whch make the dyamc characterstcs of teso structures are obvously dfferet from those of brdges ad hgh-rsg buldgs, so tradtoal methods of radom vbrato

Transcription

1 The Seveth Iteratoal Colloquum o Bluff Body Aerodyamcs ad Applcatos (BBAA7) Shagha, Cha; September -6, 01 Numercal studes o the behavors of wd-structure teracto for membrae structures Xao-Yg SUN a, Zhao-Qg CEN b, Yue WU c ad Sh-Zhao SEN d a School of Cvl Egeerg, arb Isttuted of Techology, Cha, s _ht@163.com b School of Cvl Egeerg, arb Isttuted of Techology, Cha, chezhq004@163.com c School of Cvl Egeerg, arb Isttuted of Techology, Cha, wuyue_000@163.com d School of Cvl Egeerg, arb Isttuted of Techology, Cha, szshe@ht.edu.c ABSTRACT: I ths paper, a combed umercal approach o the tmedepedet flud-structure teracto for teso structures wth large dsplacemets s preseted. The geeral dea of ths approach s to dvde the structural respose uder wd actos to three compoets: mea respose, backgroud respose ad resoat respose. The frst compoet s a statc teracto process, whch s due to the chage of structural geometry uder mea wd pressure. The secod compoet ca be regard as a steady teracto process, whch relates to the moto of large scale eddes. The last compoet ca be called as a traset teracto process, whch the dyamc magfcato effect should be cosdered maly. Due to the dfferet characterstcs of each compoet, dfferet methods should be adopted respectvely. For statc ad steady teracto, the sutable method s CFD smulato, whch the wd pressure chage due to structural deformato wll be cosdered maly; for traset teracto, the sutable method s olear radom vbrato aalyss tme doma. Base upo the combed procedure, some umercal examples clude oe-way type roofs ad saddleshaped membrae structures are carred out fally. From the comparso wth drect umercal method, whch ca be see as a accurate method, t ca be cocluded that the results obtaed from the combed procedure are very close to the drect umercal method; moreover, the combed procedure seems easer for applcato. KEYWORDS: membrae structures; wd-structure teracto; CFD umercal smulato; aeroelastc effects; aerodyamc respose; geometrcal olearty 1 INTRODUCTION Membrae structures are the most wdely used log-spa teso structures. As beg characterzed by lghtweght ad flexble, they are hghly susceptble to the wd acto. ow to determe the aerostatc ad aerodyamc respose due to the wd acto s a major cocered problem for the desg of teso structures. Up to ow, comprehesve studes have bee performed, but the mechasm of wd-duced vbrato of membrae structures has ot bee recogzed eough detal. The ma reasos le two aspects: oe s the strogly geometrcal olearty, 34

