Atmospheric Ice Accretion on Non-Rotating Circular Cylinder

Transcription

1 197 Atmopheric Ice Accretion on Non-Rotting Circulr Cylinder Muhmmd S. Virk High North Technology Centre, Deprtment of Technology Nrvik Univerity College, Norwy Emil: Received: 5 My 011, Accepted: 3 September 011 Abtrct: Numericl tudy of tmopheric ice ccretion on non-rotting circulr cylinder w crried out t dry rime ice condition. To vlidte the numericl model, reult were compred with the experimentl dt obtined from CIGELE tmopheric icing reerch wind tunnel (CAIRWT. A good greement w found between experimentl nd numericl reult. Numericl tudy howed tht election of pproprite numericl model of ice denity nd droplet ize ditribution i importnt, thee cn ignificntly vrie the imulted ice growth. Prmetric tudy t different ir flow velocitie nd ngle howed ignificnt chnge in ice ccretion on circulr cylinder. Thi reerch work provide ueful be for further numericl invetigtion of tmopheric ice ccretion on circulr power network cble intlled in the cold region like rctic nd lpine. Keyword: Atmopheric ice, Circulr cylinder, Droplet ize ditribution, Ice denity, Velocity, Angle. 1. INTRODUCTION Humn ctivitie re increingly extending to the cold region uch rctic nd lpine, where tmopheric icing will not only mke humn inconvenience, but will lo ffect the humn ctivitie in the contruction indutry (communiction tower nd ki lift, energy ditribution (power network cble nd tower, mritime ctivitie nd vition condition on the ground. Atmopheric ice ccretion occur, when freezing rin drop, now prticle or uper cooled wter droplet come into contct with the expoed urfce of tructure [1]. The potentil for dmge to fcilitie reult of tmopheric ice ccretion i coniderble. Llinc et l. [] reported tht lrge mplitude ocilltion of ice covered cble t low frequencie i reponible for bout one third of power line mintennce nd operting cot. The lrget ice lod ever recorded on power line i 305 Kg/m. Thi w recorded on kv overhed line in Vo, Norwy on April 18, 1961 [3]. Numericl tudy of tmopheric ice ccretion on tructure include the computtion of m flux of icing prticle well determintion of the icing condition [4]. Thi cn be numericlly imulted by men of integrted thermo-fluid dynmic model. Mot development in the numericl modeling of ice ccretion re focued on eropce indutry nd very few improvement hve been reported in the field of onhore tructurl icing. The min difference between ice ccretion on n onhore tructure nd n ircrft re; firtly ircrft icing tke plce t high ir peed nd mll wter droplet, while icing on onhore tructure occur in the preence of reltively low ir velocity nd lrgely vrying droplet ize [1]. So the wter droplet behvior will be different in both ce. For wet icing condition for onhore tructure, wter film cnnot imply be umed to trt it motion from the tgntion point, i umed in irfoil icing model. Thi umption i minly vlid for the high wind peed condition, when erodynmic force re fr greter thn the grvittionl force [1]. The motion of wter film on the icing urfce in ce of wet ice i importnt to obtin it thickne ditribution, which eventully be ued n input prmeter for olving the het blnce eqution. Vriou numericl tudie relted to the tmopheric icing on tructure cn be found in literture. The firt ttempt were mde in 1980 to obtin dt for generting ice hpe on vriou

