4th Interntonl Conference on Senor, Meurement nd Intellgent Mterl (ICSMIM 015) Effect of Wnd Speed on Recton Coeffcent of Dfferent Buldng Heght Chunl Ren1,, Yun Lu,b 1 No.9 Dxuexdo. Tnghn Cty, Hebe Provnce, Chn No.30 Benhundonglu. Bejng, Chn rcl9169@163.com, bluyun@cbrtech.com Keyword: heght of buldng; convecton het trnfer coeffcent; recton coeffcent. Abtrct. The r-condtonng lod wll ncree n the room wth the me envelope ze nd me therml performnce, but n dfferent heght. Therml recton coeffcent method wdely ued n clculton of r-condtonng lod. Chnge rule of therml recton coeffcent cn be confrmed by clculton ce n th pper. Wth the ncree of the heght of buldng, the recton coeffcent wll ncree. Introducton Het trnfer on the buldng urfce gretly ffected by correpondng wnd peed. Epeclly n the hgh-re buldng, buldng urfce wnd peed wll ncree wth heght, o tht the urfce het trnfer enhncement. Menwhle ddtonl het lo ccompned by ncreed r-condtonng lod. Wth the chnge rule of recton coeffcent, the r-condtonng lod nd correpondng cpcty of r-condtonng ytem cn be clculted ccurtely. The rule lo cn be ued to nlyze nternl force nd deformton n concrete tructure buldng to reduce the rk of urfce crckng produced by olr rdton nd convecton het trnfer. Wnd Speed Dtrbuton Lw At low lttude, the wnd peed ner to the ground urfce wll ncree wth heght ncreng due to urfce frcton. Below 100m, the verge wnd peed profle ftted by the logrthmc equton. In 100m-300m heght, the verge wnd peed profle ftted by exponentl lw. And the heght bove ground 300m-500m, wnd peed cheve mxmum, becue r flowng lmot not be ffected by ground urfce frcton but cton of r preure. Concluon bove lo cn be reveled n equton (1), (). Wnd peed vrton preet logrthmc lw n 10m-100m heght, nd preet ndex lw n 100m-300m heght. Wnd peed dtrbuton n logrthmc lw (10m-100m) hown n equton (1): u lnz lnz 0 [1] u1 lnz 1 z 0 (1) Wnd peed dtrbuton n ndex lw(100m-300m) hown n equton: Z u u 1 Z1 () Where Z 0 roughne heght(in the neutrl lyer, roughne heght the heght whch vertcl wnd peed pprochng to zero, roughne heght 1.1m n Bejng), Z1 tndrd 016. The uthor - Publhed by Atlnt Pre 881
heght(stndrd heght 10m n mot nton), u verge peed n Z heght, u 1 verge peed n 10m heght, wnd peed profle ndex. Convectve Het Trnfer Coeffcent n Dfferent Heght nd Correpondent Wnd Speed Typclly, convectve het trnfer coeffcent cn be clculted nd teted n nturl convecton tte. But n fct, the wnd peed on hgh-re buldng urfce ncree wth heght. In the ce of conderng wnd drecton prllel to wll urfce, the equton (3) ued to clculte convecton het trnfer coeffcent. 5.7 3.8v [] (3) Where the het trnfer coeffcent, v[m/] the velocty on wll urfce. Accordng to equton (3), convectve het trnfer coeffcent n dfferent heght nd correpondent wnd peed n 10m, 100m, 00m nd 300m heght cn be clculted n Tble1. Tble1. convectve het trnfer coeffcent nd correpondent wnd peed n dfferent heght Z[m] 10 100 00 300 Wnd Speed[m/] 4.5 9.19 1.1 13.9 [W/m ].8 40.6 51.68 58.5 Recton Coeffcent Method The recton coeffcent method propoed by D. G. Stephenon nd G. P. Mtl n Cnd n the lte 60. In eence, recton coeffcent method ntegrte modern control theory nto the Lplce trnform nd the nvert trnform. In the preme of conderng the wll therml ytem, the het flux vrton cued by the dturbnce of trngle temperture wve cell obtned by decompong the boundry condton whch vre contnuouly nto ere of trngulr pule by multplyng the pule heght wth the trngle pule cell. In the vew tht ech pule lnerly ndependent nd therml ytem lner ytem, the whole het proce cn be obtned by pplcton of uperpoton prncple nd convoluton prncple. The Trnfer Mtrx[3] From the theory of het trnfer, the therml feld nd het flux vrton trend cn be obtned by olvng the followng prtl dfferentl equton whch hown n equton (4): (4) (x, ) t (x, ) x t(x, ) qx, x t(x,0) 0 0 x l, 0 (0 x l, 0) The equton (4) for Lplce trnform hown n equton (5): T Q x, x, ch xt0, h xq0, h x T0, ch xq0, (5) 88
