Numerical study of the movement of fine particle in sound wave field

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1 Available online at ScienceDirect Energy Proceia 75 (2015 ) The 7 th International Conference on Alie Energy ICAE2015 Numerical stuy of the movement of fine article in soun wave fiel Dong Zhou a, Zhongyang Luo a *, Mengxiang Fang a, Jianing Jiang a, Hao Chen a, Donghui Sha a, Mengshi Lu a a Zhejiang University Yuquan Camus, Hangzhou,310027, China Abstract Inhalable articulate matter, esecially PM2.5 is one of the main ollutants in China an it s harmful to both human health an atmoshere. Since the removal efficiency of traitional ust removal evices such as ESP for PM2.5 is very low, retreatment becomes necessary before the ust gets into the ust remover. Acoustic agglomeration is one of the retreatment technologies which uses soun wave with high intensity to make fine articles get agglomerate an grow u, an imroves the efficiency of traitional ust removal evices for PM 2.5. In soun wave fiel, fine articles are carrie by the meium which in this aer is air, an vibrate with ifferent amlitue because of ifferent article sizes, thus relative movement aears an then articles have more chances to collie an get agglomerate. In this aer, the movement of articles with ifferent sizes in travelling wave soun fiel an staning wave soun fiel were calculate, incluing the velocity, islacement, amlitue an so on. The situation that Re<1 was consiere an Viscous force in Stokes region was chose as the main forces here. Stuying the movement of fine article in soun fiel with ifferent conitions has great meaning in learning the mechanisms of acoustic agglomeration Publishe The Authors by Elsevier Publishe Lt. This by is Elsevier an oen Lt access article uner the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-n/4.0/). Peer-review uner resonsibility of Alie Energy Innovation Institute Keywors: fine article; soun wave fiel; numeraical stuy 1. Introuction Inhalable articulate matter is one of the main ollutants in China an it s harmful to both human health an atmoshere. Particle with an aeroynamic iameter less than or equal to 2.5μm is calle PM 2.5 or fine article. It s the main cause of haze weather in China nowaays an causes a great concern [1]. What s more, PM 2.5 has very big secific surface area an it can absorb large amount of heavy metal, PAHs an some other toxic substances. An because of its tiny size it can get into human alveolus, which efinitely hurts human boy more than larger article [2]. However, the removal efficiency for PM 2.5 of * Corresoning author. Tel.: ; fax: aress: @zju.eu.cn Publishe by Elsevier Lt. This is an oen access article uner the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-n/4.0/). Peer-review uner resonsibility of Alie Energy Innovation Institute oi: /j.egyro

2 2416 Dong Zhou et al. / Energy Proceia 75 ( 2015 ) traitional ust removal evices such as ESP is quite low, so it becomes necessary to stuy the retreatments of ust removal [3]. Acoustic agglomeration is a kin of retreatment which uses soun waves with high intensity an a certain frequency to retreat fine articles in the flue gas. The air in the soun fiel vibrates with the srea of soun, an it carries articles with ifferent sizes to vibrate with ifferent amlitue. Relative movement between articles makes them agglomerate more frequently an grow u into bigger articles, an sequentially enhance the removal efficiency for fine articles of the follow-u ust removal evices. There have been a lot of theoretical works [4-6] on acoustic agglomeration, but the conclusions are not totally consistent since the mechanisms are very comlex. Orthokinetic interaction, which is wiely recognize as the rimary acoustic mechanism, is base on the entrainment of articles with ifferent sizes cause by the intensive acoustic wave in oly-iserse aerosol [7]. Smaller article is easier to be entraine. However, in mono-iserse aerosol, there was almost no orthokinetic interaction between these similar-size articles ue to the absence of relative oscillatory motion an the Hyroynamic interaction results from the interaction of articles becomes more imortant [8]. The Hyroynamic interaction consists of Acoustic Wake Effect an Mutual Raiation Pressure Interaction. The former is base on the asymmetric flow fiel aroun the article moving in soun fiel an the latter is base on Bernoulli s rincile. There are also some other mechanisms such as Acoustically Generate Turbulence, Acoustic Raiation Force, etc. which are generally consiere unimortant comare with Orthokinetic interaction an Hyroynamic interaction [9,10]. In this aer, Orthokinetic interaction an the situation that Re<1 are consiere an Viscous force in Stokes region is chose as the main force here. The movements of articles with ifferent sizes in both travelling fiel soun wave an staning fiel soun wave are calculate. The results uner all kins of frequencies, soun ressure level (SPL), initial hases, etc. are comare. These trials were carrie out to stuy the motion of articles in soun wave fiel, which ha great significance in stuying acoustic agglomeration. 2. Theory: simulation moel of article motion in soun fiel When a article is travelling in soun wave fiel, its vibration will ten to lag behin the carrier meium. The egree of entrainment μ eens on many elements such as the size of the article, the soun frequency an so on. The generalize equation of article motion can be can be written as[11] u ug 1 ( ug u ) t ( u ) 2 g u m m m 6 R( ug u) 6R g. (1) t t 2 t t In Eq. (1), u g an u stan for the velocity of the meium an the article resectively. The left sie of the equation is the resultant force acting on the article. The first right-han sie term is ressure graient force cause by the flui in absence of article. The secon term escribes the force require to accelerate the flui in the irect vicinity of the article. The next term is viscous Stokes rag. The last term accounts for the history of the article on the acceleration receive in the receing instants of time. Since the article intensity is much bigger than the gas intensity (ρ ρ g ), the first an the secon terms can be neglecte unless the gas ressure is very high. An base on the Stokes viscous force we consiere here, the last term can also be neglecte. Then we get the following equation by limiting the article motion ue to Stokes viscous force (Re<1): F 6 R( u u ). (2) g Combine Eq.(2) with the wave equation of the meium: u u t. (3) g 0 sin The solution has this form:

3 Dong Zhou et al. / Energy Proceia 75 ( 2015 ) u u sin( t) u e t/ , (4) where ω is angular frequency, τ stans for the article relaxation time which is escribe as 2 R 9 2, (5) an φ is hase shift between the vibration of the gas meium an that of the article, an μ is ynamic viscosity of gas meium. All articles are carrie along with the meium, with a certain amount of retaration because of inertia. In Eq. (4), the secon term of the right han sie is a transient term an it can be neglecte since τ is much more less than the vibration erio of the soun. Then the article motion equation can be escribe as 1 u u0 sin( t) 1, (6) an the exression of the egree of entrainment μ in Stokes Region can be efine as [12] 1 1 =cos. (7) The vibration equation of gas meium in travelling wave soun fiel an staning wave soun fiel can be escribe resectively as yt (x, t) Asin( t kx), (8) y (x, t) 2Acos( t)sin(kx). (9) s Accoring to Eq. (6) an Eq. (7), the vibration velocity of articles in travelling wave soun fiel an staning wave soun fiel can be calculate like this u u t s (x, t) Acos( tkx ), (10) (x, t) 2Asin( t )sin(kx), (11) an the exressions of article islacement are y y t s (x, t) Acos( tkx ), (12) (x, t) 2 Acos( t)sin(kx). (13) In these exressions, A stans for the vibration amlitue of gas meium an k is wave number. They can be exresse as A k 2 e, (14) 0c0 2 f c. (15) 0 In Eq. (14) e is effective soun ressure which can be get from SPL given in calculation ue to the following exression SPL 20log e, (16) ref here ref is reference soun ressure an it is generally count as Pa.

4 2418 Dong Zhou et al. / Energy Proceia 75 ( 2015 ) In this aer, all the calculations were one uner 20 an Pa. The soun velocity c 0 in this conition was about 344m/s. Particle ensity was counte as 2600kg/m 3 an the gas meium is air. 3. Results an iscussion 3.1. The egree of entrainment Fig. 1 shows that how soun frequency an article size affect on the egree of entrainment μ. When article gets larger, the frequency that can comletely carry the article becomes lower an for relatively smaller articles it gets easier to be carrie comletely by a larger range of frequencies, an articles bigger than 1mm can harly be carrie by soun with the frequency higher than 500Hz. Fig. 1. The relationshi between Particle entrainment factor μ an article size for ifferent frequencies 3.2. Particle movement in soun wave fiel Fig. 2. Movements of articles with ifferent sizes, f=1000hz, SPL=150B, x=0.5λ. Fig. 3. Movements of articles uner ifferent SPL, f=1000hz, =2μm, x=0.5λ.

