Analysis of the Frequency-Dependent Attenuation of Transient Pressure Waves in Plastic Pipes ABSTRACT

Transcription

1 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 Anlysis of the Frequency-Dependent Attenution of Trnsient Pressure Wves in Plstic Pipes Jinzhe Gong, Mr L. Stephens, Mrtin F. Lmbert 3, Aron C. Zecchin 4 nd Angus R. Simpson 5,3,4,5 School of Civil, Environmentl nd Mining Engineering, University of Adelide, SA 55, Austrli South Austrlin Wter Corportion, Adelide, SA 5, Austrli jinzhe.gong@delide.edu.u ABSTRACT Some recent reserch proposed to use plstic pipe segments s dmpener in ter pipeline systems to mitigte extreme hydrulic trnsient pressure. Hoever, there is lc of studies on ho the ve ttenution vries ith frequency nd ho different pipe prmeters influence the ttenution in typicl polyvinyl chloride (PVC) nd high-density polyethylene (HDPE) pressure ter pipes. This reserch conducts sensitivity nlysis on the frequency-dependent ve ttenution in plstic pipes using the multi-element Kevin-Voigt (K-V) model. To highlight the effect of pipe ll viscoelsticity, the effect of friction is neglected, nd the expression of the frequencydependent ttenution fctor is derived. It is found tht, HDPE pipes generlly provide higher ttenution thn PVC pipes due to the loer elstic modulus of the HDPE mteril. For typicl PVC nd HDPE pressure ter pipes, the ttenution of lo frequency ves (<5 Hz) is moderte, hile the rtes of ttenution re similr for high frequency ves (> Hz). The ptterns of ttenution for pipes of different sizes but in the sme clss (pressure rting) re lmost the sme, since the rtios of dimeter to ll thicness re similr cross given clss. Keyords: Frequency-dependent ttenution, Plstic pipe, Wter hmmer Introduction Plstic pipelines, such s polyvinyl chloride (PVC) nd high-density polyethylene (HDPE) pipes, hve been incresingly used in ter distribution systems (WDSs). The hydrulic behvior of plstic pipes under stedy stte is the sme s conventionl metllic pipes (i.e. frictionl loss follos the sme principles); hoever, the hydrulic behvior of plstic pipes under trnsient events is different from nd more complex thn tht of metllic pipes due to the pipe ll viscoelsticity. Hydrulic trnsient nlysis in plstic pipes is gining incresing ttention, nd reserch hs been minly focused on trnsient modelling [, ], le detection [3-5], blocge nlysis nd detection [6], fluid structure interction [7], nd viscoelstic creep function clibrtion [8-]. Some studies ere on the use of plstic pipe segments to suppress pressure surges in systems minly comprised of metllic pipes [-3]. The plstic mteril is much loer in strength hich results in loer ve speed nd loer impednce, nd the viscoelsticity introduces frequency dependent effects on ve speed nd ttenution [4]. Hoever, there is lc of studies on ho the pressure ve ttenution vries ith frequency nd ho different pipe prmeters influence the ttenution in

