let./vol. 51 - št./no. 11/OB - str./pp. 673-742 zvezek/issue 487 STROJNIŠKI VESTNIK JOURNAL OF MECHANICAL ENGINEERING ^ cena BOD SIT 9"770039"248001" J/ / ISSN D039-2480 9770039248001 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 673 Vsebina - Contents Vsebina - Contents Strojniški vestnik - Journal of Mechanical Engineering letnik - volume 51, (2005), številka - number 11 ISSN 0039-2480 Izhaja mesečno - Published monthly Razprave Papers Kremljak, Z., Polajnar, A., Buchmeister, B.: Kremljak, Z., Polajnar, A., Buchmeister, B.: A Heuristic Hevristični model razvoja proizvodnih Model for the Development of Production zmogljivosti 674 Capabilities Bergant, A., Karadzic, U., Vitkovsky, J., Vušanovič, Bergant, A., Karadzic, U., Vitkovsky, J., Vušanovič, I., Simpson, A. R.: Diskretni plinski kavitacijski I., Simpson, A. R.: A Discrete Gas-Cavity model z upoštevanjem vpliva nestalnega Model that Considers the Frictional Effects kapljevinskega trenja v cevi 692 of Unsteady Pipe Flow Smrekar, J., Oman, J., Širok, B.: Statistični pristop k Smrekar, J., Oman, J., Širok, B.: A Statistical Approach analizi hladilnih sistemov s hladilnimi stolpi to the Analysis of Cooling Systems with na naravni vlek 711 Natural-Draft Cooling Towers Lahajnar, L., Žlajpah, L.: Vodenje robota na temelju Lahajnar, L., Žlajpah, L.: Robot Control Based on zaznaval sile in računalniškega vida 724 Force and Vision Sensors Strokovna literatura Professional Literature Nove knjige 737 New Books Osebne vesti Personal Events Prof. dr. Anton Kuhelj ml. - sedemdesetletnik 738 Prof. Anton Kuhelj jr. - 70th Anniversary Doktorati, magisteriji in diplome 739 Doctor’s, Master’s and Diploma Degrees Navodila avtorjem 741 Instructions for Authors 673 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 UDK - UDC 658.5:657.478.8 Izvirni znanstveni članek - Original scientific paper (1.01) Hevristični model razvoja proizvodnih zmogljivosti A Heuristic Model for the Development of Production Capabilities Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Menedžerji v proizvodnih okoljih se pri odločanju srečujejo z visoko stopnjo nezanesljivosti, zaradi hitrih in velikih sprememb, ki opredeljujejo okolja, v katerih delujejo njihove organizacije. Ta pomeni, da menedžerji pri odločanju nimajo popolnih informacij o prihodnjih dogodkih, ne poznajo vseh mogočih alternativ in ne poznajo posledic vseh mogočih odločitev. Spoprijeti se z negotovostjo pomeni razvijati hevristična orodja, ki lahko ponudijo zadovoljive rešitve, ne pa tudi optimalne. Metode simulacij, ki temeljijo na ekstrapoliranju merljivih podatkov iz preteklosti, niso ustrezne kot pomoč pri odločitvah v okoliščinah negotovosti. V zadnjem času se kot prevladujoča hevristika za reševanje odločitvenih problemov pri visoki stopnji negotovosti pojavlja teorija stvarnih možnosti. Zato se postopki stvarnih možnosti danes uporabljajo za vrednotenje investicij v raziskave in razvoj, v razvoj novih izdelkov, v proizvodno tehnologijo in preostale proizvodne vire. Na inženirskem področju smo priča intenzivnemu razvoju metod, orodij in tehnik, ki sicer po svojem poreklu spadajo na področje uporabne matematike, informacijskih znanosti, operacijskih raziskav in ekonomske teorije (genetski algoritmi, evolucijsko programiranje, genetsko programiranje, mehka logika, nevronske mreže, teorija stvarnih možnosti itn.), se pa zelo uspešno uporabljajo pri reševanju različnih tehničnih optimizacijskih problemov. Teorija stvarnih možnosti se uporablja tudi pri obravnavanju tehnologije, razvoja in raziskav ter proizvodnje. Razmišljanja o uporabnosti teorije stvarnih možnosti so se razširila tudi na področje strateškega menedžmenta. © 2005 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi proizvodni, upravljanje tveganja, teorija stvarnih možnosti, modeliranje negotovosti, mehka logika) Managers in production environments face a high level of uncertainty in their decision making due to the major, rapidly developing changes defining the environments in which their organisations operate. This means that managers do not possess complete information about future events, do not know all the possible alternatives or the consequences of all their possible decisions. Overcoming this uncertainty requires the development of heuristic tools, which can offer satisfactory, if not optimal, solutions. Simulation methods based on the extrapolation of available data from the past are unsuitable for help in decision-making processes in uncertain conditions. Lately, the dominant heuristics used for solving decision-making problems during a high level of uncertainty is the theory of real options. For this reason the real-options approach is currently used for an evaluation of the investments in research and development, the development of new products, production technologies and other production sources. As regards engineering, we are witnessing the intensive development of new methods, tools and techniques, which by their origin belong to the field of applied mathematics, information sciences, operational research and economic theory (genetic algorithms, evolution programming, genetic programming, soft logic, neuron networks, the theory of real options, etc.), and are very successfully applied in the solving of various technical optimisation problems. The theory of real options is also used in issues related to technology, research and development, and production. The thoughts on the use of the theory of real options have also spread to the area of strategic management. © 2005 Journal of Mechanical Engineering. All rights reserved. (Keywords: production systems, risk management, real option theory, uncertainty modelling, fuzzy logic) 674 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 0 UVOD Odločanje v okoliščinah velike negotovosti postaja eden najbolj raziskovanih pojavov na področjih strateškega menedžmenta, organizacijske teorije, industrijskega inženiringa in menedžmenta razvoja in raziskav. Negotovost je definirana kot značilnost pojava, ki se upira merljivosti in ga je zaradi tega nemogoče učinkovito omejiti na pripadajoče stopnje verjetnosti. V nasprotju z nezanesljivostjo je tveganje merljivo s stopnjami verjetnosti in ga je mogoče upravljati. Nobelovec Arrow [2] predlaga definicijo nezanesljivosti, po kateri ta pomeni, da nikoli nimamo popolnega opisa sveta ali stanja, za katerega verjamemo, da je resničen. Ta definicija pomeni, da verjetnosti, da se kot posledica dejavnosti zgodi dogodek, ni mogoče objektivno določiti, ampak je zgolj rezultat subjektivnih domnev. Neobvladljivost negotovosti še povečujejo človekove spoznavne omejitve. Spoznavna baza človeka sestoji iz predvidevanj o prihodnosti, poznavanja mogočih alternativ in znanja, ki omogoča poznavanje posledic odločitev. Ta spoznavna baza je izrazito omejena in jo opisuje pojav omejene racionalnosti [6]. Ta izhaja iz teorije finančnih možnosti, katere temelje sta postavila nobelovca Black in Scholes [3]. Naključnostna diferencialna enačba, ki sta jo razvila, omogoča vrednotenje finančnih možnosti v okoliščinah negotovosti. Logika finančnih možnosti se je hitro razširila na stvarne možnosti, ki jih obravnava zajeten kup znanstvene literature ([1], [5] in [10]). Finančna možnost predstavlja možnost za nakup ali prodajo finančnega premoženja, ki že obstaja in se prodaja na finančnih trgih v obliki delnic in obveznic. V nasprotju z njo pomeni stvarna možnost možnost za spremembo stvarnega premoženja, virov ali intelektualnih dejavnosti, na primer: postaviti novo tovarno, osvojiti nov trg, razviti novo tehnologijo ali izdelek. Teorija stvarnih možnosti se je uveljavila kot vodilna hevristika za obravnavanje pojavov, povezanih z negotovostjo. Na prej naštetih znanstvenih področjih se potreba po obvladovanju nezanesljivosti kaže pri razvojno-raziskovalnih projektih, razvoju novih proizvodnih tehnologij, projektih razvoja novega izdelka, investicijah v napredno proizvodno tehnologijo, odločitvah o selitvi proizvodnje in razvoju proizvodnih zmogljivosti, kakor so prilagodljivost v proizvodnji ter obvladovanje kakovosti. 0 INTRODUCTION Decision-making in high-risk conditions is becoming a common area for research within strategic management organizational theory, research and development management, and industrial engineering. Risk is measurable with probability levels and can thus be managed; however, this cannot be applied to uncertainty. The Nobel Prize winner Arrow [2] proposed an uncertainty theory that suggests that there can never be a perfect definition of the world or conditions for which we believe are real. This definition can be interpreted as such: the probability that an event will occur as a result of our activity cannot be defined objectively, but can only be an outcome of our subjective assumptions. The inability to master uncertainty only enhances human cognitive limitations. The human cognitive base comprises future predictions, potential alternative options and the ability to foresee the consequences of a decision. This cognitive base is very limited and can be described by the phenomenon called Bounded Rationality [6]. It outlines that in decision-making, managers do not have complete data on future-event occurrences and therefore cannot predict all the possible alternatives or forecast all the consequences of their decisions. It is derived from the Financial Options Theory, which was developed by the Nobel Prize winners [3] Black and Scholes. The stochastic differential equation they developed enables the assessment of financial options in uncertain conditions. Financial Options logic rapidly developed into Real Options, which is outlined in a sizable amount of scientific literature ([1], [5] and [10]). The Financial Option presents a purchase or a sales option for financial assets, which already exist and are being sold in financial markets in the form of stock and bonds. The Real Option, on the other hand, represents an option for real asset change, source and intellectual activity change, for example, building a new factory, conquering new markets and developing new products or technologies. The Real Options theory has become the leading heuristic for dealing with uncertainty phenomena. The need to manage uncertainty in the above-mentioned scientific fields is most apparent with research and development projects, new production technology development, new product development projects, advanced production technology investments, production migration decisions and production capabilities development, such as production flexibility and quality management. Hevristični model razvoja - A Heuristic Model for the Development 675 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 1 TEORETIČNO OZADJE Pomembna literatura obravnava problematiko odločanja v pogojih negotovosti le delno. Trenutno potekajo najbolj izrazite raziskave na področju večkriterijskega odločanja, podprtega z izvedenskimi sistemi. Ne glede na pomemben razvoj so problemi, povezani z izbiro ustreznih metod za zapletene in mehko strukturirane odločitvene probleme, z merskimi lestvicami, statistično interpretacijo, sistemsko optimizacijo ter ciljnimi funkcijami pri večkriterijskih problemih nezadostno obravnavani in hkrati ne rešeni. Različni avtorji ([4], [11], [12] in [15]) trdijo, da pomeni teorija stvarnih možnosti pravšnjo hevristiko za upravljanje postopka razvoja zmogljivosti. Zmogljivost je definirana kot organizacijsko znanje podjetja, ki omogoča izvajaje poslovnih postopkov [8]. Strateška šola dinamičnih zmogljivosti trdi, da zmogljivosti zaradi svojih značilnosti, kakor so sistemska zapletenost in zgodovinska odvisnost, pomenijo temelje za doseganje trajnih konkurenčnih prednosti ([7], [9], [13] in [16]). Iste značilnosti, ki delajo zmogljivosti težko posnemljive in težko prenosljive in zato strateško vredne, omejujejo možnosti uspešnega upravljanja postopka razvoja zmogljivosti. Ta je opredeljen z visoko stopnjo negotovosti in zato se teorija stvarnih možnosti pojavlja kot hevristika, s potencialom pomagati menedžerjem pri upravljanju postopka razvoja zmogljivosti. 