Geometric calibration experiences of ultrasonic flowmeters installed in hydropower stations in China

Transcription

1 IGHEM2016, Lnz, Austr Geometrc clbrton experences of ultrsonc flowmeters nstlled n hydropower sttons n Chn Hemng Hu 1, Ch Wng 1, Hyng L 2, Feng Go 1 1. Ntonl Insttute of Metrology, P. R. Chn 2. Shngh Insttute of Mesurement nd Testng Technology, P. R. Chn E-ml: huhm@nm.c.cn Abstrct: Mult-pth ultrsonc flowmeter hs become one of the best choces of flow mesurement for hydropower effcency estmton wth dvntges of no pressure loss nd hgh ccurcy. More nd more ultrsonc flowmeters re nstlled n hydropower sttons n Chn. Geometrc prmeters re very mportnt nd mnufcturers usully mesure them usng theodolte nd steel tpe fter nstllton. We hve developed geometrc clbrton system bsed on totl stton s one prt of holstc pproch of onste flowmeter ccurcy estmton, nd hve hd more thn 10 geometrc clbrton experences. Our system cn drectly scn the condut ponts, mesure the sensor ponts nd utomtclly clculte geometrc prmeters ncludng pth heghts wth hgh effcency nd good ccurcy. We estmte the uncertnty due to cylnder fttng usng Monte-Crlo smulton, nd nlyze the effect of dfferences between nstllton vlues nd desgn vlues of pth heghts bsed on mesured flow profles. Influences of the wter temperture nd pressure on dmeter of steel penstock nd other prmeters hve lso been estmted. Clbrton dt nd relted uncertnty re descrbed to show the current sttus of mnufcturer nstllton. We suggest pyng more ttenton to flowmeter nstllton nd ntroducng more promsng methods for ts nstllton nd clbrton n future. Key words: ultrsonc flowmeter, geometrc prmeter, totl stton, Fro rm, cylnder fttng, uncertnty, weght coeffcent 1 Introducton Wth dvntges of no pressure loss, hgh ccurcy nd the possblty to be nstlled on exstng conduts, mult-pth ultrsonc flowmeter hs become one of the best choces for lrge dmeter wter flow mesurement. Geometrc prmeters re very mportnt for the ultrsonc flowmeter whch clculte the flow velocty nd the flow rte bsed on tme mesurement nd length mesurement. Accordng to the bsc prncple of mult-pth ultrsonc flowmeter, the flow rte s drectly relted to the geometrc prmeters of flowmeter s follows, L q R W h f t t N 2 v d u 1 cos, (1)

2 where R s the rdus of the condut; coeffcent relted to h ; L s coustc pth length; h s the reltve heght of coustc pth; s coustc pth ngle;, IGHEM2016, Lnz, Austr d W s the weght f t t s functon relted to the ultrsonc propgton tmes. The Subscrpts denotes the dfferent coustc pths. There s strct nstllton requrement of the mult-pth ultrsonc flowmeter. The trnsducers must be nstlled crefully on the desgn postons of the condut to gurntee the ccurcy of flow rte mesurement, nd the geometrc prmeters should be mesured ccurtely nd then be nput nto the flowmeter console. For the lrge dmeter flowmeter, theodolte s usully used to locte the trnsducers, then steel tpe s used to mesure the geometrc prmeters. The coustc pth lengths nd condut dmeter re mesured by steel tpe, nd the coustc pth ngles re mesured by theodolte. The nccurte mesurement of geometrc prmeters wll ffect the flowmeter ccurcy. Currently, some mnufcturers declre tht the ccurcy of ther lrge flowmeters cn rech up to 0.5%, nd ths wll only be possble f the ccurte mesurement of geometrc prmeters s done wth scentfc method nd sophstcted nstruments. 2 Mesurement System nd Method 2.1 Mn nstrument nd method The typcl lyout of coustc pths of the flowmeter s shown s Fg.1. It s flowmeter wth confgurton of two plnes wth nne pths ech. The geometrc prmeters to be mesured nclude rdus of condut secton R, length of coustc pth of coustc pth coustc pth three prmeters of R, L whch s the dstnce between pr of trnsducers, ngle whch s the cute ngle between coustc pth nd flow drecton, nd heght of h whch s the sptl dstnce between coustc pth nd condut xs. At present, the frst L nd re generlly mesured, nd the pth heght u h s usully regrds s ts predetermned vlue fter the completon of nstllton becuse of the mesurement dffcultes. Fg.1 Schemtc Drwng of Acoustc Pth Lyout Totl stton s new generton nstrument whch could drectly obtn the 3-D coordntes of the trget ponts. Lec TCRM1201+R400 totl stton hs been dopted by our mesurng system. It cn operte n rngng mode wthout prsm wth ccurcy of 2mm+2ppm, nd ts ngle mesurement ccurcy s 1". Frst, the totl stton s used to collect the coordntes of wll ponts of flowmeter condut, nd cylnder fttng s conducted to obtn the condut rdus nd condut xs. Next, centrl-pont coordntes of the trnsducers

