Numerical study on steady aerodynamic characteristics of ice accreted transmission lines

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1 Numericl study on stedy erodynmic chrcteristics of ice ccreted trnsmission lines Shinichi Ok, Tkeshi Ishihr UMECA Jpn Co,. td., AIOS Bldg. -5-9, Kmioski, Shingw-ku, Tokyo 4-, Jpn Deprtment of Civil Engineering, School of Engineering, The University of Tokyo, 7-3- Hongo, Bunkyo-ku, Tokyo , Jpn ABSTRACT: Aerodynmic chrcteristics of ice ccreted trnsmission line hs een investigted using ES turulence model. The results show tht predicted men erodynmic coefficients for single nd 4-conductor undle fvorly gree with wind tunnel test results including cute chnge of lift coefficients. Mechnism of pek lift coefficients ws verified y investigting pressure field for comprehensive understnding of the phenomenon. A method of otining men erodynmic coefficients of 4-conductor undle converted from those of single conductor is proposed, nd verified y the numericl nlysis. INTRODUCTION The lrge mplitude wind-induced motion of ice ccreted trnsmission lines, clled glloping, could cuse inter-phse short circuit, dmge of insultors nd support structures, nd, in the worst cse, resulting shutdown of trnsmission lines. Hence, it is importnt to understnd nd predict the glloping phenomenon to estlish counter mesure to prevent n ccident. Mny studies hve performed to ssess the glloping phenomenon (Den Hrtog, 956; Prkinson, 97; Novk, 97; Cooper, 973; Kimur, et l., 999; Inoue, ; Shimizu et l., 4; Phuc et l., 5. Shimizu developed the finite element nlysis code tht requires men erodynmic coefficients s input dt. Those erodynmic coefficients dt re sed on dtse in which men erodynmic coefficients re interpolted using the pst wind tunnel tests results (Shimizu nd Sto,. Aerodynmic coefficients otined from the wind tunnel test were smll in vriety for the multi-undle conductor, nd interpoltions re used to supplement insufficient dt (Shimizu et l., 4. However, ccurcy of interpolted erodynmic coefficients for vrious kinds of ice ccreted trnsmission lines is not cler. Recently, Ok nd Ishihr (9 successfully predicted men nd fluctuting erodynmic coefficients of squre prism with vrious ngles of ttck. It ws noted tht spnwise length D is prcticlly enough for predicting men vlues. This implies tht the numericl simultion with ES turulence model cn e lterntive method to ccurtely predict erodynmic coefficients of luff ody. As reported y Shimizu et l. (4, profiles of ccreted ice significntly ffect erodynmic coefficients nd could cuse lrge negtive grdient of lift coefficient, resulting in glloping of ice ccreted trnsmission lines. The mechnism of peks lift coefficient hs not mde cler. Shimizu et l. (4 lso proposed formul to estimte erodynmic coefficients of 4-conductor undle y using those of single conductor, however, the result showed inconsistent with experiment t ngles of ttck where wke from upstrem conductors ffected the downstrem ones.

2 In this study, erodynmic chrcteristics of ice ccreted trnsmission line is investigted y ES turulence model nd compred with the mesurements from the wind tunnel test. Section descries the numericl model used in this study. Section 3 presents the predicted erodynmic coefficients of single conductor from the numericl simultion, which re compred with the experimentl dt nd the interpolted those for the cses of H=.5D nd.5d. The mechnism of pek lift coefficient is lso investigted y the pressure distriution of the ice ccreted conductor. Finlly, formul considering the velocity reduction in the wke region is proposed to estimte erodynmic coefficients of 4- conductor undle y using those of single conductor nd compred with the experiment. NUMERICA MODE. Governing equtions The governing equtions employed in ES model re otined y filtering the timedependent Nvier-Stokes equtions s follows; ρu~ i =, ( x i ~ ( ρu~ ( ~ ~ u~ i P i + ρui u τ = µ, ( t x x x xi x where u ~ nd ~ p re filtered men velocity nd filtered pressure respectively. ρ is density nd τ is sugrid-scle stress. The sugrid-scle stresses resulting from the filtering opertions re unknown, nd modeled s follows; ~ τ µ t S ~ ~ ~ = + τ kkδ, u u i S +, (3 3 x xi where µ t is sugrid-scle turulent viscosity, nd S ~ is the rte-of-strin tensor.. Smgorinsky model Smgorinsky model (Smgorinsky, 963 is used for the sugrid-scle turulent viscosity. ~ ~ ~ µ = ρ S = S S, (4 t where s ρ s s is the mixing length for sugrid-scles, nd defined s; /3 ( κδ, C V = min. (5 s s where κ is the von Krmn constnt,.4, C s is Smgorinsky constnt,.3, δ is the distnce to the closest wll, nd V is the volume of computtionl cell.

