Numerical analysis on the agglomeration behavior of fine particles in plane jet

Transcription

1 Numercal analyss on the agglomeraton behavor of fne partcles n plane et Mn Guo 1, a, Ja L 2, Xn Su 1 and Gurong Yang 1 1 Tann Academy of Envronmental Scences, Tann, , Chna; 2 The Fourth Research and Desgn Engneerng Corporaton of CNNC, Chna a @qq.com Abstract The plane turbulent et s selected as the research obect to smulate the aggregaton stuaton of the sub-mcron grade fne partcles n the plane turbulent et flow feld, analyze the movement of the fne partcles n the flow feld and the evoluton process of the partcle sze and study the nfluence of dfferent tme, nterface volume fracton and St number on the aggregaton of the fne partcles through the couplng of large-eddy smulaton and partcle populaton balance model. The results show that the fne partcles szes n the pulse-et development ncrease gradually and the number densty decreases gradually to tend to be stable. The ncrease of the nterface volume fracton has enhanced the nteracton degree between the flud and the partcles and the agglomeraton result of the fne partcles s more sgnfcant. The ncrease of the St number has affected the movement of the fne partcles n the flow feld and weakened the agglomeraton effect of the fne partcles. Keywords PM2.5; large-eddy smulaton; partcle populaton balance model; free molecular coagulaton nucleaton; plane turbulent et. 1. Introducton The study concluded that the hazard of the fne partcles on the envronment and the human body manly depends on small sze and large quantty. Among the exstng fne partcle control technologes [1-3], the turbulent agglomeraton technology s one of the technology means wth strong economcal effcency and practcal value. Ths technology has fully consdered the entranment produced by the turbulent eddy and the followng features of the fne partcles, used the eddy structure [4] to change the moton tral of the fne partcles and gude the fne partcles followng the eddy to aggregate, collde and gather so as to change them nto the partcles wth larger sze to be collected by the dedustng equpment effectvely. The two-phase et mxng flow formed by the combnaton of the gas-sold two phase flow and plane turbulent et has the broad appled value n varous felds such as envronmental engneerng and pneumatc transport process. The author uses the LES (large-eddy smulaton) and PBM(partcle populaton balance) model to study the phenomena of collson and agglomeraton of mcron and sub-mcron fne partcles n plane turbulent et and wth the combnaton of the research development of computatonal flud mechancs and partcle knetc, stmulates the movement of the fne partcles n the flow feld and the nfluence of dfferent tme, nterface volume fracton and St number on the agglomeraton of fne partcles. 260

2 2. Basc equatons and soluton methods 2.1 Equatons for flow control The large-eddy smulaton dvdes the nstantaneous movement of turbulence nto large-scale moton and small-scale moton through flter functon. The large-scale moton s solved by drect numercal smulaton and the small-scale moton s solved by the correspondng turbulence model. The detaled flow feld nformaton and nstantaneous characterstc whch are closer to the actual stuaton of turbulent flow can be gven. To flter the Naver-Stokes equaton and defne the fltered varable as: 1,, ' ' ( x, y, t) ( x, y, t) dx dy A (1) A In the equaton, s the arbtrary varable(such as partcle densty, mass fracton, etc.). A s calculaton elemental area. t s the tme. x and y are the coordnate components. Substtute (1) nto N-S equaton and convecton-dffuson equaton to obtan the control equaton of the large-eddy smulaton as shown n the follows: t u u u t x u x (2) 0 p x x x (3) u t x D s S x x (4) In the equaton, s the densty of flud, kg/ m 3. P s the flud pressure, pa. u s flud velocty (, - represents x, y components), m/s. s flud shear stress tensor (-1, 2, 3; -1, 2, 3). s sublattce stress tensor (-1, 2, 3; -1, 2, 3). s effectve dffuson coeffcent. s source term of the varable. The sub-grd stress D s uses the followng model: S kk t S (5) In the equaton, s the Kronecker operato. s stran tensor (-1, 2, 3; -1, 2, 3). s sub-grd eddy vscosty coeffcent whch uses Smagornsky-Llly model: S (6) S 2 t L s t In the equaton, L s s the sub-grd mxed length and S 2S S represents the mode of stran tensor. 2.2 Populaton balance model (PBM). The partcle populaton balance model [5] descrbes knetc events such as collson, condensaton, fragmentaton, condensaton/evaporaton, nucleaton, and deposton of partcles n the dscrete system and the detals of evoluton process of the partcle scale knetcs can be obtaned by the dscrete nterval method. Ths paper supposes that the partcles are spheres of unform densty and the partcle populaton s dvded nto eght sub-ntervals from Bn-0~Bn-7accordng to the partcle sze from large to small(bn represents the partcle sze). And consderng the nfluence of coagulaton on the dstrbuton of partcle sze(coagulaton generally refers to the process durng whch two sphercal partcles collde and bond together to form a partcle wth larger sze) and the artcle populaton balance model governng equaton s shown n the followng: 261

