds; however,it cannot predict the uctuating velocity �eld [7].

For using the k � " model in the framework ofLBM, two approaches have been used. In most earlier

3174 H. Sajjadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 3173{3182

works, a separate �nite di�erence grid is created tosolve the k � " (or other) transport equations and,then, return the calculated values into the LBM frame-work for evaluating the eddy viscosity and turbulentstresses [8,9]. Recently, a new method has beensuggested in [10-12] that introduces two additionalpopulations for k and " and solves the k � " equationswithin the LBM with no need for a new grid.

The Large Eddy Simulation (LES) is run for thelarge eddies, and it only models the uctuations thatare smaller than the grid size. The LES approachtypically provides more accurate results for air owmodeling than the RANS models do, and it alsoprovides the turbulent uctuation velocity that is largerthan the grid size. Due to these advantages, the use ofLES model for simulating indoor air ows has markedlyincreased in the last decade [13-15]. The LES modelin framework of LBM was also used to investigateturbulent ows for di�erent applications [16,17]. Themajor di�culty with using LES for simulating theindoor air ow is that resolving the problem of near-wall ows requires a very �ne grid to capture large eddies,which increase the computation cost signi�cantly [18].

As noted earlier, while the LES model leads toaccurate results, the required computation times arequite high. The RANS model, however, does notprovide information on the instantaneous uctuationvelocity �eld. To overcome the disadvantages of LESand RANS, the hybrid RANS/LES concept was intro-duced to simulate ow in the past decade [19,20]. Thebasic idea of the hybrid model is to use the LES modelin the bulk of the domain, while the RANS model isused to simulate the near-wall regions to avoid the needfor a very high-resolution grid. For the RANS region,di�erent models, such as k�", k�!, Spalart-Allmaras(SA), and v2f models, were used [21,22]. Recently,Sajjadi et al. [18] developed the hybrid RANS/LESmodel within the LBM framework to solve the problemof turbulent ows in the indoor environment, wherethe k � "-LBM and LES-LBM models were used.They concluded that the computation cost of usingthe hybrid model is considerably lower than that ofthe LES; however, it is higher than that of the RANSapproach. In this respect, the accuracy of the hybridRANS/LES predictions is much higher than that ofRANS, yet somewhat lower than that of LES. Inaddition, they showed that the new hybrid modelpredicted the large-scale uctuation velocity �eld coste�ectively when compared with the LES.

Particle dispersion and deposition in turbulent ows and, in particular, in the indoor environment hasattracted considerable attention in recent years [23-26]. Fan and Ahmadi [27] proposed a sub-layer modelto capture the e�ect of near-wall vortical structure ofturbulent ows on particle deposition in vertical ducts.Zhang and Ahmadi [28] used the direct numerical

simulation technique for simulating particle depositionin turbulent duct ows. Salmanzadeh et al. [29] showedthe e�ect of subgrid scale (SGS) model on the LargeEddy Simulation (LES) of particle deposition in turbu-lent channel ow. Recently, Sajjadi et al. [12] developeda new k� "-LBM method and simulated particle depo-sition in turbulent channel ows and found reasonableagreement with the earlier numerical and experimentalresults. In addition, Sajjadi et al. [11] investigatedparticle transport in a modeled room using the LES-LBM and the k � "-LBM approaches. They showedthat both methods predicted particle dispersion anddeposition in the indoor environment reasonably well.

Applications of hybrid RANS-LES within theLBM for particle dispersion and deposition have notbeen tested yet. The main aim of this work is touse the hybrid RANS-LES within the LBM frameworkto investigate the particle transport processes in anindoor environment. The Lagrangian particle trackingapproach was also used in these simulations, and thedispersion and deposition of particles of di�erent sizeswere studied. For nanoparticles, the e�ect of the Brow-nian excitations was included in the analysis. It wasshown that the hybrid-LES- k�"-LBM model predictedthe particle deposition more accurately than the k� "-LBM did; however, while being computationally moreeconomical, it predicted the particle deposition slightlyless accurately than the LES-LBM did.

