Modeling Submicron Particles Collection in Laminar Forced Convection Gas Flow by a Rectangular Venturi Scrubber

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1 Oen Journal of Air Pollution, 2016, 5, Publishe Online March 2016 in SciRes. htt:// htt://x.oi.org/1236/oja Moeling Submicron Particles Collection in Laminar Force Convection Gas Flow by a Rectangular Venturi Scrubber Serge Wensia Igo 1, Kokou N wuitcha 2, Belkacem Zeghmati 3, Xavier Chesneau 3 1 Déartement Energie, Institut e Recherche en Sciences Aliquées et Technologies (IRSAT/CNRST), Ouagaougou, Burkina Faso 2 GPTE-LES, Déartement e Physique, Université e Lomé, Lomé, Togo 3 Laboratoire e Mathématiques et Physique es Systèmes (LAMPS), Perignan, France Receive 11 January 2016; accete 11 March 2016; ublishe 14 March 2016 Coyright 2016 by authors an Scientific Research Publishing Inc. This work is license uner the Creative Commons Attribution International License (CC BY). htt://creativecommons.org/licenses/by/4.0/ Abstract Venturi scrubbers are usually use for large articles cleaning in turbulent gaseous flow. In this work, submicron articles scrubbing in laminar force convection usty air flow in a rectangular venturi scrubber have been numerically simulate. Hyroynamics effects an scrubbing rocess are investigate in etail. Results are resente as flow velocity, axial ressure, streamlines attern, articles an rolets mass fraction rofile, an collect efficiency. They show that venturi scrubbers can be efficient for submicron articles scrubbing. In fact, a better collect efficiency is obtaine at high articles-rolets resience time, high ratio rolets concentration/articles concentration, low venturi iameter ratioan low Reynols numbers. There is a critical Reynols number value for which the collect efficiency becomes very low an tens to be constant. Keywors Venturi Scrubber, Submicron Particles, Diffusion, Laminar Flow, Collect Efficiency 1. Introuction Venturi scrubbers are wiely use for articles an gaseous collection from inustrial exhaust. Their high collection efficiency coule with low construction an maintenance cost has le to many stuies. The large ower requirements for oeration an large ressure ro across the evice are its main rawbacks [1]. These evices How to cite this aer: Igo, S.W., N wuitcha, K., Zeghmati, B. an Chesneau, X. (2016) Moeling Submicron Particles Collection in Laminar Force Convection Gas Flow by a Rectangular Venturi Scrubber. Oen Journal of Air Pollution, 5, htt://x.oi.org/1236/oja

