Powder Technology 353 (2019) 267–275

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Parameter study of filtration characteristics of granular filters for hotgas clean-up

Fei-Long Wang a, Song-Zhen Tang a, Ya-Ling He a,⁎, Francis A. Kulacki b, Yu-Bing Tao a

a Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, Chinab Department of Mechanical Engineering, University of Minnesota, 111 Church St. S. E, Minneapolis, MN 55455, United States of America

⁎ Corresponding author.E-mail address: yalinghe@mail.xjtu.edu.cn (Y.-L. He).

https://doi.org/10.1016/j.powtec.2019.05.0080032-5910/© 2019 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 27 September 2018Received in revised form 21 April 2019Accepted 1 May 2019Available online 4 May 2019

Granular filters are a promising technology in hot gas clean-up for coal-based power generation systems. Numer-ical simulations are presented for the filtration characteristics of randomly packed granular filters. The effect offilter height is first investigated to obtain a unit height which can predict filtration characteristics of the entirefilter, and it is found that the unit height should be at least 10 times the granule diameter. The filtration perfor-mance, including filtration efficiency, pressure drop and deposition uniformity are analyzed, and the effect of gasvelocity, particle diameter and granule diameter are then investigated. The results show that the pressure dropincreases rapidlywith the increase of gas velocity and decreasewith granule diameter. Increasing the gas velocityand particle diameter leads to increased filtration efficiency and decreased deposition uniformity. The effect ofStokes number on filtration efficiency and deposition uniformity can be divided into three regimes, and filterheight and granule diameter need to be optimized according to Stokes number. A correlation of initial filtrationefficiency is obtained for use in filter design and structural optimization.

© 2019 Elsevier B.V. All rights reserved.

Keywords:Hot gas clean-upGranular filterPressure dropFiltration efficiencyDeposition uniformity

1. Introduction

With the increasingconsumptionof fossil energy, theglobal environ-mental crisis has become one of the most pressing problems in recentyears [1,2]. In coal-based power generation systems, the high tempera-ture flue gas unavoidably contains fly ash and dust which causes foulingand erosion problems in heat exchangers and downstreamsystems [3–5] resulting in significant loss of efficiency and system failure[6–9]. The development of hot gas clean-up and high-temperature dustfiltration is therefore important to ensure safe, economic and stable op-eration of systems and also to meet environmental emissionrequirements.

Common particle filtration technologies, such as cyclones, electro-static precipitators, and scrubbers are not applicable in hot gas clean-up owing to the high temperature environment. Ceramic candle filtersand granular bed filters are considered two of the most promisingmethods in hot gas clean-up [10,11]. However the ceramic candle filterelements can easily suffer from micro-crack formation due to thermalshock and mechanical fatigue [12–14]. Therefore, granular bed filterscan be more attractive because they are inexpensive and more stablein high temperature environments. Because of the advantages of granu-lar bed filters, they arewidely used in bio-oil production [15], water andwaste-water treatment [16–18] in addition to application in coal-based

power generation systems. Granular bed filters can be operated in threeforms:fixed bed,fluidized bed andmovingbed. Xiao et al. [19] have sys-tematically reviewed the basic principles, characteristics and perfor-mances of the three type of granular filters.

Filtration efficiency and pressure drop are the two main perfor-mance metrics for granular filters. Influence factors on performance in-clude granular packing, granule diameter, filter height, temperature,and operating conditions including gas velocity, the property, size andconcentration of fly ash particles.