1.1 Opredelitev termina negotovost O gotovosti v organizacijskem sistemu govorimo, kadar usposobljen posameznik sprejema odločitve, povezane z delovanjem organizacijskega sistema, pri čemer ima popolno znanje o mogočih stanjih v prihodnosti in so ta stanja popolnoma neodvisna od dejavnosti, ki jih tak sistem izvaja. Takšen organizacijski sistem je popolnoma prilagodljiv, saj se je mogoče pripraviti na vsa možna stanja. Osnutek tveganja v organizacijskem sistemu pomeni, da je možno objektivno določiti stopnje verjetnosti nekega stanja ali dogodka. Pomeni, da usposobljen posameznik pozna vsa mogoča stanja v prihodnosti in verjetnosti, da se ta stanja uresničijo. Stvarnost v organizacijskem sistemu je običajno težko opisati z osnutkoma gotovosti in tveganja. Avtor Kylaheiko [12] navaja podroben 676 1 THEORETICAL BACKGROUND The problem of decision-making in uncertain conditions is only partially presented in the relevant literature. Intensive research in the area of multi-level decision-making, supported by expert systems, is currently under way. Despite the immense importance of development, problems associated with choosing the appropriate methods for complex and soft-structured decision-making problems, measuring scales, statistical interpretation, systems optimization and multifaceted problems are inadequately handled and consequently not solved. Various authors ([4], [11], [12] and [15]) claim that the Real Options theory presents the right heuristic approach to capability-development process management. Capability is defined as the organizational know-how that enables business-process implementation [8]. The strategic school of dynamic capabilities claims that due to their characteristics, such as complexity and historical dependency, capabilities are the foundation for achieving a sustainable competitive advantage ([7], [9], [13] and [16]). The very characteristics that make it difficult to imitate and transfer capabilities, consequently adding to their strategic value, also limit the possibility of successful capability-development process management. This process is also defined by a high level of uncertainty, which makes the Real Options theory only appear as a heuristic, potentially helping managers handle the capability-development process. 1.1 Definition of the uncertainty term The term certainty in an organizational system is used when a competent individual makes decisions associated with organizational system operations based on perfect knowledge of all possible future situations, and these situations are completely independent of the activities performed by such a system. Such an organizational system is totally adaptable, as one can prepare for any possible future situations. The concept of risk in an organizational system means that an objective assessment of probability levels for an event or a situation to occur is possible. This means that a competent individual is aware of all possible future situations and of the probability that these situations will actually occur. Reality in an organizational system is difficult to describe with the concepts of certainty and Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 pregled različnih tipov negotovosti. Osnutek negotovosti je dosti bolj primeren za opisovanje stanja v organizacijskih sistemih: • Parametrična negotovost predstavlja tip negotovosti, ki ga je še mogoče matematično obvladovati. Negotovost se tiče samo subjektivnih parametrov verjetnosti. . Strukturna negotovost pomeni, da ima oseba, ki odloča, nepopolno znanje o strukturi problema. Za strukturno negotovost je značilno, da je nemogoče imeti znanje o vseh mogočih posledicah. Pomembno je poudariti, da strukturna negotovost pomeni, da stanja v prihodnosti niso neodvisna od dejavnosti. 1.2 Izzivi proučevanja negotovosti Tip strukturne negotovosti je najmanj raziskan v znanstveni literaturi [14]. Nenapovedljiva negotovost pomeni nezmožnost prepoznati ustrezne vplivne veličine in njihove funkcijske povezave. Tsoukas [18] govori o radikalni negotovosti, ko poudarja, da je v organizacijskih sistemih nemogoče vnaprej vedeti, katero znanje se bo razvilo in katere kombinacije razpršenega znanja bodo pomembne za določene okoliščine. Obsežne zamiselne razprave in izkustvene raziskave dokazujejo, da je razumevanje osnutka negotovosti ključno za razumevanje delovanja organizacijskega sistema. Kljub zavedanju o pomembnosti upravljanja organizacijskih sistemov v razmerah negotovosti, je na voljo presenetljivo malo sistemskih postopkov in hevristik, ki bi podpirale postopek sprejemanja odločitev v negotovih okoliščinah. V zadnjem času se je kot vodilna hevristika za obvladovanje postopka odločanja v okoliščinah negotovosti uveljavila teorija stvarnih možnosti. Stvarne možnosti so pomembne v različnih situacijah: • ko je projekt mogoče ustaviti; . ko je investicija prilagodljiva, npr. ko je mogoče zamenjati proizvodno tehnologijo; . ko priložnosti v prihodnosti temeljijo na odločitvah, ki so sprejete danes, npr. razvoj in raziskave. 1.3 Stvarne možnosti in razvoj zmogljivosti Postopek razvoja zmogljivosti je negotov zaradi zapletene strukture zmogljivosti in zaradi njenega dolgotrajnega razvoja. Bowman in Hurry [4] risk. The uncertainty concept is far more suitable for describing the actual state that an organizational system is in [12]: . Parametric uncertainty is a type of uncertainty that can still be mathematically mastered. Uncertainty can only be related to subjective probability parameters. . Structured uncertainty means that the decisionmaker has limited knowledge of the problem structure. In structured uncertainty it is impossible to possess knowledge of all possible consequences. It should be emphasized that structured uncertainty means that future situations are not independent of the activity. 1.2 Uncertainty research challenges The structured uncertainty type is the least researched theme in scientific literature [14]. Unforeseeable uncertainty means the inability to recognize the relevant influence variables and their functional connections. Tsoukas [18], who talks about radical uncertainty emphasizes that it is impossible to predict which proficiency will be developed and which scattered knowledge combinations will be important for the specific conditions in organizational systems. Extensive conceptual discussions and empirical research studies prove that in order to comprehend organizational system operations, it is imperative to understand the uncertainty concept. Despite the fact that there is awareness of the importance of organizational systems management in uncertain conditions, there are surprisingly few systematic approaches and heuristics in place that support the process of decision-making in uncertain environments. Recently, the Real Options theory has become the leading heuristic for decision-making process management in uncertain conditions. Real options are important in different situations: . When a project can be terminated. . When the investment is flexible. For example, when it is possible to modify the production technology. . When future opportunities are based on decisions made today. For example, research and development. 1.3 Real Options and Capability Development The capability-development process is uncertain due to the complex nature of capabilities and its lengthy development procedure. Bowman and Hevristični model razvoja - A Heuristic Model for the Development 677 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 sta ugotavljala, da menedžerji v poslovnih sistemih pravzaprav intuitivno uporabljajo logiko stvarnih možnosti, ko sprejemajo odločitve v zvezi z razvojem zmogljivosti. Uporabnost stvarnih možnosti ne bodo povečala matematična orodja, ki bodo zapleteno stvarnost omejila v nekaj spremenljivk, ampak razvoj hevristik, ki bodo upoštevale zapletenost stvarnih razmer in obenem omogočale odločitve na podlagi merljivih pokazateljev. 1.4 Sistemski postopek za obravnavanje razvoja zmogljivosti V analitičnem delu je treba podrobno analizirati vire in zmogljivosti. Ugotoviti je treba, kateri viri in zmogljivosti so že na voljo in v katerih povezavah jih je mogoče uporabiti. Ugotoviti je treba primanjkljaj virov in zmogljivosti. Strokovna literatura ponuja nekaj sistemskih postopkov, ki podpirajo analiziranje virov in zmogljivosti. Preden se izvedenska skupina loti razčlenitve razvoja zmogljivosti na kategorije in dejavnike, je treba opredeliti tipe negotovosti. Milikenova delitev na negotovost stanja, učinka in odziva je koristna, saj poenoti razumevanje pojma med različnimi člani izvedenske skupine. Razčlenjevanje obravnavanega postopka na kategorije in dejavnike negotovosti pomeni del, ki se vsebinsko razlikuje v različnih sistemskih okoljih. Izvedenska skupina, ki obravnava negotovost seljenja proizvodnje na geografsko oddaljeno lego, bo identificirala drugačne dejavnike in kategorije kakor izvedenska skupina obrambnega sistema, ki obravnava izvajanje mirovnega opravila na geografsko oddaljenem kraju. Razčlenitev na kategorije in dejavnike negotovosti pomeni razstavitev zapletenega problema in omogoča začetek izvajanja postopkovnega dela. 2 METODOLOGIJA Za pričujoč prispevek je bil uporabljen dvojni metodološki postopek zaradi potrebe po usklajevanju med celostnim obvladovanjem znanstvenega problema in analitično-numerično natančnostjo oblikovanega hevrističnega postopka. Običajno razviti numerični modeli predstavljajo zgolj abstrakten model stvarnega sistema in so razviti brez izkustvenih kakovostnih temeljev, ki določajo zapleteno 678 Hurry [4] have found that managers, when making capability-development decisions in business systems, actually use the logic of real options intuitively. The applicability of real options will not be enhanced by mathematical tools, which reduce the complex reality to a few variables, but by the development of heuristics that take into account the complexity of real conditions and simultaneously enable decisions to be based on measurable indicators. 1.4 A systematic approach to handling capability development In the analytical part of the work, the sources and abilities should be analyzed in detail. It is necessary to find out which sources and abilities have already been at disposal, and in which contextual applications they might be used. It is necessary to find out the deficiency of sources and abilities. Professional literature offers some system approaches, the application of which serves as support for analyzing sources and abilities. Before the expert team starts with ability development, broken down into categories and factors, the types of uncertainty should be defined. Miliken’s partition into the situation uncertainty, effect, and response is useful, as it unifies the understanding of the notion between the different members of the expert team. Breaking down the treated process into categories and uncertainty factors actually represents the part, the contents of which differ in various system environments. The team of experts, treating the uncertainty of production movements to a geographically distant location, will identify other factors and categories than the expert team for the protection system, treating the implementation of peace operation on the geographically distant location. The breakdown to categories and factors of uncertainty represents the decomposition of a complex issue, thus enabling the start of implementing the process work. 2 METHODOLOGY The double methodological approach was used for the underlying paper due to the need for coordination between the holistic management of a scientific issue and analytical-numerical accuracy of the formed heuristic approach. In most cases, the developed numerical models represent only an abstract model of the real system and are developed without any empirical, qualitative grounds, which Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 Študija primera / Case study - analiza zmogljivosti v izbranem sistemu / analysis of capabilities in the selected system - določanje projektov za analizo / determining projects for analysis - zbiranje podatkov o identificiranih projektih / collecting data on identified projects - interpretacija podatkov / data interpretation Modeliranje hevrističnega pristopa / Modelling of the heuristic approach - kategorizacija vplivnih dejavnikov / classification of factors of influence - zasnova in oblikovanje modela na podlagi ugotovitev iz študije primera / basing and designing the model on the basis of findings from the case study - testiranje modela na podlagi stvarnih vhodnih podatkov / testing the model on the basis of real input data Oblikovanje pristopa za učinkovito interpretacijo numeričnih rezultatov / Establishing the approach for effective interpretation of numerical data Sl. 1. Struktura dvojnega metodološkega postopka Fig. 1. The structure of the double methodological approach stvarnost sistema. Uporaba dvojnega metodološkega postopka pomeni novost v obravnavanju tovrstne problematike. Dosedanje raziskave so se predvsem naslanjale na monometodološke postopke, ki so bodisi natančno opisovali dejavnike, ki oblikujejo stvarnost organizacijskega sistema, ali pa so