3 IGHEM2016, Lnz, Austr end fces re mesured one by one. The lengths of coustc pths re clculted drectly nd the ngles nd heghts of coustc pths re clculted bsed on the condut xs nd trnsducer ponts. Trdtonl theodolte method needs reference xs determned by two trget guge ponts. The process of rrngng ths xs s qute complcted nd the ccurcy s dffcult to control. However, the totl stton method could tke dvntge of enough condut wll ponts to ft the cylndrcl surfce. It promotes the mesurement ccurcy of rdus of condut secton nd ngles of coustc pths. The softwre set up n the totl stton tself s very powerful, but ts most functons would not be used n our pplcton. The mesurement my be low-effcent nd the erroneous mesurement dt could not be dentfed tmely. Amng t the pplcton n geometrc prmeter mesurement of ultrsonc flowmeter, we hve developed dedcted softwre for the totl stton. 2.2 Softwre nd procedure Dedcted softwre hs been developed for utomtc scnnng of the condut ponts wth totl stton nd utomtc clculton of ll the geometrc prmeters. The softwre runs on portble notebook, whch cn control the totl stton to scn the condut wll ponts nd receve dt from t. It s esy to perform the cylnder fttng nd geometrc prmeters clculton ccurtely, nd t s not only comptble wth the totl stton, but lso possble to mport the dt from other 3-D coordnte mesurement nstruments for only prmeter clculton. The mn nterfce s shown n Fg.2 s follows. Cylnder fttng s performed bsed on these condut wll ponts, s shown n Fg.3(). The fttng lgorthm s used for the clculton bsed on the 3 ponts on the cross secton. The fttng result s obtned drectly. The dstnce between the mesured wll ponts nd the ftted wll could be mrked n dfferent colors, nd the outlers by n tmes of stndrd devton cn be removed utomtclly. There s specl desgn for the mesurement of the centrl pont of the trnsducer, s shown n Fg.3(b). Those ponts could not be scnned utomtclly, nd could only be mesured by mng the telescope t the center of the trnsducer. Accordng to the lyout nformton of coustc pths of the flowmeter, the plnr postons nd serl numbers of the trnsducer ponts could be generted utomtclly. The mesurement strts fter mng t the correspondng poston nd clckng the serl number. In ths wy, the confuson cused by mnul numberng cn be voded, nd the effcency of the mesurement s mproved. 2.3 Algorthm of cylnder fttng Cylnder fttng s the core lgorthm of ths mesurement system. It s the problem of how to cheve the mnmum of the squre sum of dstnces between ll smplng ponts nd the cylndrcl surfce. Snce the cylndrcl surfce equton s nonlner qudrtc equton, solvng the lest squre through qudrtc equton my not result n convergence correctly. So t s crucl to prmeterze the cylndrcl surfce resonbly.

