NUMERICAL SIMULATION OF PIPING VIBRATIONS USING AN UPDATED FE MODEL

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1 NUMERICAL SIMULATION OF PIPING VIBRATIONS USING AN UPDATED FE MODEL Heikki Haapaniemi 1), Aja Saaenheimo 1), Paul Smeekes 2) and Heli Talja 1) 1) VTT Manufactuing Technology, P O Box 1704, FIN VTT, Finland 2) Teollisuuden Voima Oy, Olkiluoto, Finland ABSTRACT Taditional design and condition monitoing of piping is mainly based on postulated events and on the application of allowable vibation levels. This appoach gives only indiect infomation on the loading at the citical locations and geneally leads to ove consevative assessments. It is essential that developing piping failues can be anticipated and/o monitoed and that any epai wok is caefully planned ahead and caied out duing egula outages. In an ongoing poject a pactical method is being developed to monito the condition and emaining lifetime of pocess piping. This method combines both measuements - using a minimum numbe of fixed continuous measuements - and an adequate computational model. Relatively simple piping in a NPP was chosen as the fist pilot case. Measued modal shapes of the stuctue wee excited using an impact hamme and a shake. Results fom expeimental modal analysis wee used in finite element (FE) model validation and updating pocess caied out using the FEMtools [1] code. This pape outlines the poject and descibes the main expeiences and esults of the model updating wok. NOMENCLATURE EMA Expeimental modal analysis { ψ a } Analytical mode shape vecto { ψ e } Measued mode shape vecto T Supescipt: Tanspose of vecto H ij Response function, which expesses the esponse at DOF i if excitation is at DOF j ω Fequency Subscipt: mode numbe N Numbe of modes ψ i Eigenvecto value at DOF i coesponding to the th mode ψ j Eigenvecto value at DOF j coesponding to the th mode ω th natual fequency Modal damping atio fo the th mode ζ 1 INTRODUCTION Condition monitoing and damage detection by means of monitoing modal paametes is based on the pinciple, that changes in modes ae sensitive indicatos of changes in the physical integity of any mechanical stuctue [2]. Vibation testing offes an oppotunity fo diffeent inspection techniques that may be able to detect stuctual failues and local stuctual damages, which can e.g. effect the stess fields of the stuctue. Nomally condition monitoing and damage detection, when done by monitoing modal paametes such as eigenfequencies, mode shapes and damping atio, has been based on compaison of esults fom expeimental modal analysis of undamaged stuctue and damaged stuctue. These measuements can be made eithe with atificial excitation, e.g. with shakes o impact impulses o with ambient excitation in opeational conditions [2-4]. Instead of using the modal popeties of an undamaged stuctue as a efeence baseline fo compaison, modal popeties of an updated FE model can also be used as a baseline. A veified, validated and usable mathematical model is the best knowledge base fo the system unde investigation [5]. In this wok the aim was to ceate such an updated FE model which could late be used as a efeence baseline and also to lean about appopiate modelling techniques and identify the difficulties concening modelling of a pipeline and its components. In the FE model updating phase a somewhat lage amount of measuements will pobably be necessay than is possible in nomal condition monitoing. Pobably seveal iteation cycles ae needed to come up to an adequately woking FE model. This pocess is descibed in Fig. 1. DESIGN FEM ANALYSIS - modelling - computation - epoting - definition of measuement locations FEM ANALYSIS - model updating using measued data - computation including fatigue assessment - epoting - definition of new measuement points CONSTRUCTION seveal iteation steps may be necessay MEASUREMENTS in cold state MEASUREMENTS - fatigue - cack gowth Figue 1. The appoach to come to an adequate model to monito the vibation behaviou of a piping system, stating fom the piping design phase [6]. DESIGN PHASE CONDITION MONITORING 193