natančno modelirale podsisteme obravnavanega sistema in pri tem numerični natančnosti žrtvovali celosten pogled na obravnavani pojav. Na sliki 1 je prikazana struktura uporabljene metodologije. Raziskava se je začela s podrobno analizo zmogljivosti v livarskem sistemu. Za obravnavanje projekta so bile kot metode zbiranja podatkov uporabljeni dokumentacija in intervjuji z usposobljenimi posamezniki. Interpretacija podatkov je bila izvedena skupaj z nekaterimi člani Laboratorija za načrtovanje proizvodnih sistemov, kar je omogočilo zmanjšanje subjektivnosti raziskovalca. Poglobljeno kakovostno delo v okviru obravnavanega projekta je pripeljalo do podatkov, na katerih je bilo mogoče oblikovati hevristični sistemski postopek. Razlogi za izbiro tega projekta so naslednji: . gre za projekt, ki zahteva razvoj strateških zmogljivosti, . projekt ni povezan zgolj z investicijami v posamične tehnične sisteme, . obravnava postopke, ki zahtevajo evolucijsko determine the complex reality of a system. The use of the double methodological approach is a novelty in dealing with such issues. Past studies have mostly relied on mono-methodological approaches, which either included a detailed description of factors shaping the reality of an organisational system or the detailed modelling of subsystems of the underlying system and sacrificed the holistic view of the phenomena in question to numerical accuracy. The structure of the used methodology is presented in Figure 1. The study started with a detailed analysis of the capabilities in a casting system. The data-collection methods used in the project were documents and interviews with qualified individuals. The data interpretation was carried out in cooperation with certain members of the Production Systems Planning Laboratory, which resulted in a lower level of subjectivity of the researcher. In-depth, qualitative work within the project in question resulted in data that could be used to form the heuristic systemic approach. The reasons for selecting the project in question were: . It is a project requiring the development of strategic capabilities; . The project is not linked solely to investments in individual technological systems; . It deals with processes requiring evolutionary Hevristični model razvoja - A Heuristic Model for the Development 679 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 učenje, projekt je omejen z visoko stopnjo negotovosti, negotovost je mogoče dojemati skozi različne vidike, matematično modeliranje stvarnih možnosti ne omogoča celovitega obravnavanja problematike. Livarski sistem v okviru proizvodnega sistema je ustrezen sistem za proučevanje. 3 UPORABA MODELA NA PRIMERU LIVARNE learning; . The project has a high level of uncertainty; . The uncertainty can be perceived through various aspects; . The mathematical modelling of real options does not enable a holistic dealing with the issue at hand. The casting system as a part of the production system is a suitable system for studying. 3 CASE STUDY ON THE MODEL OF A PRODUC-TION SYSTEM - CASTING SYSTEM K2 Talilnica/ Smelter [D4 D5fD6lD7 D8 D9 D10 D11 D12 K6 Odlitki/ Castings D23 D24 D25 D26 D27 Sl. 2. Primer strukturiranja hevrističnega modela za proizvodnji sistem - livarna Fig. 2. Example of the structuring of the heuristic model for a production system - foundry Preglednica 1. Kategorije K in dejavniki D v livarskem sistemu Table 1. Categories K and Factors D in the foundry system K1 Odprema Shipping D1 - cestni road D2 - železniški railway D3 - letalski air K4 nadzor control D13 - mehanske lastnosti mechanical properties D14 - kemijske vsebnosti D15 - trdnostna hardness D16 - razsežnostna dimensional D17 - radiografska radiographic D18 - ultrazvočna ultrasound K2 Talilnica/litje Smelter/casting D4 - indukcijske peči induction furnace D5 - vakumske peči vacuum furnace D6 - litje v jeklena orodja croning D7 - peskovno litje sand casting K5 toplotna obdelava thermal treatment D19 - nitritranje nitrating D20 - vakumska obdelava vacuum treatment D21 - popuščanje yielding D22 - normalizacija normalisation K3 Čiščenje odlitkov Cleaning of casts D8 - peskalne komore D9 - ročni strojčki manual appliances D10 - dobava od zunaj outsourcing D11 - doma home D12 - razmaščevanje fatcleaning K6 odlitki castings D23 - majhni small D24 - srednji middle D25 - veliki large D26 - oglična jekla carbon steel D27 - nerjavna jekla stainless steel 680 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 3.1 Določitev pomembnosti dejavnikov negotovosti 3.1 Definition of the importance of importance factors Razmerja med kategorijami oz. dejavniki so izražena z vprašanjem: “Kolikokrat bolj je kategorija/ dejavnik i pomemben od kategorije/dejavnika j glede na cilj oz. nadrejeno kategorijo?” S primerjavo dejavnikov in kategorij po dvojicah (po podani ocenitveni lestvici) in rabo trikotno porazdeljenih mehkih števil dobimo mehke matrike na vseh ravneh hierarhije. The ratios between the categories or factors are expressed with the question: “How many times is the category/factor i more important than category/ factor j according to the aim or the superior category?” With a pair-wise comparison of the factors and categories (according to the provided estimation scale) and the use of triangularly divided fuzzy numbers, we arrive at the following fuzzy matrix on all levels of hierarchy. Mehke matrike-» stopnja zaupanja (a) -> stopnja optimističnosti (m) -> preračun uteži Npr. za K4: K4 : MM4 = D D D D D D 13 14 15 16 17 18 D 13 " 1 ~ 2 ~-1 2 ~-1 2 ~-1 7 D 14 2 -1 1 ~ 1 ~ 2 ~ 1 D 15 2 ~ -1 1 1 ~-1 2 ~-1 5 D 16 2 ~ -1 2 ~ 2 1 ~-1 4 D 17 7 ~ -1 1 ~ 5 ~ 4 1 D 18 5 ~ 3 ~ 3 ~ 5 ~-1 3 MMa = [1 1 4 3 , 5 [4,6] L ~-1 5 ~-1 3 ~-1 3 ~-1 5 ~ 3 1 1 13 , 22 14 , 35 13 , 22 [2,4] Numerična rešitev (lastni vektorji matrike -» uteži), npr. za K4 (pri a = 0,5 in m = 0,5): Fuzzy matrix -> level of trust estimate (a)-> level of optimistic estimates (m) -> weights calculation (where K4): [2,4] K4 : MMa4 a =0,5 1 17 17 17 7 5 8 30 30 48 24 17 1 4 17 4 3 30 3 8 3 8 17 1 1 17 5 3 8 30 24 8 17 17 17 1 4 5 8 30 8 15 24 7 1 5 3 1 4 3 , 5 2 ,2 1 5 [4,6] 1 4 3 , 5 5 ,3 1 4 3 , 5 1 [3,5] 1 1 8 , 6 2 ,2 1 1 6 , 4 1 1 _5 , 3_ 1 1 1 6 , 4 1 1 4 , 2 1 1 4 , 2 1 11 _6 , 4j [2,4] [4,6] [1 , 1 Numerical solution (eigenvector of matrix -* weight) where K4 (at a = 0.5 and m = 0.5): 6/1.17.17.17.7. 5 =0,5241 8 30 30 48 24 6 17.1 4.17.4.3 =0 9640 30 3 8 3 8 , 6 17.11.17.5..3 30 24 8 0,6744 6/17.17.17.1.4.5 8 -30' 8 ' 15 24 0,7224 67-1-5-4-1-3=2,7366 6 5-3-3-5---1 =2 0943 *' 8 , ^7,7158 D D D D D D 0,0679, 0,1249, 0, 0874, 0,0936, 0,3547, 0,2715 UD13 =0,3279-0,0679 = 0,0223 UD15 =0,3279-0,0874 = 0,0287 UD17 =0,3279-0,3547 = 0,1163 UD14 =0,3279-0,1249 = 0,0410 UD16 =0,3279-0,0936 = 0,0307 UD18 =0,3279-0,2715 = 0,0890 K 4 Hevristični model razvoja - A Heuristic Model for the Development 681 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 Preglednica 2. Pomembnost kategorij negotovosti v odvisnosti od stopnje zaupanja in optimističnosti ocene Table 2. The importance of uncertainty categories in relation to the level of trust in optimistic estimates Pomembnost kategorije (utež) / Importance of category (weight) Kategorija Category a = 0 a = 0,5 a = 1 m = 0,05 m = 0,5 m = 0,95 m = 0,05 m = 0,5 m = 0,95 K1 0,1753 0,1801 0,1814 0,1641 0,1675 0,1691 0,1600 K2 0,0765 0,0737 0,0728 0,0681 0,0669 0,0662 0,0653 K3 0,0553 0,0446 0,0415 0,0446 0,0411 0,0391 0,0406 K4 0,2879 0,2828 0,2835 0,3324 0,3279 0,3264 0,3388 K5 0,1788 0,1926 0,1960 0,1809 0,1879 0,1913 0,1884 K6 0,2262 0,2262 0,2248 0,2099 0,2087 0,2079 0,2069 Preglednica 3. Pomembnost dejavnika negotovosti (utež) Table 3. Importance of the uncertainty factor (weight) Dejavnik negotovosti Factor of uncertainty a = 0 a = 0,5 a =1 m = 0,05 m = 0,5 m = 0,95 m = 0,05 m = 0,5 m = 0,95 D1 0,0295 0,0344 0,0357 0,0298 0,0318 0,0329 0,0298 D2 0,1208 0,1151 0,1132 0,1138 0,1134 0,1129 0,1099 D3 0,0249 0,0306 0,0324 0,0204 0,0222 0,0233 0,0202 D4 0,0277 0,0281 0,0282 0,0267 0,0269 0,0269 0,0253 D5 0,0296 0,0294 0,0292 0,0263 0,0262 0,0260 0,0265 D6 0,0123 0,0103 0,0098 0,0099 0,0090 0,0086 0,0088 D7 0,0069 0,0059 0,0056 0,0052 0,0048 0,0046 0,0046 D8 0,0082 0,0079 0,0077 0,0069 0,0070 0,0070 0,0063 D9 0,0255 0,0171 0,0151 0,0217 0,0185 0,0169 0,0192 D10 0,0083 0,0078 0,0075 0,0068 0,0065 0,0063 0,0063 D11 0,0068 0,0061 0,0058 0,0048 0,0048 0,0047 0,0045 D12 0,0065 0,0057 0,0054 0,0044 0,0043 0,0042 0,0043 D13 0,0213 0,0216 0,0216 0,0226 0,0223 0,0221 0,0225 D14 0,0306 0,0400 0,0433 0,0366 0,0410 0,0436 0,0380 D15 0,0254 0,0289 0,0301 0,0274 0,0287 0,0294 0,0290 D16 0,0258 0,0275 0,0282 0,0305 0,0307 0,0310 0,0310 D17 0,1059 0,0936 0,0904 0,1213 0,1163 0,1135 0,1247 D18 0,0790 0,0712 0,0699 0,0941 0,0890 0,0868 0,0936 D19 0,0648 0,0563 0,0532 0,0599 0,0578 0,0562 0,0588 D20 0,0716 0,0844 0,0881 0,0824 0,0883 0,0915 0,0894 D21 0,0209 0,0237 0,0243 0,0206 0,0217 0,0223 0,0212 D22 0,0215 0,0282 0,0304 0,0180 0,0201 0,0213 0,0191 D23 0,0997 0,0892 0,0856 0,0966 0,0932 0,0894 0,0938 D24 0,0323 0,0318 0,0315 0,0295 0,0294 0,0288 0,0287 D25 0,0523 0,0588 0,0604 0,0486 0,0490 0,0524 0,0486 D26 0,0156 0,0140 0,0134 0,0121 0,0117 0,0112 0,0113 D27 0,0263 0,0324 0,0340 0,0231 0,0254 0,0262 0,0246 682 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 Sl. 3. Pomembnost kategorij in dejavnikov negotovosti Fig. 3. Importance of factors in relation to the level of trust in optimistic estimates ."-0,05 ft =0.5 ft =0,95 Sl. 4. Pomembnost kategorij in dejavnikov negotovosti Fig. 4. Importance of categories and uncertainty factors Preglednica 3. Stopnja negotovosti kategorij v odvisnosti od stopnje zaupanja in optimističnosti ocene Table 3. The level of uncertainty of categories in relation to the level of trust in optimistic estimates Negotovost kategorije (utež) / Uncertainty of category (weight) Kategorija Category a = 0 a = 0,5 a = 1 m = 0,05 m = 0,5 m = 0,95 mm = 0,05 mm = 0,5 m = 0,95 K1 0,1101 0,1041 0,1021 0,0994 0,0991 0,0986 0,0944 K2 0,2542 0,2378 0,2328 0,2639 0,2572 0,2535 0,2613 K3 0,2423 0,2451 0,2465 0,2943 0,2944 0,2949 0,3023 K4 0,1187 0,1215 0,1224 0,1018 0,1042 0,1053 0,1028 K5 0,1190 0,1263 0,1284 0,0997 0,1015 0,1026 0,0979 K6 0,1557 0,1652 0,1678 0,1409 0,1436 0,1451 0,1413 Hevristični model razvoja - A Heuristic Model for the Development 683 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 35 30 25 20 15 10 5 35 30 25 20 15 10 1 0,67 0 0,95 Alfa Mi 0,35 0,2 0,05 Sl. 5. Prostorski diagram pomembnosti kategorije K4 Fig. 5. Space diagram of the importance of category K4 majhna srednja velika small medium high 13 6 2 ^D2 D25 D27 0 2 6 13 Pomembnost Importance 5 0 0,95 0,67 Alfa Mi 0,35 0,2 0,05 Sl. 7. Prostorski diagram stopnje negotovosti kategorije K3 Fig. 7. Space diagram of the level of uncertainty of category K3 majhna small 13 6 srednja medium velika high 2 |D21 13 0 2 6 Pomembnost Importance Sl. 8. Lega dejavnikov kategorije K5 in K6 Fig. 8. Position of the factors of categories K5 and K6 Določitev stopnje negotovosti dejavnikov: Razmerja med kategorijami oz. dejavniki so izražena z vprašanjem: “Kolikokrat bolj je kategorija/dejavnik i negotov od kategorije/dejavnika j glede na cilj oz. nadrejeno kategorijo?” S primerjavo dejavnikov in kategorij po dvojicah (po podani ocenitveni lestvici, prirejeni na stopnjo negotovosti) in rabo trikotno porazdeljenih mehkih števil dobimo mehke matrike po vseh ravneh hierarhije. The ratios between the categories or factors are expressed with the question: “How many times is the category/factor i more important than the category/factor j according to the aim or the superior category?” With a pair-wise comparison of the factors and categories (according to the provided estimation scale, adapted for the level of uncertainty) and the use of triangularly divided fuzzy numbers, we arrive at the following fuzzy matrix on all levels of hierarchy: 1 684 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 ^ = 0,5 "-------------------1-------------------i> ;l-----------------------ste-----------------------r, Sl. 6. Negotovost kategorij in dejavnikov Fig. 6. Uncertainty categories and factors 1 15 10 1 0,83 0,67 0 0,95 1 0,83 0,67 0,5 0,33 0,17 Alfa 0,35 0,2 Mi 0,05 Sl. 9. Prostorski diagrami npr.: pomembnost in stopnja negotovosti za dejavnik D20 Fig. 9. Space diagrams of the importance and level of uncertainty for the factor D20 15 Al fa 0, 2 Mi Hevristični model razvoja - A Heuristic Model for the Development 685 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 13 --------- 6 ^J 0 2 6 13 Sl. 10. Področje pozornosti (A -> večje, B -> srednje, C -> manjše) Fig. 10. Area of attention (A -> larger, B -> medium, C -> smaller) 3.2 Integralna ocena negotovosti 3.2 Integral uncertainty estimate Z metodo mehkega AHP smo določili področja stopnje pomembnosti in negotovosti za vsak dejavnik, ki so omogočila tudi ustrezen izbor bolj ali manj kritičnih dejavnikov. Omejena področja vrednosti uporabimo za: . izgradnjo vektorja pomembnosti dejavnikov, . izgradnjo vektorja negotovosti dejavnikov. Integralna (celotna) ocena negotovosti (ION) je skalarni produkt obeh vektorjev: ION = Mejno integralno oceno negotovosti dobimo z uporabo enakih povprečnih uteži pri vseh komponentah vektorjev, torej pri n dejavnikih: 100 1 I 100 IONm=L Pri konkretnem obravnavanem primeru razvoja proizvodnih zmogljivosti imamo 27 dejavnikov. Mejna integralna ocena negotovosti znaša: With the method of fuzzy AHP we have determined the areas (intervals) of the level of importance and the uncertainty for every factor, which has given us the opportunity for a correct selection of the more or less critical factors. The mentioned areas of value can be used for the following: . design of the factor importance vector, . design of the uncertainty factor vector. The integral (total) uncertainty estimate (ION) is a scalar product of vectors P and N : P-N The fringe integral uncertainty estimate can be obtained by using the same mean weights with all the vector components, therefore, with n factors: 100 100 10000 In this actual example of the development of production capacity we have 27 factors. The fringe integral uncertainty estimate is: 10000 27 370 Vektor P ima naslednje člene: Vector P has the following terms: P = {3,26; 11,54; 2,63; 2,68; 2,78; 1,05; 0,58; 0,73; 2,03; 0,73; 0,57; 0,54; 2,20; 3,71; 2,78; 2,84; 10,76; 8,2; 5,9; 8,16; 2,25; 2,42; 9,27; 3,05; 5,45; 1,34; 2,86} Vektor N ima naslednje člene: v Vector N has the following terms: Nv = {4,05; 3,88; 2,45; 4,33; 8,89; 6,66; 5,17; 5,22; 6,16; 9,56; 2,42; 3,72; 2,65; 1,03; 1,38; 2,56; 0,72; 3,05; 2,42; 5,23; 1,29; 2,46; 5,52; 1,78; 4,88; 1,43; 1,77} 686 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 4 SKLEP Prispevek obsega izvirno sintezo teorije stvarnih možnosti, upravljanja tveganja, modeliranja negotovosti, metode analitičnega hierarhičnega postopka in mehke logike ter pomeni prispevek pri izgradnji orodij za podporo odločanju pri usmerjanju razvoja zmogljivosti v organizacijskem sistemu. Postopek je zasnovan na zmernem in obvladljivem številu vplivnih veličin in zagotavlja celovito obvladovanje problematike pri iskanju sprejemljivih rešitev. Izdelan hevristični model razvoja zmogljivosti je ustrezen, kar potrjuje tudi izveden praktični primer na livarskem sistemu. V prikazanem primeru z odpravljanjem negotovosti praktično zmanjšamo možnosti negativnih učinkov in se s tem, z vidika vseh virov, približamo optimizaciji proizvodnega sistema. Postopkovni del je namenjen vrednotenju analiziranih dejavnikov. Osnovna uporabljena metoda je mehki analitični hierarhični postopek (v osnovi se uporablja za podporo večkriterijskemu odločanju), ki temelji na medsebojnem določanju razmerij med posameznimi kategorijami in dejavniki negotovosti (najprej glede pomembnosti, v naslednji fazi pa še glede stopnje negotovosti dejavnikov) in na matematičnem preračunu uteži, ki kažejo že omenjeno pomembnost in stopnjo negotovosti. Prednost metode je prav v medsebojnem določanju razmerij, saj bistveno lažje ocenjujemo s primerjanjem po dvojicah, in v uporabi mehkih števil, ko v samo ocenitev vgradimo možnost napake ocenjevalca za en razred (v levo ali desno, večja napaka je praktično izločena) in to računsko upoštevamo, saj se rezultati kažejo v določenih koračnih območjih. Pomanjkljivost uporabljene metode je v razmeroma velikem številu potrebnih ocenitev, čemur pa se izognemo s tem, da imamo dejavnike že v analitičnem delu razvrščene po kategorijah, ter v nevarnosti pretirano neskladnih ocenitev, kar bi terjalo ponovitev postopka primerjanja oziroma popravek izbranih ocenitev. V prispevku smo uporabili intervalne rezultate mehke metode AHP za izgradnjo vektorja pomembnosti dejavnikov in vektorja negotovosti dejavnikov, katerih skalarni produkt nam daje integralno oceno negotovosti, ki v primerjavi z mejno oceno opredeljuje tveganje obravnavanega postopka. Na osnovi izvirnih diagramov ‘Negotovost/Pomembnost’ je bil oblikovan diagram 4 CONCLUSION This paper encompasses the original synthesis of the theory of real options, risk management, modelling uncertainty, the method of analytic hierarchy process and fuzzy logic, and it represents a contribution to the construction of tools for decision-making support for directing the capability development process in an organisational system. The procedure is based on a moderate and manageable number of influential sizes and provides a comprehensive management of the problem by searching for suitable solutions. The designed heuristic model of the development of capabilities is appropriate, which we confirmed by the practical example on a castings system. In the presented example, with the elimination of the uncertainties, we practically minimise the possibilities of negative effects, and with it, from the viewpoint of all the sources, come close to optimisation of the production system. The processing part is intended for an evaluation of the analysed factors. The basic method used is the soft analytical hierarchical process (basically used as a support to multiple criteria decision-making), based on a mutual determining of the relationships between individual categories and the factors of uncertainty (first with regard to importance and in the second stage with regard to the uncertainty level of factors) and on the mathematical calculation of weights reflecting the aforementioned importance and level of uncertainty. The advantage of this method lies in the mutual determining of relationships, as the evaluation is much easier with a comparison by pairs, and in the use of soft numbers when the evaluation itself includes the possibility of the evaluator’s error by a class (to the left or to the right, a bigger error is virtually excluded) and the calculation takes it into account as the results are presented in particular intervals. The disadvantage of the used method lies in the relatively large number of evaluations required, which can be avoided by grouping factors in the categories already in the analytical part, and in the danger of excessively diverging evaluations, which would require repeating the procedure of the comparison and adjustment of the selected evaluations. In the paper we have used interval results of the soft AHP method to build the vector of the importance of factors and the vector of the uncertainty of factors, the scalar product of which provides us with the integral evaluation of uncertainty, which in comparison with the limit evaluation determines the risk of the underlying process. On the basis of the original diagrams “Uncertainty/Importance”, we have formed Hevristični model razvoja - A Heuristic Model for the Development 687 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 Začetek/ Beginning Določitev obravnavane sposobnosti/ Definition of treated capability 1FEE Analiza virov/ Source analysis S NT Analiza sposobnosti/ Capability analysis 1ZL Opredelitev tipov negotovosti/ Definition of types of uncertainty Razčlenitev sposobnosti na kategorije negotovosti/ Classification of capabilities into uncertainty categories Razčlenitev kategorij na dejavnike negotovosti/ Classification of categories into uncertainty factors Ocenjevanje/ Estimation Izračun pomembnosti dejavnikov/ Calculation of factor importance Ca zraun stopnje negotovos, Ovrednotenje tveganja/ Estimation of risk Oblikovanje ABC diagrama za izbor dejavnikov/ Designing of ABC diagram Konec/ End Sl. 11. Sistemski postopek za obravnavanje razvoja zmogljivosti Fig. 11. A systematic approach to handling-capability development 688 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 pozornosti ABC, ki je namenjen izbiri oziroma razvrstitvi dejavnikov negotovosti, na kateri gradi odločitveni del sistemskega postopka. Odločitveni del je najpomembnejši del postopka glede na kriterij uporabnosti modela. V tem delu je bila logika modela prenesena v resnične odločitve. Odločitveni model se prične z razvrstitvijo dejavnika. Dejavniki C so tisti, ki jim ni treba dajati večje pozornosti glede na stopnjo pomembnosti in negotovosti. Kadar tovrstni dejavniki terjajo določene odločitve ali ukrepe, je te mogoče hitro in učinkovito izvesti, ne da bi nas skrbelo, kako lahko negotovost vpliva na posledice odločitve. Dejavniki A predstavljajo nasprotni pol dejavnikov glede na pomembnost in negotovost. Tovrstnim dejavnikom je treba posvetiti izjemno pozornost. Podrobneje je treba osvetliti navodilo, naj se predlagajo dokončne odločitve. To navodilo se ne sme razumeti kot predlog za nesprejetje odločitev. Navodilo pravi, da se v tem primeru ne smejo sprejemati odločitve, ki bi bile dokončne in ne bi omogočale prilagodljivega ravnanja. Te odločitve morajo biti usmerjene v ustvarjanje širokega nabora možnosti, ki omogočajo ukrepanje v primeru različnih scenarijev razvoja. Preden se sprejmejo odločitve, ki ustvarjajo možnosti v prihodnosti, je treba razpoznati širok nabor mogočih možnosti. Dejavniki B ležijo, glede na svoj pomen in glede na stopnjo negotovosti, med dejavniki A in C. Gre vsekakor za dejavnike, ki jim je treba posvetiti ustrezno pozornost. Delež pozornosti je seveda odvisen tudi od števila dejavnikov, ki so opredeljeni kot dejavniki stopnje A. Če dobimo veliko število dejavnikov stopnje A, potem bo pozornost dejavnikom stopnje B nekoliko manjša kakor v primeru, če imamo med A zgolj nekaj dejavnikov. V primeru, ko so dejavniki prišli v kategorijo B zato, ker so pomembni, niso pa nagnjeni k negotovosti, je mogoče sprejeti iste ukrepe kakor za dejavnike C. V primeru večje negotovosti se morajo tudi za dejavnike B sprejemati odločitve, ki omogočajo prilagodljivo ravnanje v prihodnosti. Izvirni prispevek v prispevku obsega: . Obravnavanje ustreznosti - uporabnosti logike teorije stvarnih možnosti pri razvoju strateških zmogljivosti, kakor tudi ovir, ki omejujejo njeno uporabnost (na primerih odločanja v proizvodnem sistemu). . Razvoj hevrističnega sistemskega postopka, ki na podlagi teorije stvarnih možnosti podpira odločanje pri razvoju zmogljivosti v organizacijskih sistemih. the ABC diagram of attention, which is used for selecting and classifying the uncertainty factors on which the decision-making part of the systematic approach builds. The decision-making part represents the most important part of the approach with regard to the model’s applicability criterion. In this part the model’s logic was transferred to real-life decisions. The decision-making model begins by classifying factors. C factors are those that do not require larger attention with regard to the levels of importance and uncertainty. When such factors require certain decisions or measures, they can be implemented quickly and effectively without worrying about how the uncertainty might affect the consequences of the decision. A factors are the opposite pole of factors with regard to importance and uncertainty. These factors require extra attention. The instructions regarding the proposing of the final decisions should be elaborated in greater detail. These instructions should not be interpreted as a proposal for not taking any decisions. The instructions say that in such a case no decisions can be taken that would be final and prevent the flexibility of action. These decisions should be directed towards creating a wide range of options, enabling reaction in the case of different development scenarios. Before adopting decisions that create future options, the wide range of available options should be identified. B factors lie between A and C factors with regard to their importance and the level of uncertainty. These are by all means factors that require an appropriate level of attention. The proportion of attention naturally also depends on the number of factors being defined as A-level factors. If we get a large number of A-level factors, the attention given to B-level factors will be slightly lower than in cases where there are only a few A-level factors. In the case that factors are classified in the B category, because they are important but not subject to uncertainty, the same measures as for C factors can be adopted. In the case of increased uncertainty, decisions enabling the flexibility of future actions should also be adopted for B factors. The original contribution in this paper is composed of: . Dealing with suitability - usefulness