2 consist of channel with three arts: a convergent section, a throat an a ivergent section or iffuser. The ollute gas stream is accelerate in the convergent, reaches its maximum velocity in the throat an finally is ecelerate in the iverging section. A liqui or an aqueous solution (generally water) is introuce in the venturi to create a sray of rolets for the articles cature. The rolets that cature articles are searate in a evice connecte to the venturi an the cleane air is ischarge into the atmoshere. In usty gas scrubbing rocess by rolets in wet scrubbers, large articles are rincially collecte by inertial imaction [2]. Their large inertia allows them to leave the gas streamlines to imact onto water ros. Submicron articles which have iameter less than 1µm because their smallness cannot imact onto ros an are collecte by brownian iffusion [3]. If a article follows a streamline which aroaches the ro within a istance of the article raius, the article is cature by the ro; this kin of collection is calle intercetion. The size of rolets usually lies in the range of - 1 mm in iameter [4]. The moe of introuction of the scrubbing liqui has le to three tyes of venturi: The Pease-Anthony tye, the wette aroach tye an the ejector tye. In the Pease-Anthony venturi tye, the scrubbing liqui is introuce into gas stream usually at the throat an sraye by the high gas velocity. This kin of venturi is the first to be investigate [5]-[8]. Basing on the inertial imaction hyothesis, they have shown that the collect efficiency is eening on gas liqui ratio, venturi geometry, articles an rolets size; An large articles lea to a better collect efficiency. In the wette aroach tye, the scrubbing liqui is introuce as a film streaming along the venturi tube walls. Here, rolets are forme ue to the gas shear on the liqui film, articularly in the throat an a ortion of the liqui remains as a film on the wall. This tye of venturi is recommene for hot gas flow, ahesives an corrosives ust [9]-[11]. They have shown that the fraction of liqui streaming as a film influences the collect efficiency an the ressure ro across the evice. In the ejector tye, the liqui is injecte through nozzles by a ressure atomizer at the throat. This king of venturi is efficient for both articles an gaseous ollutants. Moreover, it is ieal for hanling sticky or abrasive materials [12]. Desite their angerousness for human health [13] [14], submicron articles have not been receive much attention in venturi scrubbing rocess. In these stuies cite above, only large articles are consiere an the collect hyothesis is only base on inertial imaction. To imrove the submicron articles removal efficiency by imaction, others mechanisms such as electrostatic attraction an conensation of water vaor on articles may be use [15] [16] to increase articles size. In others wet scrubbers, iffusion mechanism has been wiely stuie. Slinn [17], using imensional analysis coule with exerimental ata, gives correlation for single rain rolet collect efficiency. Jung an Lee [18] erive the collision efficiency ue to Brownian iffusion an intercetion for a multile flui shere system. As seen, iffusive effects have been neglecte in venturi scrubbing rocess. Recently, Igo et al. [19] [20] erforme a numerical coe to stuy the heat an mass transfer in venturi channels. Therefore, the objective of this work is to aat this coe for the submicron articles collection stuy in venturi scrubbers base on iffusion mechanisms. 2. Problem Formulation The venturi channel is comose of two lates of sections lengths (L1, L2, L3, L4, L5). The istance between the lates is 2R in the entrance region. The external surface lates are subjecte to a constant wall temerature T w. Temerature T o, relative humiity ϕ o, ownwar velocity U o, concentration of articles C o of usty air flow are suose to be uniform in the inlet of the venturi channel. A sray of rolets is injecte into gas stream at the inlet with an initial concentration C o. The venturi wette walls are submitte to the evaoration of water vaor. It is assume that: Transfers are two-imensional an axisymetric; The raial ressure graient comonent is neglecte; Dufour an Soret effects are neglecte; Collects mechanisms are only by iffusion an intercetion; The number of articles collecte is equal to the number of rolets lost; The mixture comose of air, articles an rolets, is consiere as an uncomressible ieal gas. The imensionless equations moeling the usty air flow through the venturi scrubber in the referential (o,x,z) (see Figure 1) are: Continuity equation 11

3 Axial-momentum equation Figure 1. Schematic reresentation of the stuie system in the (O, X, Z) referential. ( ρ V ) ( ρ U ) x ( ρ VU ) ( ρ UU ) + = z 0 U P 1 U U ρ + + = + µ µ + t x z z Re x x z z Raial-momentum equation Energy equation ( ρ VV ) ( ρ UV ) V 1 V V ρ + + = µ µ + t x z Re x x z z ( ρ cvt ) ( ρ cut ) T 1 T T ρ c + + = λ λ + t x z RePr x x z z Convection-iffusion equation of rolets ( ρ VC) ( ρ UC) C 1 C C ρ ρ ρ + + = D D + S t x z ReSc x x z z Convection-iffusion equation of articles ( ρ VC) ( ρ UC) C C C ρ ρ ρ = D D + S t x z ReSc x x z z Convection-iffusion equation of water vaor ( ρ VW ) ( ρ UW ) W 1 W W ρ + + = D D + t x z Re Sc x x z z Flow rate conservation U x Q = o + Qev (8) (1) (2) (3) (4) (5) (6) (7) 12