3 In the equaton: a V,V' t n V, nv, t t 1 2 V 0 0 B ag, a V V ', V ' n V V ', t n V ', t dv ' a V, V ' n V, t n V ', t dv ' D ag, s sngle-dgt concentraton of the partcle wth the volume ofv, I/m³. s the coagulaton nucleaton of the two partcles wth volumes as V and V '. B ag, (7) s the coagulaton generaton (to avod repeated measurements, please handle wth a factor of 1/2); s the coagulaton mssng term. The turbulence aggregaton s manly produced by the collson between the partcles because of the accumulaton of part of partcles or maldstrbuton of radal velocty between the partcles caused by velocty contrast produced by the turbulence of gas phase. The man factor affectng the turbulence aggregaton s St number (Stokes number) and the nterface volume fracton. Among them, Stokes number refers to the rato of the aerodynamc reacton tme of the partcle to the tme scale of the flud characterstc and represents the dffuson ablty non-dmensonal number of the partcles n the flud. The nterface volume fracton refers to the volume percentage for the nlet partcle under a certan St number. The research shows that the partcle sze of the fne partcles of the combuston source s 95% and dstrbuted n the range of 0.021um-0.2um. After the calculaton, St 0.1, that s, belongs to the fnte nerta partcle. Ths paper uses the free molecular condensaton nuclear model for the smulaton [6]. The equaton for St s as follows: St 2 pd pu 18H The equaton for free molecular condensaton nuclear s as follows: a d, d 2kBT 3 k D ag, p (8) d d In the equaton: H-s the nozzle heght, mm; U-s the nlet man flow velocty, m/s; s the partcle aerodynamc reacton tme, ms; s the tme scale assocated wth large-scale coherent vortex, ms; s turbulent energy dsspaton rate ; Among them, s the flud vscosty, kg / (m s); s the partcle densty, kg / m 3 ; - d s the partcle sze (, - are partcles wth the frst two szes before the coagulaton), μm; T - s the partcle phase temperature, K ; s the Boltzmann constant, s the contnuous phase vscosty, kg / (m s). 3. Physcal model and expermental verfcaton 3.1 Physcal Models and boundary condtons k Fg 1 s the structure dagram for the two-dmensonal plane turbulent et and to verfy the accuracy and feasblty of the model, the geometrc parameters and operatng condtons of the model are consstent wth the lterature [7], that s, takng flow drecton length (X) length (Y ) = 96H 68H, nozzle heght H = 10mm, nectng the gas-sold two-phase flow nto the rectangular space wth U = 10m / s, defnng the characterstc tme scale T0 = H / U, takng the calculaton tme step as 0.001s and lettng the nlet Reynolds number Re meet: 2H Re U d d 2 k B p p (9) 262

