Evaluation of the Remaining Lifetime of Steel Penstocks in ...

Evaluation of the Remaining Lifetime of Steel Penstocksin Hydropower PlantsA. Adamkowski, M. Lewandowski, S. LewandowskiAbstract: The paper describes the procedure for evaluation ofthe remaining lifetime of steel penstocks in hydroelectric powerplants using a model based on the theory of crack growth.Authors pay particular attention to several issues that have asubstantial impact on the fatigue strength evaluation of theanalyzed structures, such as stress distribution in the material ofpenstock coatings, variability of its amplitude and frequency orforecast of future operation of particular hydropower plant.Introduction.The material fatigue is a phenomenon (process) of extreme importance in terms ofreliability and safety of various types of engineering structures. This phenomenon isrecognized as one of the major causes of destruction of materials. Sometimes largesteel structures, such as steel penstocks of hydroelectric power plants, even ifdesigned properly as regards both elastic and plastic deformation, they can meetcatastrophic damage caused by a sudden rupture [1,2,3,5]. Responsible for that isthe material fatigue and this phenomenon determines penstocks remaining lifetime, aperiod of its safe operation. Assessment of the length of this period is crucial for boththe power plant and the objects and people living in its vicinity.The paper describes the procedure for evaluation of the remaining lifetime of steelpenstocks in hydroelectric power plants using a model based on the theory of crackgrowth (crack propagation) [1,3]. The authors used the experience gathered from anumber of research works connected with the analysis of fatigue life of penstocks inthe largest hydropower plants in Poland [12,13]. Special attention was paid to severalissues that have a substantial impact on the fatigue life evaluation of the analyzedstructures.Fatigue process taking place in the structure (shell) of penstocks is stronglyconditioned by the characteristics of the work of the hydropower plant and thevariability in loads on the pipeline connected with that. A wide range of servicesprovided to the electro-energy system (EES) translates directly into increasedvariability of loads relevant to the fatigue life of penstocks. This is closely related tothe frequency and quality of transient states which appear during hydropower plantoperation. The most important loads are those generated in the plants operatedduring peak demands, in particular, in pumped-storage power plants, whose primaryobjective is interventional work and very frequent start and stop or transitionsbetween different modes of operation.The analysis of cyclic loads impact on the remaining lifetime of penstocks may beuseful for long-term planning in the investment of their rehabilitation andreconstruction of penstocks as very important elements of hydraulic systems of theplant. The conclusions of this in-depth analysis can also be used to determine theoperating procedures and ways of using the power plant in the EES. This cancontribute to minimize the loads put on the penstock structure and thus to extend its

safe operation, or, in some cases, to allow power plants to conditionally continue itsoperating.Theoretical basis (fundamentals) of the crack growth model.Predicting the course of material fatigue is a complex issue and, moreover, it ispresenting the high uncertainty of calculation results. The rich literature concerningthe evaluation of fatigue life of materials, is full of many hypotheses, which are thebases of models used for describing the process of fatigue [1,2,3,4,5,8,9].Unfortunately, with the diversity of these hypotheses, large variations of the resultsobtained using the same input data is also characteristic. Hence, the proper selectionof the model to the analysed system exposed at variable loads is very important withrespect to the characteristics of the material and design of that system as well as tothe variability of the loads (amplitude, frequency).A model based on the theory of crack growth was chosen for evaluating the lifetimeof steel penstocks in hydropower plants. Solid theoretical foundations based on thephysics of the fatigue fracture of the material and common use of this model intechnical applications was a direct reason for this choice.Assumption that sudden fracture is caused by an increase of the microcracks existingin the material underlies the model used. These microcracks, exposed on someloads (stresses), increase until they become unstable what leads to a catastrophicrupture of the penstock. Basing on known criteria we can determine the criticalmagnitude of the load, which do not yet cause the sudden rupture of the material.However, for significant variability of the loads or presence of different materialimperfections (e.g. corrosion) the crack growth accompanying the fatigue processcan be caused even by stresses lower than the yield stress.Durability of almost every large welded structure (weldment) should be assessedbasing on the crack growth process. Such structures are always characterized by thepresence of cracks, which are not detected during the tests and inspections due totheir small size (microcracks). The condition for sudden fracture initiation has thefollowing, general form for various types of structures [1,3]:S a EG c(1)This condition says that the sudden fracture occurs in the material exposed to cyclicloads (stresses) with the amplitude of S, if existing cracks reach a critical value oftheir linear dimension a, or alternatively, if the material with cracks characterized bycertain value of a is exposed at loads causing stress amplitude S.Expression S ais often replaced by a quantity K called stress intensity factor,and Eq.(1) can be than formulated as follows:whereIcc K K IcK EG is a critical stress intensity factor (E stands for Young’s modulus,G – for a critical speed of energy release required to form a crack with the unitsurface, also called toughness). The phenomenon of sudden fracture occurs whenK K Ic . .

