ACUSCOMP and ACUSYS A powerful hybrid linear/non linear simulation suite to analyse pressure pulsations in piping

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1 ACUSCOMP n ACUSYS A owerful hybr lner/non lner multon ute to nlye reure ulton n ng Ing Attlo Brghent, Ing Anre Pvn, SATE Sytem n Avnce Technology Engneerng, Snt Croce 664/A, 335 Venez, Itly e-ml: ttlobrghent@te-tlycom Abtrct The m of th er to exln the theoretcl n rctcl ect of ACUSYS n ACUSCOMP, multon ute for the nly of reure ulton n ng n the recton of comreor erformnce uner reltc ng ynmc ACUSYS tool to nlye the reone of generc ng ytem to reefne nut gnl generte t ny nterfce wth the g flow ACUSYS lone llow relmnry lner nly to focu the ntrnc ng reone n flow reonnce tttue n the frequency n tme omn When the ntercton between the mchne thermoynmc, the vlve mechnc n the flu exchnge roce re to be tken nto ccount, together wth the ng flow ynmc, ACUSCOMP, n cooerton wth ACUSYS, llow the tme omn non lner moellng of the entre ytem Both thee rogrmme re lcton eveloe by the leng uthor n h collbortor for the MATLAB- Smulnk envronment of The Mthwork Inc (Ntck, M, USA) Introucton ACUSYS, eveloe formerly by the leng uthor ([], [], [3], [5]) tool to nlye the reone of generc ng ytem, uch lnt or muffler, to reefne turbnce nut gnl generte t ny nterfce wth the g flow, eg t the flnge connectng one or more comreor or engne cylner to the ng ucton n/or chrge e, or t ng obtructon or bln e brnche exctng flow vortexe t ecfc Strouhl number conton [8] Thee turbng gnl (ether n term of reure or m flow rte) cn be ether clculte or etmte n vnce by the uer be on bckgroun or revou nlye ACUSYS lone llow relmnry lner nly of the comlex reone to thee ource by the ng Alo, ACUSYS llow trnfer functon n force nly to focu the ntrnc ng reone n flow reonnce tttue n the frequency n tme omn However n ome ce, rtculrly n the comreor nutry fel, th relmnry nly focue only on the ng not uffcent, becue of the ffculty n mkng uch gnl etmte whch een not only on the genertng ource, e comreor or engne, but lo on the reone chrctertc of the lnt when coule together Wely ue trngent rule uch API 68 [] requre nee tht uch ntercton between the mchne thermoynmc, the vlve mechnc, the flu exchnge roce n the ng flow ynmc re tken nto ccount nce the egn he ACUSCOMP fulfl th further requrement n, n cooerton wth ACUSYS, llow the tme omn non-lner moellng of the entre ytem nclung ucton n chrge ng connecte to flu-hnlng mchne In th er tycl recroctng comreor exmle reente Mn feture of the ute The ACUSYS / ACUSCOMP multon ute one of the few commercl oftwre rouct cble to nlye untey flow n e ytem ntegrte wth the nternl mchne thermoynmc Outtnng feture re: Both rogrmme run on PC; Extremely mle n uer-frenly grhcl nterfce; Fully ntegrte wth the MATLAB- Smulnk envronment n MS Excel ; Full exlotton of the MATLAB- MS Excel regtere rouct of Mcrooft Cor

