THE INFLUENCE OF SURFACE INCLINATION ON THE CALIBRATION OF SURFACE TEMPERATURE SENSORS

Transcription

1 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia XVII IMEKO Wrld Cngre Metrlgy in the 3 rd Millennium June 22 27, 2003, Dubrvnik, Cratia THE INFLUENCE OF SUFACE INCLINATION ON THE CALIBATION OF SUFACE TEMPEATUE SENSOS Emee Andrá Natinal Office f Meaure (OMH), Budapet, Hungary Abtract - The OMH ha develped a reference urface temperature apparatu fr the calibratin f cntact urface temperature enr under a variety f cnditin. Thi article decribe the dependence f temperature errr n the inclinatin f a heated urface and tudie the urce f thee deviatin fr variu urface temperature and enr type. The effect f urface inclinatin ha nt been invetigated befre but ha been fund ignificant, particularly becaue f it indutrial relevance. Keywrd: temperature urface heat-tranmiin 1. INTODUCTION Our labratry wa amng the firt ne having develped a reference urface temperature apparatu uing electrical heating. It temperature range i preently the larget in the wrld: frm ambient temperature t 600 C. The reference wall are exchangeae: they can be metal r inulating material embracing a large range f thermal cnductivity value. The principle f urface enr calibratin i t cmpare the tandard urface temperature with that determined by a urface enr directly applied t ne f the reference urface. The calibratin prcedure ued invlve the determinatin f the urface temperature by extraplatin befre applying the enr [1]. There are variu urce f errr and uncertaintie aciated with the calibratin f urface enr. Bilateral cmparin carried ut in thi field between PTB and OMH and between BNM-LNE and OMH hwed a gd general cnitency f the reult and have met indutrial need in reducing uncertainty [1]. At mment OMH i c-rdinating the Eurmet Prject 635, which i a cmparin f the reference urface temperature apparatu at eleven NMI by cmparin f tranfer urface temperature tandard. The technical cperatin activitie cnit f the exchange f experience and cmparin cncerning the develpment f the baic apparatu, requirement and prcedure fr traceability, influence f the thermphyical prpertie f urface, etc. In cae f temperature meaurement made n the urface f lid bdie, the heat flux depend, n the ne hand, n the temperature difference between the lid bdy and the ambient, n the ther hand, n the heat tranmiin cefficient (which expree the effect f cnductin, cnvectin and radiatin). In rder t determine the temperature f a given urface with higher preciin, the value indicated by a urface temperature enr mut be crrected. Thi crrectin depend mainly f three factr: Prpertie f the heated wall: the gemetrical and thermphyical characteritic f the material, the temperature f the wall, the quality f the urface (rughne, xidatin); Influence f the urface enr: type, gemetrical and thermphyical characteritic f the enr [2]; Heat tranfer effect: he quality f the heat tranfer at the interface urface-enr and ambient-thermmeter influence the difference between the temperature f the urface f the heated lid bdy and that f the cntact urface f the enr. Thi crrectin i the ubject f thi paper. Fig. 1. Extreme pitin f the urface The main prtin f the reitance t heat tranfer i uually cncentrated in a thin layer immediately adjacent t the wall urface (thermal bundary layer). Heat tranfer i eentially an interplay f heat cnductin frm the lid urface and energy tranprt by the mving fluid within thi layer. Hence, the heat tranfer depend eentially n the thickne and the characteritic f thi bundary-layer (Fig. 1.).