4 IGHEM2016, Lnz, Austr Fg.2 Mn Interfce of the Mesurement Softwre () Fttng Process of Cylndrcl Surfce (b) Collecton of Trnsducer Ponts Fg.3 Mn Functonl Interfce of the Mesurement Softwre As shown n Fg.4, the coordnte orgn s pont O 0 nd the drecton vector of cylndrcl surfce xs CC 1 2 s. The foot of perpendculr of orgn O 0 on xs.. s O ', nd drecton vector of.. s n. Obvously, n s the norml vector of cylndrcl surfce, n 0. n s the nerest pont on the cylndrcl surfce from orgn O 0. s the lrgest curvture vlue t pont n, nd 1/ denotes the rdus of cylndrcl surfce. nd n re two mutully perpendculr unt vectors, whch possess 3 degrees of freedom, nd could be represented by three ngles s follows, n cos sn, sn sn, cos (2) cos cos, sn cos, sn cos sn, cos, 0 sn (3)

5 IGHEM2016, Lnz, Austr where.. s the ngle between n nd z-xs; s the ngle between the projecton of n on surfce z=0 nd x-xs; s the ngle between nd vector surfce s prmeterzed nto S (,,,, ) wth 5 degrees of freedom. cos cos, sncos, sn. In ths wy, cylndrcl C 1 O' 1 C 2 n O 0 Fg.4 Prmeterzton of Cylndrcl Surfce Levenberg-Mrqurdt lgorthm s dopted n the mnmzng process. The lgorthm converges rpdly, but t s very senstve to the ntl vlues of the prmeter especlly the three ngles relted to xs. If the ntl vlues re chosen npproprtely, t s dffcult to converge, nd even go to the ncorrect locl mnmum soluton. For the geometrc prmeter mesurement of flowmeter, t s more effcent to clculte the ntl vlues by usng group of mesurement ponts. Ths group of ponts should be locted on certn vertcl cross-secton of cylndrcl surfce. There re three ponts t lest, nd the norml vector of the plne where the ponts re locted s the xs of condut gven by lner lest squre method, nd the ntl vlues of other prmeters could be obtned further. 2.4 Determnton of the wll pont number Obvously, the more the mesured ponts on the wll, the better the fttng would be. A pproprte pont number should be decded to ensure the fttng ccurcy. Monte-Crlo smulton s employed to nlyze the relton between the number of mesured ponts nd the fttng effect. For ny gven prmeter of the cylndrcl surfce S, the xs length s set s wll ponts x, y, z L. A group of n precse would be generted by rottng the mtrx bout n xs. The ccurcy of coordnte mesurng nstrument could be converted nto the stndrd uncertnty of the coordntes, whch s. The mesurement error s ssumed to obey norml dstrbuton. A group of n rndom numbers z tht obey the norml dstrbuton nd hve the stndrd devton coordnte x x, y y, z z could be conducted to obtn rdus R nd xs mke the xs result more ntutve, Smulton dt prove tht the vlues of,.. nd could be generted. Thus, s group of possble mesured dt. Cylndrcl surfce smulton x, y, z hs been converted to ngle vlue R nd re relted wth shown n Tble 1. It could be derved tht the uncertnty of rdus s smller thn the uncertnty of the coordnte tself. Both by usng ths group of dt. In order to R R. nd n. The vlues of n re cused by coordnte mesurng nd ncrese wth nd decrese wth the ncresng of n. There s n pprox mte lner relton between R,,

6 nd. It should be noted tht IGHEM2016, Lnz, Austr s relted to the length of the mesured ponts on wll surfce projected n the xl drecton, whch s R nd L hve no ssocton. L, showng n pproxmtely nverse proporton. However Tble 1 Uncertnty of Rdus nd Axs Drecton ( L 2m ) Pont number n 1mm 2mm 5mm R /mm / o R /mm / o R /mm / o The fttng s performed bsed on the smulton dt, R 4.15 n 0.06 (4) o L 4.15 n (5) The equton could be utlzed for gudng the selecton of the number of mesured ponts on the wll. Generlly, bout 50 mesured ponts re enough. 3 Anlyss of Three Gorges Flowmeter 3.1 Mesurement detl The mesurement system s exploted to clbrte the three flowmeters of the Three Gorges Hydropower Plnt. All of them re wth dmeter of bout 12.4m. Fg.5() s pcture of trnsducers nstllton wth scffoldng usng theodolte. Fg.5(b) s pcture of conductng the clbrton of flowmeter geometrc prmeters wth totl stton. When mesurng the trnsducer pont, brght flshlght s used to lght up the trnsducer re. An ccurte lgnment of the center poston of the trnsducers s performed wth the theodolte telescope. The telescope s not vlble for lgnment when mesurng the re ner the zenth. Therefore, dgonl eyepece s used to solve the mng problem of the blnd re. There re weldng sems on the condut of the Three Gorges flowmeter, whch re tken s the reference objects. The precson of the cylnder fttng would be mproved by scnnng the ponts on ech rng. In the scnnng process of condut wll ponts nd the mesurement of trnducer ponts, fxed dtum pont hs been kept wtch on repetedly for severl tmes. The vrton of the coordntes of ths pont should not exceed 2mm, or t would men tht the totl stton mght hve been moved or some other problems hve occurred.