of the logic of the theory of real options with the development of strategic capacities, as well as obstacles, which limit its usefulness (with the examples of decision-making in the production process). . The development of a heuristic system approach which, on the basis of the theory of real options, encourages the decision-making in capabilities-development in organisational systems. Hevristični model razvoja - A Heuristic Model for the Development 689 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 . Dopolnitev hevrističnega postopka za učinkovito razlago numeričnih rezultatov in njihovo podporo postopku odločanja: o uporaba mehke metode AHP za določanje stopnje negotovosti je popolnoma izvirna zamisel, saj se omenjena metoda uporablja le za določanje pomembnosti, o izvirni sestavljeni diagrami ‘Pomembnost -Negotovost’ in diagram pozornosti ABC omogočajo izbiro in razvrstitev dejavnikov (in kategorij), o integralna ocena negotovosti (ION) je izvirni prispevek pri ovrednotenju negotovosti. Razvita je tudi metodologija za določitev mejne integralne ocene, tako da je omogočena splošna opredelitev tveganja vsake obravnavane dejavnosti. Osnovni izziv za prihodnost je izdelava enovitega programskega orodja, ki bi vključevalo vse v raziskavi uporabljene tehnike in metode in zajelo celotne preračune, od vnosa potrebnih podatkov do izpisa rezultatov in izrisa vseh diagramov ter predlaganih smernic pri sprejemanju odločitev. . The completion of a heuristic approach for the effective interpretation of numerical results and their support in the decision making process: o the use of the fuzzy AHP method for determining the uncertainty level is an entirely original idea, for the above-mentioned method it is used only for defining the importance, o the original combined diagrams “Importance -Uncertainty” and the ABC diagram of attention, which enable the selection and classification of factors (and categories), o the integral uncertainty estimation (ION) represents an original method for estimating uncertainty. There is also the methodology for determining the fringe integral estimate, which enables the common estimation of risk for every activity involved. The fundamental challenge for the future is the design of a uniform software tool that would incorporate all the used techniques and methods, and encompass all the calculations, from the input of the necessary data to the printout of results, and the design of all the diagrams and the proposed guidelines for decision-making. 5 LITERATURA 5 LITERATURE [1] Amram, M., Kulatilaka, N. (1999) Real Options: managing strategic investments in an uncertain world, Harvard Business School Press, Harvard, Cambridge, MA. Arrow, K. J. (1974) The limits of organisation, Norton, New York. Black, F., Scholes, M. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, Vol 81, pp. 637-659. Bowman, E. H., Hurry, D. (1993) Strategy through the options lens: an integrated view of resource investments and the incremental-choice process, Academy of Management Review, Vol 18, No 4, pp. 760-782. Copeland, T, Antikarov, V (2001) Real Options: a practitioner’s guide, Texere, New York. Cyert, R. M., March, J. G. (1963) A behavioral theory of the corporation, Prentice-Hall, New York. Dierickx, I., Cool, K. (1989) Asset stock accumulation and sustainability of competitive advantage, Management Science, Vol. 17, No. 1, pp. 121-154. Dosi, G., Nelson, R. R, Winter, S. G. (2000) The nature and dynamics of organizational capabilities, Oxford University Press, Oxford. Einsenhardt, K. M. (1989) Building theories from case study research, Academy of Management Review, Vol. 14, No. 4, pp. 532-550. Howell, S. Stark, A., Newton, D., Paxon, D., Cavus, M., Pereira, J., Patel, K. (2001) Real Options: evaluating corporate investment opportunities in a dynamic world, Financial Times-Prentice Hall, London. Kogut, B., Kulatilaka, N. (2001) Capabilities as real options, Organization Science, Vol. 12, No. 6, pp. 744-758. Kylaheiko, K., Sandstrom, J., Virkkunen, V (2002) Dynamic capability view in terms of real options, International Journal of Production Economics, Vol. 80, No. 1, pp. 65-83. Makadok, R. (2001) Toward a synthesis of the resource-based and dynamic-capability views of rent creation, Strategic Management Journal, Vol. 23, No. 5, pp. 387-401. [14] Mosakowski, E. (1998) Entrepreneurial resources, organizational choice, and competitive outcomes, Organization Science, Vol. 9, No. 6, pp. 652-743. [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] 690 Zvonko Kremljak - Andrej Polajnar - Borut Buchmeister Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 674-691 [15] Pandza, K., Horsburgh, S., Gorton, K., Polajnar, A. (2003) A real options approach to managing resources and capabilities, International Journal of Operations & Production Management, Vol. 23, No. 9, pp. 1010-1032. [16] Teece, D. J., Pisano, G. P., Shuen, A. (1997) Dynamic capabilities and strategic management, Strategic Management Journal, Vol. 18, No. 7, pp. 509-533. [17] Trigeorgis, L. (1996) Real Options: managerial flexibility and strategy in resource allocation, MIT Press, Cambridge, MA. [18] Tsoukas, H. (1996) The firm as a distributed knowledge system: a constructionist approach, Strategic Management Journal, Vol. 17, Winter Special Issue, pp. 11-25. Naslova avtorjev: mag. Zvonko Kremljak Ministrstvo za obrambo Direktorat za logistiko Kardeljeva ploščad 24 1000 Ljubljana zvonko.kremljak@s5.net prof.dr. Andrej Polajnar doc.dr. Borut Buchmeister Univerza v Mariboru Fakulteta za strojništvo Smetanova 17 2000 Maribor andrej.polajnar@uni-mb.si borut.buchmeister@uni-mb.si Authors’ Addresses:Mag. Zvonko Kremljak, Ministry of Defence Office of Logistics Kardeljeva ploščad 24 1000 Ljubljana, Slovenia zvonko.kremljak@s5.net ProfDr. Andrej Polajnar DocDr. Borut Buchmeister University of Maribor Faculty of Mechanical Eng. Smetanova 17 2000 Maribor, Slovenia andrej.polajnar@uni-mb.si borut.buchmeister@uni-mb.si Prejeto: Received: 2.5.2005 Sprejeto: Accepted: 29.6.2005 Odprto za diskusijo: 1 leto Open for discussion: 1 year Hevristični model razvoja - A Heuristic Model for the Development 691 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 UDK - UDC 532.528:532.542 Izvirni znanstveni članek - Original scientific paper (1.01) Diskretni plinski kavitacijski model z upoštevanjem vpliva nestalnega kapljevinskega trenja v cevi A Discrete Gas-Cavity Model that Considers the Frictional Effects of Unsteady Pipe Flow Anton Bergant - Uroš Karadzic - John Vitkovsky - Igor Vušanovič - Angus R. Simpson Prehodni kavitacijski tok pare v cevi vzbudi padec tlaka na parni tlak kapljevine. Podan je kratek oris metode karakteristik, temu slede osnove nestalnega kapljevinskega trenja in prehodnega kavitacijskega toka v cevi. Glavni cilj tega prispevka je predstavitev novega plinskega kavitacijskega modela (DPKM) z upoštevanjem vplivov nestalnega trenja. Rezultati izračuna so primerjani z rezultati meritev v laboratoriju. Upoštevanje nestalnega trenja v DPKM da bolj natančne računske rezultate. © 2005 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi cevni, udari vodni, tok kavitacijski, modeli kavitacijski diskretni plinski, trenje nestalno) Transient, vaporous, cavitating pipe flow occurs when the pressure drops to the liquid’s vapour pressure. A brief description of the method of the characteristics and fundamentals of unsteady pipe-flow friction and transient, cavitating pipe flow are given. The main objective of this paper is to present a novel, discrete gas-cavity model (DGCM) with a consideration of unsteady frictional effects. The numerical results are compared with the results from laboratory measurements. The inclusion of unsteady friction into the DGCM significantly improves the numerical results. © 2005 Journal of Mechanical Engineering. All rights reserved. (Keywords: piping systems, water hammer, cavitating flow, discrete gas cavity models, unsteady friction) 0 UVOD 0 INTRODUCTION Hidravlični cevni sistemi morajo varno delovati v širokem pasu obratovalnih režimov. Vodni udar vzbudi nihanje tlaka v cevnih sistemih, spremembo vrtilne frekvence (narastek, nasprotno vrtenje) v hidravličnih strojih in nihanje gladine vode v izravnalnikih. Prehodni pojavi v ceveh lahko povzročijo zadosten padec tlaka, ki vodi do prekinitve homogenosti in kontinuitete kapljevine (pretrganje kapljevinskega stebra). Neželeni vplivi vodnega udara lahko ustavijo obratovanje hidravličnih sistemov (hidroelektrarna, črpalni sistem) in poškodujejo elemente sistema; na primer zrušitev cevovoda. Obremenitve vodnega udara v dopustnih mejah lahko dosežemo z ustreznim krmiljenjem obratovalnih režimov, vgradnjo elementov za blažitev vodnega udara ali prerazporeditvijo elementov cevnega sistema ([1] in [2]). Umerjanje in nadzor Hydraulic piping systems should work safely over a broad range of operating regimes. Water hammer induces pressure fluctuations in piping systems, rotational speed variations (overspeed, reverse rotation) in hydraulic machinery or water-level oscillations in surge tanks. Transients in pipelines can cause a drop in pressure large enough to break the liquid’s homogeneity and continuity (liquid column separation). Undesirable water-hammer effects can disturb the overall operation of hydraulic systems (hydroelectric power plant, pumping system) and damage system components; for example, pipe rupture can occur. Water-hammer loads can be kept within the prescribed limits by the adequate control of the operational regimes, the installation of surge-control devices or the redesign of the original pipeline layout ([1] and [2]). The calibration and monitor- 692 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 hidravličnih sistemov narekujeta potrebo po globljem poznavanju fizike tlačnih valov [3]. Prvi del prispevka obravnava matematična orodja za modeliranje nestalnega kapljevinskega trenja in prehodnega parnega kavitacijskega toka (pretrganje kapljevinskega stebra). Premena enačb nestalnega toka v cevi z uporabo metode karakteristik da osnove algoritma za vodni udar. V deltoidno mrežo metode karakteristik je vgrajen konvolucijski model nestalnega trenja z uporabo zmogljivih računskih orodij [4]. Vgradnja diskretnih kavitacij v model vodnega udara da diskretni kavitacijski model ([2] in [5]). V prispevku je podan nov diskretni plinski kavitacijski model (DPKM) z upoštevanjem vpliva nestalnega kapljevinskega trenja v cevi. Podan je kratek oris preizkusne postaje za meritev vodnega udara. V zaključnem delu prispevka so podani številni primeri, iz katerih izhaja, da upoštevanje nestalnega kapljevinskega trenja v DPKM pomembno vpliva na napoved tlačnih valov v preprostem cevnem sistemu z ventilom. ing of hydraulic systems requires a detailed knowledge of water-hammer waveforms [3]. The first part of the paper deals with mathematical tools for modeling unsteady pipe-flow friction and transient vaporous cavitation (liquid column separation). The method of characteristics transformation of the unsteady pipe-flow equations gives the water-hammer solution procedure. A convolution-based unsteady friction model using state-of-the-art numerical tools [4] is explicitly incorporated into the staggered grid of the method of characteristics. Incorporating discrete cavities into the water-hammer model leads to the discrete-cavity model ([2] and [5]). A novel discrete gas-cavity model (DGCM) with consideration of the unsteady pipe-flow friction effects is presented in the paper. The experimental apparatus for measurements of the water-hammer pressure waves is briefly described. The paper concludes with a number of case studies showing how the inclusion of unsteady friction into the DGCM significantly affects the pressure traces in a simple reservoir-pipeline-valve system. 