Experimental evaluation of the energy performance of an air vortex tube when the inlet parameters are varied

Send O de s o Rep in s o ep in s@ben hamscience.ne 98 The Open Mechanical Enginee ing Jou nal, 2013, 7, 98-107 1874-155X /13 2013 Ben ham Open Open Access Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube when he Inle Pa ame e s a e Va ied E. To ella1, J. Pa iño2, D. Sánchez2, R. Llopis2 and R. Cabello*,2 1Depa men o Applied The modynamics, Camino de Ve a, 14. Poly echnic Uni e si y o Valencia, E-46022 Valencia, Spain 2Depa men o Mechanical Enginee ing and Cons uc ion, Campus de Riu Sec. Jaume I Uni e si y, E-12071 Cas ellón, Spain Abs ac : The pape p esen s he analysis o he ene gy pe o mance o an ai o ex cooling ube unde a ia ions o he ai inle p ope ies, wi h h ee independen expe imen al es s alida ed h ough he ene gy balance in he de ice. The expe imen al analysis includes he ollowing a ia ions o he inpu condi ions: Fi s , he e ec o he ai inle p essu e o he o ex ube, ocused on he analysis o empe a u e a ia ions in he ou pu cold s eam and in he cooling capaci y when he cold low ac ion a ies. Second, we s udied ai inle empe a u e a ia ions o he o ex ube unde di e en cold low ac ions, which is an analysis no ound in he li e a u e. And inally, is s udied he pe o mance o he o ex ube when he insula ion is p o ided o in absence o insula ion. Keywo ds: Vo ex ube, e ige a ion sys em, ene gy analysis. 1. INTRODUCTION The Vo ex e ec was i s obse ed by Ranque [1] while obse ing he mal di ision in a cyclone sepa a o , being his design imp o ed by Hilsch [2]. Kassne and Knoe nschild [3] pe o med a heo e ical s udy based on he assump ion ha he e ec was due o adiaba ic expansion, which led o a low empe a u e in he low p essu e a ea nea he axis o he ube. Subsequen ly, o he esea che s ha e p oposed di e en heo ies o explain he ene gy sepa a ion p ocess, some o he mos impo an e e enced in ch onological o de a e: Webs e [4], Ful on [5], Shepe [6], Ha ne e al. [7], Lay [8,9], Deissle e al. [10], Reynolds [11], Lewellen [12], Linds om [13], Ku osaka [14], Ami ani e al. [15], S ephan e al. [16], A buzo e al. [17], Gu sol e al. [18], Lewis e al. [19], Ahlbo n e al. [20], T o imo [21] and Colga e [22]. No wi hs anding hese e o s, a heo y which sa is ac o ily explains he en i e p ocess has no been de eloped ye . Despi e he abo e s a emen and he low ene gy e iciency o he o ex ube, hey a e comme cialized o di e en applica ions when compac ness, eliabili y and low cos a e he main ac o s and when ene gy e iciency becomes less impo an . Cu en ly, hey a e used o cool pa s o machines, dehumidi y gas samples, cool elec ical panels, lique y na u al gas (Fin’ko [23, 24]), cool unde ad e se condi ions (Baz e al. [25, 26]), chill labo a o y en i onmen s in *Add ess co espondence o his au ho a he Depa men o Mechanical Enginee ing and Cons uc ion, Campus de Riu Sec. Jaume I Uni e si y, E- 12071 Cas ellón, Spain; Tel. +34 964 728135; Fax: +34 964 728106; E-mail: [email protected] explosi e a mosphe es (B uno [27]), in hype ba ic chambe s (Baz e al. [28]), sepa a e pa icles (Riu e al. [29]), in nuclea magne ic esonance (NMR) (Ma in e al. [30]), pe o m apid PCR (Polyme ase Chain Reac ion) wi h eal- ime op ical de ec ion [31]. Fu he mo e, o ex