2. Hybrid LES/RANS model based on LBM

To reduce the computation cost of simulations whilemaintaining the accuracy, the hybrid LES/RANSmodel is used. In other words, the LES with a subgrid-scale model is used for bulk of the ow region, whilethe RANS model is used for the near-wall regions. Inthis study, the LBM-k � " model was used to analyzethe RANS near-wall region, and the MRT-LBM-LESmodel was used for simulating the bulk of the owregion. Sajjadi et al. [11,12,18] described details of theLBM-k� ", MRT-LBM-LES, and the hybrid models of ow simulations. Therefore, only a brief summary isoutlined.

For the LBM-k � " model, two additional distri-bution functions for the k and " are de�ned as follows:

k =Xi

gi; (1)

" =Xi

hi: (2)

The transport equations for the new distribution func-tions are:

gi�x+ ci�t; t+ �t

�� gi (x; t)

H. Sajjadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 3173{3182 3175

= � 1�k

[gi (x; t)� geqi (x; t)] + �tFi; (3)

hi�x+ ci�t; t+ �t

�� hi (x; t)

= � 1�"

[hi (x; t)� heqi (x; t)] + �tFi; (4)

For k :

Fi = !i(�tjSj2�")(1+ci:uc2s

(�k�0:5)=�k); (5)

For " :

Fi= !i(C1"k

(�tjSj2)�C2"2

k)(1+

ci:uc2s

(�"�0:5)=�"):(6)

Herein, C1 = 1:44, C2 = 1:92, and the turbulencekinematic viscosity for RANS model is given as follows:

�t = C�k2

":

For the MRT-LBM-LES, to evaluate the distribu-tion function, the following transport equation is used:

fi(x+ ci�t; t+ �t) = fi(x; t)�Mij�1:Sjk:[Rk(x; t)

�Reqk (x; t)]: (7)

Components of Rk, Reqk , Mij , Sjk, subgrid scaleviscosity �SGt = (CS�)2 jSj, and strain rate normjSj are described in [11,18], where Cs = 0:16 and� = (�x�y�z)1=3.

In the new hybrid method, the transport equa-tions for k and " are solved in the entire ow domain,and the distribution function for the MRT-LBM-LES issolved in bulk of the ow region. In addition, very closeto the walls, the standard wall function was used [12].

To switch between the MRT-LBM-LES and theLBM-k� " models, a linear interpolation based on they+ value is used [30]. In other words,

�t =

8><>:�t;LES if y+ > y+up

(1��)�t;k�"+��t;LES if y+down < y+ < y+

up

�t;k�" if y+ < y+down

(8)

where � is the weighting factor:

� =y+ � y+

down

y+up � y+

down: (9)

Herein, y+down and y+

up are respectively the lower andupper limits of transition region in wall units selectedas 60 and 300 [30].

3. Particle motions

The equation of motion of small particles is givenby [11]:

dupidt

=1�pCDRep

24(ufi � upi) + (1� 1

S)gi + ni(t);

(10)

where upi is the particle velocity, ufi is the instanta-neous air ow velocity in the particle location, �p is theparticle relaxation time, given as: �p = Sd2Cc

18� , and Sis the ratio of particle density to uid density. Herein,Cc is the Cunningham slip correction and is given asfollows:

Cc = 1 +2�d

(1:257 + 0:4e�1:1d� ):

In Eq. (10), CD is the drag coe�cient and de�ned asfollows:

CD =24

RepRep < 1; (11)

CD =24

Rep(1 + 0:15Re0:687

p ) 1 < Rep < 400;(12)

where Rep is the particle Reynolds number that isde�ned as:

Rep =d jurelj�

urel = uj � upj :In Eq. (10), the drag force, the buoyancy force, and theBrownian force are included in the particle equation ofmotion; however, the lift force, which is comparativelysmall, is neglected [11].

The �rst term on the right-hand side of Eq. (10)is the drag force caused by the relative motion betweenparticles and ow. The second term on the right-hand side of Eq. (10) represents the gravitationalforce corrected by the buoyancy force. The thirdterm represents the Brownian force. The Brownianexcitation is very important for nanoparticles and ismodeled as a Gaussian white noise random process [24].In other words,

ni(t) = �i

r�S0

�t; (13)

where So = 216�kbT�2�d5(S)2Cc

, and � is selected at every timestep from a population of zero-mean, unit-varianceindependent Gaussian random numbers.