4 Q o an Q ev are resectively the inlet gas flow rate an the cumulate evaorate flow rate. Accoring to Seinfel an Panis [21], the single ro collision efficiency is efine as the number of articles containe within the volume swet by a falling ro that are collecte. Note that one rolet swees er π 2 unit time a volume of cyliner equal to V. So, by writing mass balance for articles, the term source 4 reresenting the amount of isaearing of articles can be exresse as: EF is the overall efficiency collect by a single rolet: where Eiff (, ) an int (, ) π 2 S = ρ V EFCC (9) 4 iff (, ) int (, ) EF = E + E (10) E are the collision efficiency ue to Brownian iffusion an the collision efficiency ue to intercetion resectively. Accoring to Jung an Lee (1998), they can be exresse as: int ( 1 α)( 3σ 4) π + Eiff (, ) = 2 4 Pe J + σ K 1 α R 1 R J + σ K 1+ Rint 2 1+ R int int (, ) = + ( 3σ + 4) E where α is the acking ensity, efine as the volume fraction of ros, σ is the viscosity ratio of water to air, Rint =, J = 1 6α 5+ α 5, K = 1 9α 5+ α + α 5 an Pe is the Peclet number. Using one of the hyothesis formulate above (the number of articles collecte is equal to the number of rolets lost), S = S. Dimensionless terms sources can then be euce as: 3. Numerical Proceure 3.1. Coorinate Transformation int 2 (11) (12) π 2 S = ρ V EFC C (13) 4 π 2 S = ρ V EFCC (14) 4 In orer to avoi the non-uniformity of the mesh sacing along the venturi lane, we use a mathematical transformation which transforms the irregular surface of the late into a straight line: ( x, z ) such as ( η = x F z ) an ξ = z with F ( z ) = az + b, a an b are real number. Therefore, the Equations (2)-(7) can be rewritten in the numerical omain: ( γv ) ( γu ) aη ( γu ) Φ 1 Φ Φ Φ γ + + t aξ + b ξ aξ + b 1 χ Φ aη Φ aη Φ = B+ κ + χ + G aξ + b η aξ + b ξ aξ + b ξ aξ + b where γ, B, κ, χ, an G are efine below (Table 1). The Equations (1) an (8) are resectively: ( ρ V ) ( ρ U ) aη ( ρ U ) 1 + aξ + b ξ aξ + b ( ξ ) (15) (16) U a + b η = Qo + Qev (17) 13

5 Table 1. Exression of coefficients γ, B, κ, χ, an G of Equation (15). Φ γ B κ χ G U ρ P / ξ 1/Re μ 0 V ρ 0 1/Re μ 0 T ρ c 0 1/RePr λ 0 W ρ 0 1/ReSc D 0 C ρ 0 1/ReSc C ρ 0 1/ReSc D D S S 3.2. Initial an Bounaries Conitions Initial Conitions t < t 0 ; t 0 is the imensionless time when the mixture air-articles-rolets water enters into the venturi: U = V T = 1 W = 1 C = 1 C ( ηξ) Bounaries Conitions At the inlet (ξ, 0 < η < 1) 3 U ηξ η 2 2 (, ) ( 1 ), = 1 = V T = 1 W = 1 C = 1 C ( ηξ) At the outlet (ξ = L/DH, 0 < η < 1) U ξ V ξ At the wall (0 < ξ < L/DH, η = 1) T ξ W ξ U V ( ηξ) = V T ( ηξ) = T W ( ηξ), ev At the axis of symmetry (0 < ξ < L/DH, η ) U ( ) V ηξ =, 0 T, w W, = Ww C C C We characterize the sensible Nusselt number using the following exression: Nu S 1 1 T = T T ξ ( ) F ( ) w b w ξ The collect efficiency (CE) of the venturi is calculate using the following exression [22]: CE = 1 1 ( ) ηv C ηξ, η ( ) ηv C ηξ, η out in C C C, = 1 ξ The Equation (15) associate to initial an bounaries conitions are iscretize using an imlicite scheme base on the finite volume metho an escribe by Suhas V. Patankar [23]. The system of algebraic equation euce from iscretisation of the raial momentum equation comonent, energy an iffusion equations, is for each equation tri-iagonal; so it was solve by Thomas algorithm. The iscretisation of the axial momentum equation leas to an algebraic equation system comose of M equations an (M + 1) unknowns variables (U an P). Consequently, it was solve with Gauss algorithm. The convergence was obtaine when the following (18) (19) 14