4 The partcle phase densty = 1000kg/m 3. The structured staggered mesh s used to dsperse the computatonal regon and the SIMPLE program s used to solve the N-S equaton and the composton equaton. The spatal dscretzaton uses the Quck format. 3.2 Expermental verfcaton Fg. 1 Structure dagram for the two-dmensonal plane turbulent et Based on the development of the vortex structure from the ntal stage to the stable stage of the two-dmensonal plane et flow feld at Re=11300, the three stages of et development are the ntal, mddle and stable stages of the et development and the flow feld characterstcs of each stage are ftted well wth the smulaton results of Jn Yuhu et. al [7]. When T=40T0~160T0, there s the symmetrc spanwse vortex wth opposte rotate drecton at the upper and lower shear layers of the et at the ntal stage. Wth the development of the spanwse vortex, the vortex nteracts wth each other and gradually forms a staggered dstrbuton state, resultng n the thrd vortex created between the two vortces and producng the "cat eye structure smlar to that n the mxed layer flow. When T=200T0~ 240T0 at the md-term of et development, the small vortex gradually develops large. The downstream small vortex and the upstream subsequent vortex are gradually entraned by the large vortex and the sze of the large vortex ncreases contnuously wth the parng and coalescence by the large vortex. Durng ths process, there s even the "three-pole"phenomenon of the synchronous parng of the three vortexes. When T 280T0, under the contnuous parng and coalescence of the large vortex, these vortex pars nteract wth each other to gradually get away from the center lne and generate the staggered eddy structure wth larger sze and then gradually reach the stable state. Fg. 2 Self-smlarty of flow velocty Accordng to the statstcal method of the lterature [7], the low velocty dstrbuton of the sectons wth dfferent features are taken to defne the Um as the flow velocty on the center lne of the et and the Yu as the dstance of the velocty of the 1/2 to the velocty of the center lne and to nondmensonalze the axal parameters of the X,Y. As shown n the Fgure 3, the flow velocty dstrbuton on the secton of X/100H=0.08, 0.16, and 0.24 reflects that the flow feld has good self-smlarty, whch s consstent well wth the expermental results and shows the feasblty of ths model for the plane mxed et smulaton. 263

5 4. Smulaton results and analyss 4.1 Influence of vortex structure on partcle agglomeraton Takng the ntal partcle sze as Bn7=0.3um, St as 10-3, flud nlet Reynolds number Re as and nlet partcle volume fracton as , ths secton selects the vortex structure n the et space when the dmensonless tme T=300T0. Fgure 3(a) and (b) are the et vortcty dstrbuton dagram and the detaled vew of the vortcty contour lne and t can be seen from the 4(a) that the et are n the vortex street structure smlar to the Karman(Karman Vortex Street) at T=300T0. In the downstream of the et, the small vortex develops to large vortex gradually and tends to be stable and the vortcty ntensty gradually weakens. There s the symmetrc vortex parng structure wth opposte flow drecton n the upper and lower shear layers at the bottom of the et, whch was also confrmed n the lterature [8]. The aggregaton of the fne partcles n et space at T=300T0 has been analyzed n the followng. a. vortcty dstrbuton dagram b. Detaled vew Fg. 3 Detaled vew dstrbuton of the et space vortcty feld and the vortcty contour lne The lterature [9] ponted out that the exstence of vortex has mportant nfluence on the moton dstrbuton of the partcles and hgh vortcty ntensty has enhanced the entranment of the vortex and mproved the probablty of local collson coagulaton of the partcles. Takng the Y=H as the characterstc nterface, the Fgure 4(a) montors the sze changes on the flow drecton and fnds that the sze tends to ncrease n fluctuaton manner, that s, there are peaks and valleys. Combnng the Fgure 3(a), t can be found that the valley s n the outer edge of the vortex regon whle the peak value bascally n the vortex regon of the flow feld. It can be known that the most of the partcles wth larger szes are generated n the vortex regon, ndcatng that the exstence of the vortex and the better followng feature of the fne partcles cause the local aggregaton of the partcles n the vortex regon and the partcles wth larger szes have better effect of agglomeraton among the partcles. Wth the combnaton of the Fgure 3 (a), the (X = 5H, 10H, 30H, 35H, 50H, 60H, 85H) wth dfferent features n the drecton perpendcular to the flow drecton s taken to get the volume fracton changes of the three small, medum and large szes of (Bn7, Bn5, Bn1) along the flow drecton and get the graphs (b), (c), and (d), respectvely. From the (b), t can be seen that the volume fracton of the partcles s n parabola type n the Y drecton at X=5H and except for part dffused partcles, most of the partcles moves wth the et. There s the symmetrc vortex structure wth opposte flow drecton n the upper and lower shear layers of the et at X=10H and the small partcles are featured by small mass and strong dffuson ablty. Part of the small partcles are aggregated and the aggregaton of part of them s enhanced wth the ncrease of volume fracton. There s saddle on both sdes of the wave peak. The lterature [10] has confrmed the above. Wth the combnaton of Fgure (c) and (d), t can be seen that the volume fracton of Bn7 wth the sze of Bn 5 gradually decreases and the volume fracton of Bn1 ncreases, showng that part of the aggregated smaller partcles collde and aggregate nto larger partcles, leadng to decrease n volume fracton of the small partcles and ncrease n volume fracton of larger partcles. Wth the deepenng nfluence between the vortex, the wave peak of 35H starts to devate the medal axs at X=30H, whch s consstent wth the development of the flow feld where the symmetrcal vortex structure gradually devates the center lne and reflects the nfluence of vortex structure on the local aggregaton of the fne partcles. Moreover, the volume fracton of Bn 7 further 264