Stress increase, represented in Eq.1 by S, relates to fragments of the analyzedstructure characterized by a regular shape, with no significant geometricalimperfections responsible for the stress concentration. However it is obvious, thatthose components of the structure which are characterized by the highest stressconcentration have a critical impact on the durability of this structure. Therefore, theshape factor is introduced into Eq.1 (also called the stress concentration coefficient,or theoretical notch effect factor) k defined as k maxn , where n stands forthe nominal stress (in the absence of a notch, irregularities, imperfections, etc.) and max stands for the maximum stress.Beside the external load and the crack dimensions as well as the stressconcentration coefficient k , also geometry of the elements and the shape of crackshave significant influence on the value of the factor K. This impact is taken intoaccount using the coefficient of finite dimensions and crack shape M k. Therefore, forthe elements with irregularities (imperfections) and taking the factor of M k intoconsideration , K can be expressed as follows: K M Sa(2)kEvaluation of the safe operation period of the construction requires specifying thenumber of load cycles N that can happen without causing catastrophic growth ofexisting cracks and damage of the analysed structure. The value of N, correspondingto the length or depth of the crack a, can be calculated using the Paris and Erdoganequation defining the fatigue crack growth as follows [1,3]:kdadNm C K(3)where C and m are material constants characterizing the analyzed structure.If the initial a 0 and final a c values of crack length or depth are known , (a c is the criticaldimension at which the cracks becomes unstable and grow rapidly – it correspondsto the critical stress intensity factor K Ic ) then the safe number of cycles N c can becalculated by integrating Eq.3:Nca ca0daC(K)m(4)It has to be emphasized that no general theory describing the crack growth processin materials was formulated so far, and the Paris-Erdogan equation, like the most ofsuch equations presented in the literature, is an example of the approximaterelationship obtained experimentally. Therefore, assessment of the safe operationtime of the construction, based on Eq.4, must be conducted taking into considerationconstraints posed by the use of empirical data and formulas.The model based on the theory of crack growth makes the crack growth ratedependent on several factors, among which the most important are: The range of stress changes: S S max Smin; The coefficient of asymmetry of stress cycle: R S minSmax;

The complexity of the stress state (variation amplitude, multiaxis); Mechanical properties of the material (eg, yield stress, elasticity); Metallurgical factors (such as alloy composition, heat treatment); Environmental factors (eg temperature, humidity, radiation); Geometry of the analyzed structure.The first two factors, S and R, are of particularly importance. These factorscharacterize varying loads affecting the penstock. Usually it is rather problematic andtime consuming to take into account stress courses that are complex and diversifiedin terms of amplitude and frequency. The problem of calculating the alternative(equivalent) values of these changes will be presented below in this paper.Range of stress changes essential for evaluation of penstocklifetimeIn each hydrounits mode of operation in hydropower plant the construction ofpenstocks are exposed at loads of different intensity of their changes. Depending onmany factors, such as the kind of mode of operation or the type of transition staterealized by hydrounits, the cycles of these load changes are characterized by varyingamplitude and frequency of stresses. The theory of crack growth, as alreadymentioned, assumes that in the material of the analyzed structure there are someprimary cracks and their existence is not connected with the operational conditions ofthe construction. One of the main characteristics of these cracks is their dimensions(length or depth), which decides whether a given stress change will cause furthergrowth of these cracks. Briefly put, if the primary microcrack of a given dimension a isexposed at too small stress change S, then it will not increase. Only sufficientlylarge stress change, not less than a threshold value S th can cause primarymicrocracks growing in the material of the construction.The Paris-Erdogan formula confirms this theory. It does not recognize the full courseof cracking, and concerns the range of changes in the value of K above a certainvalue K th , called the threshold stress intensity factor, to the critical value K Ic at whichthe damage of the analyzed material ensues. It is assumed that