6 criterion was satisfie: Φ Φ n+ 1 n i, j i, j 5 10 n+ 1 Φi, j (20) where Φ= U, V, T, W, C, C. The valiation of our numerical coe has been carrie out by comaring our results with the most closely numerical solution (see Figure 2). As seen, the iscreancies between our results an those of W. M. Yan an T. F. Lin [24] o not excee 0.01%. The comutational gri is uniform in the two irections. The ste length in each irection an the ste time t = are chosen by numerical exeriments rovie by the stabilities conitions of Thomas an Gauss algorithms. To ensure that the results are gri ineenent, comutations are carrie out for several mesh size. The effect of the gri size on the Nusselt number leas to a mesh size of 60 noes in the η irection an 120 noes in the ξ irection corresoning to the ste lengths (Δη, Δξ). Δη = ; Δξ = As seen, an increase of the number of noes by a factor of four oes not influence the results significantly. The iscreancies between Nusselt values for mesh size (60 120) an mesh size ( ) reorte in Table 2 is less than 5%. 4. Results an Discussion In the resent stuy, calculations were erforme for : L 1.1 m, L 2.2 m, L 3.15 m, L 4.3 m, L 5.15 m, R.1 m, T o = K, T amb = K, = 10 2 µm, = 100 µm, the ratio rolets concentration/articles concentration (C o /C o ) varies from 1 to 9 an the Reynols number in the range of 500 to Figures 3-7 show the effect of Reynols number on the velocity an the axial ressure evolution in the venturi. We note that the venturi effect is observe (velocity an ressure graient evolution are oosite in each section Table 2. Gri ineenence. Gri (η ζ) ζ.2 ζ.4 ζ.6 ζ.8 Values of Nu s (Re = 500) (60 120) ( ) Figure 2. Valiation of the numerical coe (T o = 20 C, T w = 40 C, ϕ o = 50%, Pr.703, Sc.592, Re = 500). 15

7 Figure 3. Velocity atterns. Β.25, Re = Figure 4. Velocity atterns. Β.25, Re =

8 Figure 5. Velocity atterns. Β.25, Re = Figure 6. Axial ressure graient versus axial coorinate: effect of Reynols number. Β.25. of venturi). In fact, in the converging section there is a continuous increase of the ressure ro ue to the acceleration of the mixture air-articles-water rolets velocity resulting of the conversion of the otential energy into kinetic one of the mixture air-articles-water rolets through the venturi throat. Maximum velocity of the mixture air-articles-water rolets is reache in the throat. In aition, the increasing of Reynols number 17

9 Figure 7. Axial velocity versus axial coorinate: effect of Reynols number. β.25. increases venturi effect. Figures 8-10 illustrate the effects of Reynols number on the flow structure. The change of streamlines is observe for large Reynols numbers, consequently of the increase of flow velocity. For low Reynols number, streamlines are arallel to the channel walls. Effects of arameter β on streamlines atterns are resente on Figures β equal to 1 is relate to a classical vertical channel, streamlines are arallels to the channel walls as showing in Figure 12. When ecreasing β, channel is rogressively transforme to venturi one. We note that streamlines are very close in the convergent an ivergent section, an they are merge in the throat articularly for β equal to 5. The flow velocity in the throat is of course more imortant as β ecreases. An analyse of the effect of the ratio rolets concentration/articles concentration at the inlet (Figures 14-17) show that for equal inlet concentrations, there is no ifference between articles an rolets concentration at the venturi exit. This result is the consequence of one of our hyothesis (the number of articles collecte equal to the number of rolets lost). We note that the increase of the ratio rolets concentration/articles concentration leas to a better collect of articles because the interactions articles-rolets are eening on the rolets number an increases as the rolets number increases. So the collect efficiency is eening on the ratio (rolet concentration/articles concentration). Figure 18 show the collect efficiency versus time. Collect efficiency is more imortant as the articles-rolets resience time in the venturi scrubber is rising. This result is in agreement with results of others authors [25]. It is clear that articles staying uring a long time in the scrubber enhance their robability to be collecte by rolets. The effect of Reynols number on the collect efficiency is resente in Figure 19. The collect mechanism accoring to one of our hyothesis is suose to be only by iffusion an intercetion; The collect efficiency ecreases as the Reynols number increases because the articles-rolets resience time articles ecreases in the venturi scrubber. We note also, the existence of a critical Reynols number where the ecrease of the collect efficiency is very imortant an tens to be constant. Figure 20 show that the collect efficiency increases as β values ecreases. This result confirms that in the venturi scrubber, a better mixing articles-water rolets ue to the reuction of the channel iameter leas to an imrovement of the collect efficiency. Venturi scrubber aears to be more efficient for submicron articles scrubbing than a wall lane channel one. 5. Conclusions Submicron articles scrubbing in a vertical rectangular venturi scrubber is numerically investigate in the resent stuy. In orer to etermine the collect efficiency, transfers equations are solve using finite volume 18