4. Modeled geometry

In this study, to test the newly developed method forpredicting particle dispersion and deposition, a scaleroom model was used. This con�guration is identicalto that studied in [31] for examining the e�ectivenessof the hybrid approach for air ow simulation. Asshown in Figure 1, the scaled room is roughly one-tenth scale of a full-size o�ce with dimensions of


Figure 1. Geometry of the scaled room model used in thepresent study [31].

0:914 m � 0:305 m � 0:457 m. A partition with halfthe room height is located in the middle of the room.Ventilation air enters the room vertically from one sideof the ceiling and exits through the outlet registerlocated on the other side of the ceiling. The dimensionsof the inlet and outlet are 0:101 m � 0:101 m, andthe inlet air ow velocity is typically 0.24 m/s. Thecorresponding Reynolds number based on the inletlength and an inlet air ow velocity is 1628.

5. Results and discussion

5.1. Flow �eldResults of the air ow �eld in the modeled room, whichis used in the present work utilizing the hybrid method,were investigated by the authors in [18]. It wasshown that the hybrid LES/RANS model within theLBM framework predicted the mean ow �eld and the uctuation in RMS velocities reasonably well.

5.2. Particle dispersion and depositionIn this section, particle dispersion and depositionprocesses for various particles sizes (10 nm, 100 nm,1 �m, and 10 �m) in the room were simulated.The unsteady air ow was �rst simulated for about70 s to reach a roughly quasi-steady condition; then,the particle injection was initiated with 144 particlesinjected uniformly at the inlet with the same velocityas the air ow at every 0.05 s. Particle injection stoppedwhen the simulation time reached 100 s. Therefore, atotal of 86,400 particles were injected into the ow.

Figure 2 compares the number of suspended 1 �mparticles in the room as predicted by di�erent models.The earlier simulations of Sajjadi et al. [11] and Tianet al. [31] are shown in this �gure for comparison. TwoBoundary Conditions (BC) were used for particle-wallinteractions; the �rst boundary condition is \re ect,"for which when a particle collides with a wall, itbounces back. This is the assumption used by Tian etal. [31]. The second BC is \trap." When the distance ofparticle center from the wall reaches dp/2, it is assumedthat the particle is deposited on the wall. It shouldbe pointed out that, for 1 and 10 �m particles, the

Figure 2. Comparison of the number of suspended 1 �mparticles in the room under trap and re ect boundaryconditions (Total number of injected particles is 86,400and ReInlet is 1628).

trap boundary condition is more realistic, as the vander Waals forces cause these small particles to adhereto the surface, with a little chance for rebound [27].The re ect boundary condition here was just used tocompare the present simulation results with the earlierresults of Tian et al. [31].

Figure 2 clearly shows that the number of sus-pended particles increases with time up to t = 100 swhen the injection stops; then, it decreases graduallydue to particle deposition and those that are leavingthrough the exit register. Figure 2 also shows goodagreement between the prediction of current hybridRANS/LES model and those of the LBM-LES of [11]and LES of [31]. It is also observed that the presenthybrid RANS/LES model predicts results as muchclose as to the LES results, thus somewhat improvingthe predictions of the LBM-k � " model [11].

Figure 3 presents the predicted time variation ofthe number of suspended 10 �m particles in the roomas predicted by di�erent models. It appears that thepresent hybrid model's predictions are closer to theLBM-LES model's results than those of the LBM- k�"model are. When the trap boundary condition, which ismore realistic for 10 �m particles, is used, the numberof suspended particles declines considerably, and theamount of reduction after 160 s reaches about 50%.In addition, the deviation between the predictions ofthe present hybrid LES/RANS model and the LES ofSajjadi et al. [11] is less than 4% for t < 120 s and isabout 16% at t = 145 s.

For the trap boundary condition, the numberof suspended 10 and 100 nm particles is shown inFigures 4 and 5. The trend of variations of the numberof suspended particles shows the same pattern as those


Figure 3. Comparison of the number of suspended 10 �mparticles in the room under trap and re ect boundaryconditions (total number of injected particles is 86,400 andReInlet is 1628).

Figure 4. Comparison of the number of suspended 10 �mparticles in the room under trap boundary condition (totalnumber of injected particles is 86,400 and ReInlet is 1628).

of 1 and 10 �m particles. These �gures also showthat the hybrid model captures the dispersion anddeposition of 10 and 100 nm particles more accuratelythan the k � " model does. In addition, Figures 4and 5 show that the k � " model overestimates theparticle deposition rate as discussed in [11,12] so thatthe number of suspended particles predicted by the k�"model is less than the other models is. However, thehybrid model seems to achieve highly realistic results.