when the stressintensity factor is lower than the value of K th cracks does not develop, regardless ofthe prior load state. That means that the quantity K th represents a sort of a safetyfactor if considering crack growth. Knowledge of its value allows to specify which ofthe variable loads have an influence on the crack growth in the material of theanalyzed structure.Load cycles in penstocks of hydropower plants and their equivalentcharacteristicsThe Eq.3, as well as other formulas similar to it presented in the literature, relate tostress changes with constant amplitude. It does not recognize the effects related toirregularity of stress changes which characterizes the vast majority of engineeringstructures in operation. In the case of penstocks in hydropower plants the load cyclescan have considerably varying amplitude as well as frequency. The main reason forthese loads is transient states, realized at hydrounits whose effects are spreadthroughout the whole flow system. In this case, the load characteristics dependmainly on how the hydroelectric power station is used in the EES. Configuration ofthis system and nature of the volatility in demands for power and energy decide how

many starts and stops are realized, how frequent and fast are load changes, and alsohow frequent are transitions between different operational modes of hydrounits.Among many well-known types of hydropower plants, pumped-storage power plantsare characterized by the most diversified operation, and hence various loads exertedon flow elements of hydraulic systems. It is closely dependent on the reversiblehydrounits which are common equipments of such power plants and the way thatthey are used by the power plant operator or the transmission system operator. Thetransient states resulting from the following transitions between some operationmodes and emergency conditions of hydrounit are the most important for lifetimeanalysis of penstocks: normal start and stop at:o turbine or pumping mode of operation,o compensator mode with turbine direction of rotation; emergency shutdown from the turbine and pump modes of operation; transitions between:o compensator mode and turbine mode of operation,o turbine mode and compensator mode of operation,o compensator mode and pump mode of operation.Additionally, there should still be taken into account filling and emptying the penstockthat usually causes the greatest increase in stress in the pipeline coating.Each of the aforementioned transient states is characterized by differentcharacteristics of the loads generated in hydraulic system. Among them followingshould be distinguished: states with one or two important cycles of pressure and stress changes (eg,filling / emptying the penstock, start of turbine or pump mode of operation),with one or two pairs of maxima and minima in these changes – e.g. Figure 1states with multicycles of pressure and stress changes (such as normal stopsfrom the pumping mode or emergency shutdowns from the turbine/pumpingmode of operation), with damping phase of free oscillations after one- or twophasechange of pressure and stress – e.g. Figure 2As it was mentioned earlier, the analysis of fatigue life requires knowledge about thematerial and geometric data of the analyzed structures as well as the appropriatedetermining stress course characteristics such as the range of stress changes Sand the cycle asymmetry coefficient R. There are several simplified methods that areused to take them into account [5]. The technique of equivalent stress intensity factoris the most commonly used method in practice [4]. It is based on the assumption thatthe same crack growth caused by the time-varying stress changes S(t) can betriggered off by the loads with the constant stress amplitude S eq which is equivalentfor S(t) amplitudes. In the case of stresses with a narrow band amplitude changes,the following formula of equivalent value of S eq1 is usually adopted in the chosenmodel:Seq2NiSi1iN(5)where N i denotes the total cycle numbers of stress changes of S i .ii

Alternate cycle asymmetry coefficient is adopted in accordance with an analogousdefinition as presented in Eq.