We previously investigated filtration characteristics of granular fil-ters with two typical packings: body centered cubic (BCC) and facecentered cubic (FCC) [20]. The filtration efficiency and pressure dropof FCC packing are significantly larger than that of the BCC packing.Guan et al. [21,22] numerically investigated the filtration characteristicsof a randompacked granularfilter, and the effects of granular bed depth,granule diameter and gas velocity on the filtration efficiency weredetermined. Kuo et al. [23] experimentally investigated filtration andloading characteristics of granular filters, and the effects of the granularsize and packing parameters on both pressure drop and filtrationefficiency were investigated. Chen et al. [24] experimentally studiedthe efficiency and stability of moving granular bed filter in high-temperature environment with various operation conditions. Chenand Li et al. [25] experimentally investigated the heat transfer of gaswith coagulative particles flowing through a packed granular bed filter,and twomodified correlations are proposed to give the Nusselt number.It was found that reducing the granule diameter can effectively improve

268 F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

the filtration efficiency. Tian et al. [26] consequently proposed a newkind of dual-layer granular filter, which consists of a lower layer offine granules and an upper layer of coarse granules, and the resultsshow it can simultaneously achieve both high filtration efficiency andlow pressure drop. Yu et al. [27] experimentally investigated the perfor-mance of a fixed granular filter, and proposed a three-layer granular fil-ter, which can improve the filtration efficiency by 3.2% and reduce thepressure drop by 5%. Temperature also affects the performance of thegranular filter. Peukert et al. [28] found that the filtration efficiencyfalls from 99.97% at room temperature to 98.6% at 800 °C.

Much evidence can be found that particles which deposit and accu-mulate on the granular surface will form a dust cake, and the dust cakeformation is crucial to achieving high filtration efficiency [29]. However,with thickening of the dust cake, the filter can be clogged, and pressuredrop will increase rapidly, affecting filtration performance. Wingertet al. [30] developed a numerical model to predict clogging of a granularbed filter, which describes the changes of filtration efficiency and pres-sure drop using equivalent collector diameters. We have previously de-veloped a real-time filtration model which can well predict particledeposition and accumulation characteristics on the granular surface inreal time [31]. With this filtration model, we found that depositiongrowth leads to a gradual increase of filtration efficiency and rapid in-crease in pressure drop.

Althoughmuch research has been carried out on the performance ofgranular filters, it has been focused on filtration efficiency and pressuredrop, and few studies have investigated particle deposition uniformityinside the filter. Deposition uniformity also plays an important role inthe economic operation of the filter since the increase of deposition in-homogeneity can cause a decrease in dust holding capacity. Besides, fewstudies have been conducted on the optimization of granular filters. Thepurpose of this study is to obtain the effect of different factors on the fil-tration performance of granular filter, and to obtain the correlation offiltration efficiency, which will lay a foundation for subsequent optimi-zation research.

In this paper, we present a numerical study of the filtration charac-teristics of the randomly packed granular filter. The effect of filterheight, gas velocity, particle diameter and granule diameter on filtrationefficiency and pressure drop are investigated. Then the particle deposi-tion uniformity characteristics inside thefilter is analyzed, and the effectof each factor on the deposition uniformity is obtained. A correlation ofinitial filtration efficiency is obtained, which can be useful in the designand structural optimization of the filter, and the results of this studyhave a certain guiding significance for hot gas clean-up and the optimi-zation research of granular filters.

2. Model description and numerical method

2.1. Discrete filter model

Fig. 1 is a schematic of a randomly packed granular filter. The EDEMsoftware (V 2.6) [32] is applied to generate the granules. Granules with

Fig. 1. Schematic of simulation doma

diameterD are loaded into a bed to a height of L to create thefilter. An el-ementary volume element with a 3D× 3D cross section is chosen as thephysicalmodel.Owing toperiodicity andsymmetry, theunit volumecanbe extended by applying symmetry boundary conditions on thefour surfaces along x- and y-directions. To maintain a uniform inlet ve-locity andpreventbackflow fromtheoutlet, the inlet andoutlet domainsare extended by 4D and 10D respectively. Fly ash particles are loaded atthe inletboundaryand leave thedomain fromthepressureoutletbound-ary. The filtration characteristics of the filter are then determined withthe geometric parameters and simulation conditions listed in Table 1.