2 198 Atmopheric Ice Accretion on Non-Rotting Circulr Cylinder tructure. In 1983 Lozowki et l. [5] preented numericl model to imulte the ice ccretion proce on n unheted, non rotting cylinder for rime nd glze ice condition. In 1984, Mkkonen [6] propoed numericl model to revel the reltionhip between the ccreted ice lod nd relevnt metrologicl prmeter. In thee model Mkkonen nd Lozowki umed the thermodynmic condition nd the initil icing rte to be function of the ngle round the uptrem fce of the cylinder nd were computed uing clicl Meinger eqution [1]. Thi pper decribe the numericl tudy of tmopheric ice ccretion on non rotting cylinder in the dry rime ice condition. The min purpoe i to undertnd the ice ccretion on circulr power network cble intlled in the cold region. To mke the problem eier nd to undertnd the bic of ice ccretion on power network cble, imple circulr cylindricl object i umed in thi tudy. Initilly the ccreted ice hpe obtined from the numericl nlye re vlidted with the experimentl reult obtined from the reerch pper of Ping Fu et l. [1]. Then detiled numericl tudy i crried out to tet different numericl model of ice denity nd droplet ize ditribution nd their reultnt effect on the ice ccretion. Finlly prmetric numericl tudy i crried out to undertnd the effect of flow velocity nd the ngle vrition on ccreted ice on the circulr cylinder.. Numericl Setup Numericl modeling of tmopheric icing on tructure i complex coupled proce, which involve the fluid flow imultion, droplet behvior, urfce thermodynmic nd phe chnge. Thee numericl nlye were crried out uing finite element bed Nvier Stoke eqution olver FENSAP-ICE from NTI [7]. Fluid flow w modeled by uing following nonliner prtil differentil eqution for the conervtion of m, momentum nd energy. ρ + ( ρv= 0 t ρv ij + ( ρvv = σ + ρg t (1 ρe t ( + ij + ( ρvh = k( TA+ Viτ ρ g V where ij i the tre tenor, k i the therml conductivity, E i the internl energy nd H i the enthlpy. C-type tructured numericl grid w ued, where to ccurtely determine the boundry lyer chrcteritic (her tree nd het fluxe, y+ vlue le thn 1 were ued ner the wll. The nd grin roughne height for the iced urfce w clculted with n empiricl NASA correltion decribed by Shin et l. [8, 9]. The correponding vlue of the nd grin roughne i obtined from: K K = C K C be K C K C LWC be K C K K C c be C be TS MVD ( K C K C be MVD 1 = ( MVD MVD 0 MVD 0 K C LWC LWC K = ( ( C be LWC Journl of Computtionl Multiphe Flow

3 Muhmmd S. Virk 199 K C K C be T S = T S where MVD i the droplet men dimeter, K C The one eqution Splrt be Allmr turbulence model w ued compromie between cceptble computtionl cot nd the required ccurcy in imulting the turbulent flow. Two phe flow (ir & wter w olved uing Eulerin-Eulerin pproch in FENSAP-ICE, where uper cooled wter droplet were umed to be phericl. The min dvntge of uing Eulerin-Eulerin pproch i tht, the me meh cn be ued for multiphe flow clcultion nd ice geometry. The Eulerin two phe fluid model conit of the Nvier-Stoke eqution, ugmented by the wter droplet continuity nd momentum eqution. The wter droplet drg coefficient i bed on the empiricl correltion for the flow round the phericl droplet decribed by Clift et l. [10]. α + ( αvd = 0 t ( αvd t CD Re + ( αvd Vd= 4k d ρ 1 V V Fr g ( d+ α 1 ρ d (3 where i the wter volume frction, V d i the droplet velocity, C D i the droplet drg coefficient nd Fr i the Froude number. Surfce thermodynmic nd icing rte re imulted uing the m nd energy conervtion eqution, conidering the het fluxe due to convective cooling, evportive cooling, het of fuion, vicou heting, kinetic heting nd olr rdition [11]. Q o in = Q Qltent het + Qerodynmic het + QKE het = Qublimtive het + Qconvective het + Qdroplet,cooling het + Qrditive het rhcv α Qerodynmic, heting = Cp Q = ( LWC. β. v. L + C ( T T [ ] ltent, het α f i ir urfce v α Qdroplrt, kinetic, energy = ( LWC. β. vα Qconvection = hc ( Turfce Tir Qublim tion = χ eo( Turfce Tir 0. 6hL c χ = 066. CPL p t e Qdroplet, cooling = ρβ vc α p, w( Turfce Tir 3 Q = 4εσ T ( T T rdition r ir urfce ir where r i the dibtic recovery fctor, h c i the convective het trnfer coefficient, c i i the pecific het of ice, L f i the ltent het of fuion, L i the ltent het of ublimtion, L e i the Lewi number nd ε i the urfce emiivity. ALE (Arbitrry Lngrngin Eulerin formultion w ued for the meh diplcement due to ice ccretion in time. Thi pproch dd the grid peed term to the Nvier-Stoke eqution to ccount for the meh velocity [9]. The numericl imultion were crried out t the operting nd geometric condition pecified in Tble 1. Volume 3 Æ Number 4 Æ 011 o out (4