2 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 typicl PVC nd HDPE pressure ter pipes. This pper reports numericl study on the frequency-dependent ve ttenution cused by the pipe ll viscoelsticity in typicl plstic ter pipes. The governing equtions on ve ttenution hve been derived in the frequency domin. The effect of friction is neglected becuse it is the sme in metllic pipes nd hs been extensively studied. A DN5 PVC nd DN6 HDPE pipe re considered since they re commonly used in WDSs. Sensitivity of the ve ttenution to the ey influencers is studied by vrying one dependent prmeter t time. Implictions on field ppliction for surge suppression re discussed. The results provide better understnding of the frequency-dependent ttenution of trnsient pressure ves in typicl plstic ter pipes. Governing Equtions for Trnsient Anlysis in Pipelines This section revies the -D ter hmmer governing equtions for viscoelstic pipes. The effect of friction is neglected becuse the focus is on viscoelsticity nd short time scles of surge behvior (i.e. the first fe seconds fter surge event, here frictionl effects do not dominte). For viscoelstic pipelines, the momentum nd continuity equtions re given s [, ] Q H ga t x ga H Q r A t x t here g is grvittionl ccelertion, A is the cross-sectionl re of pipeline, Q is the flo rte, H is the piezometric hed, t is time, x is distnce long the pipeline, r is the retrded circumferentil strin, nd is the elstic ve speed defined by K / K E D T c here K is the bul modulus of elsticity of the fluid, is the density of the fluid, E is Young s modulus of the pipe ll mteril, D is the pipe internl dimeter, T is the ll thicness nd c is fctor depending on the restrint condition of the pipeline [5]. The stress-strin behvior of the viscoelstic pipe ll cn be simulted by generlized Kevin- Voigt (K-V) model [], hich provides phenomenologicl description of the mteril. The model includes one elstic element nd N number of viscoelstic elements connected in series. The elstic element is represented by single spring ith modulus of elsticity E (referred to s the elstic modulus in this pper). A viscoelstic element consists of dshpot ith viscosity nd spring ith modulus of elsticity E connected in prllel. Using the K-V model, the creep function (i.e. the function describing the time-dependent strin for given pplied stress) for viscoelstic mterils is described by N t/ ( ) ( ) J t J J e (4) here J equls / E, J equls / E nd it is the complince of the spring of the th K-V element, equls / E nd it is the retrdtion time of the dshpot of the th K-V element. () () (3)

3 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 The governing equtions cn be solved by the MOC in the time domin. Detils cn be found in the literture [, ]. The governing equtions cn lso be trnsformed to nd solved in the frequency domin using the trnsfer mtrix method, nd the generl form of the trnsfer mtrix of uniform pipe section is given s [5] q cosh( L) sinh( L) q Z h h Z sinh( L) cosh( L) n here n nd n+ represent the to boundry loctions t the donstrem nd upstrem ends of the pipe section, q nd h re the complex flo nd hed oscilltion in the frequency domin, nd L is the totl length of the pipe section. With the effect of friction neglected, the propgtion opertor nd the chrcteristic impednce Z re given by [] n (5) i T (6) Z (7) gat in hich is the ngulr frequency ( f here f is frequency in Hz), T = T ( i ) represents the frequency dependent term contributed by viscoelsticity, nd is given s T N cd J (8) T i 3 Wve Attenution due to Viscoelsticity in Plstic Pipes This section investigtes ho the pipe dimensions nd viscoelstic properties contribute to ve ttenution, nd evlutes hether the dmping cn be used for effective surge suppression. 3. Frequency-dependent ttenution nd ve speed Using the propgtion opertor t given frequency, sine ve of frequency propgting in semi-infinite uniform pipe is described s the rel prt of it x P ( x, t) Pe e (9) i t here Pe represents the ve t loction x =, nd x is the distnce of propgtion. Substituting Eq. (6) into Eq. (9), the result is P ( x, t) Pe i t T x () Using the concept of complex ve speed, sine ve in pipe cn be expressed in n lterntive formt s [6] x i t x e P ( x, t) Pe e () here is the ttenution fctor nd e is the equivlent ve speed, here both re frequencydependent rel vlues. Becuse Eq. () nd Eq. () re equivlent, nd e re derived s