2 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia The greyed element in Fig. 1 repreent the thermal bundary-layer, whe temperature i much higher than the ambient temperature. It can be een that the tructure f the bundary-layer depend trngly n the urface inclinatin and thi i the mtivatin fr thi paper. In cae f calibratin fr a hrizntal urface (α=0 ) (Figure 1a) a free flw i frmed alng the enr and the temperature in the bundary-layer i higher than the ambient temperature (ta). In cae f calibratin fr a vertical urface (α=90 ) (Figure 1b), vertical free flw i frmed arund the enr. The temperature change little except in the vicinity f the urface, in the bundary-layer. A prtin f the enr i lcated in thi warm bundarylayer. In cae f calibratin fr a hrizntal urface (α=180 ) (Figure 1c) a free flw i frmed alng the enr and it temperature i the ame a the ambient temperature. Thi paper trie t preent and interpret meaurement reult, prvide a phyical explanatin and quantify the abve-mentined effect. 2. CALIBATION METHOD FO DIFFEENT SUFACE INCLINATIONS - enr 2, type Omega 88010K, with prung thermcuple trip - enr 3, type Tet , with a mall, nn-prung meauring head The ambient temperature wa 23 C. The flat heated wall wa made f aluminium with a thermal cnductivity cefficient λ=230w/m K. The heated plane wall had a diameter f 100 mm and a thickne f 20 mm. The calibratin prcedure tart with the determinatin f the urface temperature by extraplatin befre applying the enr [1]. The urface enr i applied manually n the aluminium plate. 3. MEASUEMENT ESULTS Surface temperature were meaured with three type f urface enr, fr three different temperature between 100 C and 400 C and fr even different angle f the heated reference wall between 0 and 180. The reference urface temperature apparatu ued fr thee calibratin i preented in Fig. 2. Fig. 2. eference urface temperature apparatu at OMH Fig. 4. Calibratin curve f enr 1 Thee urface temperature meaurement were effectuated in the temperature range between 100 C and 400 C, uing a Tet temperature indicatr Type 945 with three different enr (Fig 3): Fig. 3. Different urface enr - enr 1, type Tet , with prung cr thermcuple trip Fig. 5. Calibratin curve f enr 2

3 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Fig. 6. Calibratin curve f enr 3 The achieved reult hw a ignificant difference f the meaurement errr due t the variatin f the reference urface inclinatin (Fig. 4, 5, 6.). The pint preented in each diagram are mean value f twenty meaurement, fr a given temperature and angle. The cntinuu curve are trend-line f frth-degree functin. Interrupted line embed each f the uncertaintyband. Can be een that each curve ha the ame character, independently f the urface temperature and f the enrcntructin. 4. ANALYSIS OF THE MEASUEMENT ESULTS 4.1. Theretical mdel f the urface enr The urface enr i cnidered a a heated hllw bar with finite length, having cntant temperature t w at ne end and which heat i flwing t an infinite field with cntant temperature t a. Thi heat tranfer i effectuated by cnductin, cnvectin and radiatin. Cnidering the urface enr a a hllw bar with diameter d, thickne f it wall, length h, can be determined the fllwing exprein: the area A = π d f heat-cnductin and the perimeter K = π d. Intrducing the relatin: a = α K λ A, where α i the heat tranmiin cefficient frm bar t ambient and λ i the cefficient f thermal cnductivity f the bar. The utlet heat flw by cnvectin frm the bar can be calculated with the aid f the fllwing frmula [3], [4]: a h e e Qk = λ A a ( tw ta ) (2) a h a h e + e α i btained frm the Nuelt number: a h (1) α X Nu = λ, where X i a typical gemetrical dimenin and λ a i the thermal cnductivity cefficient f the fluid. Mrever, the Nuelt number can be written [5]: n Nu = c ( Gr Pr) K (4), where c, n and K are factr depending n the gemetry f the urface and it inclinatin relative t the gravitatinal field, Gr i the Grahf number and Pr i the Prandtl number. Taking int cnideratin the relatin (3) and (4), the heat tranmiin cefficient can be calculated with the fllwing equatin: λ a n α = c Gr Pr K X ( ) (5) Practically, the factr c, n, K and X are given in [3]in tw extreme ituatin. In cae f a vertical bar Pr X = h, c = 0, 686, n = 0, 25 and K = 1+ 1, 05 Pr a 0, 25 a hrizntal bar X = d, c = 0, 47, n = 0, 25 and K = 1. (3). Fr The utlet heat flw frm the bar by radiatin can be expreed [3], [4]: 4 4 Q = σ A A ε ( T T ) (6), where σ i the Bltzmann cntant, A i the area f the radiating urface, ε i the emiivity cefficient, T m i the mean aute temperature f the urface and T a i the aute temperature f the ambient. The ttal utlet heat flw i: Q = Q + Q (7) t k The calculatin carried ut fr the enr 1, uing the fllwing parameter: d = 4mm, = 0,5mm, h = 150mm, λ = 30W / m K and ε = 0, 25 and = 23 C. t a The calculatin reult are preented in Tae I., where the index v i ued fr the vertically pitined enr and index h fr the hrizntal ne. t [ C] Q kv Q kh m TABLE I. Q a Q tv Q th 100 0,306 0,448 0,130 0,436 0, ,758 1,110 0,379 1,137 1, ,231 1,802 0,746 1,977 2, ,714 2,510 1,265 2,980 3,775