Figure 6 shows the time variation of the number ofdeposited particles on the di�erent walls, as predictedby the hybrid model for 10 nm, 100 nm, 1 �m, and

Figure 5. Comparison of the number of suspended 100nm particles in the room under trap boundary condition(total number of injected particles is 86,400 and ReInlet is1628).

10 �m particles. Figure 6(a) shows that the numberof particles deposited on the ceiling increases withtime roughly linearly. This is because, after injection,particles move up toward the outlet, and some particlesreach the ceiling and depositing. This �gure also showsthat the smaller particles have a higher deposition rateon the ceiling than the larger ones do, due to the e�ectof gravity and higher Brownian motion.

Figure 6(b) shows that the number of deposited10 �m particles on the oor is quite high, and morethan 30% of the total injected 10 �m particles aredeposited on the oor after 160 s. The amount ofthe deposition of 10 �m particles on the oor is ofhigher magnitude, as compared to particles of othersizes. This is due to the particle inertia in the inletjet toward the oor and, also, the gravitational e�ect.The smaller particles with much lower inertia follow theair ow and are not deposited on the oor. In addition,Figure 6(b) shows that when the time reaches 100 ssuch that the particle injection stops, the slope of thedeposition rate decreases. This is certainly the case for1 �m particles and smaller ones. In addition, becauseof the Brownian excitation, the number of deposited10 nm particles is slightly more than 100 nm and 1 �mparticles.

Figure 6(c), (e), (f), and (g) show, respectively,the number of deposited particles on the right, front,back, and partition walls. It is seen that the cumulativedeposition for these walls has the same trend; however,the rate of deposition varies with time and, also, fordi�erent particle sizes. After 120 s (20 s after theinjection stops), the total deposition seems to saturateand does not change considerably.


Figure 6. Number of deposited particles on the walls: (a) Ceiling, (b) oor, (c) right wall, (d) left wall, (e) front wall, (f)back wall, (g) partition, and (h) total for the hybrid RANS/LES model (total number of injected particles is 86,400 andReInlet is 1628; trap boundary condition).


Figure 6(d) shows the total number of depositedparticles of di�erent sizes on the left wall. Up tot = 100 s (30 s after injection started), the depositionrate is zero for all sizes. After 100 s, a su�cientnumber of small particles are transported to the leftside of the room, and the deposition on the left wallincreases. This �gure shows that the deposition for10 �m particles on the left side is negligible. Thesetrends are in contrast with deposition on the right wall,as shown in Figure 6(c). The reason is that a largefraction of 10 �m particles is deposited on the oor,the right wall, and the partition wall; a smaller fractionenters the left-hand side of the room.

The total number of deposited particles of di�er-ent sizes on the walls are shown in Figure 6(h). Asnoted before, due to inertia and gravity, the depositionof 10 �m particle is more than other sizes. In addition,the deposition of 10 nm particles is more than 100 nmand 1 �m because of the higher intensity of theBrownian excitation.

Figures 7-10, respectively, show the total numberof deposited particles on the walls of the room aspredicted by di�erent models for 10 nm, 100 nm,1 �m, and 10 �m. It is seen that the depositioninitiates after about 80 s and increases at di�erentslops for di�erent sizes. The deposition rate of 10 �mis the highest due to the dominance of the impactionprocess. The Brownian motion causes somewhat higherdeposition rates for 10 nm particles than that for100 nm and 1 �m particles. For particles smallerthan 1 �m, Figure 7 shows that the LES modelpredicts the lowest deposition rates, while the k � "model predicts the highest. The predictions of thepresent hybrid model for the deposition are similar

Figure 7. Comparison of the total number of deposited10 nm particles on the walls of the room for variousmodels (total number of injected particles is 86,400 andReInlet is 1628; trap boundary condition).

Figure 8. Comparison of the total number of deposited100 nm particles on the walls of the room for variousmodels (total number of injected particles is 86,400 andReInlet is 1628; trap boundary condition).

