33 3 Vol.33,No JournaloftheMeteorologicalSciences Jun.,2013 M N,N,:, ES `.,2013,33(3): SUXiaoyong,GAOTaichang,LIUXichuan,etal.N

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1 33 3 Vol.33,No JournaloftheMeteorologicalSciences Jun.,2013 M N,N,:, ES `.,2013,33(3): SUXiaoyong,GAOTaichang,LIUXichuan,etal.Numericalsimulationoftheraindrophorizontalvelocityafectedbythewind.Jour nalofthemeteorologicalsciences,2013,33(3): doi: /2012jms.0087 Y 4 Y 456 1, :; 1 1 (1 7 ]0 PU,, ; I,T ) "# #+bc, ^, -, 6,!! bc, P! [\D O [\, ^85)*./01:T V,, ^85 OF 85, Q, ;3D 8 E E;,, ^8 5 ] V ( 15s) => ; 84,7>: 5>T,, V ^ 854!>, >.! S $^ a )*, $%& ;3 ; E; [ ; ` ' :P doi: /2012jms.0087 (:A Numericalsimulationoftheraindrophorizontal velocityafectedbythewind SUXiaoyong 1,2 GAO Taichang 1 LIUXichuan 1 ZHAO Shijun 1 (1InstituteofMeteorologyandOceanography,PLAUniversityofScienceandTechnology,Nanjing211101,China; 2No.68028ofPLA,Lanzhou730058,China) Abstract Toinvestigatetheraindrophorizontalvelocityinwind,theraindrophorizontalmovingve locityunderdiferentatmosphericconditionswassimulatedbasedonthestresofraindropinwindandthe relationshipofdragcoeficientandreynoldsnumbersinthispaper.simulationresultsindicatedthatthe raindrophorizontalvelocityisunequaltothevelocityofwind,andtheraindropterminalhorizontalveloci tyvarieswiththeraindropdiameterandthevelocityofwind;theraindropcanreachasteadyhorizontal velocityinashortperiodoftime(commonlylesthan15s)afectedbythewind;underthesamewind condition,thehigherthealtitudeisandthelowertheairpresureandenvironmenttemperatureare,the higherterminalhorizontalvelocityofraindropis,andviceversa.theseconclusionsareofgreatpractical importancetoraindropimagemosaicforautomaticopticalprecipitation measuringsystem basedonthe principleofimageacquisition. Keywords Raindrop;Horizontalwind;Velocity;Dragcoeficient;Numericalsimulation 6 7 S 7 2 E 6 _ 23\ ]*+S4c\, D F2 3S\ ] Y S_ 0 S*+ 4cS [1 3] )*+,(Received): ;-.*+,(Revised): ;/01 +,(Publishedon line): /01 :htp:// := T()* K(GYHY ) 2345(Corespondingauthor):N (GAOTaichang).2009gaotc@gmail.com

2 3 M N,:3 4 3 ES ` 283 S2 E./ 23 S X CDY JS Q9 S 8 X^T NS 2, 6 S 23 X = 8 2DVD- HVSDa 23YB b 2 E 6 7, S U : 3 R, R3 S X, S 8, D 2 ES*+ 2 E,D 3 WX E S*+,A S 2DVD HVSD 23 X S 5 Kruger,etal [4], 3 S, S U 8 -, 8 S `8 ; Schonhuber,etal [5] IJ 2DVDS 2]! DN D3 S ;Huang,etal [6] D N D 2DVD80m`() S 9 J [7] 2mmS, S D =*+;Barthazy,etal [8]! X S D3 S,R S 1 bm1s 3 S3 F E, ' ] D 9 =? csd, 3 4 `8S3 X E BCR ] ( SG, `S!= ] 3 X ES r(θ)=r 0 [ c n cos(nθ )], (1) n=0,r(θ) -E θd S,r 0 S,c n [ 1 IJ BC( =,R!S mm S U! 1 0mm UGB' 8, ; 1 0mm,Q9 S, 8 = S, S,(, A,R3 4 3 E*+S 1 _ P 1 0mm S D3 WX ES S% D *+ ] 4cS, c5 () 3 WX ES4c _ BC( % = [2] c 2 n [ ] n=1 S=πr c 0 +c , (2) S BC( % *+,8 S : 6mm,A, 1!= F 1~6mm S BC( S%,, C S,BC( S% S%,(Q9 S, S = V( S, J 1 J, K ) S! 1 0~ 6 0mm D S BC( % S 9 [( (3) ),); 2 S= d d 2.(3) 1 P 1 1 = US 9(, 0PR 19\ S 9 ] D U * Beard ChuangR PW X D SG, U C 1S 10b6 S,!= BC( [9], ] ( S ( 9 S ( L, ( S S8 U [ 1 BC( D S U Fig.1 TheraindropshapeofBCmodelfordiferentdiameters