2 Smulnk functonlte, tht men the oblty of nertng tonl block, for exmle to nlye the rotry hft mechnc or to ntegrte the moel wth control routne, ether of the mchne ee or of the vlve (eg to mlement vrble flow ccty control) Png Png 3 Plenum Cylner effect Png Plenum,3 Plenum 4 Cylner effect Fg Exmle of ytem ute for ACUSYS - ACUSCOMP multon Sngle or ouble effect cylner (Mgent n Fg ), whch nclue, nete ne: o Sucton n chrge vlve ynmc, functon of ether mechncl commn (e cm hft) or fferentl reure rve, between the cylner n the lnt e (both ynmclly clculte by ACUSCOMP) o Cylner thermoynmc, whch nclue both the oen he (exchnge wth the ng) n cloe he (cloe vlve) Plen (Green n Fg ), rereentng the buffer volume tht re t the nterfce of the mchne, between vlve n ng Retrcton, rereentng equvlent reure lo element tht cn be ue n lce of the entre ng block to nlye the behvour of the mchne wthout the multmol ynmc behvour of the ng In the fle only menonl n engneerng rmeter mut be efne 3 The oftwre rchtecture for comlete ulton nly The oertve equence to erform comlete nly n the nut-outut reltonh between the two rogrmme cn be ummre n the cheme of Fg 3 Anly wth ACUSYS: Clculton of the tte mtrxe of the ng ytem Fg ACUSCOMP moel n the Smulnk envronment of the ytem of Fg The uer cn bul u the ACUSCOMP n ACUSYS Smulnk moel by ely emblng by very few vectore lne the vrou comonent block (Fg ), or choong one n lbrry of reemble confgurton The block cn be: Png tte ce mtrxe (Blue n Fg ), e the overll ynmc chrctertc of ech ng e (ucton, chrge or ntermete) connecte to one or more cylner Thee tte ce mtrxe re clculte by ACUSYS Anly wth ACUSCOMP: Determnton of the ctul forcng reure gnl n of the comreor ncte cycle n m flow rte uner the nfluence of the ng recton Anly wth ACUSYS: Determnton of the reone n every ecton of the ng to the reure n m flow gnl obtne from ACUSCOMP n the tte mtrxe clculte n ACUSYS Anly wth ACUSYS: Determnton of the force on ng Fg 3 Scheme for comlete ulton nly

3 Dt re trnferre to/from one rogrm to the other ung the otentlte of the MATLAB envronment or through workheet fle, utomtclly ete n flle n by ACUSCOMP n ACUSYS Th hel the uer lo n mngng the n etng freely ther rereentton 4 Theoretcl roch of the moel In the followng ecton the mthemtcl roch, whch w followe n the mlementton of the moel comonent, ecrbe The electro coutc nlogy llow mlfcton of the contnuty n momentum equton of the untey comreble flow n n elementry tube [7], f they were wrtten for n electrc crcut lke tht of Fg 4, tkng nto ccount lo the frcton loe effect m R C L m 4 Pulton rogton The moel of lnt mlemente n ACUSYS eentlly fnte element moel of monomenonl fel of rogton Th hyothe of lne wve rogton vl when the wvelength uffcently greter thn the tube meter or thn the chrctertc menon orthogonl to the rogton recton, nmely when: f c < 6 () D In Eq f the frequency (Hz) of generc gnl comonent, c the oun ee ne the flu e (m/), correcte to ccount for the e hoo comlnce n D the mxmum e cro ecton menon, orthogonl to the rogton recton of the oun wve (m) Th conton uully verfe ne comreor ng For exmle for ng hvng meter of 4 mm n oun ee of 45 m/ th cut-off frequency of 35 Hz, whle the comreor ee funmentl tyclly rnge from to Hz The hgher frequence re mene by the vcou effect n the oun wve ctterng The flu meum conere boune n e n contner, rg n the xl n benng moe, wth even vrble meter n rbtrry he, uch ulton mer, het exchnger, etc Bee the lne wve rogton moel, octe to the rnge of frequence tue, ACUSYS run uner the hyothe of lner reltonh between mltue of reure vrton n locl flu velocte, vl untl the ltter n the men flu velocty re mll enough comre to the oun ee Such hyothe better known the conton for the electro-coutc nlogy Fg 4 Electro-coutc nlogy ote n ACUSYS R + L ; x x L ; R A D C Ax C c A () (3) In Eq () n (3), whch reectvely rereent the contnuty n momentum blnce fter the bove-mentone roxmton, the followng notton n efnton re le (n SI unt): R: equvlent retnce erve from the lnerzton of the turbulent frcton reltonh cue below (Eq 4), L, C: equvlent nuctnce n ccty of the element reectvely, : flow rte n reure of the flu t ecton n t: tme A: e cro ecton re x: element length c: oun ee of the flu n the element : frcton he lo fctor er unt length D: e meter : m enty of the flu : ubcrt nctng the men vlue n ero of tme (eg the t hrmonc ero)