2 2 GENERAL DESCRIPTION OF THE STRUCTURE The fist pilot system, pat of the auxiliay feed wate system piping at the Olkiluoto NPP (OL1) was chosen based upon the following equiements: Reasonable in size, Cold in opeation condition, no tempeatue effects no insulation, Easy to access and measue in both opeational and standstill condition (modal analysis), A clealy defined excitation (ecipocating pump). Duing nomal opeation the auxiliay feed wate system is not in use except fo the peiodically pefomed tests lasting fo five minutes each month. The expected - and measued - vibation amplitudes wee so small that no integity poblems ae anticipated due to this vibation. The pat of the piping system being unde consideation is located on the outside of the containment between the containment penetation and the auxiliay feed wate system pumps. The pumps ae 3 piston plunge pumps unning at a fequency of 4 Hz. The length of the modelled pat of the pipeline is about 56 metes including two majo banches attached to it. The length of the measued pat of the pipeline is about 44 metes. Thee ae also 17 suppots and thee diffeent actuatos (valves o estictos) in the measued pat of the pipeline. Suppot locations and geneal desciption of the pipeline can be seen in Fig. 2. Thee wee basically fou diffeent types of piping suppots, which wee modified depending on thei position and/o pupose. The pupose of suppots was eithe to act as a suppot in all loading conditions o act as a suppot in case of a piping o neighbouing suppot failue. In latte case, the design dawings usually indicated a gap between pipe and suppot stuctue. Duing walk-down inspections it was found out, that visible gaps seldom existed between pipe and suppot stuctue. 3 MEASUREMENTS Modal testing was done using both impact hamme [7] and shake excitation [8], based upon 29 measuement locations and 76 measued DOFs. These measuement locations ae shown in Fig. 3 along with the FE model. Modal testing was pefomed to expeimentally chaacteise the dynamic behaviou of the piping. The mode shapes and associated fequencies wee detemined both duing opeation and in standstill condition. Thus, both opeational and natual mode shapes wee obtained. ' # 4 $ # 4 #, " J $ # Figue 3. Measuement points (left) and the FE model (ight). 3.1 Natual mode shapes ; : % = I B Figue 2. FE model and suppot locations. This pipeline is made fom DN 100 stainless steel pipe with nominal diamete of mm and wall thickness of 6.02 mm. The design pessue, which is effective duing the use of the pump, is 90 ba and the design tempeatue is 100 C. Howeve, the piping is filled with wate that does not exceed the oom tempeatue duing any anticipated tansient. This means that the piping is not insulated and that tempeatue is not an issue. The natual mode shapes wee excited, in case of impact test, with hamme impacts causing shot time impulses with moe o less unifom enegy input ove the significant fequency band [9]. The mode shapes themselves wee then ecoded but the data immediately afte the impulses was neglected. The data, afte the diect influence of the excitation has become negligible, wee used to detemine the modes and associated fequencies. In case of shake excitation a andom noise signal was used to contol the shake output. shapes wee calculated with the Rational-Faction-Polynomial-cuve fitting method [8]. All measued FRFs wee used togethe duing this so-called global cuve fitting. Most significant (i.e. lowest) eigenfequencies fom both impact and shake measuements ae listed in Table1, excluding the lowest measued eigenfeguency (19.0 Hz) fom impact tests due to measuement eos connected to that mode shape. 194

3 Table 1. The most significant eigenfequencies fom impact and shake measuements. Impact (Hz) Shake (Hz) Impact (Hz) Shake (Hz) The mode shapes with hamme impact measuements and with the shake excitations wee quite close to each othe and it seemed that in this case esults wee not dependent of the type of excitation (impact o shake) used. It should also be noted that some of the deviation in the esults could be explained by the fact that the wate height in the piping was not necessaily the same duing these tests. 