4 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 here Im T () e (3) ReT Re nd Im re the rel nd imginry prts of the term in brcets, respectively. For ny given frequency, lrger vlue of represents lrger ttenution rte. Substituting Eqs. (3) nd (8) into Eq. (), the ttenution fctor is derived s N KcD / T J Im / / K E D T c i K / K / E D / T c Eq. (4) shos tht, in ddition to frequency, the ttenution fctor is relted to the elstic modulus E ), the rtio of internl dimeter nd ll thicness ( D T ), the viscoelstic complince ( J ), ( the constrint fctor ( c ), nd the retrdtion time ( ). 3. Cse studies on ttenution To benchmr plstic pipelines re considered HDPE pressure pipe ith mteril code of PE, nominl pressure of PN6, stndrd dimension rtio of SDR nd nominl dimeter of DN6; nd n unplsticized PVC (PVC-U) pressure pipe ith PN8 nd DN5. Detiled specifictions of the pipe properties re given in Tble. The dimeter nd ll thicness vlues re from Austrlin Stndrd AS/NZS 43:9 for PE pipes nd AS/AZS 477:6 for PVC pipes. The vlues of E, J, nd Poisson s rtio for the HDPE pipe re sourced from published results by Covs, et l. [], nd for the PVC pipe from Sores, et l. [7]. The constrint fctor c is clculted for thic-lled pipe ( D T < 5) ith restrint throughout [5]. The bul modulus / nd density of ter re ten s the vlues t degrees Celsius. The elstic ve speed is clculted using Eq. (3). Note tht PVC-M nd PVC-O pipes re more commonly used nodys thn PVC-U for ter supply. Hoever, clibrted viscoelstic complince of PVC-M or PVC-O pipes is not redily vilble. The PVC-U pipe studied in this reserch (referred to s PVC in the rest of the pper for brevity) represents n extreme cse of viscoelstic behvior in comprison to most types of PVC pipes, becuse PVC-M nd PVC-O mterils re non to be more rigid, therefore expected to hve less of viscoelstic response. The vrition of the ttenution fctor over rnge of prcticl frequency vlues for the to benchmr pipes re shon in Fig.. It cn be seen tht the ttenution fctor increses ith n increse in frequency, nd reches nerly constnt vlue t Hz nd bove for both cses. The results in Fig. sho tht, ttenution of lo frequency ves (<5 Hz) is limited even fter m of propgtion. The ttenution rte increses ith frequency nd is similr for ves ith frequencies higher thn Hz for either cse. / (4)

5 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 Tble Specifictions of the benchmr HDPE nd PVC pipelines Specifiction DN6 HDPE pipe DN5 PVC-U pipe Internl dimeter D (mm) Wll thicness T (mm) Elstic modulus E (GP) Complince prmeter J (P-).44E-.5E- Complince prmeter J (P-).37E- N/A Complince prmeter J 3 (P-).45E- N/A Retrdtion time (m).5.5 Retrdtion time (m).5 N/A Retrdtion time 3 (m).5 N/A Poisson s rtio ( ).46.4 Constrint fctor c ( ).5.3 Bul modulus of ter K (GP).. Density of ter (g/m3) Elstic ve speed (m/s) x -3 Attenution fctor (m - ) 4 3 HDPE PVC Reltive mgnitude HDPE PVC Frequency (Hz) Frequency (Hz) Fig. Vrition of the ttenution fctor ith frequency for the benchmr HDPE nd PVC pipes. 3.3 Sensitivity nlysis of the ttenution behvior Fig. Reltive mgnitude of ves of different frequencies fter propgtion distnce of m in the benchmr HDPE nd PVC pipes. The folloing sensitivity nlysis hs been conducted by vrying one prmeter t time in Eq. (4), hile eeping other prmeters the sme s for the benchmr PVC pipe. The vrition of the constrint fctor is not considered. Fig. 3 (), (b) nd (c) sho the vrition of the ttenution fctor for vrying E, D/ T nd J, respectively. The rnges of E, D/ T nd J considered re.5 to 5 GP, 5 to 3, nd - to 5 - P -, respectively. These rnges cover the possible vlues for most stndrd PVC nd PE ter pipes.