2.2. Mathematical model

The continuum (gas) phase flow is treated as a three-dimensionalincompressible flow, and the governing equations for conservation ofmass and momentum are,

∇ � U ¼ 0 ð1Þ

∂U∂t

þ ρU � ∇U ¼ −∇pþ μ∇2U ð2Þ

Gas flow through the granules is turbulent, and the SST k-ω turbu-lence model [33–35] is employed to describe the effect of turbulenceflow. The transport equations for turbulent kinetic energy k and the spe-cific dissipation rate ω are,

∂∂t

ρkð Þ þ ∂∂xi

Uiρkð Þ ¼ ∂∂xj

μk∂∂xj

k

!þ ~Pk−β�ρωk ð3Þ

∂∂t

ρωð Þ þ ∂∂xi

Uiρωð Þ ¼ ∂∂xj

μω∂∂xj

ω

!þ Pω−βρω2

þ 2ρ 1−F1ð Þ 1ω

1σω;2

∂∂xj

k∂∂xj

ω ð4Þ

where μk and μω are the effective viscosities,

μk ¼ μ þ μ t1σk

ð5Þ

μω ¼ μ þ μt1σω

ð6Þ

μt is the modified turbulent viscosity, σk and σω are diffusion constants.Pω is the rate of production of ω,

Pω ¼ γ 2ρSij � Sij−23ρω

∂∂xj

Ui

!δij

" #ð7Þ

γ is a model constant, and δij is the Kronecker delta.

in for random packed granules.

Table 1Physical quantities and operating conditions.

Parameters Units Range

Granule diameter, D mm 1–5Filter height, L mm N5DAverage porosity, ε – 0.41Inlet velocity, uin m/s 0.2–1Particle diameter, dp μm 1–5Particle concentration, C mg/m3 2000

Fig. 2. Schematic representation of the uniformity index.

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Fly ash particles are the disperse phase, and a Lagrangian method isemployed to predict their motion and trajectories. The forces acting onfly ash particles in fluids mainly include drag force, gravity,thermophoretic force, Brownian force, Saffman lift, Basset force, etc.The fly ash particle size ranges from 1 to 5 μm in this work (Table 1). Ac-cording to Ref. [36], the drag force of particles within this size range is atleast one order of magnitude larger than the other forces. Therefore,only the drag force is consideredwhen calculating themotion of fly par-ticles in the fluid. The force balance on a particle is,

dup

dt¼ FD u−up

� � ð8Þ

where FD(u − up) is the drag force, and FD is,

FD ¼ 3μCD Rep4ρpd

2p

ð9Þ

CD is the non-linear drag coefficient, and Rep is the relative particleReynolds number,

CD ¼24 1þ 0:15 Re0:687p

� �Rep

; Rep≤1000

0:43 ; RepN1000

8><>: ð10Þ

Rep ¼ ρ u−up�� ��dp

μð11Þ

u and up are the fluid and particle velocity respectively, ρp is the particledensity, μ is dynamic viscosity of fluid, and dp is the diameter of particle.

2.3. Filtration model

The mechanisms of particle deposition on the granular surface in-clude interception, inertial impaction, diffusion, gravitational settlingand electrostatic attraction [19]. The electrostatic attraction are not con-sidered in this work. The gravitational settling usually dominates forlarge particles when the gas velocity is b0.01 m/s. In present work, thegas velocity ranges from 0.2 to 1m/s, and the fly ash particle size rangesfrom 1 to 5 μm. Thus, the gravitational settling can be ignored in thiswork. While the effect of diffusion increases slowly as the particle sizefalls within submicron ranges and is dominated by nano-particles[19], so the diffusion can also be neglected in our work. As for intercep-tion, it occurs when the radius of particle exceeds the distance betweenits trajectory and the granules, and its influence decreases with the in-crease of clearance size. In this paper, the granule diameter rangesfrom 1 to 5 mm, and it's 1000 times larger than that of fly ash particlesize, so the interception can also be neglected. It is reported that the in-ertial separation is generally thought to be the dominating depositionmechanism when the granule diameter D ≥ 1 mm, and fly ash particlediameter dp ≤ 50 μm [15,37]. Therefore, only inertial impaction is con-sidered in present work.