Figure 9. Comparison of the total number of deposited1 �m particles on the walls of the room for various models(total number of injected particles is 86,400 and ReInlet is1628; trap boundary condition).

between the two, yet are closer to the predictions ofLES model. The over-prediction of the depositionrate by the k � " model is well known. Tian andAhmadi [1] reported that the k�" model overestimatedthe deposition velocity in turbulent duct ows, sincethis model cannot properly capture the anisotropicturbulence uctuations. They showed that accountingfor the anisotropy of turbulence uctuations and thenear-wall e�ects can improve the results. Figures 7-9 show similar over-estimation patterns of the k � "model. However, by using the hybrid model, whichcan capture the uctuation velocity in the bulk of the


Figure 10. Comparison of the total number of deposited10 �m particles on the walls of the room for variousmodels (total number of injected particles is 86,400 andReInlet is 1628; trap boundary condition).

domain correctly, the particle deposition decreases andis closer to the LES results.

For 10 �m particles, Figure 10 shows that thepredictions of total deposition by the three models arecloser to each other; however, similar but milder di�er-ences are seen. The reason is that for 10 �m particles,the impaction dominates the deposition process, andthe in uence of turbulence deposition becomes smaller.

6. Conclusions

The hybrid RANS/LES in conjunction with the latticeBoltzmann method was used to simulate particle dis-persion and deposition in a room. For the LES model,the sub-grid scale turbulence e�ects were included inthe Smagorinsky model. For using the k�" turbulencemodel within the framework of LBM, the formulationwas enhanced by the addition of two populations for kand ". For the hybrid RANS/LES method, the near-wall region was simulated using the k � " model, andthe bulk of the ow region was analyzed by the LESmodel using the LBM. Deposition and dispersion ofparticles with diameters of 10 nm-10 �m in a room wereanalyzed. Based on the presented results, the followingconclusions are drawn:

� The predictions of the hybrid RANS/LES for parti-cle deposition and dispersion are more accurate thanthat of RANS is, yet somewhat less accurate thanthe LES results. Average deviations of predictionsof the present hybrid model and the RANS methodfor deposition of 10 �m particle in comparison withthe LES results are, respectively, 8% and 12%.

� The k � " model overestimates the deposition rate,

because this model cannot capture the anisotropy ofturbulence uctuations correctly.

� With the increase of particle diameter from 10 nmto 1 �m, the total number of deposited particles inthe room decreases by about 15% due to the declineof the intensity of the Brownian excitation.

� The number of depositions for 10 �m particle ismore than other studied sizes. This is due to thegravitational sedimentation and inertial impaction.

Nomenclature

fi Density distribution functionsgi Turbulence kinematic energy

distribution functionshi Dissipation distribution functionsk Turbulence kinematic energy" Dissipation!i Weighted factor indirection i�k Relaxation time for k�" Relaxation time for "� Molecular mean free path of the gasd Particle's diameterg Gravity accelerationT Fluid temperature� Density� Kinematic viscosity

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Biographies

Hasan Sajjadi received his PhD degree in Mechani-cal Engineering from the Shahid Bahonar University,Kerman, I.R, and is now an Assistance Professor ofMechanical Engineering at University of Bojnord, Iran.His research work concerns uid mechanics, particle


deposition and dispersion, turbulent ow, and latticeBoltzmann method.

Mazyar Salmanzadeh received his PhD degree inMechanical Engineering from the Shahid Bahonar Uni-versity, Kerman, I.R, and is now an Associate Pro-fessor of Mechanical Engineering at Shahid BahonarUniversity, Iran. His research work concerns particledeposition and dispersion as well as turbulent ow.

Goodarz Ahmadi received his PhD degree in Me-chanical Engineering from the Purdue University, WestLafayette, IN, USA and is now a Professor of Me-

chanical Engineering at Clarkson University, USA. Hisresearch work concerns particle transport, depositionand removal, aerosol mechanics, stochastic processes inengineering, advance theory of turbulence, and multi-phase ow modeling.

Saeed Jafari received his PhD degree in MechanicalEngineering from the Shahid Bahonar University, Ker-man, I.R, and is now an Associate Professor of Mechan-ical Engineering at Shahid Bahonar University, Iran.His research work concerns particle deposition anddispersion, turbulent ow, lattice Boltzmann method,and multiphase ow modeling.

investigation of particle deposition and dispersion...

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