2 whch make the dyamc characterstcs of teso structures are obvously dfferet from those of brdges ad hgh-rsg buldgs, so tradtoal methods of radom vbrato aalyss frequecy doma ca ot be used drectly. The other reaso s the weak local rgdty, whch ca make membrae structures produce rather large vbrato uder wd exctato. Sometme, these large vbratos ca eve affect the surroudg flud feld remarkably; that s to say, the wd-structure teracto or the aeroelastc effects ca ot be eglected. To solve the prevous problem, some olear radom vbrato aalyss methods tme doma have bee developed successfully [1]. But all those methods are based o the codto that the let flow or the wd pressure process has bee determed beforehad, so they ca ot cosder the fludstructure teracto actually. To determe the actual wd loads o teso structures, especally to reveal the mechasm of wd-structure teracto, some sem-emprcal methods have bee developed [], also some wd tuel tests has bee carred out [3]. owever, some uavodable errors wll occur whe usg smplfed methods, ad wd tuel tests are too expesve to carry out extesve studes, therefore those methods are oly lmted to certa specal structures. I recet years, wth the developmet of hgh speed computer ad umercal computatoal methods, t has bee avalable to tegrate computatoal flud dyamcs (CFD) ad computatoal structure dyamcs (CSD) techque to smulate structures ad surroudg flow smultaeously, whch s called as umercal wd tuel method. Comparg to those smplfed methods ad wd tuel tests, umercal wd tuel method ca solve flowg problems of complex geometrcal bodes wthout dsturbg the flud feld, costruct computatoal models whose dmeso are same as that of orgal structures so as to avod the smlarty requremets wd tuel test, completely cotrol the propertes of flud ad provde great flexblty for selectg flowg parameters to carry out parametrc aalyss. Because of these superor characterstcs, umercal wd tuel method s hghly valued by researches ad developed quckly. Now ths method has bee appled to solve some aeroelastc problems, such as for brdges [4] ad also for membrae structures [5]. But due to the tremedous calculate work, ths method also ca ot be used egeerg practce. I ths paper, a overvew of the studes o wd-structure teracto of teso structures s provded frstly. The a combed umercal approach based o CFD smulato method ad radom vbrato aalyss method s preseted. Fally, Base upo the combed procedure, some umercal examples clude oe-way type roofs ad saddle-shaped membrae structures are carred out. METODOOGY Wd-duced respose of teso structures ca be theoretcally descrbed as a problem of usteady couplg vbrato betwee compressble vscous flud ad geometrcal olear elastc body. Due to the flud forces ad structure dsplacemets o the terface betwee flud ad structure are ukow, t s mpossble to solve the flud feld ad structural feld separately, so we have to fd some methods that ca solve these two felds smultaeously. Udoubtedly, the umercal wd tuel method provdes a good platform for solvg ths problem. I Ref. [6], the author had developed a FEM program for calculatg two-dmeso problem. There were three modules cluded ths program, each for CFD, CSD ad CMD (Computatoal Mesh Dyamcs) calculato, respectvely. The flowchart s show fg.1. The dyamc flud-structure teracto was performed by a parttoed soluto approach, ad the tmedepedet smulato process was cotrolled by a terato procedure betwee these three modules utl covergece was reached each tme-step. Based o ths program, the aeroelastc re- 35

3 The Seveth Iteratoal Colloquum o Bluff Body Aerodyamcs ad Applcatos (BBAA7) Shagha, Cha; September -6, 01 spose of oe-way type pretesoed membrae roofs has bee studed. The effects of several factors, such as heght-spa rato, roof slope, roof mass ad preteso force et al, were vestgated. From these studes, some prelmary but very mportat coclusos about the mechasm of wd-structure teracto were obtaed [7]. Fg. 1 Flowchart of CFD smulato program The practcal cable/membrae structures are 3-dmesoal wth complcated surfaces. Usg the CFD smulato approach as metoed above to study the aeroelastc effects of 3-D structures has theoretcally possble, but wll be very dffcult practce at preset. Frstly, the tme-cosumg of smulatg 3-D problem s hudreds tmes of -D problem, whch ca ot be tolerated for systemcally studes. Secodly, the creasg computg tme wll cause lots of umercal dsspato ad error cumulato. So f we use the method proposed Ref. [9] to solve 3-D problem, t meas that all the umercal methods ths -D program should be mproved to get more computg effcecy ad precso, however the work s obvously eormous. At the same tme, there are two facts: (1) Varous CFD commercal software are developg quckly, they have provde more effcet umercal platform to solve flud problem, however, the problem of flud-structure teracto ca hardly be resolved by these software. () From the vewpot of egeerg, egeers usually do t cocer about the detals of couplg vbrato process but some statstc formato, such as the mea ad peak value, ad whether or whe wll the aeroelastc stablty occur. So t s possble to solve the couplg problem by aother ew method, whch s to adopt some smplfed aalytcal methods ad umercal methods to get the statstcal formato of the couplg process, ad gve up the smulato o wdstructure teracto detal. The precodto of ths method s to gve a reasoable explaato about the couplg mechasm of wd-structure teracto. Accordg to the wd-duced structural vbrato theory proposed by Daveport [8], the structural respose ca be broke to three compoets: mea respose r, backgroud respose r B ad resoat respose r R (Fg.). The mea respose s duced by average wd pressure, ad does ot chage wth tme. The backgroud resposes relates to the moto of large scale eddes, ad vary slowly ad rregularly wth tme. It s essetally a quas-statc process ad has o dyamc amplfcatory effect. The resoat respose usually happes at frequeces adjacet wth the structural atural frequecy, ad has obvous dyamc amplfcatory effect. If we assume that the wd-duced vbrato respose of membrae structures has the same characterstcs as metoed above, the dfferet methods ca be adopted for dfferet compoets to get the statstc formato separately. 36