6 decreases and the volume fracton of the large partcles further ncreases n Fgure 4(b). At the same tme, the peak curve changes from hgh to short, showng that the range of local aggregaton s enlarged correspondngly wth the vortex movement. Taken together, the et vortex structure has further enhanced the local aggregaton and collson effect between the partcles to some extent. There s parng and aggregaton of the orgnal vortex at X=50H to generate large-scale vortex, whch can enhance the perturbaton acton on the flow feld. The vortex parng and aggregaton ncreases the aggregaton of the partcles at the center lne and the aggregaton effect s sgnfcant, resultng n the double-peak structure. When X=60H, 85H, there are further ncreased vortex scale, weakened ntensty, ncreased partcle nerta, decreased nteracton of the vortex, poor aggregaton effect, slow ncrease of volume fracton of the larger partcles and outflow of most part of them, whch shows that the partcle aggregaton s closely related to the partcle dffuson characterstcs and gas phase turbulence. Meanwhle, t s found that n the flow process, the number densty of partcles s ncreased from the center of the et to the perphery, whch s confrmed b the results of Lu Ynhua et al. [11]. (a) Partcle sze changes n the drecton of et flow drecton ( b) Volume fracton changes of Bn7 (small partcle sze) n the drecton of flow drecton (c) Volume fracton changes of Bn5 (medum partcle sze) n the flow drecton 265

7 (d) Volume fracton changes of Bn1 (large partcle sze) n the flow drecton Fg 4 (a)~(b):partcle sze changes n the flow drecton and partcle volume fracton changes on the sectons wth vertcal flow drecton Fgure 5 and Fgure 6 show the partcle sze change wth tme and evoluton of partcle number densty wth tme. Wth the tme and development of the flow feld, the sze ncreases gradually and tends to be stable and the number densty gradually decreases and tends to be stable, whch ndcates that under the acton of the plane turbulent et flow feld, the fne partcles collde and aggregate wth the vortex aggregaton to gradually coalesce to be the larger partcles and decrease the number densty of the partcles. Fg 5 Partcle sze changes wth tme 4.2 Influence of St number on the agglomeraton of fne partcle Fg 6: Evoluton of partcle number densty over tme Takng Re=11300 and nlet partcle volume fracton as , the Stokes numbers are smulated as , , , , , respectvely and the flow feld at T=280T0 has been fully developed. Fgure 7 shows the volume fracton change of the nlet partcles wth the ntal partcle sze at T = 280T0 n the flow drecton. Wth the ncrease of St number, the volume fracton of the partcles wth ntal partcle sze of the et flow feld has decreased and the aggregaton effect s gettng weak wth gradual declne. When St=1 10-3, the volume fracton decreases rapdly wth large varaton range and the small partcle agglomeraton effect s sgnfcant. Same to the change tendency of curve X=5H n Fgure. 4(b), due to the small ntal fne partcle sze, good followablty and faster response to the flow feld, the entranment and aggregaton effect of the partcles s good. Meanwhle, there are much more partcles wth small sze n the et flow feld to make the local aggregaton remarkable and further mprove the aggregaton effect of partcles wth larger sze. When the St number ncreases, the partcle sze ncrease durng partcle agglomeraton gradually slows down, ndcatng that the ncrease of partcle sze enhances the nertal force of the partcles and the response to the flow feld s weakened, resultng n that the larger partcles are easy to be out of the vortex to flow to the downstream. There are less partcles n the et flow feld, whch has weakened the nteractons between the flud and the partcles and reduced the aggregaton and agglomeraton effect of the partcles wth 266