Besides, the granular filter investigated in this paper are used forhigh temperatureflue gas clean-up, and it usually works at temperaturehigher than 1000 °C. In such high temperature, the fly ash particles arein a semi-molten state, and they can be sticky enough and will be

captured once they hit the granular surface. Besides, in practicalapplication, regular blowing and cleaning is required for fixed bed gran-ular filters, while for moving bed granular filters it is also necessary toreplace the fouled granules with clean ones. Therefore, we mainlyfocus on the initial stage of the filtration progress and the detachmentof deposited particles in the later stage are not considered in presentwork. Most of the theoretical and simulation works in existing litera-tures [19,21,22,38] are also based on such simplification, and it leadsto satisfactory results.

In our simulation, the particle deposition mass flow rate _md on thegranular surface is recorded at the end of each time step in the solution.The filtration efficiency is defined,

η ¼ _md

CuinSinð12Þ

where C is the concentration of injected particles, and uin and Sin areinlet velocity and inlet surface area, respectively.

The particle deposition fraction along the filter, φ, is monitored,

φ ¼ mxR L0 mxdx

ð13Þ

wheremx is the depositionmass at x position along the granularfilter (0≤ x ≤ L).

The dust holding capacity is an important performance for a granularfilter, which represents the mass of dust retained by the filter until at-tainment of the specified final pressure drop increase. It is conceivedas a test property serving as an indicator of a filter's service life or serviceperiod. The filter with higher dust holding capacity has a longer servicelife (service period). However, there is no formula for calculating thedust holding capacity. It is easy to understand that, the greater deposi-tion uniformity, the smaller increase of pressure drop caused by deposi-tion of dust of the same quality, so the dust holding capacity will behigher. Therefore, in this paper, the deposition uniformity is employedto evaluate the dust holding capacity of granular filters.

The index, γ, is introduced to evaluate the degree of uniformity ofthe particle deposition characteristics along the filter,

γ ¼ 1−12n

Xni¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimi−mð Þ2

qm

ð14Þ

wheremi is the depositionmass of each observation section (Fig. 2), andm is the average depositionmass for all observation sections. The unifor-mity index, γ, varies from 0 to 1, and a larger γ represents the betteruniformity.

2.4. Numerical method and boundary conditions

The computational (Fig. 1) includes six boundaries: velocity inlet,pressure outlet, and symmetric boundaries for the four side surfaces.Additional inlet and outlet domains are extended by four and tentimes granule diameters, respectively, tomaintain a uniform inlet veloc-ity and prevent the backflow from outlet.

Fig. 3. Comparison of initial pressure drop.

Fig. 4. Effect of filter height on initial pressure drop at uin = 0.2 m/s.

270 F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

The flue gas components are: N2 75.07%, O2 5.85%, CO2 8.88% andH2O 10.2%,which keeps the samewith our previouswork [31]. A typicalhigh temperature (1000 °C) flue gas from a copper smelting process isselected as the continuum phase, and density and viscosity are calcu-lated according to the volume fraction of each component: ρ =0.27 kg/m3 and μ=4.9 × 10−5 kg/(m·s). Thematerial of thefly ash par-ticles is regarded as Bi2O3, which usually exists in the flue gas of bothcopper and lead smelting processes. The density of fly ash particles is8900 kg/m3, and the typical particle loading concentration is2000 mg/m3.

Fly ash particles are loaded at the velocity inlet boundary and leavethe simulation domain from the pressure outlet boundary. For the par-ticles hit on the granular surface, theywill deposit on thewall and be re-moved from the computational domain. The discrete phase model(DPM) is used to track particle behavior in the fluid flow. Because theparticle mass loading is quite low and the particle size is small(Table 1), the particle-particle interaction and effect of the particles onthe fluid flow field are neglected. Thus, one-way coupling is employedfor the particle phase with random walk stochastic tracking [39].