4 In lnerng the frcton loe ttenton mut be to the crteron by whch th erforme, t mut comly wth the tey tte reltonh: x ( ) D A (4) where : Inee the correct uul roch for ynmc mng lnerton woul be by the frt ervtve of Eq (4) n the ont of verge oertng flow (Fg 5), yelng n exreon for R, ouble comre to the one n Eq () ue by ACUSYS ṁ Fg 5 Grhcl rereentton of the two flow frcton lnerton oton (t tngent or ervtve, ecnt or verge) t m woul yel 5% error n the m flow rte (Fg 6) To mtch th conton t nte convenent to ue the exreon for R gven n Eq (), whch men to lnere Eq (4) by the ecnt roch rther thn the tngent one (Fg 5) n to uneretmte the mng of the reure ulton n the ng It mut be hghlghte, however, tht th roxmton oe not mr the vlty of the ynmc nly Inee the ynmc reone of very low mng ytem ffecte by the mng fctor only wthn very nrrow frequency bnwh roun the nturl frequence Oute th t well known tht the reone motly etermne by the rectng comonent of the ytem mence, e cctnce n nuctnce, whch re not ffecte by the bove crteron for the mng efnton On the other hn, when uch ytem reonte, the reure n flow mltue woul be nywy o hgh tht the whole electrocoutc nlogy woul looe t vlty n quntfyng the ctul reone mltue Neverthele uner thee conton the outut of the moel woul fulfl nywy the nee for hghlghtng crtcl tuton 4 Comreor In the ACUSCOMP moel of comreor, element wth fxe volume, lke len, n wth vrble volume, lke cylner, re both conere, rereente n Fg 7 For hgh flow rte reltve to the volume or, more recely, for hort reence tme of the g n the volume, they cn be conere btc t m, h t T,,, V m, h t 5 m m m Fg 6 Error n the clculton of the men flow when ung the ervtve (tngent) frcton retnce fctor (Ref to Fg 5) Th woul well roxmte the mng of ech hrmonc comonent of the ynmc reone, but uner tey tte conton, eg contnt reure fference gnl between the two en, t Work Fg 7 Generl m-energy blnce rereentton of n element wth vrble volume In generl the m blnce for ngle element cn be wrtten n Eq (5), where the flu

5 enty n the volume V n the ubcrt n refer to the ucton n chrge ort reectvely n n V (5) V Eq (6) nte the generl exreon of the energy blnce, where U the totl nternl energy, h the ecfc enthly of the g flow n L the work erforme by the g n the btc volume U n n L h m h t & t (6) In the ce of rel g wth comreblty fctor z, ume contnt for the g conton t the temerture n reure n the volume V, the exreon of the ecfc nternl energy u n enthly h cn be wrtten lke for n el g, n Eq (7) n (8) reectvely Conerng the work erforme by the g n the volume V, ee Eq (9), n the rel g tte equton () n combnng together Eq (6), (7), (8), (9) n (), the fnl exreon () of the energy blnce ne V cn be obtne, where c cv U u cvt (7) V h c T (8) L V (9) zrt () When conerng olytroc of exonent m nte of the reverble btc trnformton, t cn be emontrte tht Eq () mofe nto Eq () The Eq (5) n () cn be further te to the ecfc comonent to be moelle, e cylner or len, er the followng ubecton 4 Cylner thermoynmc y mx y y mn m &, h t m &, h Fg 8 Cylner cheme For cylner, rereente n Fg 8, only one nut n one outut mut be conere, whle the vrton of the volume V een only on the ton troke Thu, cllng A the ton re, y the ton oton, T the temerture n the enty ne the cylner, the Eq (5) n () cn be rewrtten (3) n (4) t, T T T n n V T T m + + t & () V V V n n m V T T m + + t & () V V V y A A y (3) T m Tt T A y A y + y y + (4)