8 the vortex gradually. Ths result has been also confrmed by the gentle change tendency of volume fracton of the curve X=60H n Fgure. 4(b). 5. Concluson Fg 7 volume fracton changes of ntal partcle n the flow drecton at T=280T0 Combnng the local aggregaton of mcron and submcron fne partcles n the large-eddy smulaton and populaton balance model smulaton n the plane turbulent et process, ths paper has studes the agglomeraton effects of fne partcles at dfferent tmes, volume fractons and St numbers. The results show that the fne partcles are affected by the vortex structure durng the turbulent et process and the partcles wth smaller sze have good followablty to be able to move wth the vortex better. There s local aggregaton for the fne partcles and the probablty of collson between partcles ncreases. The partcles wth larger sze have better aggregaton effect and wth the ncrease of the sze, the partcles gradually reverse the effects of turbulence vortex under the acton of the centrfugal force, resultng n that the nlet sze mgrates toward the large partcle sze. The nteracton effect of the fne partcles wth larger nlet volume fracton and the flow feld s sgnfcant, whch can promote the development of vortex structure n the flow feld and mprove the agglomeraton collson effect of the partcles. Partcles wth smaller St-numbers have stronger dffuson capacty and movement speed, and the degree of response to the flow feld s hgher, whch enhances the effect of local aggregaton and collson of the partcles. The partcle sze changes greatly, and wth the ncrease of the St-number, the partcle sze s n lower growng rate, reflectng that the effect of the flow feld on the partcles decreases gradually and the response senstvty s ncreasngly weakened. References [1] YAN J, CHEN L, YANG L. Combned effect of acoustc agglomeraton and vapor condensaton on fne partcles removal[j]. Chemcal Engneerng Journal, 2016, 290: [2] LIU Jan-png. Research progress on agglomeraton of fne partcles from coal fred flue gas [J]. Shandong chemcal ndustry, 2014, 43 (8): [3] GE Yang-zhen, LIU X-pu, ZHANG Peng-fe, et al. Inhalable partcles agglomeraton technology [C]// The ffteenth conference of Chna electrc dust collecton, Anhu: Chna Envronmental Protecton Industry Assocaton, 2013: [4] YE Fe. Unsteady vortex moton and ts mechansm [D]. Tann :Tann Unversty, [5] SU Jun-we, GU Zhao-ln, XU. dscrete phase system populaton balance model solvng algorthm [J]. Chnese Scence: Chemstry, 2010, 40 (2): [6] XU Jun-bo, ZHANG L, YUE Ren-lang, et al. The computatonal flud dynamcs smulaton of PM 2.5 fne partcle coagulaton [J]. computer and appled chemstry, 2013,30 (8): [7] KIM Han-hu. Large eddy smulaton of coherent structure of Zheang Unversty [D]. Zheang: Zheang Unversty, [8] LUO Kun, LIU Xao-yun,, et al. Drect numercal smulaton of gas sold turbulent et wth hgh Reynolds number [J]. Journal of engneerng thermal physcs, 2004 (3):

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