1 TEORETIČNI MODEL 1 THEORETICAL MODEL Vodni udar popisuje potovanje tlačnih valov v ceveh s kapljevino. Nestalni tok v cevi popišemo s kontinuitetno in gibalno enačbo [2]: Water hammer is the transmission of pressure waves in liquid-filled pipelines. Unsteady pipe flow is described by the continuity equation and the equation of motion [2]: dJH +VdJH -V dt dx dH dV g----+ — + V dx dt Naj omenimo, da so vse označbe definirane v poglavju 6. Postavimo tok v eni razsežnosti (po prerezu povprečena hitrost in tlak), tlak večji od parnega tlaka kapljevine, linearen elastični odziv stene cevi in kapljevine, nestalno trenje kapljevine nadomeščamo s stalnim, zanemarljivo količino prostih plinskih kavitacij v kapljevini inšibko interakcijo med kapljevino in ogrado. Konvektivni členi V(dH/dx), V(dV/dx) in Vsin^so majhni v primerjavi s preostalimi členi in jih v inženirski uporabi lahko zanemarimo ([1] in [2]). Z vpeljavo pretoka Q = VA namesto povprečne pretočne hitrosti V se poenostavljeni sistem enačb (1) in (2) glasi: a a 8V sin# +--------= 0 g 8x dx 2D (1) (2). Note that all the symbols are defined in Section 6. The flow in the pipe is assumed to be one-dimensional (cross-sectional averaged velocity and pressure distributions), the pressure is greater than the liquid vapour pressure, the pipe wall and the liquid behave linearly elastically, unsteady friction losses are approximated as steady friction losses, the amount of free gas in the liquid is negligible and the fluid-structure coupling is weak. For most engineering applications, the transport terms V(dH/dx), V(3V/3x) and Vsinč, are very small compared to the other terms and can be neglected ([1] and [2]). A simplified form of Eqs. (1) and (2) using the discharge Q=VA instead of the flow velocity V is: dH a2 dQ ----+------— = 0 dt gA dx dH + 1 dQ Q\Q\ dx gA dt 2gDA 2 (3) (4). Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 693 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 Premena poenostavljenih enačb (3) in (4) z metodo karakteristik (MK) da združljivostne enačbe vodnega udara, ki veljajo vzdolž karakterističnih krivulj. Združljivostne enačbe v koračni obliki so numerično stabilne razen v primeru velikih izgub zaradi trenja in redke računske mreže. Obravnavane enačbe, zapisane za računsko točko i (sl. 1), se glase [2]: - vzdolž C+ karakteristike (Dx/Dt = a) The method of characteristics (MOC) transformation of the simplified equations (3) and (4) produces the water-hammer compatibility equations, which are valid along the characteristics lines. The compatibility equations in finite-difference form are numerically stable unless the friction is large and the computational grid is coarse and, when written for a computational section i (Fig. 1), are [2] - along the C+ characteristic line (Dx/Dt = a) gA - vzdolž C- karakteristike (Dx/Dt = -a) H-H + (Q i,t -Q i-1,t-Dt )+ Q i,t Q a () ( ) f Dx ( )( i,t i-1,t-Dt u d 2u d 2gDA2 d i-1,t-Dt H-H - (Q i,t -Q i+1,t-Dt )- Q i,t Q a ( ) () f Dx ( )( i,t i+1,t-Dt d u 2 d u - along the C- characteristic line (Dx/Dt = -a) f Dx gA V primeru vodnega udara sta pretok na navzgornjem koncu računske točke i ((Q )i) in pretok na navzdolnjem koncu točke ((Qd)) u enaka (nestalni kapljevinski tok). Na robu (rezervoar, ventil) enačba robnega pogoja nadomesti eno od združljivostnih enačb vodnega udara. V tem prispevku bomo uporabili deltoidno mrežo metode karakteristik [2]. 1.1 Nestalno kapljevinsko trenje v cevi V algoritmih za vodni udar običajno uporabimo stalni ali navidezno stalni člen trenja. Ta (5), (6). 2gDA The discharge at the upstream side of the computational section i ((Qu)i) and the discharge at the downstream side of the section ((Qd)i) are identical for the water-hammer case (unsteady liquid flow). At a boundary (reservoir, valve), a device-specific equation replaces one of the water-hammer compatibility equations. The staggered grid in applying the method of characteristics [2] is used in this paper. 1.1 Unsteady Pipe Flow Friction Traditionally, the steady or quasi-steady friction terms are incorporated into the water-hammer t t-Dt 1 -4-----> J L \ C C \ 1—> 0 jsn i-1o io i+1o J Sl. 1. Deltoidna mreža metode karakteristik za sistem hram - cevovod - ventil Fig. 1. The method of characteristics staggered grid for a reservoir-pipe-valve system L x 694 Bergant A. - Karadzic U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 postavka velja za počasne prehode, pri katerih so strižne sile navidezno stalne. Uporaba navidezno stalnega modela trenja za hitre prehode da, kakor so pokazale primerjave med rezultati izračuna in meritev ([6] do [8]), znatna odstopanja v dušenju, obliki in času poteka tlačnih valov. Koeficient trenja, zapisan neposredno v enačbah (5) in (6), lahko izrazimo kot vsoto navidezno stalnega dela fq in nestalnega dela Navidezno stalni koeficient trenja fq je odvisen od Reynoldsovega števila in relativne hrapavosti cevi. V literaturi so predlagani številni modeli nestalnega trenja, ki jih delimo na enorazsežne (1D) in dvorazsežne (2D) modele. V 1D modelih približamo dejanski 2D prečni profil hitrosti in ustrezajoče izgube trenja. Z 2D modeli računamo dejanski prečni profil hitrosti med prehodnim pojavom. Modele trenja lahko razporedimo v šest skupin [7]: 1) člen trenja je odvisen od trenutne povprečne hitrosti V, 2) člen trenja je odvisen od trenutne povprečne hitrosti V in trenutnega krajevnega pospeška dV/dt, 3) člen trenja je odvisen od trenutne povprečne hitrosti V, trenutnega krajevnega pospeška dV/ dt in trenutnega konvektivnega pospeška adV/ x (Brunonejev model), 4) člen trenja je odvisen od trenutne povprečne hitrosti V in difuzije d2V/dx2, 5) člen trenja je odvisen od trenutne povprečne hitrosti V in uteži za hitrostne spremembe v preteklosti W(z) (konvolucijski model), 6) člen trenja je odvisen od trenutne porazdelitve hitrosti po prerezu (2D modeli). V prispevku bomo obravnavali konvolucijski model nestalnega trenja ([4], [10] do [12]). 1.2 Prehodni kavitacijski tok Kavitacijski tok v cevi se pojavi pri nizkih tlakih med prehodnimi pojavi. Prehodna kavitacija znatno vpliva na obliko tlačnega vala. Enačbe vodnega udara postavljene za enofazni prehodni tok, ne veljajo za dvofazni prehodni tok. Prehodna kavitacija v ceveh se pojavi v dveh algorithms. This assumption is satisfactory for slow transients where the wall shear stress has a quasi-steady behaviour. Previous investigations using the quasi-steady friction approximation for rapid transients ([6] to [8]) showed significant discrepancies in the attenuation, the shape and the timing of the pressure traces when computational results were compared with measurements. The friction factor, explicitly used in Eqs. (5) and (6), can be expressed as the sum of the quasi-steady part fq and the unsteady part fu [9]: The quasi-steady friction factor, fq, depends on the Reynolds number and the relative pipe roughness. A number of unsteady-friction models have been proposed in the literature including one-dimensional (1D) and two-dimensional (2D) models. The 1D models approximate the actual 2D cross-sectional velocity profile and the corresponding viscous losses in different ways. The 2D models compute the actual cross-sectional velocity profile continuously during the water-hammer event. The friction term can be classified into six groups [7]: 1) The friction term is dependent on instantaneous mean flow velocity, V, 2) The friction term is dependent on instantaneous mean flow velocity, V, and the instantaneous local acceleration, d V/dt, 3) The friction term is dependent on the instantaneous mean flow velocity, V, the instantaneous local acceleration, dV/dt, and the instantaneous con-vective acceleration, adV/dx (Brunone’s model), 4) The friction term is dependent on the instantaneous mean flow velocity, V, and the diffusion, FV/dx2, 5) The friction term is dependent on the instantaneous mean flow velocity, V, and the weights for past velocity changes, W(t) (convolution-based model), 6) The friction term is based on the cross-sectional distribution of instantaneous flow velocity (2D models). This paper deals with the convolution-based unsteady-friction model ([4], [10] to [12]). 1.2 Transient Cavitating Pipe Flow Cavitating pipe flow usually occurs as a result of low pressures during a transient event. Transient cavitation significantly changes the water-hammer waveform. Water-hammer equations developed for a one-phase liquid are not valid for the two-phase transient fluid flow. There are two basic types of f=fq+ f u (7). Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 695 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 oblikah ([2] in [3]): 1) enokomponentni dvofazni tok (parna kavitacija, pretrganje stebra), 2) dvokomponentni dvofazni tok (plinska kavitacija, prost plin v kapljevinskem toku). V prispevku obravnavamo parno kavitacijo v ceveh. Kavitacija se lahko pojavi kot krajevna kavitacija z velikim kavitacijskim razmernikom -kavitacija na robu ali visokem kolenu vzdolž cevi, ali kot nepretrgani kavitacijski tok z majhnim kavitacijskim razmernikom - enakomerno porazdeljeni mehurčki v kapljevini. Parna kavitacija v ceveh se pojavi, ko se tlak kapljevine zniža na parni tlak kapljevine. Postavimo zanemarljivo majhno količino prostega in/ali izločenega plina v kapljevini. Ta postavka velja v večini industrijskih cevnih sistemov. Tlačni val v cevi potuje s stalno hitrostjo pri tlaku, večjem od parnega tlaka kapljevine. Tlačni valovi ne obstajajo v področju nepretrganega parnega kavitacijskega toka. Nezmožnost potovanja tlačnega vala v področju nepretrganega parnega toka je karakteristična ločnica med parno in plinsko kavitacijo. Razviti so bili številni modeli za popis parne kavitacije, to so diskretni parni kavitacijski model (DPAKM), diskretni plinski kavitacijski model (DPKM) z upoštevanjem majhnega plinskega razmernika (a < 10-) in kombinirani parni kavitacijski model ([2] in [5]). Diskretni plinski kavitacijski model je preprost in daje natančne rezultate v širokem pasu obratovanja sistema [13]. V prispevku podajamo nov DPKM z upoštevanjem nestalnega kapljevinskega trenja v cevi. 2 DISKRETNI PLINSKI KAVITACIJSKI MODEL Z UPOŠTEVANJEM NESTALNEGA TRENJA Diskretni plinski kavitacijski model (DPKM) dopušča plinske kavitacije v računskih točkah numerične mreže metode karakteristik. V cevnih odsekih med numeričnimi točkami obstaja kapljevina, kjer potujejo udarni valovi s stalno hitrostjo a. Diskretno plinsko kavitacijo popišemo z združljivostnima enačbama vodnega udara (5) in (6), kontinuitetno enačbo za prostornino plinske kavitacije in plinsko enačbo [14]. V računski točki deltoidne mreže metode karakteristik se kontinuitetna enačba za prostornino plinske kavitacije in plinska enačba glasita: - kontinuitetna enačba za prostornino plinske kavitacije transient cavitating flow in pipelines ([2] and [3]): 1) One-component two-phase transient flow (vaporous cavitation, column separation), 2) Two-component two-phase transient flow (gaseous cavitation, free gas in liquid flow). This paper deals with vaporous cavitating pipe flow. Cavitation can occur as localized cavitation with a large void fraction, such as when a cavity forms at a boundary or at a high point along the pipeline, or as distributed cavitation with a small void fraction, such as when cavity bubbles are distributed homogeneously in a liquid. Vaporous cavitation occurs in pipelines when the liquid pressure drops to the vapour pressure of the liquid. The amount of free and/or released gas in the liquid is assumed to be small. This is usually the case in most industrial piping systems. The water-hammer wave propagates at a constant speed as long as the pressure is above the vapour pressure. Pressure waves do not propagate through an established mixture of liquid and vapour bubbles. The inability of pressure waves to propagate through a distributed vaporous cavitation zone is a major feature distinguishing the flow with vaporous cavitation from the flow with gaseous cavitation. A number of numerical models have been developed to describe vaporous cavitation, including the discrete vapour-cavity model (DVCM), the discrete gas-cavity model (DGCM) by utilizing a low gas void fraction (a < 10 7) and the interface vaporous cavita-tion model g ([2] and [5]). The discrete gas-cavity model is simple and performs accurately over a broad range of input parameters [13]. An improved DGCM that considers unsteady pipe friction is presented in this paper. 2 A DISCRETE GAS-CAVITY MODEL THAT CONSIDERS UNSTEADY FRICTION The discrete gas-cavity model (DGCM) allows gas cavities to form at computational sections in the method of characteristics numerical grid. A liquid phase with a constant wave speed a is assumed to occupy the computational reach. The discrete gas-cavity model is described by the water-hammer compatibility equations (5) and (6), the continuity equation for the gas volume, and the ideal-gas equation [14]. Numerical forms of the continuity equation for the gas volume and the ideal gas equation within the staggered grid of the method of characteristics are: - the continuity equation for the gas volume 696 Bergant A. - Karadzic U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 ( "g ) i,t= ( "g ) 2Dt+(y((Qd)i,t-(Qu)i,t)+(1-y)((Qd )i,t-2Dt-(Qu)i,t-2Dt))2 D t (8), - plinska enačba - the ideal-gas equation () (H0-z0-H) DPKM se uspešno uporablja za simuliranje The DGCM model has been successfully used plinske in parne (ag < 10-) kavitacije. V slednjem for the simulation of both gaseous and vaporous (ag primeru se izračun prostornine diskretne kavitacije < 10-) cavitation. In the latter case, when the discrete po enačbi (9) ponovi, ko je izračunana prostornina cavity volume calculated by Eq. (8) is negative, then po enačbi (8) negativna. the cavity volume is recalculated by Equation (9). 