ubes ope a e as suc ion de ices (Alhbo n e al. [32]) and as expande s in ansc i ical CO2 cycles (Sa ka e al. [33]). Recen ly, Sachin e al. [34] and O han e al. [35] s udied di e en geome ies o he cold end o imp o e he ene gy pe o mance o he o ex ube. In con as o he exis ing expe imen al analysis o ai o ex ubes, which mainly ocuses on s udying hei pe o mance unde a ia ions o he cold low ac ion wi h cons an inle empe a u e p ope ies, he objec i e o his wo k is o analyse he incidence o he ai low inpu pa ame e s (inle p essu e and inle empe a u e) on i s ene gy pe o mance. Speci ically, we analyse he ou le empe a u e o he cold s eam, he cooling capaci y p o ide and he COP eached by he e ige a ing de ice. Acco dingly, his wo k p e ends o con ibu e o he unde s anding o he eal pe o mance o ai o ex ubes. 2. EXPERIMENTAL TEST BENCH AND ANALYSIS The expe imen al es bench de eloped o his wo k is shown in Fig. (1). This expe imen al se up inco po a es an EXAIR BP3215 o ex ube (maximum olume ic low a e 0,007078 m3/s in s anda d condi ions a 690 kPa o inle p essu e). The assembly is he mally isola ed om he comp essed ai en ance in he cold and ho ou le s. We measu e empe a u e wi h K- ype he mocouples and p essu e wi h piezoelec ic ansduce s placed a he inle and ho and cold exi s. The unce ain ies, calib a ed using Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 99 ce i ied e e ences, a e o ± 0.5 ºC o he he mocouples and o ± 0.1% o he ull scale ange (0-1000 kPa) o he p essu e ansduce s. We measu e empe a u e on he ou e su ace o he ubes, since acco ding o Ahlbo n [36], o measu e he empe a u e o mo ing luids, a de ice mo ing a he speed o he low should be used so as o achie e he mal equilib ium. We use wo mass low me e s, one o he inle ai (Tes o 6441, wi h p ecision ± 0,3 % o ull scale) and o he o he ho exi ai (B onkho s model EL-Flow F112AC, wi h p ecision ±0.1% ull scale). The signals a e ga he ed by an AGILENT 34970A da a acquisi ion sys em. 3. VORTEX TUBE CHARACTERIZATION The main pa ame e s ha cha ac e ize he ope a ion o a o ex ube a e he ollowing: 3.1. Cold Flow F ac ion Cold low ac ion a io is he a io be ween cold low and inle low: =mc min ; 0 ! !1 (1) 3.2. COP As o any e ige a ion plan , COP is he a io be ween he cooling capaci y p oduced and he powe consump ion equi ed in he ins alla ion, as p esen ed by equa ion (2). COP =Q0 PCs (2) whe e he cooling capaci y is calcula ed in he same way as in he case o a hea exchange , aking in o accoun he ene gy abso bed o cool he cold s eam (3). Q 0 =m c !c p !(T in "T c ) (3) Supply o comp essed ai , in he case o o ex ubes, is usually p o ided by an independen ai comp esso , making i di icul o es ima e he powe consump ion o compu e he COP i a wa me e is no a ailable o i he ai comp essed is no used exclusi ely in he o ex acili y. Acco ding o Boswell [37], he powe equi ed o comp ess ai om a mosphe ic condi ions, assuming an isen opic p ocess, can be calcula ed acco ding o exp ession (4), whe e he subsc ip s “2” and “1” indica e he comp esso ou pu and inpu condi ions. PCs = ! ! "1#min #R#(T2"T1) (4) Using he ela ionships inhe en in an adiaba ic comp ession p ocess (5) and (6), T 2 T 1 =p 2 p 1 ! " #$ % & ' (1 ' (5) R! " " #1=c p (6) and conside ing ha ai is cooled un il p ac ically o an a mosphe ic empe a u e (T1), wha means ha his is he o ex inle empe a u e “Tin”, he exp ession o powe consump ion can be w i en as de ailed by exp ession (7). P Cs =m in !c p !