4 00 Atmopheric Ice Accretion on Non-Rotting Circulr Cylinder Tble 1: Operting condition ued for the imultion. Free Strem Wind Velocity [m/] 5,10 Droplet Size, MVD [µm] 35 Liquid Wter Content, LWC [g/m 3 ] 1. Atmopheric Air Temperture [ C] 15 Simultion Time [minute] 30 Cylinder Dimeter [m] Figure 1: C-type tructured type numericl meh 3. MODEL VALIDATION Detiled nlye were crried out to vlidte the numericl reult with the experimentl tet, crried out in the CIGELE tmopheric icing reerch wind tunnel (CAIRWT, t v 5 m/ec, MVD 35 µm nd circulr cylinder dimeter of 35 mm. Thi experimentl dt w obtined from the reerch rticle publihed by Ping Fu et l. [1] in 006. Figure how the comprion of ccreted ice hpe obtined from the numericl nd experimentl tudy. A good greement w found between both numericl nd experimentl reult, which lo vlidted the numericl model for the further tudie. After the vlidtion of model, detiled prmetric numericl tudy w crried out to undertnd the effect of vriou operting prmeter on rte nd hpe of ccreted ice on the circulr cylinder. 4. PARAMETRIC ANALYSES 4.1. Effect of Ice Denity Vrition Ice denity cn ffect the ccreted ice hpe nd growth. Since ice denity vrie from 300 kg/m 3 to 90 kg/m 3, depending on the pecific icing condition, the predicted ice thickne my ccordingly differ to lrge extent [1, 1]. Therefore detiled prmetric tudy i crried out to tet different numericl model of tmopheric ice denity. Three different numericl model of ice denity were teted in thi tudy, 1 contnt vlue of 917 kg/m 3, Mcklin formul, 3 Jone formul. Ice denity by Mcklin formul i decribed : ρ ice = log 10( R M 8. 3(log 10( R M for 0.<R M R M dv. d = T wll < 170 (5 Journl of Computtionl Multiphe Flow

5 Muhmmd S. Virk 01 Figure : Comprion of ccreted ice hpe, obtined from numericl imultion with experiment, t v = 5 m/ec, MVD = 35 m, T = -15C & t = 30 min. where d i the droplet dimeter in micron, V d i the droplet impct velocity (m/ec nd T wll i the wll temperture. Similrly ice denity by Jone formul i defined : ρ ice RM RM 10 R = M ( 115. RM RM RM 60 Thee numericl nlye were crried out t v 5 m/ec, MVD 35 µm nd circulr cylinder dimeter of 35 mm. Reult howed vrition in imulted ice hpe for ech ce. For thi prticulr tudy of ice ccretion on non rotting circulr cylinder, Jone formul of ice denity predicted the bet ice hpe in comprion with the experimentl dt, but we cnnot pply thi to ll other tructurl hpe. A detiled prmetric tudy i necery for ech different tructurl hpe. Figure 3 how the comprion of ice hpe for ech ice denity formul t two different droplet ize ditribution (Mono-dipered & Lngmuir-D. Reult howed tht for numericl (6 Figure 3: Comprion of ccreted ice hpe, for vriou ice denity model with experiment, t v = 5 m/ec, MVD = 35 m, T = 15C & t = 30 min. Volume 3 Æ Number 4 Æ 011