4 FE MODELS The FE models wee oiginally geneated with FPIPE [10] pogam and the models wee tanslated into ABAQUS [11], which was then used as a solve. These analyses wee conducted as a MSc. thesis [12]. The fist FE model, efeed hee as Case 1, was modelled accoding to design dawings. This would also be the nomal appoach in the design phase and this model would also be used in fist petest analysis when the fist measuements ae planned. Of couse, it was clea fom the beginning that thee ae always diffeences between the actual stuctue and the ideal design dawing. Popeties of the FE model wee vaied in ode to find out how diffeent modifications affect the behavio of the model. Because it was known on befoehand that the citical aspect was to find suitable stiffness values fo the piping suppots, mainly thei sping constants wee modified. The stiffness values fo the suppots wee estimated by using vey simple FE models loaded by unit foces and moments. Also, moe elevant infomation concening the actual piping geomety was obtained by diect measuement and so-called walk down inspections made to the piping. This infomation was then applied in futhe analysis based on updated input data (Case 2 and Case 3). The FE model used in the ABAQUS [11] analyses, main dimensions of the pipe line and suppot locations ae shown in Fig. 2. The model consists of 180 elbow and pipe elements, 3 beam elements and 123 sping elements. Both pipe bends and adjacent staight segments ae modeled with ELBOW31 elements and the bends wee modeled with 2 elements. Thee ae 5 integation points though the wall thickness and 20 integation points aound the cicumfeence of the section; six ovalization modes ae used. The middle segments of long, staight pipe uns ae modeled with PIPE31 type elements. To join the pipe segments modeled with diffeent element types, waping of the ELBOW31 elements is pohibited at the nodes connecting the ELBOW31 elements to the PIPE31 elements. 1-dimensional sping elements ae used in the appopiate diections to model the suppots. Six SPRING1 elements with diffeent stiffness values (one fo each degee of feedom) ae needed to descibe one pipe suppot. One B31 element was needed to model an extension attached to the pipeline and two B31 elements wee needed to model beam connecting two diffeent pipe segments. The locations and stiffness values of the suppots as well as the pipe wall thickness values wee modified accoding to inspection and measuements in Cases 2 and 3. In Cases 1 and 2 the pipe is assumed to be completely filled with wate wheeas in Case 3 the pipe is assumed to be filled only up to m (see Fig. 2). This is done because, if the system has a height of moe than 10 metes and the isolation valves at the top of the piping ae pefectly tight, one may assume that thee will be a vacuum in the uppe pat of the piping. The mateial popeties used in Cases 1-3 ae listed in Table Table 2. Mateial popeties. Popety Case 1-3 Young's modulus 206 GPa Steel density 7850 kg/m 3 Wate density 1000 kg/m 3 Poisson's atio 0.3 Tempeatue 20 C Geneal desciptions of Cases 1-3 ae listed in Table Table 3. Analysed basic cases. Popety Case 1 Case 2 Case 3 Suppots design measued measued documents Suppots simple FE models simple FE 1 models simple FE 1 models Gaps low stiffness updated updated 1 sping 2 stiff- sping 2 stiff- ness ness Wall thickness nominal measued measued Wate level full full level +15 m 1) Gaps in suppots accoding to design documents ae descibed using sping elements with low stiffness value. 2) Obseved gaps in suppots ae descibed using sping elements with low stiffness value. 5 CORRELATION ANALYSIS BETWEEN ORIGINAL FE MODELS AND EXPERIMENTAL DATA In ode to validate the FE models, thei coelation against expeimental esults needs to be evaluated and thei quality must be eviewed numeically. Also, if esults of coelation analysis ae not satisfactoy models must be modified and updated. Pio to any updating coect mode pais must be identified, which can be a vey poblematic task. The coelation was evaluated by compaing esults fom an impact hamme test [7] against the esults fom FE analysis. These analyses wee conducted as a pat of MSc. thesis [12]. As a fist task the coelation between expeimental and numeical esults was evaluated in tems of modal assuance citeion () values and matices. In the beginning it was decided to filte tems with a value less than 15 % of maximum displacement fom expeimental eigenvectos and also to use 5 % double fequency toleance. Filteing focuses the coelation analysis to aeas whee majo modal displacements take place and double fequency toleance enables combining fequencies within 195