4 Fg. Respose to wd For the mea respose, the couplg effects are maly duced by the structural average deformato, whch wll make the mea wd pressure chage cosequetly. It s a statc process ad ca be solved drectly by steady CFD umercal smulato wth several teratve steps. For the backgroud respose, the couplg effects are maly duced by the effect of the spatal correlato of fluctuatg wd, that s to say, we have to fd these crtcal dstrbutos of fluctuatg wd pressure whch ca make structure produce maxmum or mmum steady respose. It s a quas-statc process whch the dyamc amplfcatory effect ca be gored ad oly some modes of steady deformato are cosdered. For the resoat resposes, dyamc couplg betwee the hgher frequecy parts of fluctuatg wd ad structure s maly cosdered, t meas that the resoat respose of structure s maly duced by those small-scale eddes. Due to the effect of those small-scale eddes s a radom process, the sutable method for solvg the resoat resposes s olear radom vbrato aalyss methods tme doma. It s worth to expla that the calculato of each compoet wll based o the result of the calculato o the former compoet. To sum up, the wd-structure teracto ca be dvded to three parts (Fg.3): statc teracto, steady teracto ad traset teracto. Mea respose belogs to the statc teracto, backgroud respose belogs to the steady teracto, ad resoat respose belogs to traset teracto. The statc teracto ad the steady teracto should be studed specally by meas of CFD umercal smulato. The traset teracto should be studed by meas of olear radom smulato tme doma. Fg. 3 the sketch of wd-structure teracto 3 GENNERA FORMUATIONS 3.1 Statc Iteracto Statc teracto s expressed as follow: 37

5 The Seveth Iteratoal Colloquum o Bluff Body Aerodyamcs ad Applcatos (BBAA7) Shagha, Cha; September -6, 01 Ks0 x0 p (1) Where x0 s the mea respose; Ks0 ad p are the stffess ad mea wd pressure correspodg to the mea deformato respectvely; p ca be calculated by meas of CFD smulato. 3. Steady Iteracto Steady teracto s expressed as follow: Ks1 x1 () t p() t () Where p() t s the fluctuatg wd pressure, whch ca be calculated by CFD smulato. Accordg to the Proper Orthogoal Decomposto (POD) techque, p() t ca be decomposed as follow: pxyzt (,,, ) pˆ ( xyzt,,, ) a( t)g 1 1 (3) whereg s the th egemode of the wd pressure feld, ak () t s the correspodg prcpal coordate, pˆ () t s the wd pressure tme hstory correspodg to the th egemode, represets the domat wd pressure dstrbuto o structural surface. Substtute Eq.(3) to Eq.(), Eq.()ca be rewrtte as: s1 1 1 K x t pˆ t (4) Assumg the steady deformato s the summato of the effects of each egemode ˆ s1 1 K x t p t x 1 () t x 1 () t (5) 1 where x () 1 t s defed as the tme-hstory of the quas-statc respose duced by the th egemode. The the varace of backgroud respose 1 ca be expressed as (6) s1 where 1 s the varace of steady deformato x 1 () t duced by the th egemode. So the followg formula ca be used to estmate the cotrbuto of each egemode to the whole steady deformato. 1 1 (7) 1 Accordg to the POD techque, Eq. (4) ca be expressed as: Ks 1 x1 t a()g t (8) From Eq. (8), t s educed that the vbrato mode of x 1 () t s determed by the stffess K ad the th egemode G, ad the vbrato ampltude of x () 1 t s determed by the prcpal coordate () fdg the momet a t. So the maxmal steady deformato 1 j t, whch s correspodg to the peak value of a () t. j x t of x () 1 t ca be determed by 38