3 .3 Boundry conditions When wll-dcent cell is in the lminr sulyer, the wll sher stress is otined from the lminr stress-strin reltionship. If the mesh cnnot resolve the lminr sulyer, it is ssumed tht the centroid of the wll-dcent cells flls within the logrithmic region of the oundry lyer, nd the lw-of-the-wll is employed. u ~ = u τ u ρ τ µ y, u~ = ρuτ y ln E uτ κ µ τ where u% is filtered velocity tht is tngentil to the wll, u τ is friction velocity, κ is von Kármán constnt, nd constnt E is 9.8. Uniform velocity condition is specified t inlet oundry, nd zero diffusive conditions re used t the outlet oundry. Symmetry conditions re given for oth sides nd upper/lower oundries..4 umericl method Finite volume method nd unstructured collocted mesh re used for the present simultions. The second order centrl difference scheme is used for the convective nd viscosity term, nd the second order implicit scheme for the unstedy term. SIMPE (Semi-Implicit Pressure inked Equtions lgorithm is employed for solving the discritized equtions (Ferziger nd Peric,..5 Modeling conditions nd system configurtions The models of ice ccreted trnsmission line in the present study re sed on the wind tunnel test y Shimizu (Shimizu et l., 4. Figure shows the section of profile of ice ccreted single conductor trnsmission line models in which the heights of ccreted ice, H, re respectively,d,.5d, nd.5d, where D denotes dimeter of the conductor. Figure shows the computtionl domin for the single conductor nd mesh used in the present study. The computtionl domin is squre s shown in Figure(, nd length of ech side of the domin is 6D. Mesh density is higher t the tip of ccreted ice nd totl 88 grids re distriuted in the circumference s shown in Figure(. Figure 3( shows 4-conductor undle model in which typicl dimeter B, intervl etween conductor centers, is 3D. Mesh distriution in the vicinity of ech ccreted ice nd conductor is the sme s tht of single conductor trnsmission line model. As shown in Figure 3(, structured uniform size grids re distriuted etween conductors to minimize numericl viscosity. Tle. shows the conditions of the simultions. (6 H=9.5 D=9 c H=9 D=9 H=4.75 D=9 Figure. Cross sectionl dimensions of conductors nd ccreted ice model geometry: ( height of ccreted ice H=D; ( H=.5D; (c H=.5D

Figure. Computtionl domin nd mesh: ( computtionl domin of single conductor; ( mesh ner the ice ccreted single conductor Figure 3.

Prmeter used in this study Conductor type Single conductor 4-conductor undle Height of ccreted ice H D.5D.

4 Spnwise length D D The numer of mesh in spnwise direction 4 The numer of the mesh 8, 349,5 3 MEAN AERODYNAMICS FOR SINGE CONDUCTOR Negtive

Hence, it is importnt to predict pek of men lift coefficients.

4 Figure. Computtionl domin nd mesh: ( computtionl domin of single conductor; ( mesh ner the ice ccreted single conductor Figure 3. Computtionl domin nd mesh: ( computtionl domin of 4-conductor undle; ( mesh etween ice ccreted conductors of 4-conductor undle Tle. Prmeter used in this study Conductor type Single conductor 4-conductor undle Height of ccreted ice H D.5D.5D D Reynolds numer UD / ν 3, Non-dimensionl time step size tu / D.4 Spnwise length D D The numer of mesh in spnwise direction 4 The numer of the mesh 8, 349,5 3 MEAN AERODYNAMICS FOR SINGE CONDUCTOR Negtive grdient of men lift coefficients could cuse negtive dmping resulting in glloping (Den Hrtog, 956; Prkinson, 97. Hence, it is importnt to predict pek of men lift coefficients. In this section, men erodynmic coefficients of single conductor trnsmission line re predicted for the height of ccreted ice, H=D,.5D, nd.5d, nd compred with the wind tunnel test results. Figure 4 shows men erodynmic coefficients, C D, C, C M, vry with ngles of ttck in different heights of ccreted ice plotted with Shimizu (Shimizu et l., 4. As shown in Figure 4(, predicted C D for H=D show flt curve in the rnge from α = to