7 IGHEM2016, Lnz, Austr () Trnsducer Instllton wth Theodolte (b) Geometrc Mesurement wth Totl Stton Fg. 5 Mult-pth Flowmeter of Three Gorges Power Stton 3.2 Anlyss of result nd ts uncertnty As the geometrc prmeters of flowmeters used for the Three Gorges re the dt mesured by the mnufcturer, the flow rte mesurement errors brought by the dfference between mnufcturer dt nd clbrton dt re nlyzed. The flow error due to rdus mesurement s two tmes of tht of rdus error, nd the errors of pth length nd pth ngle re relted to the flow rte dstrbuton nd weght coeffcents correspondng to the coustc pths. Accordng to u 1 r 1/9 m, the formul of flow rte dstrbuton of fully-developed turbulent flow n the crculr ppe, together wth the weght coeffcents of dfferent pths of the correspondng flowmeters, the flow mesurement errors cused by fctory defults of geometrc prmeters of the three flowmeters re respectvely clculted, s shown n Tble 3. From the dt we cn see rdus error s most possbly the mn error of the geometrc prmeters. The pth ngle errors re not so lrge becuse of compenston effect of the two-plne pth confgurton. Tble 2 Flow Errors due to Geometrc Prmeter Mesurements Flowmeter Rdus Pth length Pth ngle Totl error A 0.12% 0.03% 0.01% 0.16% B 0.13% 0.01% 0.00% 0.14% C 0.03% 0.01% 0.03% 0.07% As ll of the geometrc prmeters re mesured by the sme nstrument, the pth lengths re strongly correlted nd the pth ngles re lso strongly correlted. Moreover, the tme-relted terms cn be expressed s the relton between pth velocty um nd length of coustc pths, f t 1 1 c u cos c u cos 2u cos (6) t t L L L m m m d, tu d u Therefore, the compostng formul of the uncertnty relted to the geometrc quntty s smplfed nto N N N 2 Wu m Wu m tnu Wu m (7) uc qv u R u L qv R 1 L 1 1 Bsed on formul (7), uncertnty contrbuton of geometrc prmeter to flow rte mesurement s clculted. The stndrd uncertnty s bout 0.10%, nd the contrbuton mgntudes of ech source re n tble 3 s below. In the short-dstnce pplcton of totl stton, ngle mesurement error hs smll contrbuton to mesurement uncertnty, nd there s only the dstnce mesurement error wth 2mm+2ppm.

8 IGHEM2016, Lnz, Austr When the trnsducer centrl ponts re mesured, telescope s requred to m t the mesured pont, nd n ddtonl mng error wll be ncluded. Condut rdus Pth length Pth ngle Tble 3 Flow Uncertnty Introduced by Geometrc Prmeters Flowmeter Uncertnty components A B C Repetblty 0.01% 0.01% 0.02% Totl stton 0.07% 0.07% 0.07% Cylnder fttng 0.01% 0.01% 0.03% Repetblty 0.01% 0.00% 0.01% Totl stton 0.03% 0.03% 0.03% Repetblty 0.01% 0.00% 0.04% Totl stton 0.03% 0.03% 0.03% Telescope mng 0.04% 0.04% 0.04% Combned uncertnty 0.09% 0.09% 0.10% 3.3 Confrmton of uncertnty of totl stton Our length mesurement deprtment only provdes certfcton of ngle mesurement nd prsm rngng for totl sttons, whch cnnot reflect the ccurcy of rngng wthout prsm. Therefore, set of evluton system for comprson s desgned. The centers of end fces of two smll cylnders re dopted to determne stndrd dstnce. FroArm pltnum s used to mesure the stndrd dstnce, wth ccurcy of 0.035mm. The stndrd dstnce s compred to the mesured vlue by totl stton n non-prsm mode to nlyze the rngng error s n fg.6(). n 1 () Test for Non-prsm Mode (b) Locton of Totl Stton n Condut Fg.6 Schemtc Dgrm of Rngng n Non-prsm Mode Fg.7 shows the rngng error of the totl stton under dfferent ncdent dstnces nd ngles, ncludng the mesured dt over long perod. It cn be found tht the ncdent ngle hrdly ffects the rngng error when the ncdent dstnce s lrger. But when the ncdent dstnce s smller, the rngng ccurcy tends to be worse wth smll ncdent ngle. Ths s lucky tht only the lrge ncdent dstnces nd smll ncdent ngles cn meet together s shown n fg.6(b). On the whole, the resonble use of the totl stton should ensure 2mm rngng ccurcy n non-prsm mode.

