Atmospheric n Climte ciences,,, 86-9 oi:436/cs39 Publishe Online July (http://wwwscirporg/journl/cs) he Clous Microstructure n the Rin timultion by Acoustic Wes Abstrct Oik Nlbnyn Moscow ocil-humnitrin Institute, Moscow, Russi E-mil: hoikjn@yhoocom Receie My, ; reise June 5, ; ccepte June 9, A simplifie moel of clous microstructure ynmics uner turbulent conitions is presente he nture of rin stimultion by coustic wes, bse on the rops injection in the region of turbulent cogultion, is escribe he conitions for effectie rin stimulting re estimte Keywors: Clou, rop, urbulence, Conenstion, Cogultion, Rin timultion Introuction he inestigtions of clous microstructure represent significnt step for stuying the possibilities n prospects to stimulte rin n ultimtely to control wether ptterns he most commonly use methos he been by seeing the clou by rious gents tht cuses lrge scle frcture within its structure or by irect injecting of lrge rops of wter into the clou Howeer, these methos require the use of rtillery n rocket systems or flying eices which cn be pretty costly cientists he been serching for cost-effectie lterntie methos o bring the chnges in the clous microstructure by using the impct of coustic wes were n interesting ie from the strt heoreticl clcultions he estimte tht the impct of intense coustic wes upon clou woul initite the cogultion of the rops which woul crete shift of the mximum in the istribution of the rops towrs lrger sizes he experiments, conucte with both, oerln fog n rtificil fog in chmber he confirme these estimtions [,] Wht becme pprent, tht the impct of coustic wes hs to be extremely intense (~4 B) n hs to lst for long time (minutes) Howeer, it woul not be relistic to obtin the require prmeters of the coustic wes in the clous while the source of soun wes is on the groun But the clous in nture, comprtie to n rtificil fog or n oerln fog my, intrinsiclly be operting uner turbulent conitions An the turbulent conitions combine with coustic wes coul sufficiently enhnce the effectieness of stimulting the rin here re mny theoreticl n empiricl moels escribing the clous' microstructure n its ynmics ue to the rops cogultion n conenstionl growth [, ] hese moels represent rious pproches to the moement of the rops n their interction In the present pper simplifie moel of the rops moement, cogultion n conenstionl growth uner turbulent conitions is represente On the bsis of the represente moel, the possibilities of rin stimulting by the impct of coustic wes uner turbulent conitions re exmine he Motion of rops uner urbulent Conitions in the Air After the nucletion of rops in supersturte ir the min processes tht he been inole in the formtion of the clous microstructure re: - Conenstionl growth n eportion of rops; - Cogultion of the rops by colliing; - Pulerizing of the rops he spee of the rop reltie to the ir prticles plys the min role in these ynmics ue to the ir iscosity the rop gets inole by the turbulent strems of the ir But the ensity of the rops is much greter thn the ir ensity n ue to inerti of rops their trjectory eite from the ir prticles trjectory It mens tht rops moe reltie to the surrouning ir he reltie elocity of sphericl rop in the iscous ir is etermine by the following eqution: () t t Copyright cires
O NALBANYAN E AL 87 Here is the rop elocity reltie to the surrouning ir prticles, r 9 () is the time of tokes relxtion of the rop s elocity in the iscous ir, is the locl elocity of the ir prticles t the position of the rop, n re the ensities of the wter n the ir corresponingly, is the kinemtic iscosity of the ir, r is the rius of the rop he ir resistnce, proportionl to the rop's ccelertion is neglecte he mss of the ir in hyroynmic bounry lyer is neglecte s well he pttern of the rnom turbulent flows is superposition of numerous ortices of rious sptil scles n the rince of the ir prticle elocity E k is etermine by the sptil spectrl ensity of the rnom fiel of rtes Ek, where k π / l is the sptil we number of the ortex, l is the ortex size For tmospheric turbulence we he k 5/3 π /, k k k k le k πc k,, m where k n km re the sptil we numbers which correspon to the outer L n the inner l m scles of turbulence corresponingly he ir prticles being inole with ortices of rious sizes he curiliner trjectories of moement o the ccelertion of the ir prticles in some irection my be represente s superposition of ccelertions of rious