The effect of filter height on filtration characteristics is first investi-gated to obtain a unit height which can well predict the filtration effi-ciency of a whole filter. After the unit height is obtained, the effect ofgranule diameter and flue gas velocity are investigated. The pressuredrop, filtration efficiency, particle deposition fraction and the depositionuniformity index along the filter are all monitored at each time step.

All simulations are performed with FLUENT (V 18.0) [40]. The filtra-tionmodel, calculation of particle deposition fraction and theuniformityindex along the filter, as well as the monitoring procedure are all writ-ten in form of user-defined functions. The SIMPLE algorithm isemployed for the velocity-pressure coupling, with a second order up-wind discretization scheme for the convective and diffusive terms. Itcan be regarded as converged when the normalized residuals areb10−4 for each governing equation.

2.5. Numerical validation

The grid independence validation is first conducted before simula-tion. The actual point contacts between granules usually leads to themeshingproblems and poormesh quality. So the area contact treatmentbetween granules is applied in this paper, because it is more accuratethan the tiny gap treatment and also can maintain mesh quality andeconomy in the CFD calculations [41]. Fine meshes are applied nearthe granular surface, while the mesh size in the inlet and outlet zonesare properly enlarged to decrease computing time. Additionally, poly-hedral meshes have been applied which can reduce the number ofgrids. For example, the case with a granule diameter of 1 mm and filterheight of 10D,different sizes of grid systems are generated. The pressuredrop and collection efficiency are calculated for grid independence val-idation. When changes in pressure drop and collection efficiency areb5%with the increase in grid number, the results are regarded as grid in-dependence, and the final adopted grid number is ~350,000. The samegrid size and mesh generation method are applied to other cases withdifferent filter heights and granule diameters to ensure that all casesare grid independent.

A numerical validation of initial pressure drop is conducted forfilterswith a height of 10D, gas velocity from 0.2 to 1 m/s, and granular diam-eter from1 to 5mm. All simulation conditions andmethods are kept thesame as Section 2.4. The Ergun equation [42,43], which can be used todetermine the pressure drop of packed bed, is employed to comparewith the simulation results,

ΔpL

¼ 1501−εð Þ2ε3

μUD2 þ 1:75

1−εε3

ρU2

Dð15Þ

The comparison is shown in Fig. 3 where the simulations for differ-ent cases fit well with the predict results of Ergun equation. The

maximum deviation is within 6%, which indicates the reliability of thesimulation. Additional validation for different random packing modelsand filtration efficiency can be found in our previous work [20,31] andare not presented here for brevity.

3. Results and discussion

As the pressure drop, filtration efficiency and deposition uniformityare changing with time, and the changing characteristics are related tothe gas velocity, particle diameter and the filter structures. It is difficultor even impossible to obtain correlations to well describe the filtrationperformance of the granular filter in the later stage. In present work,wemainly focus on the initial stage of the granularfilter, and investigateeach factors on the filtration performance.

3.1. Effect of filter height

The effect of filter height on pressure drop and filtration efficiency isfirst investigated to obtain a unit height which can predict the filtrationcharacteristics of a whole filter. For uin = 0.2 m/s and dp = 1 μm, forexample, the filtration characteristics with filter heights of 5D - 50Dare obtained. Fig. 4 shows the effect of filter height on initial pressure

Fig. 5. Effect of filter height on initial filtration efficiency at uin = 0.2 m/s and dp = 1 μm.

Fig. 6. Effect of gas velocity on initial pressure drop.

Fig. 7. Effect of gas velocity on initial filtration efficiency.

271F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

drop of the filters with different granule diameters. For each granule di-ameter, the initial pressure drop increases linearly with filter height,whichmeans any height can be used as a unit height to predict the pres-sure drop across the whole filter.

Fig. 5 shows the effect of filter height on the initial filtration effi-ciency. The efficiency results of filter height 5D, 10D and 20D are usedto predict the efficiency of other heights according to,

η ¼ 1− 1−ηL0� �L=L0 ð16Þ

where ηL0represents the filtration efficiency of a filter with height of L0.