5 , then linerly increses with increse inα, which is in good greement with the experiments. Predicted C for H=D shows negtive grdient etweenα = nd s oserved in experiment s shown in Figure 4(. The cute chnge of C round α = s oserved in the experiment is well cptured y the present numericl pproch. Predicted C is underestimted the experiment etween α = nd 3. In the rnge from α = 3 or lrger, the predicted C curve is lmost flt nd in good greement with experiment. As shown in Figure 4(, predicted CM grees with experiment for ll ngles of ttck. Regrding the reltion etween the height of ccreted ice nd erodynmic coefficients, s shown in Figure 4(, ngle of ttck t pek lift coefficient, α = for H=D, is shifted to t H=.5D, nd the mgnitude of the pek ecomes smller. The pek is lmost dispper t H=.5D. The ngle of ttck corresponding to the peks increse when the height of ccreted ice reduces. Similr tendency is oserved in the predicted moment coefficients s shown in Figure 4(. Those predicted results re in good greement with experiments. Tle present men lift coefficients otined y interpoltions t α = vry with the height of ccreted ice t H=,.5D,.5D, nd.d respectively. As shown in the tle, significnt discrepncies re oserved etween C y interpoltions nd experiment for oth H=.5D nd.5d, nd present numericl nlysis hs dvntge over conventionl interpoltions. Negtive grdient of lift coefficients nd pek lift coefficients re oserved in the experiment (Shimizu et. l, 4. However, the mechnism of the phenomenon is not discussed in the study ecuse pressure field dt re not ville. One of the dvntges of the numericl nlysis is tht comprehensive flow nd pressure fields cn e otined from n nlysis result. C D 4 3 Shimizu et.l.(d Present(D Shimizu et.l.(.5d Present(.5D Simizu et.l.(.5d Present(.5D C C M Shimizu et.l.(d, C Shimizu et l.(d, C M Present(D, C Present(D, C M Shimizu et l.(.5d, C Shimizu et l.(.5d, C M Present(.5D, C Present(.5D, C M Shimizu et.l.(.5d, C M Shimizu et l.(.5d, C M Present(.5D, C Present(.5D,C M Angle of ttck (deg Angle of ttck (deg. Figure 4. Vritions of erodynmic coefficients with ngles of ttck : ( C D, ( C nd conductor t H=D,.5D, nd.5d C M for single Tle. Men erodynmic coefficients otined y interpoltions t α = H C experiment numericl interpoltion -.5D D D

6 C p - c α= o α=6 o c x/b Figure 5. Men pressure field : ( α = ; ( α = 6 ; (c men surfce pressure coefficients distriutions Figure 5 shows men pressure field nd men surfce pressure coefficients distriutions in the vicinity of ice ccreted single conductor t α = nd 6 for H=D. As shown in Figure 5 ( nd (, mgnitude of negtive pressure t round leding edge of lower fce t α = is lrger thn tht t α = 6. This indictes tht lrger negtive lift force is generted round α =, which resulted in the pek lift coefficient. As shown in Figure 5 (c, mgnitude of negtive pressure t round leding edge of lower fce, x/b=.6 to.9, is lrger thn tht t α = 6. This indictes tht lrger negtive lift force is generted tα =. 4 MEAN AERODYNAMICS FOR 4-CONDUCTOR BUNDE In this section, men erodynmic coefficients of 4-conductor undle trnsmission line re estimted y the numericl simultion nd y proposed formul sed on the predicted erodynmic coefficients for the single conductor. The predicted erodynmic coefficients y the numericl simultion with ngles of ttck for 4-conductor undle with H=D re in good greement with the experiment s shown in Figure 6. Aerodynmic coefficients of 4-conductor undle cn e descried s follows; CD = ( CD+ CD+ CD3+ CD4 (8 where suscript denotes 4-conductor undle, nd suscript to 4 denote ech conductor for 4-conductor undle. Aerodynmic coefficients of ech conductor mye modified y using reduce fctor, γ i, from tht of single conductor;