2.1 Konvolucijski nestalni model trenja 2.1 Convolution-Based Unsteady Friction Model Zielke [10] je s pomočjo analitičnih orodij razvil Zielke [10] analytically developed the convo- konvolucijski model (KM) nestalnega trenja za lution-based model (CBM) of unsteady friction for prehodni laminarni tok. Nestalni del koeficienta trenja transient laminar flow. The unsteady part of the fric- v enačbi (7) popišemo kot konvolucijo utežne funkcije tion factor in Eq. (7) is defined by the convolution of s krajevnimi pospeški v opazovanem časovnem pasu: a weighting function with past temporal accelerations: = 32nA trdQ ( t ** (10) dq\q\0 * WA- t ) d t . Zielke je rešil enačbo (10) z upoštevanjem Zielke evaluated Eq. (10) using the full convo- polne konvolucije, ki pa je računsko obsežna, saj lution scheme, which is computationally intensive be- obsega hitrosti v celotnem opazovanem časovnem cause it requires convolution with a complete history pasu. Prispevek avtorjev k računsko učinkoviti in of past velocities. The most recent approach to evalu- dovolj natančni rešitvi KM je v aproksimaciji utežne ate the CBM, which is efficient and accurate, makes funkcije W(t) kot končne vsote z N eksponentnimi an approximation of the weighting function W(t) by a členi [4]: finite sum of N exponential terms [4]: N Nestalni del koeficienta trenja je tedaj The unsteady part of the friction factor is definiran kot: now defined as: fu= DQQ N y k ( t ) (12), kjer so Heni yk(t) izraženi: where the component yk(t) is expressed as follows: t ( \ f VQ - n k K[t - t * yk(t=*mke d t (13). Pri tem konstanta K (= 4n/D2) spremeničas t And where the constant K (= 4 n/D2) converts v brezrazsežni čas t = 4 nt/D2. V času t + 2Dt člen yk the time t into the dimensionless time t = 4 nt/D2. At izrazimo z enačbo: time t + 2Dt the component yk is: yk ( t + 2Dt ) =j*m k e n k K t + 2 D t - t d t * (14). Rešitev gornjega integrala v obliki zapisa z Solving the integral and writing it in terms of brezrazsežnim časovnim korakom Dt (= KDt) da the dimensionless time step Dt (= KDt) finally gives učinkovit vrnilni izraz za člen yk in s tem tudi za fu: an efficient recursive expression for the component yk and hence for fu: Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 697 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 yk(t + 2Dt) = e- nkKDt -nkKDt yk(t) + mk[Q(t + 2D t ) - Q ( t )]} (15). Člen yk(t) je izračunan v predhodnem časovnem koraku in je znan v času t + 2Dt. Tako ni treba izvajati konvolucije v celotnem opazovanem pasu. Izpeljali smo koeficiente eksponente vrste mk in nk za Zielkejevo utežno funkcijo za prehodni laminarni tok [10] in za Vardy-Brownove utežne funkcije za prehodni turbulentni tok ([11] in [12]), dobimo jih v [4]. CBM model nestalnega trenja ne napove rahlega faznega odmika tlaka, ki ga razberemo iz rezultatov meritev ([15] in [16]). Fazni odmik je posledica nizkofrekvenčnih komponent karakteristik prehodnega pojava, ki so običajno reda velikosti osnovne frekvence. Iz tega izhaja, da je dejanska hitrost širjenja valov rahlo nižja od napovedane. Kapljevina ima dodatno vztrajnost zaradi nestalne porazdelitve hitrosti po prerezu, ki jo popišemo z vztrajnostnim popravnim koeficientom fi [16]. Vztrajnostni popravni koeficient (VPF) definiramo: P = AV Dejansko se /?malo spreminja med prehodnim pojavom ([17] in [18]). Postavimo, da je koeficient/? nespremenjen in sloni na začetnih pretočnih pogojih, tj. p=R. Obravnavni postopek je uporabljen tudi v podobnih primerih, kakor je izpeljava Vardy-Brownove utežne funkcije. VPF lahko določimo iz logaritmičnega ali potenčnega zakona porazdelitve hitrosti [19]. Uporabimo Reynoldsov transportni teorem, postavimo nespremenljivo vrednost VPF in dobimo gibalno enačbo, ki se razlikuje od enačbe (4): 8x gA 8t 2gDA 2 The component yk(t) was calculated during a previous time step and is known at time t + 2Dt. There is now no convolution with the complete history of velocities required. The coefficients of the exponential sum mk and nk were developed both for Zielke’s weighting function for transient laminar flow [10] and for Vardy-Brown’s weighting functions for transient turbulent flow ([11] and [12]) and can be found in [4]. The CBM of unsteady friction cannot produce the small low-frequency shift observed in experimental results ([15] and [16]). The low-frequency shift is related to the lowest-frequency components of the transient event, which are normally at the fundamental frequency. This suggests that the true wave speed is slightly lower than expected and the liquid has an extra inertia due to the velocity distribution, which is related to the momentum correction factor/?[16]. The momentum correction factor (MCF) is defined as: \v 2 d A (16). A Realistic values of /3do not vary greatly during a transient event ([17] and [18]). It is assumed that/?is constant and based on the steady conditions preceding the transient event, i.e., /?=/?. This is common to other analyses, such as the Vardy and Brown unsteady-friction weighting function. The MCF can be determined from either the log or power laws for the velocity distribution [19]. Using the Reynolds transport theorem, it can be shown that if the constant MCF is considered then the equation of motion (4) becomes: Q\Q\ (17). Premena enačb (3) in (17) z metodo karakteristik da združljivostne enačbe vodnega udara, ki se v koračni obliki glase: - vzdolž C+ karakteristike (Dx/ Dt = a/ Jf0) ^((Qu )i,t-(aUjf Dx The finite-difference form of water-hammer compatibility equations obtained by the MOC transformation of Equations (3) and (17) is - along the C+ characteristic line (Dx/ Dt = a /jfi0) H -H Qu i,t Qd i-1,t-Dt = 0 ( )( ) (18), gA u i,t d i-1,t-Dt 2gDA vzdolž C karakteristike [Dx/ Dt = -a / -^PA - along the C characteristic line [Dx / Dt = -a / -JfiA - aJK() - ( Qu ) )- f Dx gA (Qdi-< WW H -H Qd Qu ( )i,t ()i (19). Vpeljava R v enačbe vodnega udara da manj strme karakteristike, ki upočasnijo potek prehodnega pojava. 2gDA2 The inclusion of b0 in the water-hammer equations causes the slope of the characteristics to decrease, representing a slowing of the transient. 698 Bergant A. - Karadžič U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 3 PREIZKUSNA POSTAJA 3 EXPERIMENTAL APPARATUS Preizkusna postaja za raziskave vodnega udara in kavitacijskega toka v ceveh je postavljena v Robinovem hidravličnem laboratoriju univerze v Adelaidi, Avstralija [20]. Merilna postaja je sestavljena iz ravnega bakrenega cevovoda z nagnjeno strmino dolžine 37,23 m (U = ± 0,01 m), notranjega premera 22,1 mm (U = ± 0,1 mm) in debeline stene cevi 1,63 mm (U = ± 0,05 mm). Cevovod je priključen na tlačni hram z leve in tlačni hram z desne strani (sl. 2). Merilna negotovost U je definirana kot kvadratni koren vsote kvadratov relativne in absolutne napake [21]. Strmina cevovoda je nagnjena s 5,45 % (Ux = ± 0,01 %). Želeni tlak v obeh tlačnih hramih krmilimo z računalnikom. Neto prostornina vode v obeh tlačnih hramih in zmogljivost kompresorja omejujeta največjo stalno hitrost na 1,5 m/s in največji delovni tlak (tlačno višino) v obeh hramih na 400 kPa (40 m). Prehodni pojav na postaji je vzbujen s hitrim zapiranjem kroglastega zasuna. Hitro zaprtje ventila se lahko izvede z zapiralnim mehanizmom na torzijsko vzmet (čas zapiranja ventila t je nastavljiv od 5 do 10 milisekund) ali pa ročno. Vsak preizkus je izveden v dveh fazah. V prvi fazi dosežemo stalno pretočno hitrost (U = ± 1 % za prostorninsko metodo). V drugi fazi hitro zapiranje ventila vzbudi prehodni pojav. Hitrost širjenja udarnih valov (Ux = ± 0,1 % ) je določena iz časa potovanja primarnega udarnega vala (prvi val, ki ga zazna tlačno zaznavalo) med zaprtim ventilom in bližnjo četrtino dolžine cevovoda. Tlačni hram T1 Pressurized reservoir T1 Laboratory apparatus for investigating water-hammer and column-separation events in pipelines was constructed in the Robin Hydraulics Laboratory at the University of Adelaide, Australia [20]. The apparatus comprises a straight 37.23 m (U = ±0.01 m) long sloping copper pipe of 22.1 mm (U = ±0.1 mm) internal diameter and of 1.63 mm (U = ±0.05 mm) wall thickness connecting two pressurized tanks (Fig. 2). The uncertainty in a measurement, U, is expressed as a root-sum-square combination of the bias and precision error [21]. The pipe slope is constant at 5.45% (U = ±0.01 %). A specified pressure in each of the tanks is controlled by a computerized pressure-control system. The net water volume in both tanks and the capacity of the air compressor limits the maximum steady-state velocity to 1.5 m/s and the maximum operating pressure (pressure head) in each tank to 400 kPa (40 m). A transient event in the apparatus is initiated by a rapid closure of the ball valve. Fast closure of the valve is carried out either by a torsional spring actuator (the valve closure time tc may be set from 5 to 10 milliseconds) or manually by hand. Each experiment using the apparatus consists of two phases. First, an initial steady-state velocity condition (U = ±1% for the volumetric method) is established. Second, a transient event is initiated by a rapid closure of the valve. The wave-propagation velocity (U = ±0.1% ) is obtained from the measured time for the initial pressure wave (the first pressure wave passing the transducers) to travel between the closed valve and the quarter point nearest to the valve. JSE 2.03 m J2Z Tlačni hram T2 Tlačno zaznavalo Pressurized reservoir T2 ^Pressure transducer H v2 Ventil Valve Pipeline Cevovod D = 22.1 mm L = 37.23 m Sl. 2. Preizkusna postaja Fig. 2. Experimental apparatus layout Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 699 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 Na navzgornjem in navzdolnjem koncu cevovoda ter na polovici dolžine cevovoda so na notranji premer cevi vgrajena piezoelektrična tlačna zaznavala (Kistler 610 B, U = ± 0,7 %). Temperatura vode (U = ± 0,5 oC) je stalno merjena v hramu T1. Lega ventila med zapiranjem je merjena z optičnimi zaznavali (U = ± 0,0001 s). Meritev je registrirana in analizirana z merilnim računalnikom Concurrent 6655 v okolju UNIX. 4 PRIMERJAVA REZULTATOV IZRAČUNA IN MERITEV Rezultati izračunov in meritev prehodnih pojavov v preizkusni postaji (sl. 2) so podani za dva primera z začetnima pretočnima hitrostima V0 = {0,30; 1,40} m/s pri stalni statični višini v tlačnem hramu T2 H = 22 m [5]. Računski rezultati, dobljeni z DPKM z upoštevanjem nestalnega trenja po KM in vztrajnostnega popravnega koeficienta (DPKM + KM + VPF), so primerjani z rezultati meritev. Izračuni in meritve so bili izdelani za primer hitrega zapiranja ventila na navzdolnjem koncu cevovoda s pozitivno strmino pri tlačnem hramu T1 (sl. 2). Čas zapiranja ventila za oba primera je bil enak, t = 0,009 s, kar je precej krajše od odbojnega časa udarnega vala 2L/a = 2x37,23/1319 = 0,056 s (a = 1319 m/s je izmerjena hitrost udarnega vala). Ventil začne hitro zapirati v času t = 0,0 s. V izračunu je izbran nabor števila cevnih odsekov N = {16, 32, 64, 128, 256}, da se preveri grobost računskega modela [22]. V enačbi (8) je bil izbran utežni koeficient Y= 1,0, v enačbi (9) pa je bila izbrana dovolj majhna vrednost plinskega kavitacijskega razmernika a = 107 ([13] in [14]). Vztrajnostni koeficient v enačbah (18) in (19) je odvisen od začetne pretočne hitrosti [19]; za V0 = 0,30 m/s znaša A = 1,0332, za V0 = 1,40 m/s pa A = 1,0224. Izdelali smo tudi izračune z DPKM z upoštevanjem navidezno stalnega modela trenja (DPKM+NST), da bi izluščili vpliv modelov trenja na rezultate izračuna. Izračunani in izmerjeni rezultati so primerjani pri ventilu (H1) in na polovici dolžine cevovoda (H ) (sl. 2). Primerjava rezultatov izračuna in meritev za primer z začetno pretočno hitrostjo V0 = 0,30 m/s in dveh števil računskih cevnih odsekov N = {32, 128} je podana na slikah 3 in 4. Manjše število cevnih odsekov je običajno izbrano v inženirskih analizah vodnega udara. Večje število cevnih odsekov bi moralo dati bolj natančne rezultate izračuna (konvergenčni in stabilnostni kriterij). Three flush-mounted piezoelectric-type pressure transducers (Kistler 610 B, U = ± 0.7 %) are positioned at the endpoints and at the midpoint. The water temperature (U = ±0.5oC) in reservoir T1 is continuously monitored and the valve position during closure is measured using optical sensors (U = ±0.0001 s). Data acquisition and processing were performed with a Concurrent 6655 real-time UNIX data-acquisition computer. 