9 IGHEM2016, Lnz, Austr Fg.7 Dstnce Mesurement Error of Totl Stton 3.4 Errors cused by vcnt condut mesurement It s worth notng tht conduts of the flowmeters re vcnt when mesurng geometrc prmeters, but re full wth pressure n the opertng condton. The chnges of upstrem wter hed wll led to moderte deformton of the conduts. The prts outsde steel penstocks where the flowmeters re locted re concrete nd there re cushons mde of other mterls n locl re. The complex structure wll led to rregulr deformton. Here prelmnry estmton of the nfluence of wter pressure on the rdus chnge s gven s follows, 2 2 PR (0.8 ~ 1.18)MP (6.2m) R (3 0.6)mm Et 210GP 60mm S where P s the nternl pressure of the condut; Es s the elstc modulus of the mterl; t s the condut thckness. Due to lrge dfference n nternl pressure, the expnson of the rdus s bout 3mm, wth reltve vlue of 0.048%, nd the rdus vlue needs to be corrected bsed on the ctully mesured vlue. The expnson of conduts lso mpcts on the lengths nd ngles of coustc pths. Under hydrulc expnson, only rdl expnson s consdered but not xl expnson, nd the reltve ncrement of length of coustc pth s 0.039%. The ngle of coustc pth wll lso ncrese by o, nd the correspondng flow rte ncrement s tn 0.039%. Therefore, the rdus s ncresed by 3mm due to nternl pressure, whch further ncreses the ctul flow rte by 0.18% s shown n tble 4. Due to the possble chnge of the nternl pressure nd temperture, the uncertnty of the flow rte mesurement should dd term of 0.04%. Reltve stndrd uncertnty Tble 4 Influence of the Chnge of Pressure nd Temperture Fctor of nfluence rdus Pth length Pth ngle Totl Flow rte error % % % % Pressure 0.023% 0.009% 0.009% 0.026% Temperture 0.026% 0.013% / 0.029% Totl 0.034% 0.016% 0.009% 0.039% (8)

10 4 Anlyss of Pth Heght error nd Weght Coeffcent Correcton 4.1 Assessment of nstllton error of pth heght IGHEM2016, Lnz, Austr The mesured coustc pth heghts cn be used to ssess the flow rte mesurement error cused by the dfference between the mesured coustc pth heght nd the desgn vlue bsed on the possble velocty dstrbuton n the condut of flowmeter. The nfluence of heght devton s not only relevnt to weght coeffcents, but lso to the grdent of velocty dstrbuton curve of coustc pths t the heghts. Although the weght coeffcent of coustc pth ner the edge s smll, ts velocty grdent s usully lrger, nd the nfluence of nstllton errors of coustc pth heght t ths pont s lso greter. Bsed on the bove formul for fully-developed turbulent flow, the nfluence cused by the heght devton s prelmnrly ssessed s shown n tble 5. It s found tht the bsolute vlues of coustc pth heght of flowmeter A nd B re lrger or smller thn the desgn vlue, nd the resultng flow rte mesurement errors re smll. However, ll the pth heght of flowmeter C re smller thn the desgned vlues, whch leds to nelgble postve error of flow rte mesurement. 4.2 Correcton of weght coeffcents Tble 5 Assessment of Instllton Errors of Acoustc Pth Heght Flowmeter Instllton error Stndrd devton A -0.01% 0.03% B -0.01% 0.01% C 0.05% 0.01% In ddton to the overll correcton of the mesured flow rte, the nstllton errors of coustc pth heght cn be reduced by usng the new weght coeffcents of coustc pths. In the Guss ntegrl, the weght coeffcent where W cn be clculted through the followng ntegrl expresson: 1 N h hk W h dh 1 h h k0, k k h s the weght functon. Snce the ntegrl expresson of the formul s complex to use, the explct expresson of the weght coeffcents s deduced s below: W N 1 2 j1 1,, nd g f h j j k N k N h h hj j1, j where for Guss-Jccob method, 0.5, but for OWICS method, 0.6. N+1-2j th power fter the expnson of the polynoml h h N 1 m1 m f j, nd cn be expressed s h k (9) (10) s the term wth the f h sum prod nchoosek h,j,2 (11) j k k 2 2 j1 n mtlb. In ddton, j 1 g 1 x x d x, nd the dt n tble 6 cn be used drectly. 1