4 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia 4.2. Cmparin f the theretical and the meaured deviatin Fig. 7. Mdel f urface meaurement The meaurement errr i related t the temperature f the heated wall t w and t the inclinatin angle ϕ (Fig. 7.) and defined a: dtm = t tw (8), where t i the temperature indicated by the thermmeter. The meaured temperature errr dt m a a functin f the angle ϕ and fr a given t w i hwn in Fig. 8. In the vertical pitin (v) f the enr, the heat flw Q tv can be written: Q tv dt th ( 180 ) = f (10) The factr f can be determined: Qtv f = (11) dt 180 m ( ) Mrever, the theretical errr can be written uing the ttal heat flw Q th related t t w (Fig. 8.): Qth dtth ( 90 ) = (12) Thi i a ymmetrical curve with repect t the vertical = 90 dt = dt 180 ). ϕ ( ( ) ( ) th 0 th Mathematical frmulae can be fund in the pecialied literature nly fr extreme angle. Cnidering the fllwing equatin: dt = a ϕ 2 th + b ϕ + c (13) and knwing the pair f value [ ϕ = 0 ( )], dt 0 th, [ ϕ = ( )], dt 90 and [ ϕ = ( )], dt 180, the 90 th 180 th cefficient a, b and c can be calculated. The deviatin ddt between the theretical and the meaured th temperature errr i: ddt f th dtm dt th = (14) Fig. 9. Deviatin f the theretical temperature errr frm the meaured ne Fig. 8. Meaured and theretical temperature-errr a a functin f the inclinatin angle The flw develping near the heated wall defrm the temperature field f the ambient. In cae f the extreme pitin f the urface, thi thermal bundary-layer can be een in Fig. 1. It can be berved that the bundary-layer near the enr-head i the mt thin fr ϕ = 180, in thi pint the theretical curve can be cnnected t the curve f the meaurement errr with gd apprximatin: dt 180 = dt 180 (9) th ( ) ( ) m Here the cncrete calculatin f dt th and ddt th fr enr 1 i preented, uing (13) and (14) which can be een in Fig.9. Cnidering the fllwing equatin: 2 ddtth = ( 180 ϕ) ( ak + bk ϕ + ck ϕ ) (15), cefficient a k, bk and ck can be calculated Phyical interpretatin f the difference between the theretical and the meaured deviatin The enr-head f length h and fr certain angle interval al a part f the enr-bar are ituated in the thermal bundary-layer develpment alng the heated wall (Fig. 7.). The temperature ditributin in a thermal

5 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia bundary-layer develpment alng a flat plate can be written a [6]: t ta = ( tw ta ) 1 2 y δ t (16), where δt i the thickne f the bundary-layer. The heat-flw field and thermal bundary-layer develpment, urrunding the heated wall and the enr, are ketched fr variu angle interval in Fig. 10 and Fig. 11. and baed n (17) and (18), it can be een that the difference between theretical and meaured errr can be attributed t the bundary-layer: Q = dtth dtm = ddt th (20) f Baed n the analyi f the heat flw Q a a functin f the angle, the qualitative behaviur f ddt th can be determined. The cnvective heat-flux Q wk frm the heated wall bey [1][2]: Q ϕ = 0 Q ϕ = 90 Q ϕ = 180 (21) wk ( ) ( ) ( ) wk Hence, the heat flw Q wk can be expreed by a mntnically decreaing functin (Fig. 12.) wk Fig. 10. Flw field and thermal bundary-layer in cae f ϕ [ 0, 90 ] Fig. 11. Flw field and thermal bundary-layer in cae f ϕ [ 90, 180 ] Equatin (16) i valid nly in the ϕ [ ϕ kr1 ϕ kr 2 ], interval. In cae f the enr, the utlet heat flw huld be equal with inlet heat flw. In particular, the heat flw thrugh heated wall / enr-head interface can be expreed: Q = f (17) w dt m, where dtm = t tw i the meaurement errr and f i the invere value f the thermal reitance. Due t the fact, that the enr-head get heat additin nt nly frm the cntact urface, but al frm the thermal bundary-layer, the fllwing relatin i valid: Q = Q + Q (18) t w, where Q t i the utlet heat flw frm the enr-bar, Qw and Q are inlet heat flw frm the cntacted urface and frm the bundary-layer repectively. Taking int cnideratin that = f (19) Q t dt th Fig. 12. Qualitative analyi f the heat tranfer frm the bundary layer t the enr A a cnequence f the temperature ditributin f the bundary-layer, the pecific rate f heat flw q i inverely prprtinal with the thickne δt f the bundary-layer, therefre δt can be expreed with the aid f a mntnically increaing functin in the interval ϕ ϕ, ϕ. Fr ymmetrical ϕ value with repect t [ 1 2 ] kr kr (ϕ = 90 ϕ, ϕ = 90 + ϕ ), i fllw that δ t δ t. Fig. 7 hw that fr the mean temperature 1 2 relative t the layer f thickne h, the fllwing inequality i valid: t t (22) mh2 mh1 We have indicated t mh a mntnically increaing functin f ϕ (Fig. 12.). The mean flw velcity u mh relative t the layer f thickne h i the highet fr ϕ = 90 (Fig. 12.). The heat flw frm the bundary-layer t the enr-head i prprtinal with the velcity u mh and with the temperature t mh : Q u mh h t mh (23)