6 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 () (b) (c) Fig. 3 Vrition of the ttenution fctor ith vritions of: () E, (b) D/ T nd (c) J. Figure 3 shos tht, for ny specific frequency considered in the rnge, the ttenution fctor behves pproximtely linerly proportionl to the elstic modulus, the rtio of internl dimeter to ll thicness, nd the viscoelstic complince. The rte of the chnge in the ttenution fctor increses ith n increse in frequency. Tht is, for lo frequencies, the ttenution fctor is smll (on the order of -4 ) nd nerly constnt for chnges in these prmeters, heres t 3 Hz, the ttenution fctor chnges from to.49-3, to.98-3, nd to.66 - over the rnge of E, D/ T nd J respectively. 4 Discussion on Surge Suppression using Viscoelstic Attenution Common trnsient sources in customer premises include solenoid vlves, bll flot vlves nd pumps. Although the opertion of vlves nd pumps typiclly induces step trnsient ves t its source, the user s pipe netor modifies the ves nd sometimes outputs shrp pulses to the ter min. Fig. 4 shos n exmple of the trnsient ves generted by customer in the Centrl Business District (CBD) of Adelide, Austrli. The pressure trce s collected in the ter min in front of building. Positive nd negtive pulse pressure ves ith mplitude of bout 9 m nd durtion bout s ere continuously generted. For stndrd PVC nd HDPE ter pipelines, the vlues of E, properties (e.g. PE pipe should hve similr E nd J re dictted by the mteril J ), nd the vlue of D/ T is relted to the pressure rting (typiclly PN6, or higher, re used for ter distribution systems), so the rnge of vrition for these prmeters is limited. The ttenution chrcteristics of stndrd PVC nd HDPE ter pipes re reflected in the benchmr cse studies nd the sensitivity nlysis. According to Figs. to 3, the ttenution is limited for lo frequency ves (<5 Hz) despite the chnges in the ey prmeters. Hoever, in rel ter netors, the energy of most pressure oscilltions induced by hydrulic devices (e.g. customer vlve opertions, or pump opertions) re concentrted in lo frequencies, becuse the opertions typiclly te hundreds of milliseconds to minutes. Fig. 5 shos the normlized mplitude spectr of pulse signls ith durtions of.,.4, nd s, confirming tht the mjority of the energy is in the frequency rnge of less thn 5 Hz. Overll, this study indictes tht it is not sufficient or cost-effective to use the viscoelstic ttenution lone for surge suppression in ter netors. Hoever, it should lso be noted tht due to the lo impednce of plstic pipes, the sme flo perturbtion ill induce smller pressure

7 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 oscilltion in plstic section hen compred ith metllic section of the sme size, nd the pproprite use of the impednce difference cn help ith surge suppression [3]. Amplitude spectrum s.4 s s 5 5 Frequency (Hz) Fig. 4 Customer-induced trnsient pressure ves recorded in Adelide CBD. Fig. 5 Amplitude spectr of unit pulse signls ith durtions of.,.4 nd s. 5 Conclusions A numericl study on the frequency-dependent ttenution of hydrulic trnsient ves in plstic ter pipelines hs been conducted. The governing eqution for viscoelsticity-induced ve ttenution hs been derived in the frequency domin, nd it demonstrtes tht the ttenution is relted to the elstic modulus ( E ), the rtio of internl dimeter nd ll thicness ( D/ T ), the viscoelstic complince ( J ), the retrdtion time ( ), nd the pipe constrint fctor ( c ). Wve ttenution hs been simulted for to commonly used plstic ter pipes (DN5 PVC nd DN6 HDPE). The results sho tht the ttenution of lo frequency ves (<5 Hz) is limited. While the ttenution rte increses ith frequency, the rtes re similr for ves ith frequencies higher thn Hz. The ptterns of ttenution for pipes of difference sizes but of the sme clss (pressure rting) re similr, since the rtios of dimeter to ll thicness re similr cross given clss. Bsed on the PVC pipe cse, sensitivity nlysis hs been conducted to investigte the vrition of the ttenution fctor for vrying E, D/ T nd J. The results sho tht the ttenution fctor is pproximtely linerly proportionl to ech of the three prmeters, ith the rte of the chnge increses ith n increse in frequency. Hoever, for lo frequencies (<5 Hz), the ttenution fctor is smll nd nerly constnt for chnges in these prmeters. In rel ter netors, the energy of most pressure oscilltions induced by hydrulic devices (e.g. customer vlve opertions, or pump opertions) re concentrted t lo frequencies. As result, it is concluded tht the ve ttenution effect in plstic pipes lone is not cost-effective for surge suppression. Hoever, the combined use of plstic nd metllic pipe sections cn be helpful. 6 Acnoledgements The reserch presented in this pper hs been supported by the Austrlin Reserch Council (DP7375) nd by the South Austrlin Wter Corportion (UA68).