frequencies k which epen on the ortex size Aksin k t k t Let s ssume moel of ynmic turbulence Accoring to the moel kinetic energy of the ir prticles is sttionry n the prticles he only tngentil ccelertion cuse be the curilinerity of their trjectories In this cse the mgnitue of tngentil ccelertion equls to the ir elocity in the ortex rise to the secon power n iie by the size of the ortex, while the frequency equls to the ir elocity in the ortex iie by the size of the ortex /3 Ak Ck /3, k 6πCk In this cse the qusisttionry solution of Eqution () hs the form /3 k m Ck k k (3) sin ktkcos kt k Let s nlyze the obtine solution For smll rops the time of tokes relxtion () is much less thn the chrcteristic time of smll-scle turbulent pulstions k n the mplitue of reltie elocity of the rop hs the squre-lw epenence on the rius of the rop Ck C k r (4) /3 /3 m 3 m 3 For lrger rop if the time of tokes relxtion is in the rnge of the turbulent pulstion s k km the epenence of the reltie elocity on the rius of the rop becme liner /4 π 3C 3/4 /4 π 3C 3/4 (5) r 9 Very lrge rop with k is too inertil to moe with the ir prticles n its reltie elocity correspons to the elocity of the turbulent flows 6πC k /3 3 Conenstionl Growth of the rops he clous rise in supersturte ir consequently to the heterogeneous nucletion of rops he bounry between the wter n the ir is subjecte to the moleculr uneenness, so the kinetic coefficient of the conenstion q, etermining the epenency of the growth rte u on the supercooling woul be quite high n we cn isregr the kinetic supercooling n; ccoringly kinetic supersturtion It mens tht the supersturtion t the growing surfce correspons to the equilibrium conitions he process of conenstion gets lwys ccompnie by the ltent het relese, n the lue of the rop s oerheting, reltiely to the ir is t exctly the correct leel, which is neee to trnsfer the ltent het of conenstion from the growing surfce of the rop to the clou n cn be obtine by the conition of the het trnsfer Here H ur H ck (6) u r is the growth rte of the rop, H is the specific het of eportion, c is the specific het cpcity of the ir, K is the therml iffusiity of the ir, is the thickness of the therml bounry lyer t the surfce of the moing rop o, the lue of the stem concentrtion t the growing surfce C iffers from the concentrtion of sturtion in the clou ue to C Copyright cires
88 O NALBANYAN E AL the curture of the rop s surfce n the oerheting of the rop Vm C C C C H (7) rr Here is the surfce energy of the wter-ir bounry, Vm is the molr olume of the wter, R is the gs constnt, is the bsolute temperture he stem trnsfer from the clou to the growing surfce of the rop tkes plce ue to the ifference between the stem concentrtion in the clou C eq n t the rop s growing surfce u r C C C eq (8) Here is the stem moleculr iffusion coefficient in the ir, is the thickness of the iffusie bounry lyer t the surfce of the moing rop he thickness of the bounry lyers epens on the reltie elocity of the rop he estimtions he shown tht the irflow of the rops in the clou hs lminr chrcter n the following expression cn be use rk, r (9) ubstituting (7) n (8) in (6) n tking into ccount (9) the expression for the rop s growth rte cn be obtine u r C V m R req r H C c K r () Here req is the rius of the rop which is uner the equilibrium conitions, ie o not grow n o not eporte It is obious, tht the conenstionl growth rte epens on the rop s elocity, reltie to the ir n the tmospheric turbulence consierbly intensifies the conenstionl growth Howeer the efining fctor remins in the ifference of the lues between the rop s rius n the criticl rius he lue of the criticl rius is etermine by the lue of the supersturtion Vm Ceq Ceq C C r R Although size of n iniiul rop is minute, combine surfce s up to rther lrge mount For exmple, in cubic meter of the clou with g of wter cpcity n the erge rop size bout µm, the totl eq surfce of the rops is bout 3 m In the course of few secons, ll the stem tht mkes the supersturtion conenses on the growing surfce of the rops he spersturtion in the clou ecreses to some qusi equilibrium leel which is much less thn the wter olume content of the clou M It mens tht t the sttionry conitions the growth of the lrger rops occurs ue to the eportion of smller rops n the wter content of the clou prcticlly oes not chnge n 4πu r W r r r () W r t u r W r r () Here W r is the ensity of the size istribution