It can be seen from Fig. 5 that the initial filtration efficiency increaseswith filter height, while the growth rate gradually decreases. Filtrationefficiency will finally reach a constant value (100%) when the filterheight is large enough. We also see that the 5D prediction results arehigher than the simulation results,while the 10D and 20D prediction re-sults agree well with the simulation results. Therefore, the unit heightshould be at least 10D, and we choose 10D as our unit height to predictthe pressure drop and filtration efficiency of the filters with differentheights.

3.2. Effect of uin and D on initial pressure drop

The fly ash particle diameter does not affect the initial pressure dropof the granular filters. To investigate the effect of gas velocity uin andgranule diameter D on the initial pressure drop, the filter height isfixed at 10D (unit height), and the gas velocity is varied from 0.2 to1m/s at 0.2m/s steps. Fig. 6 shows the effect of gas velocity on the initialpressure drop of filters with different granule diameters. Pressure dropincreases with gas velocity and can be explained well according toEq. (15). With the same filter height and granule diameter, pressuredrop increases quadratically with gas velocity. It also can be seen fromFig. 6 that the smaller the granule diameter, the faster the pressuredrop grows with gas velocity, and for each gas velocity, pressure dropincreases rapidly with a decrease of granule diameter. The smaller thegranule diameter, the larger the specific surface area, which leads to arapid increase in pressure drop.

3.3. Effect of uin, dp and D on initial filtration efficiency

Figs. 7 and 8 show the effect of gas velocity uin and particle diameterdp on the initial filtration efficiency of filters with different granule di-ameters, respectively. For each particle size (Fig. 7), filtration efficiencyincreases with gas velocity, and the larger the particles are, the faster itincreases. In Fig. 8, we can see that the efficiency also grows rapidlywithparticle diameter. The similar pattern occurs with different granule di-ameters, and the smaller the granule diameter, the faster the efficiencygrows.

The reasonwhyefficiency increaseswith gas velocity andparticle di-ameter can be explained appealing to the Stokes number, Stk. TheStokes number characterizes the behavior of the particle suspended inthe flow, defined as the ratio of particle inertia to the fluid drag,

Stk ¼ t0uin

D¼ ρpd

2puin

9μDð17Þ

It can be seen that with the same granule diameter, the increase ofgas velocity and particle diameter will both lead to the increase ofparticle's Stokes number. Particles with larger Stokes number havelarger inertia and longer relaxation time t0 (the time constant in the ex-ponential decay of the particle velocity due to drag), whichmakes themless influenced by the flow. Thus a larger number of particles will tendto impact the granules and thus increase efficiency.

Increasing the granule diameter will also increase the filter height,because the filter height is fixed at 10D (unit height). Fig. 9 shows theeffect of Stokes number on initial filtration efficiency at the same rela-tive height L/D= 10. It can be seen from Fig. 9 that efficiency generallyshows an upward trendwith Stokes number. There are deviations alongthe upward trend, and the deviation decreases with an increase ofStokes number.

Fig. 9 can be divided into three particle regimes. Regime I corre-sponds to particles with Stk ≤ 0.01. In this regime, the efficiency is rela-tively low, and the growth trend is slow. This is because the particleStokes number is small, and the corresponding inertia and relaxationtime are also small, which makes the particles easily moved with the

Fig. 8. Effect of particle diameter on initial filtration efficiency.

Fig. 10. Effect of granule diameter on initial filtration efficiency.

272 F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

flowwith few particles deposited on the granular surface. In the secondregime, 0.01 b Stk b 0.05, filtration efficiency increases rapidly withStokes number. Particles with large Stokes number have high inertiaand kinetic energy and are more likely to break away from flow field,leading to a higher deposition rate. In the third regime, the Stokes num-ber is N0.05, and the growth trend of efficiency gradually slows down,tending to 100%.