Where T(x, ) the Lplce trnform from temperture to tme t the poton x, Q(x, ) the Lplce trnform from het flux to tme t the x ecton, the Lplce trnform of ( repreentng tme), therml dffuvty, m /, λ therml conductvty, W/(m K), x [m] coordnte on the clculted urfce, l [m] the thckne of wll. From equton (4), (5), the temperture repond nd het flux repond n ny poton cn be obtned by Lplce trnform method once boundry condton t(0,τ) nd q(0,τ) re known. And equton (5) cn be olved by Lplce trnform of T(x, ) nd Q(x, ) whch hown n equton (6). When x=1, then: T l, Q l, Where: A() B A C ch / l B D T 0, Q 0, ; C / h / l h / l/ / ; D ch / l A B G When C D, G trnfer mtrx of wll ytem repreentng therml chrctertc of wll ytem, nd not relted to temperture nd het flux on both de of the wll. Het Trnfer Coeffcent In olvng the het trnfer coeffcent, B()=0 n the trnfer mtrx, nd 100 n trncendentl equton. Then het trnfer equton hown n equton (7): y y 0 n K 1 1 B B 1 e n1 1 e e n 0 n 1 Where Δτ the dcrete tme ntervl,δτ=1h, B the coeffcent,be equl to 1/ B' -, the I-th root, n the number of recton coeffcent, n=40, K the het trnfer coeffcent of wll, W/(m K), Δτ the dcrete tme ntervl, Δτ=1h, B the coeffcent,be equl to B' - 1/, the I-th root, n the number of recton coeffcent, n=40, K the het trnfer coeffcent of wll, W/(m K). Ce Reerch For one type of wll, the wll mterl re hown n Tble: Tble. Wll mterl Wll type Therml Dffuvty [W/m ] Het trnfer coeffcent[kg/m 3 ] 1. brck ettng(40mm) 0.00184 0.81. Lme plter (0mm) 0.00179 0.7. ; (6) (7) 883
Root of Equton B() Dfferent heght root dtrbuton fgure re hown n Fg.1-Fg.4, n whch the horzontl coordnte re the root of B(), nd the longtudnl coordnte re the vlue of B(). Fg.1 Root of B() n 10m heght Fg. Root of B() n 100m heght Fg.3 Root of B() n 00m heght 884
Fg.4 Root of B() n 300m heght Repreent the bove fgure by dt n Tble3: Tble3. The root dt of B() Heght Heght Heght Heght Root Root Root 10m 100m 00m 300m Root 1-0.19 1-0.141 1-0.136 1-0.137-0.59-0.646-0.599-0.598 3-1.48 3-1.58 3-1.515 3-1.513 4 -.89 4-3.01 4 -.993 4 -.99 5-4.941 5-5.041 5-5.086 5-5.084 6-7.641 6-7.717 6-7.87 6-7.84 7-11.03 7-11.06 7-11.3 7-11.3 8-15.1 8-15.1 8-15.9 8-15.3 9-19.85 9-19.85 9-0.0 9-0.0 10-5.7 10-5.7 10-5.4 10-5.4 11-31.34 11-31.34 11-31.4 11-31.4 1-38.04 1-38.04 1-38.8 1-38.8 13-45.36 13-45.36 13-45.36 13-45.36 14-53.3 14-53.3 14-53.7 14-53.7 15-61.84 15-61.84 15-61.8 15-61.8 16-71 16-71 16-70.95 16-70.95 17-80.78 17-80.78 17-80.74 17-80.74 18-91.18 18-91.18 18-91.14 18-91.14 885
Repone Coeffcent Accordng to equton (7), the recton coeffcent clculted Tble4: Tble4. Recton coeffcent vlue n dfferent heght Heght 10m Heght 100m Heght 00m Heght 300m j Y j Y j Y j Y 1 0.0017 1 0.0067 1 0.0066 1 0.0083 0.045 0.0556 0.051 0.0536 3 0.1048 3 0.19 3 0.108 3 0.14 4 0.1481 4 0.1754 4 0.166 4 0.1679 5 0.1661 5 0.1905 5 0.1834 5 0.185 6 0.167 6 0.1866 6 0.18 6 0.1836 7 0.1587 7 0.1733 7 0.1715 7 0.177 8 0.146 8 0.1565 8 0.1565 8 0.1575 9 0.13 9 0.139 9 0.1404 9 0.141 10 0.118 10 0.14 10 0.147 10 0.15 11 0.105 11 0.107 11 0.1099 11 0.1103 1 0.093 1 0.0935 1 0.0966 1 0.0969 13 0.081 13 0.0815 13 0.0847 13 0.0848 14 0.073 14 0.0709 14 0.0741 14 0.0741 Concluon Recton coeffcent pper to ncreng trend whch ccord to the ctul tuton n bove nly. It cn be deduced tht hetng lod nd coolng lod wll ncree wth the ncree of the buldng heght. In the clculton of coolng lod nd hetng lod, the recton coeffcent hould be djuted wth the buldng heght regrdle of multon method or tbulr computton. The djuted route wll help to mprove the ccurcy of degn, epeclly be benefcl to optmze conultton. Reference [1] Tntn Yng, Dxue Lu, Ruojng Wng, Zhnhn Wng. The Influence on Low-E Gl of Wnd Speed Chngng wth Buldng Heght, 007, 6():79 [] S.E.G.JAYAMAHA, N.E.WIJEYSUNDERA, S.K.CHOU. Meurement of the Het Trnfer Coeffcent for Wll, Buldng nd Envronment, 1996,31(5),399 [3] Qen Yn, Qngzhu Zho. Buldng Het Proce. Bejng :Chn Archtecture & Buldng Pre,1986. 886