6 3.3 Traset Iteracto Traset teracto s expressed as follow: M x t C x t K x t p t, x t, x t, x t (9) s s s,,,,, p t x t x t x t p t f x t x t x t (10) Where x () t s traset deformato relatve to the peak steady deformato of the th egemode; ~ p ( ) represets the hgh frequecy part fluctuatg wd cludg the moto-duced aerodyamc force; ~ p ( ) ca be decomposed to p () t whch does ot cosder the structure vbrato ad f ( ) whch s duced by structure vbrato. p () t s gaed from the hgh frequecy parts of results of CFD smulato, whch based o the form correspodg to each peak steady respose; f ( ) s added aerodyamc term whch ca be trasformed to added mass M a ad aerodyamc damp Eq.(8)ca be rewrtte as: C a by meas of smplfed aeroelastc model theory[9]. So ( M s M ) a x() t ( Cs Ca) x () t Ksx() t p () t (11) It s especally emphaszed that traset teracto s based o the possble peak steady deformato of the th egemode x x ( ) 1 tj,.e. dfferet x x ( ) 1 tj correspod to dfferet traset teracto respose. 3.4 Peak Respose The peak respose of structure s solved by meas of superposto theory after gettg x, x1 t ad x t : xmax x 1 max (1) 1 Based o the theory metoed above, the flowchart of the combed umercal approach s show as fgure 4. Fg. 4 Flowchart of the combed umercal approach 39

7 The Seveth Iteratoal Colloquum o Bluff Body Aerodyamcs ad Applcatos (BBAA7) Shagha, Cha; September -6, 01 4 NUMERICA EXAMPE 4.1 Couplg Effects of Oe-Way type roofs The roof spa s 40m ad 10m hgh, the computatoal doma s show fgure 5. The flow 0.16 velocty profle s defed by V ( y) 30( y /10) m/s leadg to a velocty value of 30m/s at 7 roof level. Thus, the Reyolds umber becomes Re The fxed wall s assumed as oslp flow boudary, local oe-way codto s adopted o the boudary of the outlet, ad the gradet of flow speed of the outlet s zero; o-dmesoal tme step t ere we assume the roof s a cable structure, the mass per legth g s 5kg/m, the prestressg teso force T s 0kN. Accordg to the results of computato, the frst ad secod frequecy of structure s 0.8z ad.34z, respectvely. Fgure 6 shows the streamle drawg of flow aroud the fxed roof, t meas that the couplg effect does ot bee cosdered. Fgure 7 shows the streamle drawg of flow aroud the elastc roof wth the cosderato of couplg effect. It ca be see that, because the shape of the elastc roof chages wth wd acto, whch drectly chage the boudary of the flud feld, so the characterstcs of flow aroud a elastc roof s much dfferet from those of rgd roof. For the elastc roof, the separato pot of arflow appears at the back of the frot of the roof, ad the effects of vortex droppg weake sgfcatly. The whole average wg pressure o the elastc roof s close to that of rgd roof, but the pulse wd pressure decrease sgfcatly, whch llustrates that whe vortex dowstream alog the roof, couplg effect duced eergy dsspato lead to mor pulse pressure. Fg. 5 Computatoal doma for flow aroud a oe-way type roof It worth to be explaed that the above result was gotte from the method ref. [6], here we call t as drect umercal method, whch ca be see as a accurate method. It ca be see that by the drect umercal method, we ca get the etre formato of the couplg process. But from the vewpot of egeerg, we usually oly cocer about those statstc formato, such as the mea ad peak value, t meas that we sped a large amout of tme to get those useless formato. Next, the combed procedure proposed ths paper wll be adopted to calculate that statstc formato. The result s show fgure 8. It ca be see that the result of combed approach seems very close to that of drect umercal method, but qute dfferet to the result of radom vbrato aalyss. It shows that by usg the combed approach we ca also get farly accurate result, ad the tme cosumg by ths method s qute small compare to the drect umercal method. 40