6 0 Atmopheric Ice Accretion on Non-Rotting Circulr Cylinder modeling of ice ccretion on tructure, election of pproprite numericl model of ice denity i very importnt. It lo highlighted the importnce of election of proper droplet ize ditribution. 4.. Effect of Droplet Size Ditribution Selection of pproprite ditribution of wter droplet dimeter in ir, for numericl modeling of tmopheric icing on tructure i very importnt. The droplet dimeter in ir re not uniformly ditributed. For numericl modeling, the droplet dimeter ditribution cn be decribed vi droplet pectr tting the frction of the individul droplet dimeter [4, 13]. Clcultion of the motion for every ingle dimeter, frction of prticle would be computtionlly very expenive. Therefore different numericl model of the droplet ize ditribution re vilble nd proper election of thee model for prticulr ce i very vitl in pproprite prediction of rte nd hpe of ice growth on ny tructure. A detiled prmetric numericl tudy w crried out to elect the pproprite numericl model of droplet ize ditribution for circulr cylinder. Medin volume dimeter of 35 µm i umed for thi tudy. Medin volume dimeter (MVD i ttiticl repreenttion of the dipered wter droplet dimeter for which the cumultive ditribution i 0.5. Thi method help in electing the droplet dimeter in reonble ccurcy for numericl imultion, it i very difficult to numericlly compute lrge pectr of droplet with different dimeter. Four different dipered droplet pectrum were nlyzed during thi reerch work (mono dipered, Lngmuir B, Lngmuir C & Lngmuir D. A medin volume dimeter of 35 µm w ued for ll thee 4 ce. For ech Lngmuir ditribution ce, 7 different vlue of droplet dimeter were ued to ttiticlly improve the medin volume dimeter ditribution. Tble how the Lngmuir droplet ize ditribution ued for thi tudy. Tble : Lngmuir Droplet ize ditribution ued for MVD = 35 µm Droplet Dimeter (mm Lngmuir B Lngmuir C Lngmuir D An importnt prmeter for numericlly imulting the ice ccretion on ny tructure i the droplet colliion efficiency. The wter droplet collection efficiency t the urfce or normlized flux of wter t the urfce with repect to the wter flux t infinity, determine the mount of wter flowing on the urfce. In the Eulerin pproch the droplet collection efficiency i clculted t every urfce point uing [14]: β = αu n (7 where n i the urfce norml. The wter flux t the urfce i clculted by: m = w LWC U β (8 To undertnd the effect of droplet ize ditribution during numericl modeling of ice ccretion on circulr cylinder, detiled prmetric tudy i crried out for four different droplet ize ditribution in the pectr. Reult howed mll chnge in the ice growth, when comprion i mde between mono-dipered nd the Lngmuir droplet ditribution. Comprion between Lngmuir B, C & D Journl of Computtionl Multiphe Flow

7 Muhmmd S. Virk 03 Figure 4: Comprion of ccreted ice hpe, for vriou droplet ize ditribution model with experiment, t v = 5 m/ec, MVD = 35 m, T = 15C & t = 30 min. ditribution did not howed ignificnt difference in the ice growth. A n overll Lngmuir D ditribution howed the bet greement with the experimentl dt in ce of circulr cylinder. Figure 4 how the droplet colliion efficiency nd ice growth for ech droplet ize ce Effect of Flow Velocity Vrition Chnge in irflow velocity cn ffect the droplet behvior nd rte of tmopheric ice growth on tructure. To nlyze thi phenomenon, numericl nlye re crried out t two different ir velocitie (5 & 10 m/ec. Generlly droplet moving in the ir trem i influenced by it drg nd inerti, when neglecting the grvity nd buoyncy, if drg dominte the inerti the droplet follow the trem line where for the ce, where inerti dominte the prticle hit the object. The rtio of inerti to drg depend upon the droplet ize, velocity of ir trem nd dimenion of the object in quetion [15]. Reult how n incree in the droplet colliion efficiency with the incree of flow velocity, which i minly due to incree in the inerti of the droplet, which dominte the droplet drg nd led to n incree in the number of droplet colliding with the cylinder. Such incree in the droplet colliion efficiency, led to n incree in the ice growth on the cylinder. Figure 5 how comprion of droplet colliion efficiency nd ice growth on circulr cylinder t two different ir flow velocitie Effect of Flow Angle Vrition Numericl nlye were crried out to undertnd the effect of free trem flow ngle vrition on loction nd hpe of ice growth. Three different flow ngle (0, 15 & 30 degree were nlyzed t Figure 5: Effect of flow velocity vrition on droplet colliion efficiency nd ice growth. Volume 3 Æ Number 4 Æ 011