4 this toleance limit. Coelation evaluations wee mainly pefomed with the FEMtools [1] code. The following equation is used fo evaluating values: ( ψ, ψ ) T ({ ψa} { ψe} ) { } { } a e = (1) T T ( ψa ψa )({ ψe} { ψe} ) In geneal highe value indicates bette coelation between modes, although it is difficult to povide pecise values that the should take in ode to guaantee good esults. Ewins [13] has suggested following intepetation fo the values value less than 5 % indicates uncoelated mode shapes and value highe than 90 % coelated mode shapes. Anothe estimate povided by Ingemansson Education [14] in thei couse mateial is that the value below 50 % indicates poo coelation and values highe o equal as 70 % good coelation. This latte suggestion may also be easonable in case of piping systems, whee it may be difficult to define the actual measuement locations and diections accuately and whee distances between measuement locations may be lage. Hee the mode pai selection is based on visual inspection of mode shapes, values and fequency eos. Usually the mode paiing is based on maximising values and minimising fequency eos but in some cases this is not a feasible appoach because it may cause mode paiing poblems as descibed in efeence [15]. Note, that expeimental mode 1 is left out of all compaisons due to a measuement eo in it's mode shape. pais fo Cases 1-3 ae pesented in Tables 4-6. Table 4. pais fo Case 1.The aveage fequency eo and value ae pesented in the last line. Case 1 EMA Aveage Fom Table 4 it can be seen that even if thee ae some acceptable mode pais like pai 2 and 8 this model is not acceptable and it needs futhe efinement. This was not a supise because the model used in Case 1 was based solely on design dawings, which wee not always as accuate as hoped. Duing visual inspection of the pipeline and measuement of the suppot locations it was found out that the actual suppot locations diffeed sometimes significantly fom locations suggested by design dawings. Also some of the suppots have been alteed fom oiginal design dawing. So it is extemely impotant, that design dawings used duing the modelling phase ae coect and up to date. Fom the esults pesented in Tables 4-6 it is easy to conclude that both Case 2 and Case 3 have an impoved situation ove the oiginal Case 1. Geneally, esults ae bette although in some mode pais significant tade off has occued between fequency eos and values. Especially the lagest fequency eos ae educed and the lowest values impoved while the highest values have slightly deteioated due to the tade off mentioned ealie. In view of these esults it is still somewhat unclea which one of the models, Case 2 o Case 3, would eventually povide the best possible base fo futhe model updating. Also, it is impossible to detemine with any cetainty the actual wate level in the piping fom these esults. The selection to use Case 3 in model updating is based mainly on two factos: 1) knowledge that it is not likely that the piping is completely filled with wate and 2) on engineeing judgement based on maginally bette coelation povided by Case 3. Table 5. pais fo Case 2. Case 2 EMA Aveage Table 6. pais fo Case 3. Case 3 EMA Aveage

5 6 RESULTS FROM MODEL UPDATING The Case 3 was selected as base model fo the updating pocess and the main focus was concentated to piping suppots which wee known as the most uncetain and ambiguous pat of the pipeline. The updated vesion of Case 3 is efeed as. All tanslational suppot sping constants wee selected to be alteable paametes and expeimental fequencies fom 2 to 9 as well as coesponding modes wee selected to act as esponses. Late also the Young's modulus was also chosen as a paamete to be modified in ode to impove the updating esults. So-called automated model updating was in this case impossible due to incoect stiffness matix, caused by use of the SPRING elements. This caused some seious difficulties to the updating pocedue, which could be descibed as a loop, whee cetain steps wee pefomed as follows: (i) Impoting of the ABAQUS [11] esults into the FEMtools [1]. (ii) Pefoming coelation analysis and mode paiing in the FEMtools [1]. (iii) Sensitivity and updating analysis pefomed by FEMtools [1]. (iv) Re-editing of the oiginal ABAQUS [11] input with the modifications suggested in pevious step. (v) Re-un of updated input in the ABAQUS [11]. Due to the incoect stiffness matix this loop was equied to un seveal times and in ode to avoid instability duing the updating analysis the FEMtools [1] was allowed to make only small changes to the updating paametes. Main changes caused by the updating analysis wee in the stiffness of the tanslational