3 R3 S Fig.3 Thehorizontalforceofraindrop % ) Fig.2 Fitingpictureofsectionarea R2 S 1, 3 R, 3 S4 S94, -, W R T S E,N S3 X E *+, WX S J,A, R3 4 8 S3 X 1 $%S, 1 1, R2 1 _ S, A,R( 1 _ P D 3 WX ES =*+3 D 3 WX ES,BC GS] ( G : (1) P3, P S ; (2)D d 1mmS, D d>1mms S U, BC( U( ; (3) R2 3 X 1 R 8 /, RWX 1 Y R3 X 1 S 3, F 3 D S4,F=ρ A (V-v) 2 S;F D, F D =0 5ρ A v 2 SC D ρ A E,v S3 X E,S %,C D [,V 3 D d 1mmS, % S=πd 2 /4,D 1mm<d 6mmS, % IJ(3) IJ, G WX 1 m dv dt =F-F D, (4),m D ds, R2 3 X 1 R 8 /,A, S C,m=ρ w πd 3 /6(ρ w 3S E), 9,D d 1mmS (4) ] : dv dt = 3 ρ A (V-v) 2 2 ρ w d -3 ρ A v 2 C D 4 ρ w d. (5) D 1mm<d 6mmS (4) ] dv dt = 3β A (0 5369d d ) πd 3 ρ w [2(V-v) 2 -v 2 C D ]. (6) (5) (6) X S\ 1, S3 X E v [ C D T 0, (, C D Y C S,A, 1S! [ C D 2 ]T $T [ WX S4c,C S, [ [ [ Y AF :(1) S L, μ,μ, SWX ; (2) S E L( d ) WX E vs,l S,v WX,] J = 1 Table1 Thesectionareaofraindropfordiferentdiameters d/mm S/mm BC(

4 3 M N,:3 4 3 ES ` 285 S WX μ vdd WX 4 C, Y Re=vd/μ, c, Y WX, [, Y WX, [ [10] A η=μρ A, Y = Re=ρ A vd/η, (7) η SX L[,Q E TS ^ ^ E T 0 η=( T) (8) Y [ D [S*+ (,PR 1910 CW Osen 1S!=Y - [ SD [, [ R Re 1 8 J) ;Q,LeClair,et al [11] =T W Y Re D S [ ;Gunn,etal [12] () 9! =Y Re>1 Y [ S 9 J Foote,etal [13] DaviesS J!, C, E 3 SY [ S [ S;Warnica,etal [14] 7S 9 = 20<Re<120 \ 8 W R 0 J1 S [, 9 R J 1 W C Reynolds T R 0J S GBC Ceylan,etal [15] = STU YB TU YB E Y [ SD 9=, ] 2!=[ TU YB TU YB W S [ 9=, C 89 JD!S 9= S [ 2!= [ S 9= : 4 J 2 S YB [ Y S 7, Gunn Kinzer 3 8 J!TU YBS 7 Osen= Gunn Kinzer8 J, TU YBS 7 Osen= Gunn Kinzer8 J R Re 1000 TU YBS) Gunn Kinzer8 JGB), Re>1000, A S3 RW X E 8 S, 3 C STUYB, [ 8 N ` ;S ce,bc J Gunn Kinzer3 8 J, K )S! = 1000<Re 3500 W S [ 9= (13),); 5 4 YBY - [ Fig.4 Thedragcoeficient-Reynoldsnumberscurve ofdiferentparticletypes = 2 T 8 Table2 Calculationformulaofdragcoeficient YB Y 9= C D =K 1 +K 2 (9) TU YB [15] 0 1<Re 10 6 K 1 =1-0 5exp(0 182)+10 11Re -2 3exp ( 0 952Re - 4) Re -4 3exp ( 1 3Re - 2) 1 1 K 2 = Reexp( Re) Re 2 exp( Re) Re 10 4 C D =24/Re+6 48 Re (10) C D =K 11 +K 22 (11) TU YB [15] 0 1<Re 10 6 K 11 =1+4 44Re -2 3exp ( 0 684Re - 8) 1 K 22 = Reexp( Re) Re 2 exp( Re) W Re 1 0 C D = 24 Re ( 1+ 3 Re(C.W.Oseen= ) 16 ) (12)