(5):Req2NiRi1iN(6)The method for estimating the equivalent quantities directly from the formulas (5) and(6) can be successfully used for the first group of transient states realized in thesample pumped-storage power plant for which one or two important cycles of stresschanges can be distinguished - for example, Figure 0-1 . However, this method doesnot work for broadband load processes characterized by significant variability withinthe amplitude or frequency domain (so-called. multicycle loads) – e.g. Fig 0-2 .According to [4], for courses with these characteristics the equivalent range of stresschanges S eq2 should be calculated as follows:in which:SS2rmsS2iiS eq 2 2 S (7)- standard deviation for load changes in time S(t),S - mean value of stress changes in time S(t),S rms – root mean square value of stress changes in time S(t).Consequently, the equivalent cycle asymmetry coefficient is taken as defined below:RS 0.5SS 0.5Seq 2eq 2(8)S 0.5Seq 2 S 0.5SQuantities S , S and S rms are determined considering only those cycles of stresschanges, which are relevant to evaluating the fatigue life of the pipeline – this meansthat only those changes in stress amplitudes which are large enough to have causedthe growth of cracks in material exposed on such stress is taken into account.Forecast of the plant operation as an important element inevaluating the penstock lifetimeIn Egs.5 and 6 quantity N, standing for the total number of cycles of stress changesS, can be examined on a yearly basis, which allows to determine the permissiblenumber of years, during which (while maintaining the other important criteria ofoperation) safe operation of the penstock is guaranteed. In this case, the value of Nis determined by multiplying the projected annual average number of transient statesn state and the number of cycles of stress changes (relevant to evaluation of fatiguelife) n cycle occurring in these states:N n staten cycle(9)

egardless of the adopted model. Thus allows to obtain results coming in the safeside of this evaluation.The course of the remaining lifetime calculationsAll the above mentioned data allow to estimate the penstock lifetime using the crackgrowth model. At firstS eq and R eq need to bedetermined using Eqs.5 and 6. It requires calculation of both the number of stresscycles n cycle and the range S and the asymmetry R of these cycles for each of theanalyzed transient states. The total number of cycles of stress changes (N) per yearshall be determined using Eq.9 taking into account the projected number of transientstates n state in the future operation of the hydrounit.The equivalent characteristics used in Eq.4 allow to determine a safe number ofcycles N c . The ratio of this value and the annual total number of cycles of stresschanges N:N cLifetimenew (10)Nis the lifetime (in years) of a new penstock that have not been yet exposed at anyloads resulting from the hydrounit operation, which will be working according to theassumed forecast.For objects already in the operation, there is a need to take into account theoperation of plant conducted so far and its impact on the remaining lifetime of theanalyzed structure. The fatigue level of the pipeline construction resulting fromvariable loads during its historical operation can be included using followingrelationship:NpN 2Seq pS 2where the index p refers to quantities, whose value is determined basing on ahistorical course of the penstock operation.Finally, the remaining lifetime of the penstock including a previous course of thepenstock work, and assuming its further operation according to the assumedforecast, can be calculated using formula:Lifetime oldeqp2eq,22Seq Np Seq pN S 22N Nc p SeqNc (11)NN SAccording to the Eq.11 the estimated number of years of the remaining safeoperation of the penstock is calculated taking account of the difference between asafe number of load cycles N c for the stress changes with the amplitude equal S eqand the number of load cycles N p for the stress changes with the amplitude equalS eq p made during the previous course of the penstock operation.eq

ConclusionsThe paper demonstrates the way of evaluating the remaining lifetime of steelpenstocks of hydropower plants using the model based on the theory of crack growthin materials. Solid theoretical foundation based on the physics of the fatigue fractureof materials and widespread technical applications underlay the selection of thismodel. However, it has to be stressed that the general lack of experimentalverification of the estimates concerns the chosen model as well as many othermodels of fatigue life evaluation which abounds in the literature. Using the modeldescribed in this paper there is a need for knowing the strength data of the materialbuilding pipeline coatings. In the absence of such data it is required to carry outappropriate laboratory research of material.When determining the remaining lifetime of the penstock construction it is importantto: determine correctly the equivalent values of S eq and R eq for the projected andprevious stress changes exerted on the structure, determine stress concentration coefficients for areas with excessive materialand geometric imperfections – it is carried out basing on visual inspection andnon-destructive diagnostic tests of the external surfaces as well as numericalanalysis of stress distribution in these places, consider