8 Fg. 6 Streamle aroud the fxed roof Fg. 7 Streamle aroud the elastc roof We also calculate the oe-way type roof wth 1/10 sag (as show fg. 9) ad wth 1/10 rse (as show fg. 10). It ca be see that for these two dfferet shape roofs, the combed procedure ca get very close results to that of accurate method. For the arch-shaped roof, the effect of flud-structure teracto seams very small, t ca be explaed that the roof shape plays a mportat role to the couplg effect. The couplg effect wll chage the structural shape from bluff body to streamled body, f the structural shape close to streamle body, the the couplg effect wll be small. Dsplacemet (m) Drect Numercal Smulato(cosderg FSI) Radom Smulato tme doma(wthout cosderg FSI) Combed Numercal Approach(cosderg FSI) x/ Dsplacemet (m) Drect Numercal Smulato(cosderg FSI) Radom Smulato tme doma(wthout cosderg FSI) Combed Numercal Approach(cosderg FSI) x/ Dsplacemet (m) Drect Numercal Smulato(cosderg FSI) Radom Smulato tme doma(wthout cosderg FSI) Combed Numercal Approach(cosderg FSI) x/ Fg. 8 Maxmum respose of flat roof Fg. 9 Maxmum respose of suspeso roof Fg. 10 Maxmum respose of arch roof 4. Couplg Effects of Shaddle-Shape Membrae Structures The roof spa s 8m, the rato of sag to spa (f/) s 1/16, the mass per area s 1.5kg/m, the teso force s.5kn/m. The frst ad secod frequecy of structure s.6z ad 3.03z, respectvely. The calculate model s show fgure 10. The other calculate parameters are same as the two-way type roof. Fg. 10 The calculate model Fgure 11 shows the maxmum dsplacemet of membrae structure calculated by these three methods. It ca be see that the couplg effect of 3-D structures seems more complcate tha - D structures, but f we compare the maxmum dsplacemet pot betwee the results of these three methods, t s also show that the result from combed procedure seems farly close to the drect umercal method, but larger tha the result of radom vbrato aalyss. 41

9 The Seveth Iteratoal Colloquum o Bluff Body Aerodyamcs ad Applcatos (BBAA7) Shagha, Cha; September -6, 01 a) Combed Approach b) Drect Numercal Method c) Radom vbrato aalyss Fg. 11 Maxmum dsplacemet o roof by dfferet methods 5 CONCUSION I ths paper, a combed umercal approach for solvg the flud-structure teracto for teso structures was proposed. Wth the comparso to the drect umercal method ad radom vbrato method, t ca be see that the combed approach seems more accurate tha the radom vbrato method ad more effcet tha the drect umercal method. Accordg to the calculate result of two-way type, t ca be coclude that the couplg effect tred to chage the structural shape from bluff body to streamled body, so f the structural shape close to streamle body, the the couplg effect wll be small. ACKNOWEDGEMENTS The vestgato s supported by the Natoal Scece Fud Coucl of People s Republc of Cha uder Cotract No ad No REFERENCE 1 S.Z. She ad Q.S. Yag (1999), Wd-duced Respose Aalyss ad Wd-resstat Desg of yperbolc Parabolod Cable Net Structures, It. J. Space Structures, 14(1), T. Matsumoto (1990), Self-excted Oscllato of a Pretesoed Cable Roof wth Sgle Curvature Smooth Flow, J. Wd Eg. Id. Aerody., 34 (3), P. A.. Irw ad R.. Wardlaw (1981), A Wd Tuel Ivestgato of a Retractable Fabrc Roof for the Motreal Olympc Stadum, Proc. 5th It. Cof. o Wd Eg., Pergamo, A. arse (1998), Computer Smulato of Wd-Structure Iteracto Brdge Aerodyamcs, J. Struct. Egrg. IABSE, 8(), M. Glück, M. Breuer, F. Durst, A. alfma, E. Rak (001), Computato of Flud- Structure Iteracto o ghtweght Structures, J. Wd Eg. Id. Aerody, 89(14-15): Y. Wu ad S. Z. She (005), Computato of Wd-Structure Iteracto o Teso Structures, Proc. 6th Asa-Pacfc Coferece o Wd Egeerg. Seoul, Korea, Y. Wu ad S. Z. She (006). Numercal studes o the behavors of wd-structure teracto for oe-way type roofs. Proc. 4th It. Cof. o Computatoal Wd 4

10 Egeerg. Yokohama, Japa, A. G. Daveport (1967), Gust oadg Factor, J. Struct. Dv. ASCE., 93(ST3), Wu, Y., Yag, Q. S. et al, Studes o Wd-Structure Iteracto by Wd Tuel Tests, Proceedgs of the 11th Natoal Coferece o Wd Egeerg, Saya, Cha, 003. ( Chese) 43