5 C D = Re Re (9) 9,BCR ` 1,, Re 1000 TU YBS [, 2 Re 10 4 S 9= `, 1000<Re 3500 (13) `, 8 ` 1 Re 3500,A D Re>3500S P 3 ^ R [ 9= SG,D3 4 S 3 X E ` 3, R V 3 X E v=0,f z=0,r3 D S4 F F D S 4, T 3 X E 1 2 S, XS \ 1 d 1mm { dz dt =v. (14) dv dt = 3 ρ A (V-v) 2 2 ρ W d -3 ρ A v 2 C D 4 ρ w d 1mm<d 6mm : dz dt =v dv dt = 3ρ A (0 5369d d ) πd 3 ρ w [2(V-v) 2 -v 2 C D ]. (15 ) BC (Runge Kuta) D(14) (15), V t=0,v=0,z=0, 1 S3 X E v E _cs 5 [ ); Fig.5 Fitingpictureofdragcoeficient SGB2] [16] 8 ]4 f(x n,y n ), f(x n,y n )R ] 5 x n S f(x n,y n )S 8 ] y n+1 S = y n+1 =y n + x n+1 x n f(x,y)dx. (16) S (16),! S ; BC 4b = y n+1 =y n + h 6 (K 1 +2K 2 +2K 3 +K 4 ), (17),K 1 =f(x n,y n ),K 2 =fx ( n + h 2,y n + h 2 K 1 ), K 3 =fx ( n + h 2,y n + h 2 K 2 ),K 4 =φ(x n +h,y n +hk 3 ). B h,h=t n+1 -t n, S E ρ W =1000kg/m 3,4 E g=9 8m/s 2, [ C D ^ )= O,ρ A E2,η^(8) R (p=1013hpa,t= 20 ) E ρ A =1 205kg/m 3, SX L [ η= kg/(m s) R ` 1, C 3 X E S m/s 3 X E 4 CD'E 4 1 Y < CD BC S S p= 1013hPa, E T=20 S *+,8 S : 6mm,A BCR ` 1 S 0 1~ 5 8mm, 3!=,3 3m/s 8m/s S ` ; 3!, S3 X E 3 SWX E,Q9 3 S ^, S3 X E S m/s W S3 X ED 6!, 3 5m/s, S3 X EQ9 S 3 5m/s, S3 X E Q9 S, " 3,R Re= ,d=3 8mm, S 3 X E m/s,Q, Y, S [ Q

6 3 M N,:3 4 3 ES ` 287 = 3 CD(p=1013hPa,T=20 ) Table1 Numericalsimulationresults(p=1013hPa,T=20 ) d/mm V=3m/s V=8m/s v/(m/s) Re v/(m/s) Re X ED Fig.6 Thecomparisonofraindropterminal horizontalvelocityunderdiferentwinds Y S,C S 5 S 5,Q9 [ S, 3 D S4, S3 X E 7 5mmS YBR 3 3 X EQ ^S 7!,R3 S4, S3 X E R \( 15s) ] 7 5mm S3 X EQ ^ Fig.7 Variationof5mmraindrophorizontalvelocitywith timeunderdiferentwinds S, S3 X E (3, 3 X ES 4 2 < CD S & E ρ A X L[ ηd SWX 9 S, E ρ A X L[ η S,A, 3, S3 X E 4!= E X L[ = 4 < H T Table4 Airdensityandairviscositycoeficientunder diferentatmosphericconditions ρ A /(kg m -3 ) η/(kg m -1 s -1 ) p=1013hpa,t= p=1013hpa,t= p=900hpa, T= p=700hpa, T= p=600hpa, T=

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