5 Dong Zhou et al. / Energy Proceia 75 ( 2015 ) Fig. 4. Movements of articles uner ifferent frequencies, SPL=150B, =2μm, x=0.5λ. Fig. 2 shows the movements of articles with ifferent sizes. It s obviously that the bigger the article is, the lower the article vibration amlitue is. An there is a hase shift between the motion of the meium an articles which becomes bigger for lager article iameter. Fig. 3 shows the effect of SPL. The eak velocity of the article increases with the increase of SPL, an when it comes to 160B, the eak velocity of 2μm article can reach more 6m/s. The influence of frequency is shown in Fig. 4. In inicates that a higher frequency means a longer erio, an for the same article with a iameter of 2μm, the increase of the frequency makes the eak velocity of the article ecreases a little bit since entrainment factor is a little change. Fig. 5. Movements of articles at ifferent initial laces in travelling wave soun fiel, f=1000hz, SPL=150B, =2μm. Fig. 6. Movements of articles at ifferent initial laces in staning wave soun fiel, f=1000hz, SPL=150B, =2μm. In Fig. 5 it is clear that in the same conition, the movement of articles at ifferent initial laces in a travelling wave soun fiel only have ifference in initial hase. However, when articles are in a staning wave soun fiel, as shown in Fig. 6 there are wave noes an antinoes. At the wave noes articles on t vibrate at all an at the antinoes articles vibrate with the largest amlitue all the time. Particles will move towars to the wave noes for a relatively stable state, which might be quite helful for the agglomeration. But the real ifferences of travelling wave soun fiel an staning wave soun fiel in agglomeration is still not clearly stuie yet.

6 2420 Dong Zhou et al. / Energy Proceia 75 ( 2015 ) Conclusion In this aer, the movements of articles in both travelling wave soun fiel an staning wave soun fiel were calculate, an the influences of article size, soun frequency, SPL an the initial lace were consiere. The results showe that article size an frequency have great effect on the entrainment factor an a higher SPL cause larger vibration amlitue. The existences of wave noes an antinoes mae a staning wave soun fiel quite ifferent from a travelling one. In the future work, the rocess of acoustic agglomeration between two articles will be focuse on an exeriments on article motion etecting in soun wave fiel will be carrie out to verify the numerical result. Acknowlegements This work was suorte by a grant from the Major State Basic Research Develoment Program of China (973 Program) (No. 2013CB228500) an the Program of Introucing Talents of Disciline to University (No. B08026). References [1]Wu D., Hazy weather research in China in the last ecae: A review. Acta Scientiae Circumstantiae. 2012, 32, (2), [2]Wang J., Stuy of combine acoustic agglomeration with other means to remove coal-fire fine articles. Ph, Zhejiang University, [3]Heienreich, S. ;E. F., Conensational rolet growth as a reconitioning technique for the searation of submicron articles from gases. Chemical Engineering an Processing: Process Intensification 1995, 34, (3), [4]Song, L.; Koomann, G. H.; Hoffmann, T. L., An imrove theoretical moel of acoustic agglomeration. Journal of vibration an acoustics 1994, 116, (2), [5]Hoffmann, T. L.; Scaroni, A. W.; Song, L.; Chen, W.; Koomann, G. H., Exerimental an numerical analysis of bimoal acoustic agglomeration. Journal of vibration an acoustics 1993, 115, (3), [6]Zhang, G.; Liu, J.; Wang, J.; Zhou, J.; Cen, K., Numerical simulation of acoustic wake effect in acoustic agglomeration uner Oseen flow conition. Chinese Science Bulletin 2012, 57, (19), [7]Sheng, C.; Shen, X., Simulation of Acoustic Agglomeration Processes of Poly-Diserse Soli Particles. Aerosol Science an Technology 2007, 41, (1), [8]Liu, J.; Wang, J.; Zhang, G.; Zhou, J.; Cen, K., Frequency comarative stuy of coal-fire fly ash acoustic agglomeration. Journal of Environmental Sciences 2011, 23, (11), [9]Chou, K. H.; Lee, P. S.; Shaw, D. T., Acoustically inuce turbulence an shock waves uner a traveling-wave conition. The Journal of the Acoustical Society of America 1980, 68, (6), [10]Townsen, R. J.; Hill, M.; Harris, N. R.; White, N. M., Moelling of article aths assing through an ultrasonic staning wave. Ultrasonics 2004, 42, (1-9), [11]Patel, S.N.; Low intencity (155 DB) acoustic agglomeration-bench-scale exeriments. Ph. State University of New York at Buffalo [12]González, I. A.; Hoffmann, T. L.; Gallego, J. A., Precise measurements of article entrainment in a staning-wave acoustic fiel between 20 an 3500Hz. Journal of Aerosol Science 2000, 31, (12), Biograhy Prof. Zhongyang Luo, Director of CEU, Cheung Kong Scholar, Winner of National Funs for Talente Professionals. Research fiels inclues Clean coal combustion science an technology, Utilization of bio-energy an solar energy, Pollutants control uring coal/biomass combustion an gasification, etc.