6 Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia Prceeding, XVII IMEKO Wrld Cngre, June 22 27, 2003, Dubrvnik, Cratia It ha been thu demntrated that Q i nt ymmetrical with repect t ϕ = 90, explain the aymmetry f the ddt th. In particular the variatin f [ ϕ ] Q in the angle interval ϕ 0, kr 1 can al be explained with the aid f Fig. 10. In cae f ϕ = 0, the whle enr i immered in the thermal bundary-layer (Fig. 1.). Increaing the angle ϕ, a larger and larger part f the enr-bar emerge frm the bundary-layer. Fr thi rean Q i a mntnically increaing functin f the angle interval. The variatin f Q in the interval ϕ [ ϕ kr2, 180 ] can be interpreted uing Fig. 11. In the cae f ϕ = 180 (Fig. 3.), the cld air w away the bundary-layer frm the enr-head, therefre Q ( ϕ = 180 ) 0. Thu, a een in Fig. 11 that q i a mntnically decreaing functin f ϕ in thi angle interval. In Fig. 12 we have btained a Q (ϕ) ddt ϕ functin in Fig. 8. functin imilar t the ( ) th 5. CONCLUSIONS Surface enr meaurement, cmpunded by cniderae errr, which were nt quantified, can nwaday be crrected by value determined during calibratin. One f thee ignificant errr i etimated in thi wrk. The meaurement reult prve unambiguuly the influence f urface inclinatin n the meaurement errr. In thi firt tep f the invetigatin, a theretical analyi ha been carried ut t etimate the temperature-errr related t urface inclinatin. Thee invetigatin led t a better apprach f urface temperature meaurement uing cntact enr and imprvement in the calibratin methd and prcedure. EFEENCES [1]. Mrice, E. Andrá, E. Devin, T. Kvác, "Cntributin fr the calibratin and the ue f urface temperature enr", Tempmek Prceeding, vl. 2, pp , [2] F. Bernhard, S. Augutin, H. Mammen, K.D. Smmer, E. Tegeler, M. Wagner, U. Demich, "Calibratin f cntacting enr fr temperature meaurement n urface", Tempmek Prceeding, vl. 1, pp , [3] M.A. Mihejev, "Bae f practical calculatin cncerning the heat-tranfer", "A hõátadá gyakrlati zámítáának alapjai" Tankönyvkiadó, Budapet, [4] T. Környey, "Tranmiin f heat", "Hõátvitel", Mûegyetemi kiadó, Budapet, [5] H. Y. Wng, "Heat tranfer fr engineer", Lngman Grup Limited, Lndn, [6] E.. G. Eckert,. M. Drake Jr., "Heat and Ma Tranfer", Mc Graw - Hill Bk Cmpany, Inc., New Yrk, Trnt, Lndn, AUTHO: Emee Andrá, Thermmetry Diviin, Natinal Office f Meaure, 1124 Budapet, Hungary, phne: , fax: , e.andra@mh.hu