of the rops, Wr r M he Equtions () n () escribe the ynmics of the size istribution of the rops t the sttionry conitions Estimtions gie tht the conenstionl growth rte uner the sttionry conitions is ery low n it is oubtful tht conenstionl growth cn proie forble conitions for the rin to occur he rte of conenstionl growth uner the sttionry conitions oes not rnk oer μm/h n it woul tke too much time for the rin rops to form At the sme time the conenstionl growth uner the nonsttionry conitions is ery importnt n efficiently chnges the rops' sizes 4 he rops Colescence he reltie motion of the rops cn le to their collisions n colescence he isppernce of two colliing rops n the ppernce of the rop with the common olume le to the chnge in the size istribution of the rops he moluchowski eqution escribing the ynmics of the size istribution ue to rops collisions cn be represente t the following form W r r Wr rpr, rw r t W r r P r, r W r () r r 3 3 3 3 3 3 rp r, r r W r W r r Here the first term correspons to the isppernce of the rops of rius r ue to their collisions with the smller rops; the secon term correspons to the isppernce of the rops of rius r ue to their collisions with the lrger rops, n the thir term correspons to Copyright cires
O NALBANYAN E AL 89 the ppernce of the rops of rius r ue to collisions of the smller rops he function Pr, r correspons to the spce olume tht in time unit becomes free of the rops of rius r ue to their cpture by lrger rop of rius r In generl the etermintion of Pr, r is ery knotty problem becuse it is necessry to tke into ccounting the interction between colliing rops he cse of the rops moement cuse by the tmospheric turbulence is simpler becuse the rius of sptil correltion of turbulent rnom fiel of elocities is consierbly greter thn istnce between rops, prticipte in colescence It mens tht the rops tht he possibility to collie moe t the sme irection n the lrger rop hing greter elocity runs own the smller one In tht simplifie moel function Pr, r cn be represente s, π P r r R, (4) mx Here n re the elocities of the lrger n the smller rops corresponingly, Rmx is the mximl trnsersl istnce between trjectories of rops which coul he collision If hyroynmic interction between the rops is neglecte then R mx r r Howeer the moing rop in rel iscous ir is surroune by lminr hyroynmic bounry lyer with thickness r he opposite irs prticles n rops he to flow roun the moing rop he tngentil shift of the inertiless rop equls, r r where is the hyroynmic bounry lyer thickness of the opposite rop king into ccount inerti of the opposite rop n ssuming for the simplicity the circulr motion of ir roun the lrger rop we he the less lue of its tngentil shift where r rr π exp r, π, r r is the time of tokes relxtion of the opposite rop hen the mximl trnserse istnce between trjectories of rops which coul he collision equls: Rmx r r rr π rr exp r r (5) hus the possibility of collision epens on the rops sizes n elocities he elocities of the rops epen on the intensity of turbulent mixing n for ny intensity of turbulence; there exists miniml rius for the rop tht llows it to bsorb smller rops For exmple, for the following prmeters of turbulence L = m, L m = mm n the root men squre elocity of the turbulent flows = 3 m/s, the low borerline of the ipson for the turbulent colescence r c equls 43 µm, while t = 5 m/s we he r c = 3 µm n t = m/s - rc = µm If the rops in the clou re istribute in the rnge of ipson of the riuses, smller thn r c, the colescence oes not tke plce, the clou remin stble n the rops he continue to grow slowly through the conenstionl mechnism he rte of growth in such clou coul he pick up for exmple, with the chnge temperture or increse intensity of turbulence he rin conition cn be cuse lso by injecting the clou with rops of the riuses substntilly lrger thn rc he require number of injecte rops tht cn intke ll the wter content of the clou is bout in cubic meter If the rius of the injecte rop is significntly greter thn the erge rius of wter rops in the clou its exponentil growth woul he occurre 5 he Rin timultion by Acoustic Wes A propgting soun we eokes wy motion of ir prticles P πt sin (6) c s Here P is the soun we s pressure, is the we perio of soun, c s is the soun spee ue to ir iscosity the rops he wy motion s well he mplitue of reltie elocity of the rop is P (7) cs s Awkene by soun we, the moement of the rops intensifies the het n the mss trnsfer n ccoring to () increses the conenstionl growth rte Howeer, the effect of soun we coul be een more inispensble for the cogultion of the rops he mechnism tht is inole in the colescence uner the impct of coustic we is ctully similr to the mechnism tht is inole in the colescence uner the turbulent conitions For exmple, the effectieness of the coles- Copyright cires