10 - 0 Figure 8. Streamlines atterns. Re = 500, β Figure 9. Streamlines atterns. Re = 1000, β

11 - 0 Figure 10. Streamlines atterns. Re = 2000, β Figure 11. Streamlines atterns. Re = 2000, β = 1. 20

12 - 0 Figure 12. Streamlines atterns. Re = 2000, β Figure 13. Streamlines atterns. Re = 2000, β

13 Figure 14. Particles an rolets mass fraction at the venturi outlet versus time. C o /C o = 1, Re = 500, β.25. Figure 15. Particles an rolets mass fraction at the venturi outlet versus time. C o /C o = 3, Re = 500, β.25. Figure 16. Particles an rolets mass fraction at the venturi outlet versus time. C o /C o = 6, Re = 500, β

14 Figure 17. Particles an rolets mass fraction at the venturi outlet versus time. C o /C o = 9, Re = 500, β.25. Figure 18. Collect efficiency versus time. C o /C o = 9, Re = 500, β.25. Figure 19. Collect efficiency versus Reynols number. C o /C o = 1, β

15 Figure 20. Collect efficiency versus β. Re = 500, C o /C o = 9. metho, Gauss an Thomas algorithm. The effects of inlet Reynols number, flow structure, inlet ratio rolet concentration/articles concentration, venturi iameter ratio an secies resience time on the collect efficiency are been investigate in etails. The major results are: A venturi scrubber is more efficient for submicron articles scrubbing than a wall lane channel one. Collect efficiency is better at low Reynols numbers, high ratio rolet concentration/articles iameter, low venturi iameter ratio an high resience time of secies. There is a critical Reynols number, where the collect efficiency ecreases significantly an tens to be constant. Acknowlegements The authors acknowlege the embassy of France in Burkina Faso for his financial suort. References [1] Viswanathan, S. (1997) Moeling of Venturi Scrubber Performance. Inustrial & Engineering Chemistry Research, 36, htt://x.oi.org/1021/ie970235s [2] Chate, D.M an Kamra, A.K. (1997) Collection Efficiencies of Large Water Dros Collecting Aerosol Particles of Various Densities. Atmosheric Environment, 31, htt://x.oi.org/1016/s (96)00338-x [3] Dullien, F.A.L. (1989) Inustrial Gas Cleaning. Acaemic Press, New York. [4] Park, S.H., Jung, C.H., Jung, K.R., Lee, B.K. an Lee, K.W. (2005) Wet Scrubbing of Polyiserse Aerosols by Freely Falling Drolets. Aerosols Science, 36, htt://x.oi.org/1016/j.jaerosci [5] Johnstone, H.F., Fie, R.B. an Tassler, M.C. (1954) Gas Absortion an Aerosol Collection in Venturi Atomiser. Inustrial an Engineering Chemistry, 45, [6] Calvert, S. (1970) Venturi an Other Atomizing Scrubbers Efficiency an Pressure Dro. AICHE Journal, 16, htt://x.oi.org/1002/aic [7] Boll, R.H. (1973) Particles Collection an Pressure Dro in Venturis Scrubbers. Inustrial & Engineering Chemistry Funamentals, 12, htt://x.oi.org/1021/i160045a008 [8] Leith, D.E. an Cooer, D.W. (1980) Venturi Scrubbers Otimization. Atmosheric Environment, 44, htt://x.oi.org/1016/ (80) [9] Azzoari, B.J. an Govan, A.H. (1984) The Moelling of Venturi Scrubbers. Filtration & Searation, 21, [10] Pulley, R.A. (1997) Moelling the Performance of Venturi Scrubbers. Chemical Engineering Journal, 67, htt://x.oi.org/1016/s (97) [11] Rahimi, A., Taheri, M. an Fathikaljahi, J. (2005) Mathematical Moelling of Non-Isothermal Venturi Scrubbers. The Canaian Journal of Chemical Engineering, 83, htt://x.oi.org/1002/cjce [12] Gamisans, X., Sarrà, M. an Lafuente, F.J. (2004) Flui Flow an Puming Efficiency in an Ejector-Venturi Scrubber. 24