11 Tble 6 The Coeffcent g j n Formul (10) j = 1 j = 2 j = 3 j = 4 j = IGHEM2016, Lnz, Austr Although formul (10) s stll complex n form, t could be red by the softwre progrm. For the flowmeters wth 3 coustc pths, the formul of weght coeffcent cn be expnded nto g g h h h hk k 1, k 3 k k 1, k 1,2,3 For the flowmeters wth 4 coustc pths, the formul of weght coeffcent cn be expnded nto (12) 4 g h g h 2 k 1 k k 1, k k 1, k h h hk k 1, k 4 1,,4 (13) nd so on. For the flowmeter C, the weght coeffcents cn be corrected by the bove lgorthm, nd the flow rte mesurement error fter correcton cn reduce from 0.05% to below 0.01%. 5 Concluson The nstllton nd geometrc prmeter mesurement of trnsducers of ultrsonc flowmeters re very mportnt. The nstllton personnel should tke serous tttude nd strctly follow the procedures, otherwse nccurte mesurement of geometrc prmeters wll ffect the ccurcy of flowmeters. A set of utomted mesurement system of geometrc prmeters for lrge ultrsonc flowmeters s bult bsed on Lec totl stton. It cn scn condut wll surfce nd trnsducer locton, yeldng n ntegrted descrpton of geometrc morphology of flowmeters. The condut rdus, s well s ngles nd lengths of coustc pths re clculted, nd the ccurcy nd effcency of geometrc prmeter mesurement re mproved. Especlly, the weght coeffcents could be corrected n lne wth the ctully mesured heght of coustc pth. At present, ths system cn only be ppled to geometrc prmeter mesurement of flowmeters n crculr condut. It wll be ppled to the locton nd nstllton of trnsducers fter slght modfcton, nd the lgorthm wll be extended to flowmeters n squre condut nd open chnnel. References [1] BROQUET P, CONTI L, VATERLAUS H P. Use of totl Stton Theodolte for the Instllton of Ultrsonc Flow- Meters n lrge Dmeter Penstocks. Proc. IGHEM2000. [2] VOSER A. Anlyse und Fehleroptmerung der mehrpfdgen kustschen Durchflussmesung n Wsserkrftnlgen. Dss. ETH Nr.13102, [3] ISO Clbrton of vertcl cylndrcl tnks, nternl electro-optcl dstnce-rngng method. [4] LUKÁCS G, MARTIN R R, MARSHALL D. Fthful lest-squres fttng of spheres, cylnders, cones, nd tor for

12 IGHEM2016, Lnz, Austr relble segmentton. Proc. 15th Europen Conf. Computer Vson, 1998, [5] STEFAN B. Dscusson of Instllton Methods nd Errors of Multpth Acoustc Dschrge Mesurements n Closed Conduts. Proc. IGHEM2004. [6] TRESCH T, GRUBER P, STAUBLI T. Comprson of ntegrton methods for multpth coustc dschrge mesurements. Proc. IGHEM2006. [7] Tresch T, et l. Presentton of optmzed ntegrton methods nd weghtng correctons for the coustc dschrge mesurement. Proc. IGHEM 2008.