With the same relative filter height, L/D = 10, Fig. 10 shows the ef-fect of granule diameter D on initial filtration efficiency in the three re-gimes. It can be seen that the filtration efficiency for regimes II and IIIdecreases with granule diameter even if the filter height increases.While for regime I, efficiency increases with granule diameter. There-fore, in the application process, when the Stokes number is located inregime II, reducing the granule diameter can significantly increase effi-ciency and reduce thefilter size (height).When the Stokes number is lo-cated in regime I, reducing the granule diameter will slightly decreasethe efficiency with the same relative filter height. However, for thesame filter height, reducing the granule diameter will significantly in-crease efficiency and pressure drop, and thus optimization is needed.For Stokes number located in regime III, the efficiency is close to 100%,and does not change much with the granule diameter. Therefore, inthis case appropriately increasing the granule diameter can significantlyreduce the pressure drop while ensuring the efficiency does notchange much.

3.4. Effect of uin, dp and D on particle deposition uniformity

In our previous work [20,31], we found that the particle depositionfraction decreases with filter depth and shows large spatial

Fig. 9. Effect of Stokes number on initial filtration efficiency.

inhomogeneity. Inhomogeneity of the particle deposition can cause adecrease in dust holding capacity. When the front part of the filter isclogged by the accumulated particles, pressure drop increases signifi-cantly, and it is necessary to either shut down the filter system or re-place the fouled granules. Therefore, the uniformity of the particledeposition plays an important role in the economic operation of thefilter.

The effect of gas velocity uin and particle diameter dp on depositionuniformity are shown in Fig. 11 and Fig. 12. For larger particles, deposi-tion uniformity decreases with gas velocity, and the larger the particlesare, the faster it decreases.While for small particles, e.g., dp= 1 μm, de-position uniformity slightly increases with gas velocity in large granulediameter filters. Larger particles have large inertia, and as gas velocityincreases, the Stokes number increases, whichmakes themmore easilydeposited in the front part of the filter. Thus deposition uniformity de-creases. Small particles are more strongly advected with the flow, andincreasing the gas velocity may cause them run farther in filters withlarge diameter granules, thus the deposition uniformity slightly in-creases. Deposition uniformity decreases rapidly with particle diameterin different granule diameter filters (Fig. 12).

With the same relative filter height L/D=10, Fig. 13 shows the effectof Stokes number on the deposition uniformity, where the depositionuniformity decreases with Stokes number. The graphs in Fig. 13 alsocan be divided into three Stokes-number regimes. In regime I, Stk ≤0.01, and deposition uniformity does not strongly vary with Stokesnumber and remains at a high value. In regime II, 0.01 b Stk b 0.2,

Fig. 11. Effect of gas velocity on deposition uniformity.

Fig. 12. Effect of particle diameter on the deposition uniformity.Fig. 14. Probability density function of particle deposition fraction along the filter.

273F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

deposition uniformity decreases rapidly with the increase of Stokesnumber. When Stk N 0.2 (regime III), the downward trend graduallydecreases.

To show the inhomogeneous deposition distribution of fly ash parti-cles in thefilter, we choose three cases for Stokes numbers in each of thethree regimes. The probability density function of particle depositionfraction along the three filters are shown in Fig. 14 wherein the particledeposition fraction decreases with filter depth for all the cases, andthe inhomogeneity of deposition become pronounced with largerStoke number. Fig. 14a shows the case with Stk=0.004 (regime I). Par-ticles deposit along thewhole of thefilter, and overall deposition unifor-mity is relatively good with γ = 0.65. Fig. 14b shows the case withStokes number located in regime II, where the particle deposition frac-tion shows a more pronounced peak than in Fig. 14a. For regime III(Fig. 14c), almost all of the particles deposit in the first half part ofthe filter with the dust holding capacity of the latter half part notutilized.

With the same relative filter height, L/D = 10, Fig. 15 shows the ef-fect of granule diameter D on deposition uniformity in the three re-gimes. Deposition uniformity for all cases increases with granulediameter, which means increasing the granule diameter can signifi-cantly increase the deposition uniformity and the dust holding capacityof the filters. Combining the results in Figs. 10 and 15, the efficiency is ~100% for large Stokes number (Stk ≥ 0.05), and increasing the granule di-ameter at the same relative height L/D improves deposition uniformity,

Fig. 13. Effect of Stokes number on deposition uniformity.

reduces pressure drop and ensures that the filtration efficiency does notvary much. For medium and small Stokes number (Stk b 0.05) at thesame filter height L, reducing the granule diameter can significantly in-crease the filtration efficiency, but it also will decrease deposition uni-formity and increase the pressure drop. Thus for filter designpurposes, optimization is needed.