6 4 Plen A lenum n element of fxe volume nterfce wth the ng (or retrcton) on one e n the vlve (ucton or chrge), on the other, whch ut n communcton wth the cylner volume when the vlve oen In ouble effect cylner ngle lenum cn urroun r of vlve of the me tye (ucton or chrge) Eq (5) n (6) re erve from (5) n () eletng the ervtve of V th contnt T n n V (5) n n m T T m + t & V V (6) 43 Vlve ynmc ACUSCOMP clculte the oenng of ech comreor vlve olvng the ngle egree of freeom equton of the hutter oton The force conere re thoe ue to the reure fference between the cylner n the jcent lenum, ctng on the effectve hutter re, the retorng force by non-lner rng n frcton mng En troke hock contrnt re moelle too, whch yel bouncng behvour to be vble when of relevnce Be on the bove blnce the vlve oen only when otve reure fference excee the rng relo n the frcton force, lke n the rel comreor The m flow through the vlve orfce clculte functon of the ntntneou vlve oenng, the reure utrem n owntrem n the temerture utrem the vlve, e n the cylner or lenum Be on well-known lterture [9] the vlve reference flow ecton clculte by Eq (7) A r 44 3 X v AvC + ( ) M + ( ) (7) In the bove X v the vlve oenng, erve by the bove hutter moton equton, A v the equvlent vlve, full oenng, flow coeffcent rove by the vlve mnufcturer for wter flow tet, C the g correcton fctor n M the Mch number utrem the vlve, uully neglgble, comre to the ven contrct conton Snce n the flow through n obtructon ll reure loe re locle owntrem the ven contrct, the totl reure n the ltter equl tht of the utrem flow Knowng th reure, from the jcent volume blnce ecrbe bove, bckolvng Eq (8) llow the clculton of the Mch number n ny ecton, n rtculr the ven contrct, whle the other Eq (9), (), () n () efne ll the ttc n totl thermoynmc vrble n the me ecton Uner chokng conton, e crtcl flow t Mch, the m flow reche t mxmum vlue, eenng on the utrem conton ( ) RTt A t ( ) M M Tt T + M + ( ) F( M ) (8) (9) t + M () t t () zrtt () zrt The g comreblty fctor z ue n the bove equton ume the men vlue between thoe clculte t ucton n chrge conton The bove generle orfce moel llow clcultng both the flow through comreor vlve, whch normlly ubcrtcl, n tht through lekng el or vlve et, whch nte cn be chocke, functon of the ntntneou g conton on the two e of the obtructon (eg the reure n the two volume of ouble effect cylner) 44 Retrcton The generc orfce moel, whch w reente n the revou ecton, cn lo be ue to moel the flow through ny other retrcton, eg equvlent obtructon or lo element tht cn be ue n lce of n entre ng Th woul llow to relmnrly nlye the behvour n cycle of