the current fatigue wear of the analysed construction appropriately,what allows to adjust the evaluation of the number of remaining years of itssafe operation, forecast future operation of considered hydropower plant accurately.High sensitivity of results of the analysis, in relation to the above factors, causes, thatthese factors are crucial for the credibility of evaluation of the remaining lifetime ofthe structure. It should be emphasized that the proper treatment of these issuesshould first and foremost enable to obtain the results coming in the safe side of theanalysis.The proceedings of the method used for the evaluation of the penstock lifetime pointon factors which make it possible to extend the penstock safe operation time. Thefirst one is a forecast of future operation of the plant. As it was mentioned earliersome transient states realized within the confines of hydrounit operation arecharacterized by a considerable number of cycles of stress changes, and large rangeand asymmetry of these changes. So it is clear that reducing the number of suchtransients will prolong the remaining lifetime of the penstock.Another possibility of extending the lifetime of the penstock can be achieved byreducing the range of stress changes in the construction. It leads directly todecreasing the range of pressure changes in the penstocks during the transient thatcan be completed for example by implementing the appropriate modifications to themachine control system which do not require interference with the flow systemconstruction. That is why it is very attractive way particularly because on the onehand it needs low capital intensity and on the other hand it gives measurable gainsmanifesting in extending the total safe operation time of the penstock.Reducing the stress concentration coefficients in critical points of the structure canalso bring some significant extending the penstock lifetime. An example of that isstrengthening the construction of pipelines branching, resulting in a reduction ofmaximal stresses in such elements [10,11]. It should be emphasized that anychanges in technology and design should take account of their impact on theoperation conditions of the penstock and its lifetime.

These observations can provide crucial guidance for operators and owners ofhydroelectric power plants, equipped with a penstock (pipeline derivation). They mayenable: to determine optimal way for operation of these type of plants in terms of thesmallest possible load exerted on the penstock construction, therebyextending its lifetime, to plan expenditures for rehabilitation and replacement of critical componentsof the plant, and to support the sustainable operation of the plant consisting in, inter alia, theoptimal usage of hydrounits, considering the remaining lifetime of a penstockas a goal of such optimization.References1. Ashby, M., F., Jones DRH: Engineering Materials. Properties and applications.WNT, Warsaw 1995 (in polish).2. Dyląg, Z., Jakubowicz A. Orłoś, Z.: Strength of Materials, Volume II, WNT,Warsaw 1997 (in polish).3. Kocańda S., Shawn J.: Fundamentals of fatigue calculation, WydawnictwoNaukowe PWN, Warsaw 1997 (in polish).4. Sobczak, K. Spencer, Billie F.: Stochastic models of materials fatigue, WNT,Warsaw 1996 (in polish).5. Wyrzykowski, J, W., Pleszakow, E. Sieniawski J.: Deformation and fracture ofmetals, WNT, Warsaw 1999 (in polish).6. Assessment of strength of the penstock in Żarnowiec PSPP, work by prof. JAKonig, Institute of Fundamental Technological Problems, Warsaw 1983 (inpolish).7. BS7910.1999. "Guide on Methods for assessing the acceptability of flaws instructure." British Standards Institution.8. Rykaluk K.: "Cracks in steel structures - Dolnośląskie Wydawnictwo Edukacyjne1999 (in polish).9. Dexter RJ, Pilarski PJ, Mahmound HN, "Analysis of crack propagation in weldedstiffened panels", Int Journal of Fracture, 25 (2003).10. Kwapisz, L., Adamkowski, A..: Stress concentration in pipeline connections, (inPolish), International Conference HYDROFORUM'2000, Czorsztyn, 18-20.10.2000, p. 177-182.11. Adamkowski, A., Kwapisz, L.: Strength analysis of Penstock bifurcations inHydropower plants, Proc. Conference. 12. Internatnales SeminarWASSERKRAFTANLAGEN - Sicherheit und / oder Risiko ", TU Wien, 27-29November 2002, p. 125-156.12. Adamkowski, A.: Evaluation of strength of the penstock No. 1 in Żydowo PSPP,IMP PAN, No. 342 / 99, Gdańsk 1999 (in polish).13. Adamkowski, A., Janicki, W., Lewandowski, M.: Research of hydrostatic andhydrodynamic loads in the penstock No 3 in Żarnowiec PSPP, IMP PAN, No767/09, Gdańsk 2009 (in polish).14. Adamkowski A., Lewandowski, M.: Evaluation of strength and lifetime of thepenstock No. 3 in Żarnowiec PSPP, IMP PAN No arch 883/09, Gdańsk, 2009 (inpolish).