7 C = C γ, γ = U / U (9 Di D i i i where suscript i demotes ech conductor. U i nd U denote upstrem wind velocity for ech conductor nd inflow velocity respectively. Aerodynmic force coefficients in the wke region re proportionl to velocity pressure. Suppose tht distriution of velocity pressure in the wke region is in sinusoidl wveform where minimum nd mximum velocity pressure re denoted s / ρu min nd / ρu mx respectively. Men velocity pressure in the wke region cn e estimted s follows: / ρ U = / ρ( U min + U mx / ( Normlized men velocity pressure y the velocity pressure in the inflow, e expressed s: ρ cn / U o γ = ( γ min + γ mx / ( Figure 7 shows predicted non-dimensionl men velocity profile in y direction, norml to inflow direction in the upstrem side of rer conductor. Minimum reduce rtio is estimted. t α = 9 nd mximum one is.86 resulting in γ =.63. Similrly, γ =.867 is otined t α =. Tle 3 shows men drg coefficient of 4-conductor undle from the experiment nd the formul. Drg coefficients y present formul re closer to experiment, compring with those otined y conventionl one C D, C Present (C -6 D Present (C Present (C M Angle of ttck (deg. Sihimizu et l.(c D Shimizu et l.(c Shimizu et l.(c M C M Figure 6. Vrition of erodynmic coefficients with ngles of ttck for 4-conductor undle with H=D.5.5 U/U o U/U o y/d Figure 7. Non-dimensionl men velocity profile in y direction in the upstrem side of rer conductor: ( α = ; ( α = 9. y/d

8 Tle 3. Men erodynmic coefficient of 4-conductor undle α Experiment Conventionl Present CONCUSION Aerodynmic coefficients of ice ccreted single nd 4-conductor trnsmission line hve een investigted using ES turulence model. Following summrizes the findings nd conclusions of this study; The predicted men erodynmic coefficients of ice ccreted single conductor with curved surfces y the numericl simultion show good greement with experiments, while lift coefficients otined y interpoltions significntly overestimted the experiments in some ngle of ttck. It ws found tht pek negtive lift coefficient for H=D cse is cused y negtive pressures ner the tip of the lower fce. Negtive pressures increse with increse in ngle of ttck nd recovers t ngle lrger thn due to the vortex shedding. Intensive nd concentrted negtive pressure region ws oserved t α =, ccording to the pek lift coefficient t round this ngle of ttck. 3 A formul ws proposed to estimte erodynmic coefficients of 4-conductor undle from corresponding those of single conductor, considering velocity reduction in the wke region. The predicted drg coefficients t α = nd 9 for 4-conductor gree well with the experiment nd overestimtions y the conventionl formul re improved. 6 REFERENCES Cooper, K. R., 973. Wind tunnel nd theoreticl investigtion into the erodynmic stility of smooth nd strnded twin undled power conductors, Ntionl eronuticl estlishment, Report TR-A-5. Den Hrtog, J. P., 956. Mechnicl virtions, McGrw-Hill. Ferziger, J., Peric, M,. Computtionl method for fluid dynmics, 3rd Edition, Springer. Inoue, M.,. Formultion of unstedy erodynmic forces on n ice-ccreted 4-conductor undle trnsmission line nd prediction of the wind-induced response mplitude. Kimur, K., Inoue,M., Fuino, Y., Yukino, T., Inoue, H., Morishim, H., 999. Unstedy forces on n iceccreted four conductor undle trnsmission line, , ISMB Novk, M., 97. Glloping Oscilltions of Prismtic Structure, Proc. ASCE, Vol. 98, No. EM. Ok, S., Ishihr, T., 9. Numericl study of erodynmic chrcteristics of squre prism in uniform flow, Journl of Wind Engineering nd Industril Aerodynmics 97, Prkinson,G. V., 97. Wind-induced instility of structure, Phil. Trns. Roy. Soc. und. A 69, Phuc, P.V., Ishihr, T., Shimizu, M., 5. A wind tunnel study on unstedy forces of ice ccreted trnsmission lines, 5 th Interntionl colloquium on luff ody erodynmics nd pplictions, Ottw. Shimizu, M., Sto, J.,, Glloping oservtions nd simultion of -4condictor undle trnsmission line, Jour nil of Structurl Engineering, Vol. 47A, Shimizu, M., Ishihr, T., Phuc, P. V., 4. A Wind tunnel study of erodynmic chrcteristics of ice ccreted trnsmission lines, 5 th Interntionl colloquium on luff ody erodynmics nd pplictions, Ottw. Smgorinsky, J., 963. Generl circultion experiments with the primitive equtions. I. The sic experiment, Month. We. Rev. 9,

Numerical study of turbulent flow over complex topography by LES model

Numerical study of turbulent flow over complex topography by LES model Numericl study of turulent flow over complex topogrphy y LES model Zhenqing Liu* ), Tkeshi Ishihr** ),)Deprtment of Civil Engineering, The University of Tokyo, Tokyo, Jpn, *) Zhenqing Liu, liu@ridge.t.u-tokyo.c.jp