16 Chemical Engineering an Processing, 43, htt://x.oi.org/1016/s (03) [13] Clye, M.A., Guttor, P. an Sullivan, E. (2000) Effects of Ambient Fine an Coarse Particles on Mortality in Phoenix, Arizona. NRCSE Technical Reort Series, No. 40, [14] Vermont Air Pollution Control Division (1997) Fine Particles: The Microscoic Menace. Air Matters, 2, 1-8. [15] Bologa, A., Paur, H. an Wäscher, T. (2001) Electrostatic Charging of Aerosol as a Mechanism of Gas Cleaning from Submicron Particles. Filtration & Searation, 38, htt://x.oi.org/1016/s (01) [16] Huang, C.-H., Tsai, C.-J. an Wang, Y.-M. (2007) Control Efficiency of Submicron Particles by an Efficient Venturi Scrubber System. Journal of Environmental Engineering, 133, htt://x.oi.org/1061/(asce) (2007)133:4(454) [17] Slinn, W.G.N. (1983) Preciitation Scavenging. Atmosheric Sciences an Power Prouction Division of Biomeical Environmental Research, US Deartment of Energy, Washington DC. [18] Jung, C.H. an Lee, K.W. (1998) Filtration of Fine Particles by Multiles Liqui Dro an Gas Bubble Systems. Aerosols Sciences an Technology, 29, htt://x.oi.org/1080/ [19] Igo, S.W., Kokou, N., Ouéraogo, I., Dieuonné, J.B. an Belkacem, Z. (2014) Numerical Simulation of Laminar Force Convection Air Flow in a Rectangular Venturi Channel. Journal of Engineering Stuies an Research, 20, [20] Igo, S.W., Dieuonné, J.B., Palm, K., Kokou, N., Belkacem, Z. an Chesneau, X. (2011) Laminar Force Convection Heat an Mass Transfer in Venturi Tube with Wette Walls. Frontiers in Heat an Mass Transfer, 2, Article ID: htt://x.oi.org/1098/hmt.v [21] Seinfel, J.H. an Panis, S.N. (1998) Atmosheric Chemistry an Physics: From Air Pollution to Climate Change. Wiley, New York. [22] Mohebbi, A., Taheri, M., Fathikaljahi, J. an Talaie, M.R. (2003) Simulation of an Orifice Scrubber Performance Base on Eulerian/Lagragian Metho. Journal of Hazarous Materials, 100, htt://x.oi.org/1016/s (03) [23] Suhas, V.P. (1980) Numerical Heat Transfer an Flui Flow. Hemishere Publishing Cororation, New York. [24] Yan, W.M. an Lin, T.F. (1998) Combine Heat an Mass Transfer in Laminar Force Convection Channel Flows. International Communications in Heat an Mass Transfer, 15, htt://x.oi.org/1016/ (88) [25] Koo, J., Hong, J., Lee, H. an Shin, S. (2010) Effect of the Particle Resience Time an the Sray Drolet Size on the Particle Removal Efficiencies in a Wet Scrubber. Heat an Mass Transfer, 46, htt://x.oi.org/1007/s

17 Nomenclature C imensionless concentration = C/C o c imensionless secific heat = c /c o iameter (m) D imensionless mass iffusion coefficient = D/D o DH hyraulic iameter (m) = 2R M molar mass (kg mol 1 ) Pr Prantl number = μ o c o /λ o Re Reynols number = ρ o U o DH/μ o Sc Schmit number= μ o /ρ o D o T imensionless temerature = T/T o t imensionless time = tu o /DH U gas imensionless axial velocity comonent = U/U o S imensionless source term = S/S o V gas imensionless raial velocity comonent = V/U o X imensionless raial coorinate = X/DH Z imensionless axial coorinate = Z/DH Greek symbols β venturi iameter ratio=throat iameter/2r λ imensionless thermal conuctivity = λ/λ o ρ air imensionless ensity = ρ/ρ o µ air imensionless viscosity = μ/μ o Subscrits a air amb ambient b bulk quantity rolets ev evaoration o inlet articles w wall W imensionless water vaor mass fraction = W/W o 26