sping suppots, which wee inceased in some cases seveal hunded pecent. Also the Young's modulus was inceased in the lowe (below level ) pat of the stuctue fom 206 GPa to 210 GPa. The mode paiing table of updated model and expeimental esults based on 15 % filteing and 5 % double fequency toleance can be seen Table 7. This table indicates impovement in the fequency coelation in geneal and also slight impovement in the lowest values (mode pais 2 and 3) ove the situation with Case 3 (see Table 6). If mode pais in Tables 6 and 7 ae compaed it can noticed that thee has been some tade-off between fequency eo and values in pais with high values in Case 3 (Table 6). Table 7. pais fo. EMA Aveage Intoducing damping In ode to evaluate possible effects caused by damping following pocedue was pefomed: (i) Analytical FRFs wee synthesised fom natual fequencies and coesponding mode shapes obtained fom FE model used in with the FEMtools [1] code. Hee modal damping model with 1.5 % modal damping atio was used and the FRF synthesis was pefomed accoding to following equation: N ψ 2 i ψ j Hij ( ω) = ω. (2) 2 2 = 1ω ω + 2iωωζ (ii) Resulting FRFs wee impoted into I-DEAS Test [16] softwae was used to pefom modal analysis to the analytical FRFs obtained fom pevious step. This new model with damping is efeed as Case 5. (iii) Resulting natual fequencies and coesponding mode shapes wee impoted in to the FEMtools [1] fo new coelation analysis. The FRF synthesis was made by using thee excitation coodinates (all thee diections x, y and z wee used) and by using all nodes of the FE modes as esponse co-odinates. Modal analysis was pefomed with I-DEAS Test [16] by using so-called polyefeence technique fo extaction of the modal paametes (natual fequencies, damping and esidue) and coesponding mode shapes wee extacted with the fequency polyefeence technique. Both techniques can be found summaised in I-DEAS Test [16]: Theoy manual. The esulting mode pais fo the new model, efeed as Case 5, is pesented in Table 8. Also hee 15 % filteing was used and 1.85 % was used as a double fequency toleance fo mode pais 1-5 and 4 % fo mode pais

6 Table 8. pais fo Case 5. Case 5 EMA Aveage % avg. pai Case 1 Case 2 Case 3 Case 5 Figue 5. Fequency eos fo mode pais in Cases 1-5 and aveage eos in pecentages. The fequency eo is pesented in Fig. 4 in tems of a 45 line whee in the ideal situation all makes indicating mode pais should lie on this line. These esults indicate bette fequency coelation fo the updated Cases 4 and 5 than fo the oiginal Cases 1, 2 and 3. The poduces best esults in mode pais 2, 5, 6 and 8 along with Case 5. In mode pai 1 thee is vey little diffeence between diffeent cases. In mode pais 3 and 4 the best esults is achieved with Cases 2, 4 and 5. Cases 3 and 4 gives the best esults fo mode pai 4 and fo mode pai 7 the best esult is achieved with Case Case 1 Case 2 Case 3 Case 5 Both the actual fequency eos fo all mode pais in Cases 1-5 and the aveage fequency eos fo individual cases ae pesented in Fig. 5. Also in Fig. 6 all the values fo mode pais in Cases 1-5 as well as the aveage values fo individual cases ae shown. FEA (Hz) EMA (Hz) Case 1 Case 2 Case 3 45 line Case 5 Figue line compaison fo eigenfequencies in Cases avg. pai Figue 6. values fo mode pais fom Cases 1-5 and aveage values. Figues 5 and 6 as well as Table 7 confim the impovement of the FEA esults in ove the oiginal Cases 1-3 especially in view of the fequency eo. In case of values the situation is not so clea due to the tadeoff mentioned ealie. In geneal updating of the FE model impoved the values in mode pais with low oiginal values and in mode pais with high oiginal values some loss of coelation did occu. When the damping was intoduced into the FE model in Case 5 also the values impoved as can be seen fom Figues 5 and 6 and Table 8. On the othe hand this caused some gowth in the fequency eos, especially in mode pai 3. In geneal the aveage fequency eo did not deteioate significantly if compaed with situation in. 7 CONCLUSIONS It is faily clea that the discepancy, in case of piping with seveal suppots, between FE models and eal man made stuctues comes mainly fom the uncetainties of the pipe suppots. So fom this point of view they ae also the most suitable pats fo modifications fo updating a FE model. In ode to enhance the possibilities of successful model updating some measuements should also be made fom the suppots and coesponding locations of the pipe. These measuements may eveal impotant infomation about the dynamic behaviou of the suppots and about the inteactions between the pipe and it's suppots. Special attention should be given to locating the actual measuement points accuately fom the eal stuctue. 198