4. Multiple correlation

The simulation results for initial filtration efficiency can be repre-sented in compact form via correlation. The Reynolds number, Re,Stokes number, Stk, and dimensionless diameter, dp /D are the dimen-sionless groups used in correlation to describe the effects of gas velocity,particle diameter and granule diameter. Recall that we fixed the filterheight at 10D (unit height) and have investigated the effect of each fac-tor on the initial efficiency. The correlation form of initial efficiency forthe filter with unit height, L0, is assumed to be,

ηL0 ¼ 1‐exp C1−C2 ReC3StkC4 dpD

� C5" #

ð18Þ

The four coefficients C1, C2, C3 and C4 are determined by means ofmultiple linear regression using the simulation results. The correlationis,

ηL0 ¼ 1‐exp −0:453−6:286 Re−0:206Stk3:346dpD

� −1:495" #

ð19Þ

Fig. 15. Effect of granule diameter on deposition uniformity.

Fig. 16. Comparison of filtration efficiency between correlation and simulation data.

274 F.-L. Wang et al. / Powder Technology 353 (2019) 267–275

where 0.2 ≤ uin ≤ 1 m/s, 1 ≤ dp ≤ 5 μm, and 1 ≤ D ≤ 5 mm. Fig. 16 showsefficiency predicted results by the correlation and the simulation data.The average deviation is b6%, which indicated that the correlation hasgood prediction accuracy.

With Eq. (16), the correlation of initial efficiency for the filter with aunit height (L0 = 10D) in Eq. (19) can be extended to any filter height,

η ¼ 1− 1−ηL0� �L=10D

¼ 1− exp −0:0453LD−0:6286

LD

Re−0:206Stk3:346dpD

� −1:495" #

ð20Þ

For uin = 0.2 m/s, dp = 1 μmand D = 5 mm, as an example, thesimulation results offilterswith differentfilter height are applied to ver-ify the accuracy of the correlation in Fig. 17. The predicted resultsfit wellwith the simulation,which indicates the correlation is of sufficient accu-racy for engineering purposes and useful for the design and structuraloptimization of the filter.

Fig. 17. Predicted results for cases with uin = 0.2 m/s, dp = 1 μm and D = 5 mm.

5. Conclusions

A numerical investigation has been carried out on the filtration per-formance of randomly packed granular filters used in hot gas clean-up.Our main conclusions are,

(1) A unit filter height of 10 times the granule diameter (10D) cansufficiently well predict the filtration characteristics of the entirefilter.

(2) Pressure drop increases rapidly with an increase of gas velocityand decrease of granule diameter.

(3) Filtration efficiency increases with gas velocity and particle di-ameter. Reducing the granule diameter increases filtration effi-ciency at a given filter height.

(4) Particle deposition uniformity increases with the decrease of gasvelocity and particle diameter. Increasing the granule diameterimproves deposition uniformity and consequently increase thedust holding capacity of the filter.

(5) The effect of Stokes number on efficiency and deposition unifor-mity can be divided into three regimes dependent on Stokesnumber. For medium and small Stokes number (Stk b 0.05), thefilter height and granule diameter need to be optimized for de-sign purposes.

(6) A correlation of initial filtration efficiency is obtained, and can beuseful in the design and structural optimization of granularfilters.

Acknowledgements

The present work is supported by the National Key R&D Program ofChina (2016YFB0601100).

The authors would also like to thank the Foundation for InnovativeResearch Groups of the National Natural Science Foundation of China(No.51721004), and the Science and Technology Planning Project ofXi'an (201809160CX1JC2-02).

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