AuthorsProf. Adam AdamkowskiThe Szewalski Institute of Fluid-Flow Machinery, PASci (IMP PAN)Centre for Mechanics of Liquids, Department of Hydraulic Machineryul. Fiszera 14;80-952 Gdańsk, PolandPhone: +48 58 69 95 205Fax: +48 58 341 61 44E-mail: aadam@imp.gda.plDr. Mariusz LewandowskiThe Szewalski Institute of Fluid-Flow Machinery, PASci (IMP PAN)Centre for Mechanics of Liquids, Department of Hydraulic Machineryul. Fiszera 14;80-952 Gdańsk, PolandPhone: +48 58 69 95 186Fax: +48 58 341 61 44E-mail: mlew@imp.gda.plMEng. Stanisław LewandowskiL.S.HydroConsultul. Glińskiego 13;84-239 Bolszewo, PolandPhone/Fax: +48 58 572 05 41E-mail: hydroconsult@gmail.comAdam Adamkowski, PhD, DSc. Received his MEng. degree in 1978 from the Institute of Shipbuildingof the Gdansk University of Technology (Poland) in the field of naval machinery, equipment and powerplants. The Institute of Fluid-Flow Machinery of the Polish Academy of Sciences granted him a PhDdegree in 1989 and a DSc degree in 2005. Currently: an Associate Professor and a head of theCentre for Mechanics of Liquids and a head of the Department of Hydraulic Machinery in theSzewalski Institute of Fluid-Flow Machinery of the Polish Academy of Sciences (IMP PAN). Mainprofessional interests: hydraulic transients in closed conduits (analysis and control), problems ofhydraulic turbomachinery design and operation, flow rate measurements in hydropower plants.Mariusz Lewandowski, PhD. Received his MEng. degree in 2000 from the Faculty of EnvironmentalEngineering of the Technical University of Gdansk in the field of water resources management andhydraulics. The Institute of Fluid-Flow Machinery of the Polish Academy of Sciences granted him aPhD degree in 2009 for research into unsteady fluid flow in closed conduits. Currently, he works in theDepartment of Hydraulic Machinery in the Szewalski Institute of Fluid-Flow Machinery of the PolishAcademy of Sciences (IMP PAN) Centre for Mechanics of Liquids from 2000. Professional interests:hydraulic transients in closed conduits.Stanisław Lewandowski, MEng. graduated from the Faculty of Electrical Engineering of theTechnical University of Wroclaw. He has been working in the electric power sector since 1973. From1979 to 1992 he was working as the Chief of the Operation and Maintenance Section in the ŻarnowiecPumped-Storage Power Plant. Between 1992 and 1993 he was a Deputy Director of HYDROMEX Ltd.In the period between 1993 and 2003 he was Director of Plants Operation in the Pumped StoragePower Plants Co (ESP SA). After that he was Director of the Department of Operation in the UpperOder Power Plants Ltd. (Elektrownie Górnej Odry sp z o.o.) and then he worked as a Director ofHydropower Plants Maintenance in ENERGA Straszyn Hydropower Plants Ltd. (ENERGA ElektrownieStraszyn Sp. z o.o.). Currently he leads his own firm L.S. HydroConsult offering his to hydropowerplant sector widely understood. He has been strongly involved in activities of the Polish HydropowerAssociation since its origin. Between 1992 and 1996 he was a Deputy Chairman and in periods 1996-1999 and 2003-2008 the President of this Association. He is an author of numerous papers dealingwith the contribution of hydro plants to regulation of the electric power system.