7 Also it is impotant to ensue, as caefully as possible, that the actual measuement diections ae coect. If the planned measuement diection is X then it is impotant that the measuement sensos ae set in this diection. Both of these seemingly simple tasks can be extemely difficult in case of complex piping systems and some discepancies and eos will always exist, which may cause seious and unexpected poblems in coelation analysis and in late model updating. Duing the FE modelling phase of a pipeline enough emphasis should be given to the bounday conditions, like suppots o pipe-ends, and it should be emembeed that a pipeline seldom ends with eally igid bounday conditions. When the FE model (geomety) ends, the effect of masses beyond this end point should also be taken into consideation if the pipeline is not igidly anchoed in this point. Intoduction of damping into the FE model had some impoving effect to the modal coelation but these effect should be studied moe caefully and with some othe damping model like stuctual damping model befoe any conclusions can be dawn. Duing the updating pocess it must be emembeed that, although the updating is usually based on modifying some physically ealisable popeties such as Young's modulus, coss-section aea, density, etc., thee is no one-to-one coespondence between expeimental and analytical models. In othe wods, the actual modelling eos ae in fact compensated by adjusting design paametes selected fo updating, athe than actually identifying and eliminating these modelling eos. ACKNOWLEDGEMENTS This epot is pat of the poject Plant life management (XVO), which is co-odinated by VTT Manufactuing Technology. The wok has been funded by the National Technology Agency (TEKES), Teollisuuden Voima Oy, FEMdata Oy, Fotum Engineeing, Neste Engineeing and VTT Manufactuing Technology. Thei funding is gatefully acknowledged. Measuements and Numeical Simulation, Poc. of Baltica Confeence 2001, 12 p., [7] Rostedt, J. Desciption of the Dynamic Popeties of Pipeline 327 with Help of Vibation Animation, Kankaanpää: J. Rostedt Oy. Repot RR Doc, 5 p. + App. 21 p. (in Finnish), [8] Nuutila, O. & Rostedt, J. OL1, - Modal Analysis of a Pat of System 327 Using Shake Excitation, Kankaanpää: J. Rostedt Oy. Repot Doc, 5 p. + App., [9] Smeekes, P., Talja, H., Saaenheimo, A. & Haapaniemi, H. Numeical Simulation of Piping Using Modal Coelation, Tansactions of the 16th Intenational Confeence on Stuctual Mechanics in Reacto Technology, SMiRT 16, Washington DC, USA, [10] FPIPE Use's Manual, FEMdata oy, Espoo [11] ABAQUS Theoy Manual, Vesion 5.8. (1998). Hibbit, Kalsson & Soensen Inc. RI. [12] Haapaniemi, H. A Case Study fo Validating and Updating the Dynamic FE l of a Pipeline. MSc. Thesis, 101 p., Helsinki Univesity of Technology, [13] Ewins, D. J. Modal Testing: Theoy and Pactice, Reseach Studies Pess Ltd. Letchwoth, Hets, U.K, ISBN X, 269 p [14] Ingemansson Education. LMS Gateway, Coelation and Updating Couse Book, Held at Gothenbug [15] Mölle, P. W. & Fibeg, O. An Appoach to the ing Poblem, Mechanical Systems and Signal Pocessing, Vol. 12, No. 4, pp , [16] I-DEAS Test: Modal Analysis Use's Guide. I-DEAS Maste Seies 7, Stuctual Dynamics Reseach Copoation, USA, REFERENCES [1] FEMtools Use's Guide. Vesion Dynamic Design Solutions N.V. (DDS). Leuven, Belgium, June [2] Mannan, M. A., McHague, P. & Richadson, M. H. Continuous Monitoing of Modal Paametes to Quantify Stuctual Damage, Poc. of I XII, 6 p, [3] Mattheis, A., Tobitz, M., Kussmaul, K., Kekhof, K., Bonn, R. & Bey, K. Diagnostics of Piping by Ambient Vibation Analysis, Nuclea Engineeing and Design, Vol. 198, pp , [4] Mevel, L., Hemans, L. & Van De Auweae, H. Application of a Subspace-based Fault Detection Method to Industial Stuctues, Mechanical Systems and Signal Pocessing, Vol. 13, No. 6, pp , [5] Natke, H. G. Poblems of l Updating Pocedues: A Pespective Resumption, Mechanical Systems and Signal Pocessing, Vol. 12, No. 1, pp , [6] Smeekes, P., Talja, H., Saaenheimo, A. & Haapaniemi, H. Piping Vibation Management Combining 199