(T 2 "T 1 ) (7) Ob aining “T2” by means o (5), he inal exp ession o calcula ing he COP wi h expe imen al da a, easible measu able, is shown in equa ion (8) COP =Q 0 P Cs = !(T in "T c ) T in !p in p 1 # $ %& ' ( ( ) "1)/ ) "T in # $ % % & ' ( ( = !(T in "T c ) T in !p in p 1 # $ %& ' ( ( ) "1)/ ) "1 # $ % % & ' ( ( (8) Fig. (1). Tes bench and senso s loca ion. 100 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al. 4. EXPERIMENTAL ANALYSIS The wo ks a ailable in li e a u e demons a e ha he main magni udes which a ec he ene gy pe o mance o a o ex ube a e he inle p essu e (pin) and he low a io ( ). The e o e, we e alua e he ene gy pe o mance o he o ex ube wi h a se ies o ials in which he low a io a ies inside he ope a ing ange o he de ice. 4.1. Expe imen al Tes Range We conside h ee di e en expe imen s o e alua e he pe o mance o he o ex ube. Fi s , i was pu h ough h ee di e en inle p essu e le els, condi ions a e de ailed in Table 1. Second, he in luence o he inle ai empe a u e was e alua ed, a ied using a he mos a ic wa e ba h (as shown in Fig. 1) by using a small hea exchange placed in he inpu cu en . The e alua ion ange o he o ex ube in his es is shown in Table 2. Finally, he e ec o he he mal insula ion o he o ex ube was e alua ed o cons an ai inle condi ions, as de ailed in Table 3. 4.2. Valida ion o Expe imen al Measu emen s Fi s , o check he alidi y o he expe imen al esul s we analyse he ene gy balance on he o ex ube, i exp essed by ela ion (9). In he ene gy balance he hea ans e o he en i onmen is neglec ed and po en ial ene gies a e conside ed equal o he inpu and ou pu cu en s ( ue in he expe imen al plan ). Pin =min !(hin +Ec,in )=mc!(hc+Ec,c)+m !(h +Ec, )=Pou (9) As i is illus a ed by Fig. (2), he expe imen al es s co obo a e he ene gy balance o equa ion (9). As can be obse ed in Fig. (2), o e all ene gy balance shows a de ia ion o ± 5% be ween he o al powe o he de ice inpu and ou pu . The h ee cloud o poin s co espond o he h ee inle p essu e le els (Table 1). The he modynamic p ope ies o he ai we e e alua ed using Re p op ou ines [38] neglec ing he mois u e o he inle ai , since i p esen ed a low mois u e a io. 4.3. Inle P essu e Va ia ion Tes Fi s , we p esen he analysis o he expe imen al pe o mance o he o ex ube o he inle p essu e a ia ion es (Table 1). In Fig. (3), he measu ed ai ou le empe a u es o he o ex ube a e depic ed. The expe imen al e olu ions a e consis en wi h p e ious expe imen al s udies, such as hose o P om onge [39] and Saidi [40]. As i can be obse ed in he e olu ion o he ou le cold low in Fig. (3), a minimum in empe a u e exis s in each es . This minimum in empe a u e is ansla ed o wo coinciden minimums in he powe o he cold low a he o ex ou le , p esen ed in Fig. (4). In Fig. (4), we p esen he o al powe and he con ibu ion due o he p oduc o he mass low by i s speci ic en halpy. The di e ence be ween hem is he p oduc o he mass low by he kine ic ene gy. In Fig. (5), we depic he alues o cold mass low and i speci ic en halpy o he s eady-s a e co esponding o he highes p essu e in he es . I can be deduced om Fig. (5) ha