7 comreor regrng the multmol ynmc behvour of the ng cue n ecton 4, t ecrbe n ec 5 43 Force on ng The ntegrte ACUSYS-ACUSCOMP ute llow lo, the fnl te, to clculte n nlye the force generte by the reure ulton t the e ben or juncton, the nut for ynmc tructurl nly, to verfy oble tructurl reonnt vbrton, foreeen for ntnce by the API 68 rule [] The elementry noe of Fg 9 rereent the ben between two nterectng e element Uner the hyothe tht the ben or jont extenon mll comre to the oun wve length n the frequency bnwh conere, the reure contnt long the noe t ech tme; the totl force ctng on t cn then be clculte the um of two contrbuton, efne by Eq (3) n (4) The former the vector um of the reure force; the ltter the chnge of momentum of the flow, between the two noe en t tme t F u F r u Fg 9 Elementry noe rereentton F The reultnt recte long the bectng lne of the ngle forme by the two ng element, rereente n Fg 9 In Eq (5) the reure n the m flow re functon of tme, whle n A re ume to be contnt n the noe F r F F ev A ( u ) u (3) A A + ( u u A ) ( u u ) (4) (5) 5 Reult In th chter the mn tycl reult, whch cn be obtne by men of ACUSYS n ACUSCOMP, re reente An exmle two-tge/two-effect r comreor conere, nterfce wth ucton, ntertge n chrge ng (Fg ), wth the followng nomnl chrctertc: M flow rte 69 kg/ Inlet reure 8 br Intercooler reure br Outlet reure 46 br Revoluton ee 7 rm A exlne bove the tme omn nly w erforme n ACUSCOMP, fter clcultng by ACUSYS the three et of the ng tte ce mtrxe After long the fle n runnng the ACUSCOMP moel, the followng cylner vrble, referre to ech effect, cn be lotte: Pton troke; Pton velocty; Cylner reure; Cylner temerture; Sucton n chrge vlve bounry reure; Sucton n chrge vlve fferentl reure; Sucton n chrge vlve flow rte; Sucton n chrge vlve oenng For ech lenum the followng lot re vlble: Preure; Temerture; Inut m flow rte; Outut m flow rte The ng en reure n flow rte, or equvlent retrcton one, cn be lotte well Prmeter DP Retr Incte work (kj) Incte torque (Nm) Incte ower (kw) Volumetrc effcency Comreon rto Ave m flow rte (kg/) 94 9 Tble Globl erformnce reult: t tge t effect cylner (DP Dynmc Png, Retr Png equvlent retrcton)

8 55 x 6 ACUSCOMP Cyl Eff cyl (P) Cyl Eff cyl (P) Cyl Eff cyl (P) Cyl Eff cyl (P) Volume (m 3 ) x -3 Fg Incte cycle clculte wth ACUSCOMP n ynmc ng, for the exmle ce Ech of the vrble lte bove cn be comre n the me lot wth ll the other n cn be lye veru four fferent bc: Tme; Cylner volume Crnk ngle; Pton oton For the exmle conere, the reult for tble cycle of the frt effect of the frt tge cylner re hown n Tble The ncte cycle for ll the tge n effect re nte rereente n Fg Th ce how the nfluence of the ynmc ng chrctertc wvy reure gnl bove ll urng the chrge he of the n tge The two effect how lo ome obvou gnl he hft Bee the n-cylner vrble, the mot mortnt outcomng for the reure ulton nlye re the nut gnl to be rove to the thr te of the nly (Fg 3), nmely the reure gnl t the nut ecton of the ng, e the reure n the len Thee cn be exorte to ACUSYS, for the tme n frequency nly n ll ng ecton, yelng the reone n term of reure (Fg ) or m flow rte To hghlght the nfluence of the ng ynmc on the comreor erformnce n gnl generte t the nterfce wth the ng, mlr nly hown for the me comreor, wth ure retrcton nte of the comlete ynmc ng moel, mentone n Sec 44 The other chrctertc of the ytem, uch cylner, vlve n len re ket unvre The globl erformnce o not vry recbly n th ce (Tble ) comre to the one revouly ecrbe, no gret ulton occur: wth the ng ynmc moel the erformnce recte re lghtly better (lower ncte ower) Th reltve nvrnce of erformnce cn be exlne by the lck of gret reure ulton n the ng n len Inee from the ubequent ACUSYS nly t reult tht the reone t the ntermete ng ecton re lower thn the nut gnl (Fg ) The lghtly lower torque n ower wth the ynmc ng moel cn be exlne by the fvorble ereon wve t the en of the g chrge (Fg n Fg 3) rtculrly n the t tge