9 O NALBANYAN E AL cence uner turbulence with prmeters C = 65 m 4/3 s n L m = mm cn be mtche up by the soun we with P = 8 P n frequency 7 Hz he colescence of the rops uner the effect of coustic we cn be escribe by the sme Equtions (3-5), s it were uner the turbulent conitions, howeer, the lue of the rops elocities he to correspon to (7) It is eient, the best result in the colescence cn be chiee if the perio of the soun equls to the time of tokes elocity relxtion of the lrger of the two colescing rops ht woul secure the mximum reltie elocity for the lrger rop, proie the minimum thickness for its bounry hyroynmic lyer n ensure the mximum contrst of elocities between the lrger n the smller rops Note, tht the turbulence frequency of 7 Hz is the optimum for the rops with the rius 67 µm For the smller rops the effectieness of turbulent colescence ecreses (proportionl to r ) n coustic wes with the corresponent frequency woul be more effectie As it were in the cse of the colescence uner the effect of turbulence, for ny intensity of the soun we, there exists minimum rius for the rop tht is ble to consume smller rop Or, in other wors, for rop of ny size, there exists threshol point of intensity for the soun we which woul he just ensure consumption of smller rops For exmple, for the rops with the rius 3, the threshol point of intensity for the soun we hs to be 5 P with the frequency Hz, for the rops with the rius 5 μm we he 6 P with the frequency 75 Hz n for the rops with the rius μm we he 8 P with the frequency 65 Hz he impct of soun we is especilly effectie for the sizes of the rops, which re unble to colesce uner turbulent conitions, in other wors for the rops, which re in the rnge for the stble clou In Figure the chnge of the ensity of the size istribution of the rops W r ( 9 m 4 ) uner the impct of coustic we is represente In the represente cse the wter cpcity is g/m 3, the riuses of the rops were initilly istribute in the rnge from µm to 3 µm Acoustic we hs the intensity P = P, frequency is 3 Hz, the impct urtion is s It cn be seen the isppernce of the rops in the rnges from 7 to 9 µm n from 4 to 5 µm heir colescence les to formtion of the rops with the rius roun 3 µm A totl number of ppere single colesce rops is bout 68 in cubic meter If the size of ppere rops is in the rnge of n effectie colescence uner turbulence they coul represent the bse for the follow up rin Note tht t = P Figure he chnge of the ensity of the size istribution of δw r uner the impct of coustic we the rops P the number of the newly forme in cubic meter rops cme to n t P = 4 P cme to 35 hus the stimulting effect of coustic we results in proucing not ctully the rin rops, but the rops which re goo n rey to colesce uner the turbulent conitions he impct of coustic wes becomes especilly effectie with ner-rin clou It mens tht the rops re istribute in close proximity to the borerline of the ipson for successful turbulent colescence n single colescence woul be sufficient he min concern in the reliztion of the coustic we rin stimultion is the ctul eliery of the right intensity soun we to the clou For exmple, the intensity of P with the rius of the coustic spot of m correspons to the coustic power of 3 MW ht power coul not ery likely be chiee by the mens of electro-mechnicl trnsltors Howeer, certin perspecties he become isible with connection to the soun we s genertion by mens of the fuel gs explosion For exmple, the energy of single impulse of inicte intensity n the urtion corresponent to necessry frequency is bout 3 kj, which correspons to mechnicl energy, relese from the explosion of g of propne 6 Acknowlegements he uthor wnts to cknowlege r AVrnyn initite the present inestigtion, r IChunchuzo for numerous iscussions n r OKrymo for the interest to the present inestigtion n the technicl support 7 References [] L G Kchurin, Fizicheskie Osnoi Vozeisti N tmjcfernie Processi, Girometeoizt, Leningr, 99 [] V uliko, A V Mischenko n R Amiro, Akusticheskie oji, Fizmtknig, Moscow, Copyright cires