8 st Interntionl WDSA / CCWI 8 Joint Conference, Kingston, Ontrio, Cnd July 3-5, 8 7 References [] D. Covs, I. Stoinov, J. Mno, H. Rmos, N. Grhm, nd C. Msimovic, "The dynmic effect of pipe-ll viscoelsticity in hydrulic trnsients. Prt II - Model development, clibrtion nd verifiction," J. Hydrulic Res., vol. 43, pp. 56-7, 5. [] H. Rmos, S. Tmminen, nd D. Covs, "Wter supply system performnce for different pipe mterils prt II: sensitivity nlysis to pressure vrition," Wter Resour. Mnge., vol. 3, pp , 9. [3] D. Covs nd H. Rmos, "Cse studies of le detection nd loction in ter pipe systems by inverse trnsient nlysis," J. Wter Resour. Pln. Mnge., vol. 36, pp ,. [4] M. Ferrnte, B. Brunone, S. Meniconi, B. W. Krney, nd C. Mssri, "Le size, detectbility nd test conditions in pressurized pipe systems," Wter Resour. Mnge., vol. 8, pp , 4. [5] C. Cpponi, M. Ferrnte, A. C. Zecchin, nd J. Gong, "Le detection in brnched system by inverse trnsient nlysis ith the dmittnce mtrix method," Wter Resour. Mnge., vol. 3, pp , 7. [6] S. Meniconi, B. Brunone, M. Ferrnte, nd C. Mssri, "Smll mplitude shrp pressure ves to dignose pipe systems," Wter Resour. Mnge., vol. 5, pp ,. [7] A. Kermt, A. S. Tijsseling, Q. Hou, nd A. Ahmdi, "Fluid-structure interction ith pipe-ll viscoelsticity during ter hmmer," J. Fluids Struct., vol. 8, pp ,. [8] A. Kermt nd A. Hghighi, "Strightforrd trnsient-bsed pproch for the creep function determintion in viscoelstic pipes," J. Hydrulic Eng., vol. 4, p. 4458, 4. [9] G. Pezzing, "Evlution of time evolution of mechnicl prmeters of polymeric pipes by unstedy flo runs," J. Hydrulic Eng., vol. 4, p. 4457, 4. [] J. Gong, A. C. Zecchin, M. F. Lmbert, nd A. R. Simpson, "Determintion of the creep function of viscoelstic pipelines using system resonnt frequencies ith hydrulic trnsient nlysis," J. Hydrulic Eng., vol. 4, p. 463, 6. [] A. M. Al-Khomiri, "Plstic ter hmmer dmper," Aust. J. Civ. Eng., vol. 8, pp. 73-8,. [] G. Pezzing nd P. Scndur, "Unstedy flo in instlltions ith polymeric dditionl pipe," J. Hydrulic Eng., vol., pp. 8-8, 995. [3] J. Gong, M. L. Stephens, M. F. Lmbert, A. C. Zecchin, nd A. R. Simpson, "Pressure surge suppression using metllic-plstic-metllic pipe configurtion," J. Hydrulic Eng., vol. 44, p. 485, 8. [4] D. Covs, I. Stoinov, J. F. Mno, H. Rmos, N. Grhm, nd C. Msimovic, "The dynmic effect of pipe-ll viscoelsticity in hydrulic trnsients. Prt I - Experimentl nlysis nd creep chrcteriztion," J. Hydrulic Res., vol. 4, pp , 4. [5] E. B. Wylie nd V. L. Streeter, Fluid Trnsients in Systems. Engleood Cliffs, Ne Jersey, USA: Prentice Hll Inc., 993. [6] L. Suo nd E. B. Wylie, "Complex vespeed nd hydrulic trnsients in viscoelstic pipes," J. Fluids Eng., vol., pp , 99. [7] A. K. Sores, D. I. C. Covs, nd L. F. R. Reis, "Anlysis of PVC pipe-ll viscoelsticity during ter hmmer," J. Hydrulic Eng., vol. 34, pp , 8.