he cause o he minimum in he ou le empe a u e o he cold ai and in he ou pu powe s is he ou le mass low e olu ion o he cold low. Table 1. Inle P essu e Va ia ion Tes Range Tes A e age pin [kPa] Va ia ion pin [%] A e age Vin [m3/h] Va ia ion Vin [%] A e age Tin [ºC] Va ia ion. Tin [%] A e age min [kg/h] Va ia ion. min [%] HP 563.35 -0.27 ÷ 0.22 16.35 -5.13 ÷ 3.31 20.08 -2.48 ÷ 3.00 109.45 -4.96 ÷ 3.23 MP 409.22 -0.76 ÷ 0.76 11.33 -2.97 ÷ 3.41 21.08 -2.60 ÷ 1.20 54.91 -2.48 ÷ 3.68 LP 256.86 -0.74 ÷ 0.88 6.19 -4.77 ÷ 3.35 21.61 -0.65 ÷ 0.84 18.79 -4.24 ÷ 2.77 Table 2. Inle Tempe a u e Va ia ion Tes Range Tes A e age pin [kPa] Va ia ion pin [%] A e age Vin [m3/h] Va ia ion Vin [%] A e age Tin [ºC] Va ia ion. Tin [%] A e age min [kg/h] Va ia ion. min [%] HT 572.93 -0.46 ÷ 0.28 16.22 -5.84 ÷ 3.59 38.98 -1.57 ÷ 1.01 103.75 -6.05 ÷ 3.93 MT 549.15 -0.46 ÷ 0.57 16.02 -6.14 ÷ 2.90 19.33 -0.56 ÷ 0.60 104.8 -6.00 ÷ 2.98 LT 550.42 -0.63 ÷ 0.73 15.89 -6.17 ÷ 4.22 14.37 -8.87 ÷ 2.67 105.95 -5.21 ÷ 3.85 Table 3. Tes Condi ions wi h and wi hou Insula ion Tes A e age pin [kPa] Va ia ion pin [%] A e age Vin [m3/h] Va ia ion Vin [%] A e age Tin [ºC] Va ia ion. Tin [%] A e age min [kg/h] Va ia ion. min [%] WITH 575.06 -7.72 ÷ 10.4 16.12 -5.47 ÷ 11.7 20.98 -1.66 ÷ 1.25 109.96 -11.48 ÷ 20.78 WITHOUT 577.14 -9.05 ÷ 11.07 16.41 -10.02 ÷ 8.94 21.56 -1.68 ÷ 1.39 112.17 -13.50 ÷ 18.28 Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 101 On he o he side, ega ding he ene gy pa ame e s, we p esen he cooling capaci y in Fig. (6) and he COP in Fig. (7) o he h ee inle p essu es o he o ex ube conside ed. They ha e been ep esen ed e sus he low a io (1). As can be obse ed in Fig. (7), a maximum in COP exis s o each inle p essu e le el. This is because he exis en ela ion be ween he cooling capaci y and he empe a u e o he cold ou le low (equa ion 3). None heless, he alue o he low a io ‘ ’ co esponding o he minimum empe a u e Fig. (2). Ini ial check. O e all ene gy balance in he o ex ube. Fig. (3). Ai ou le empe a u es o he cold and ho s eams s low a io o he inle p essu e a ia ion es . 0 2 4 6 8 10 12 0 P ou [Kw] 2 4 6 P in [Kw] 810 -5% +5% 12 200 220 240 260 280 300 320 340 360 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 T ou [K] T_OUTc HP T_OUTc MP T_OUTc LP T_OUTh HP T_OUTh MP T_OUTh LP 102 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al. o he ou le cold low does no coincide wi h he alue o he low a io ‘ ’ co esponding o he maximum cooling capaci y, since a a ia ion o he mass low exis s. De eloping equa ion (3), Q 0 =m c !c p !(T in "T c )= !m in !c p !(T in "T c ) (10) de i ing (3) wi h espec o he low a io ‘ ’, dQ 0 d =m in !c p !(T in "T c )" !m in !c p !dT c d (11) and equalling o ze o, (T in !T c )= "dT c d (12) Exp ession (12) es ablishes he alue o he low a io ‘ ’ which maximizes he cooling capaci y. F om a de ailed obse a ion o equa ion (12), i can be said ha he alue o ‘ ’ which maximizes he cooling capaci y di e s om he alue o ‘ ’ which minimizes cold exi empe a u e, since i hey we e he same he alue o he di e en ial dTc d would be equal o ce o. Acco dingly, he alue o ‘ ’ which minimizes he cold exi empe a u e is lowe han he alue HP = 563.35 kPa 5 5.5 6 6.5 7 7.5 8 8.5 9 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 P [kW] PT_ou ,c m_ou ,c * hou ,c Fig. (4). Ou pu powe s o he p essu e es . HP = 563.35 kPa 0 5 10 15 20 25 30 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 m ou ,c [kg/s] 285 287 289 291 293 295 297 299 h ou ,c [kJ/kg] m_ou ,c h_ou ,c Fig. (5). Mass low a e and speci ic en halpy o he cold ou pu cu en s low a io o he maximum p essu e alue. Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 103 o ‘ ’ which maximizes he cooling capaci y. This easoning can be obse ed on he ep esen a ion o he cooling capaci y and cold exi empe a u e dependence on he low a io ‘ ’ on Figs. (3, 6) espec i ely. Rega ding he COP e olu ions p esen ed in Fig. (7), i needs o be men ioned ha hei alues a e highe han hey would be in an ac ual ins alla ions, since he cooling capaci y has been ela ed wi h an ideal powe o he comp ession p ocess, which in his assay is conside ed o be cons an o each inle p essu e. 4.4. Inle Tempe a u e Va ia ion Tes The second expe imen al analysis which is pe o med wi h he o ex ube co esponds o he empe a u e a ia ion o he ai inle (Table 2). This analysis has no been ound in li e a u e, acco dingly his sec ion aims o highligh he 0 0.2 0.4 0.6 0.8 1 1.2 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Q 0 [kW] Q0 HP Q0 MP Q0 LP Fig. (6). Cooling capaci y s low a io o he p essu e a ia ion es . 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 COP COP HP COP MP COP LP Fig. (7). COP s low a io o he h ee inle p essu es. 104 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al. impac o he ai inle empe a u e on he ene gy pe o mance o he de ice. Fi s , in Fig. (8), we p esen he e olu ion o he cold ou le empe a u e o h ee di e en ai inle empe a u es e sus he low a io. I can be obse ed ha he cold ou le empe a u e is as lowe he ai inle empe a u e is. The abo e discussed minimum empe a u e o a gi en low a io exis s in he expe imen al e olu ions. Rega ding he cooling capaci y, we p esen i s e olu ion in Fig. (9) o he h ee inle empe a u es e sus he low a io. A ligh inc ease on he cooling capaci y wi h he inc ease o he ai inle empe a u e o he o ex ube can be 240 250 260 270 280 290 300 310 0.7 0.75 0.8 0.85 0.9 0.95 1 Tou ,c [K] HT MT LT Fig. (8). Cold ou le empe a u e s low a io in he inle empe a u e a ia ion es . 0 0.2 0.4 0.6 0.8 1 1.2 0.7 0.75 0.8 0.85 0.9 0.95 1 Q 0 [kW] Q0 HT Q0 MT Q0 LT Fig. (9). Cooling capaci y s low a io o he inle empe a u e a ia ion es . Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 105 obse ed. Tha is because he di e ence be ween he inle empe a u e and ha a he cold ou le is highe when highe he ai inle empe a u e is. 4.5. Insula ion Tes Finally, we analyse he e ec o he insula ion in he o ex ube. We e alua e his e ec by compa ing he ene gy pe o mance o he o ex ube wi h insula ion and wi h no unde simila inle condi ions (Table 3). We p esen he expe imen al e olu ion o he cooling capaci y in Fig. (10) and he COP in Fig. (11). F om he analysis o he expe imen al e olu ions, i can be a i med ha no app eciable di e ence exis s be ween he esul s wi h and wi hou insula ion, and he li le di e ences can be associa ed wi h small de ia ions o he es condi ions. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Q 0 [kW] Q0 WITH Q0 WITHOUT Fig. (10). Cooling capaci y s low a io wi h and wi hou insula ion. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 COP COP WITH COP WITHOUT Fig. (11). COP s low a io wi h and wi hou insula ion. 106 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al. 5. CONCLUSIONS We p esen a es bench o an ai o ex ube in he p esen wo k. I allows o modi y he inle condi ions o he ai in o de o analyze hei in luence in he ene gy pe o mance o he de ice. The pape p esen s he expe imen al e alua ion o he ai o ex ube unde inle p essu e and empe a u e a ia ions o he inle ai o e a wide ange o a ia ion o he cold and ho lows, i. e., a ia ion o he low a io. We alida ed all he expe imen al esul s wi h he o e all ene gy balance in he de ice, ob aining an e o below 5%. We obse ed a minimum in he ou pu empe a u e o he cold low in he inle p essu e a ia ion es . This minimum was al eady e idenced in p e ious wo ks, as well as i s ans e o he COP alues, howe e , his pape analyses he causes which p oduce his minimum. We concluded ha i is associa ed wi h he a ia ion o he mass low a e o he cold ou pu cu en . Fu he mo e, we analyse he alues o he low a ios a which he minimum in empe a u e and cooling capaci y a e ob ained. We s udied expe imen ally he in luence o he inle empe a u e o he ai o he o ex ube, and conclude ha he ou le empe a u e o he cold low is lowe as lowe he inle empe a u e is. Addi ionally, he cooling capaci y is highe when highe he inle empe a u e is, since he di e ence in empe a u e be ween he inle ai and he cold ou le ai is highe . Finally, we e alua ed he e ec o he insula ion o he o ex ube o cons an inle condi ions, and we concluded ha he insula ion does no modi y app eciably he ene gy pe o mance o he de ice. NOMENCLATURE COP = Coe icien o pe o mance cp = Speci ic hea a cons an p essu e, kJ·kg-1·K-1 Ec = Speci ic kine ic ene gy, J·kg-1 h = Speci ic en halpy, J·kg-1 m = Mass low a e, kg·s-1 p = P essu e, kPa PC = Comp ession powe consump ion, kW Q0 = Cooling capaci y, kW R = Gas cons an = Gold low ac ion T = Tempe a u e, K G eek Symbols ΔT = Tempe a u e di e ence γ = Speci ic hea a io Subsc ip s c = Cold low in = Inle low h = Ho low ou = Ou le Flow s = Isen opic p ocess CONFLICT OF INTEREST The au ho s con i m ha his a icle con en has no con lic o in e es . ACKNOWLEDGEMENTS The au ho s a e indeb ed o he Spanish Minis y o Educa ion and Science (CTM2008-06468-C02-02/TECNO) and o he Spanish Minis y o he En i onmen and Ru al and Ma ine A ai s (200800050084716) o hei economic suppo o his wo k. REFERENCES [1] G.J. Ranque, “Expe iences su la de en e gi a oi e a ec simul anes d’un echappemen d’ai chaud e d’un enchappemen d’ai oid”, J. Phys. Radium., ol. 4, pp. 112-114, 1933. [2] R. Hilsch, “Die expansion on gasen im zen i ugal eld als käl ep oze”, Z. Na u o schung, ol. 1, pp. 208-214, 1946. [3] R. Kassne , and E. Knoe nschild, “F ic ion laws and ene gy ans e in ci cula low. W igh -Pa e son ai o ce base”, Technical epo F-TR-2198ND OH, 1948. [4] D.S. Webs e , “An analysis o he Hilsch o ex ube”, J. ASRE Re ig. Eng., ol. 58, pp. 163-70, 1950. [5] C.D. Ful on, “Ranque’s ube”, J. ASRE Re ig. Eng., ol. 58, pp. 473-9, 1950. [6] G.W. Shepe , “The o ex ube in e nal low da a and a hea ans e heo y”, Re ige a ion Eng., ol. 59, pp. 985-989, 1951. [7] J. 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