9 Sect Tme reone (Preure (br)) Hrmonc mltue x 5 4 x x x x x x x Tme () Frequency (Hz) Run: -Jun- 6:6:4 Fg ACUSYS reure ulton n the ucton ng of the tet ce (the re lne ncte the reone, whle the blue n green lne ncte the nut gnl) t tge Cylner - t effect - Incte cycle t tge ucton lenum - reure 3 83 Retrcton Dynmc Png 8 Retrcton Dynmc Png 9 8 Preure (br) Preure (br) Volume (m 3 ) Tme () Fg t tge P-V grm; ynmc v retrcton ng Fg 4 t tge ucton lenum reure; ynmc v retrcton ng n tge Cylner - t effect - Incte cycle t tge chrge lenum - reure Retrcton Dynmc Png Retrcton Dynmc Png 4 95 Preure (br) 35 3 Preure (br) Volume (m3) Tme () Fg 3 n tge P-V grm; ynmc v retrcton ng Dete the rent equvlence of the two moel when lookng t the overll erformnce, Fg 5 t tge chrge lenum reure; ynmc v retrcton ng mortnt fference between them re event when lookng t the reure gnl n the len

10 (Fg 4 n Fg 5), whch mly mortnt fference n the reult from the ACUSYS nly of the ulton n the whole ng The fnl te of tycl reure ulton nly then the clculton of the force generte by the flu t the noe of the ng The lyout of the ltter cn be vule n ACUSYS, hown n Fg 6, 3D coloure e howng lo the reure or flow rte ntntneou vlue n the noe of force reucton A n exmle of the outut, Fg 7 rereent the force long x, y n z n four noe of the nlet ng of the comreor moel Fg 6 ACUSYS - 3D rereentton wth colore reure level of the t tge ucton ng of the exmle comreor; the button llow crollng of reure ttern long wth tme 6 Concluon 3 4 Noo Fx (N) Fy (N) Fz (N) x x x Tme () Tme () Tme () -Jun- Run: 6::6 x Fg 7 ACUSYS - Force t four noe of the nlet ng of the exmle comreor The work reente n th er the reult of multyer eveloment me t rovng engneer flexble n effectve tool for the nly of reure ulton n lnt ACUSYS n ACUSCOMP, ete ther rent mlcty embe ohtcte moellng roch tht llow relble multon of recroctng comreor erformnce, well the nly of other flu ng ytem, when trnent or other ource of reure ulton re of concern The t uthor exerence n ung thee tool lo for ther ervce n vrety of tuton howe the effectvene n uefulne of the multon to

11 revent ngerou tuton or to unertn revouly unexlne e vbrton henomen foun n the rel lnt oerton The work on th ubject n contnuou rogre n wll encom lo new tet n comron mong moel n exermentl [] API STANDARD 68 Recroctng Comreor for Petroleum, Chemcl n G nutry Servce, 4th E, June 995 Acknowlegement The uthor wh to thnk SIAD Mcchne Imnt SA (Bergmo Itly), who tmulte n rove the oortunty to evelo n mrket ACUSYS n ACUSCOMP n rove tycl comreor egn n erformnce rmeter for the nly reente n th er Reference [] Brghent A, Ot P: ACUSYS - Alcton of MATLAB-SIMULINK for the multon of coutc ulton n lnt (n Itln), t Itln MATLAB Conference, Bologn, 4 Oct 994 [] Brghent A: ACUSYS - Alcton of MAT- LAB-SIMULINK for the multon of coutc ulton wthn lnt (n Itln), 3r Congre of the Itln Acoutc Aocton, Bologn, -4 Se 995 [3] Brghent A: ACUSYS - Uer mnul, Coyrght Ing Attlo Brghent, Dec 994 [4] Brghent A, Pvn A: ACUSCOMP - Uer mnul, Coyrght Ing Attlo Brghent, Dec 994 [5] Brghent A, Contero D: Prelmnry vlon of ACUSYS to nlye ntblte n the non lner combuton zone lnt coutc ntercton, ISMA t Noe n Vbrton Engneerng Conference, Leuven, 8-/9/96 [6] Crwfor F S: Wve, McGrw-Hll book Co, USA, 965, 968, 969 [7] Heywoo J B: Internl Combuton Engne Funmentl, McGrw-Hll Intl E Automotve technology Sere, USA, 988, 989 [8] Pelne n Comreor Reerch Councl/ South Wet Reerch Inttute, Pulton & Vbrton Short Coure, 99 [9] Mller, DS "Internl flow ytem", BHRA, n e