8 04 Atmopheric Ice Accretion on Non-Rotting Circulr Cylinder Figure 6: Effect of ir flow ngle vrition on droplet colliion efficiency nd ice growth. contnt free trem ir velocity of 5 m/ec & t 15 min. Reult howed chnge in ice growth with the chnge of flow ngle. Such chnge in flow ngle minly ffect the tgntion point nd the droplet colliion loction nd efficiency. With the incree of flow ngle, reult howed the colliion of droplet even t the bckide of the circulr cylinder. Figure 6 how the chnge in droplet colliion efficiency nd hpe of ice growth with the chnge in ir flow ngle. 5. CONCLUSIONS Thi reerch tudy provided the ueful informtion nd inight of the numericl modeling of ice ccretion on non rotting circulr cylinder. Thi informtion cn provide ueful be for further numericl invetigtion of tmopheric ice ccretion on circulr power network cble, intlled in the cold region. Following re ome importnt finding of thi reerch work. For numericl modeling of ice ccretion, election of pproprite numericl model of ice denity i very importnt. In ce of circulr cylinder, Jone formul of ice denity predicted the bet ice hpe in comprion with the experimentl dt. A mll chnge in the ice growth i oberved, when comprion i mde between monodipered nd the Lngmuir droplet ize ditribution, but comprion between Lngmuir B, C & D ditribution did not howed ignificnt difference in the ice growth. A n overll Lngmuir D ditribution howed the bet greement with the experimentl dt in ce of circulr cylinder. With the incree of ir velocity droplet inerti dominte the droplet drg, therefore more droplet hit the circulr cylinder, which led to n incree in the ice ccretion. Chnge in ir flow ngle effect the tgntion point loction nd droplet colliion efficiency. At higher ngle, the ice ccretion i found even t bckide of the circulr cylinder. REFERENCES [1] Ping Fu, Moud Frzneh, nd G. Bouchrd., Two dimenionl modelling of the ice ccretion proce on trnmiion line wire nd conductor. Cold Region Science & Technology, : p [] A Llinc, F Llinc, nd L. Ignt. Numericl tudy of iced conductor erodynmic. in 7th Interntionl Workhop on Atmopheric Icing on Structure [3] Drge, M.A., Atmopheric icing nd meteorologicl vrible Full cle experiment nd teting of model, in Deprtment of Geophyic. 005, Univerity of Bergen: Bergen, Norwy. [4] T Wgner, U. PEil, nd C. Borri, Numericl invetigtion of conductor bundle icing, in EACWE : Florence, Itly. [5] E P Lozowki, J R Stllbr, nd F.P. Herty., The Icing of nunheted, Non-rotting Cylinder, Prt I: A Simultion Model. Journl of Climte nd Applied Meteorology, : p [6] Mkkonen, L., Modelling of ice ccretion on wire. Journl of climte ppl, Metoer, : p Journl of Computtionl Multiphe Flow

9 Muhmmd S. Virk 05 [7] [8] J Shin nd T.H. Bind., Experimentl nd computtionl ice hpe nd reulting drg incree for NACA 001 irfoil. 199, NASA technicl memorndum [9] Mnul, N.S.U. 010, NTI. [10] R Clift, J R Grce, nd M.E. Weber, Bubble, Drop nd Prticle. 1978, New York: Acdemic Pre. [11] Sözgen nd Æ.M. Cnibek, Ice ccretion imultion on multi-element irfoil uing extended Meinger model. Het M Trnfer, : p [1] M Frzneh, J Kiernicki, nd J. Drpeu., Ice ccretion on energized line inultor. Interntionl Journl of Offhore nd Polr Engineering, 199. (3. [13] I Lngmuir nd K.B. Boldgett., A mthemticl invetigtion of wter droplet trjectorie, in AAF Technicl Report [14] Boutnio, Z., An Eulerin 3D nlyi of wter droplet impingement on Convir-580 noe nd cockpit geometry, in Deprtment of Mechnicl Engineering. 1999, Concordi Univerity, Cnd: Montrel. [15] Mortenen, K., CFD imultion of n irfoil with leding edge ice ccretion, in Deprtment of Mechnicl Engineering. 008, Technicl Univerity of Denmrk. p Volume 3 Æ Number 4 Æ 011