4 COMPARISON OF COMPUTATIONAL AND EXPERIMENTAL RESULTS A numerical and experimental analysis of the transient events in the laboratory apparatus (Fig. 2) is presented for two different initial flow-velocity cases K = {0.30; 1.40} m/s at a constant static head in the pressurized reservoir T2M = 22 m [5]. The numerical results from the DGCM and the CBM of unsteady friction with the momentum correction factor (DGCM+CBM+MCF) are compared with the results of measurements. Computational and experimental runs were performed for a rapid closure of the valve positioned at the downstream end of the upward sloping pipe at the pressurized tank T1 (Fig. 2). The valve closure time for the two runs was identical, t = 0.009 s, which is significantly shorter than the water-hammer wave-reflection time of 2Z/a = 2x37.23/1319 = 0.056 s (a = 1319 m/s is the measured water-hammer wave speed). The rapid valve closure begins at time t = 0.0 s. Different numbers of reaches were selected for each com-putational run N = {16, 32, 64, 128, 256} to examine the numerical robustness of the model [22]. The value of the weighting factor = 1.0 was used in Eq (8), and a small gas void fraction of a = 107 was selected in Eq (9) ([13] and [14]). The momentum correction factor depends on the initial flow velocity [19] and its value used in Eqs. (18) and (19) is/? = 1.0332 for K = 0.30 m/s and/? = 1.0224 for K = 1.40 m/s. In addition, the DGCM and the quasi-steady friction model (DGCM+QSF) results are included in the analysis to compare the effect of friction modelling on the computational results. The computational and experimental results are compared at the valve (//1) and at the midpoint (// ) (Fig. 2). A comparison of the numerical and experimental results for an initial flow velocityK= 0.30 m/s and differ-ent numbers of computational reaches N = {32, 128} is presented in Figs. 3 and 4 respectively. Traditionally, a lower number of reaches is used in water-hammer analysis. A higher number of reaches should give more accurate results (convergence and stability criteria). 700 Bergant A. - Karadzic U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 Hitro zapiranje ventila v primeru za H = 22 m in začetno hitrost V0 = 0,30 m/s vzbudi vodni udar s pretrganjem kapljevinskega stebra. Največjo izmerjeno višino pri ventilu Hv1 = 95,6 m razberemo po zrušitvi prve kavitacije v obliki ozkega tlačnega utripa. Obremenitev z največjo višino je kratkotrajna (0,00628 s). Največja izračunana višina z DPKM+NST je H1 = 99,6 m in z DPKM+KM+VPF H1 = 95,1m. Rezultati izračuna, dobljeni z DPKM+NST, se dobro ujemajo z izmerjenimi rezultati za prvi in drugi tlačni utrip. Odstopanja med rezultati se večajo s časom prehoda. Rezultati, dobljeni z DPKM+KM+VPF, se dobro ujemajo z izmerjenimi rezultati v širokem pasu opazovanja prehodnega pojava. Primerjava rezultatov izračuna in meritev za primer z začetno pretočno hitrostjo V0 = 1,40 m/s in dveh števil računskih cevnih odsekov N = {32, 128} je podana na slikah 5 in 6. V obravnavanem primeru je največja višina pri ventilu enaka višini vodnega udara v času 2L/a po zaprtju ventila. Izmerjena največja višina je H1 = 210,9 m. Največji višini, določeni z DPKM+NST in DPKM+KM+VPF, se dobro ujemata A rapid valve closure for HT2 = 22 m and an initial flow velocity V0 = 0.30 m/s generates a water-hammer event with liquid column separation. The maximum measured head at the valve Hv1; max = 95.6 m occurs as a short-duration pressure pulse after the first cavity collapses. The duration of the maximum head is very short (0.00628 s). The maximum computed heads predicted by DGCM+QSF and DGCM+CBM+MCF are Hv 1; max = 99.6 m and Hv1; max = 95.1m, respectively. The computational results obtained by the DGCM+QSF agree well with the experimental results for the first and the second pressure-head pulse. The discrepancies between the results are greater for later times. The results obtained using the DGCM+CBM+MCF give pressure histories that are in good agreement with the experimental results for longer time periods. A comparison of the numerical and experimental results for an initial flow velocity V0 = 1.40 m/s and different numbers of computational reaches N = {32, 128} is presented in Figs. 5 and 6, respectively. The maximum head at the valve for this case is the water-hammer head generated at a time of 2L/a after the valve closure. The value of the maximum measured head is Hv1; max = 210.9 m. The maximum head predicted by the DGCM+QSF and 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 a) 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 c) Meritev Measurement -DPKM+NST DGCM+QSF 0.00 0.20 0.40 0.60 0.80 t (s) Meritev Measurement DPKM+NST DGCM+QSF 0.00 0.20 0.40 0.60 0.80 t (s) 100.0 80.0 ~ 60.0 % 40.0 * 20.0 0.0 -20.0 b) 100.0 80.0 ^ 60.0 w! 40.0 * 20.0 0.0 -20.0 d) 0.00 0.20 0.40 0.60 0.80 t (s) 0.00 0.20 0.40 0.60 0.80 t (s) Sl. 3. Primerjava višin pri ventilu (H) in na polovici dolžine cevovoda (H p): Fig. 3. Comparison of heads at the valve (H ) and at the midpoint (H )T V0 = 0.30 m/s, HT2 = 22 m, N = 32 Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 701 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 80.0 60.0 40.0 20.0 0.0 -20.0 c) 100.0 80.0 o 60.0 % 40.0 ^ 20.0 0.0 -20.0 0.00 0.20 0.40 0.60 0.80 a) t (s) b) 100.0 ] -------Meritev t 1 100.0 Measurement 80.0 60.0 100.0 Meritev p i Measurement 80.0 | --------DPKM+NST li i DGCM+QSF 60.0 40.0 i |a 1S, /;_, ,u ^ M fM i^i yj\i 20.0 —1 : w y y \ 0.0 __ i L IN Meritev Measurement - DPKM+NST DGCM+QSF i j Ji A Mi H jfi M Wi w la i 40.0 i L ^ 20.0- 0.0 -20.0 v 0.00 0.20 0.40 0.60 0.80 t (s) d) i Meritev Measurement DPKM+KM+VPF DGCM+CBM+MCF M\ m, fi w u 0.00 0.20 0.40 0.60 0.80 t (s) _ Meritev Measurement DPKM+KM+VPF DGCM+CBM+MCF ,lfi /1 f\ fi f, U 1 Wkj J; W U fj; W! V 0.00 0.20 0.40 0.60 0.80 t (s) Sl. 4. Primerjava višin pri ventilu (H) in na polovici dolžine cevovoda (H p): Fig. 4. Comparison of heads at the valve (H ) and at the midpoint (H )T V0 = 0.30 m/s, HT2 = 22 m, N = 128 260.0 220.0 180.0 140.0 100.0 60.0 20.0 -20.0 a) 260.0 220.0 180.0 140.0 100.0 60.0 20.0 -20.0 c) Meritev Measurement DPKM+NST iDGCM+QSF,, 260.0 220.0 180.0 f 140.0 Meritev Measurement DPKM+KM+VPF DGCM+CBM+MCF I 0.00 0.20 0.40 0.60 0.80 1.00 1.20 t (s) * 100.0-03 60.0-20.0 -20.0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 b) t (s) 260.0 220.0-180.0-? 140.0 5 100.0 ^ 60.0 20.0--20.0-0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 t (s) d) t (s) Meritev Measurement DPKM+KM+VPF DGCM+CBM+MCF IftlfA^A i iliJ jffW \MwIm Sl. 5. Primerjava višin pri ventilu (H) in na polovici dolžine cevovoda (H p): Fig. 5. Comparison of heads at the valve (H ) and at the midpoint (H )T V0 = 1.40 m/s, HT2 = 22 m, N = 32 702 Bergant A. - Karadzic U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 260.0 220.0 180.0 140.0 100.0 60.0 20.0 -20.0 a) 260.0 220.0 180.0 140.0 100.0 60.0 20.0 -20.0 c) Meritev Measurement DPKM+NST IDGCM+QSF 0.00 0.20 0.40 0.60 0.80 1.00 1.20 t (s) _ Meritev Measurement DPKM+NST «DGCM+QSF /iJvVw yywfe^ 0.00 0.20 0.40 0.60 0.80 1.00 1.20 t (s) Meritev Measurement DPKM+KM+VPF DGCM+CBM+MCF 260.0-220.0 : 180.0- f 140.0: ~* 100.0: ^ 60.0: 20.0: -20.0- 0.00 0.20 0.40 0.60 0.80 1.00 1.20 b) t (s) 260.0- 220.0- 180.0^ ? 140.0: 5 100.0-^ 60.0- 20.0: -20.0- 0.00 0.20 0.40 0.60 0.80 1.00 1.20 d) t (s) Sl. 6. Primerjava višin pri ventilu (H) in na polovici dolžine cevovoda (H p): Fig. 6. Comparison of heads at the valve (H ) and at the midpoint (H )T V0 = 1.40 m/s, HT2 = 22 m, N = 128 z izmerjeno višino. Čas obstoja prve kavitacije pri ventilu, določen z DPKM+KM+VPF, se bolje ujema od časa, določenega z DPKM+NST (meritev: 0,318 s; DPKM+NST: 0,331 s; DPKM+KM+VPF: 0,325 s). Rezultati izračuna, dobljeni z DPKM+NST, se dobro ujemajo z rezultati meritve do zrušitve prve kavitacije pri ventilu. Iz rezultatov, dobljenih z DPKM+KM+VPF, razberemo znatno izboljšanje napovedi dušenja in faznega odmika tlačnih utripov v primerjavi z rezultati, dobljenimi z DPKM+NST. Rezultati izračuna z večjim številom cevnih odsekov se bolje ujemajo z rezultati meritev. Sklepamo, da upoštevanje modela nestalnega trenja v DPKM (DPKM+KM+VPF) da bolj natančne rezultate v primerjavi z rezultati, dobljenimi z upoštevanjem modela navidezno stalnega trenja (DPKM+NST). 4.1 Konvergenca in stabilnost Numerični model DPKM+KM+VPF, vgrajen v MK računsko mrežo, mora zadostiti konvergenčnim in stabilnostnim kriterijem. Konvergenca definira stalno rešitev, ko se Dx in DGCM+CBM+MCF closely matches the measured head. The duration of the first cavity at the valve is predicted better by the DGCM+CBM+MCF than by the DGCM+QSF (measurement: 0.318 s; DGCM+QSF: 0.331 s; DGCM+CBM+MCF: 0.325 s). Computational results obtained with the DGCM+QSF agree well with experimental results until the first cavity at the valve collapses. The results from the DGCM+CBM+MCF show significant improvement in terms of both the attenuation and phase shift of the pressure-head traces when compared to the DGCM+QSF results. When the number of computational reaches is increased, the computational and measured results agree better. Inclusion of the unsteady-friction model into the DGCM (DGCM+CBM+MCF) significantly improves the results compared to those using the quasi-steady friction model (DGCM+QSF). 4.1 Convergence and Stability The numerical solution of the DGCM+CBM+MCF incorporated into the MOC computational grid should satisfy the convergence and stability criteria. Convergence relates to the behaviour of Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 703 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 Dt približujeta ničli, stabilnost rešitve pa je odvisna od napake zaokrožitve [1]. V tem prispevku sta konvergenca in stabilnost DPKM+KM+VP in DPKM+NST preverjena z metodo nabora cevnih odsekov [22] v pasu N = {16, 32, 64, 128, 256}. Na sliki 7 so podani rezultati izračuna za primer z the solution as Dx and Dt tends to zero, while stability is concerned with the round-off error growth [1]. The influence of the different numbers of computational reaches N = {16, 32, 64, 128, 256} is investigated for the DGCM+CBM+MCF [22]. In addition, a numerical analysis of the DGCM+QSF model is included as well. Fig. 7 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 100.0 80.0 60.0 40.0 20.0 0.0 -20.0 DPKM+NST DGCM+QSF f N=16 -N=32 -N=64 U WJ In DPKM+NST DGCM+QSF N=64 - N=128 - N=256 \l Ittl \a A\ A UN u ^ \ DPKM+NST DGCM+QSF N=16 -N=32 -N=64 DPKM+NST DGCM+QSF N=64 - N=128 - N=256 u M f V r \ i DPKM+KM+VPF DGCM+CBM+MCF J N=16 -N=32 -N=64 DPKM+KM+VPF DGCM+CBM+MCF, N=64 - N=128 - N=256 DPKM+KM+VPF DGCM+CBM+MCF N=16 -N=32 -N=64 DPKM+KM+VPF DGCM+CBM+MCF N=64 - N=128 - N=256 (1 0.00 0.20 0.40 0.60 0.80 0.00 0.20 t (s) Sl. 7. RaAunska analiza: V0 = 0,30 m/s, HT2 = 22 m Fig. 7. Numerical analysis: V0 = 0.30 m/s, HT2 = 22 m 0.40 t (s) 0.60 0.80 704 Bergant A. - Karadžič U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 začetno pretočno hitrostjo V0 = 0,30 m/s z blago kavitacijo. Rezultati, dobljeni z obema modeloma so konzistentni s povečanjem števila odsekov. To pa ne velja za rezultate izračuna v primeru z začetno hitrostjo V0 = 1,40 m/s na sliki 8. Intenzivna kavitacija vzdolž cevi v obliki področij 280.0 240.0 200.0 160.0 shows the numerical results for the case with an initial flow velocity V0 = 0.30 m/s with moderate cavitation. The results for both models are consistent as the number of reaches is increased. This is not the case for the numerical runs with initial velocity V0 = 1.40 m/s in Fig. 8. Severe cavitation along the pipeline forms distributed, 120.0 80.0 40.0 0.0 280.0 240.0 200.0 160.0 DPKM+NST DGCM+QSF 120.0 80.0 40.0 0.0 280.0 240.0 200.0 160.0 120.0 80.0 40.0 0.0 280.0 240.0 200.0 160.0 120.0 80.0 40.0 0.0 DPKM+NST DGCM+QSF UUUUW DPKM+KM+VPF DGCM+CBM+MCF DPKM+KM+VPF DGCM+CBM+MCF y'tjR^vV^- «=16 -«=32 -«=64 DPKM+NST DGCM+QSF «=16 -«=32 -«=64 !l DPKM+NST DGCM+QSF LjwWWAahJ LI «=16 -«=32 -«=64 DPKM+KM+VPF DGCM+CBM+MCF «=16 -«=32 -«=64 DPKM+KM+VPF DGCM+CBM+MCF MfaV- mrt* «=64 - «=128 - «=256 «=64 - «=128 - «=256 «=64 - «=128 - «=256 «=64 - «=128 - «=256 jm* um 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 t (s) t (s) Sl. 8. Računska analiza: V0 = 1,40 m/s, HT = 22 m Fig. 8. Numerical analysis: V0 = 1.40 m/s, HT2 = 22 m Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 705 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 nepretrganega parnega kavitacijskega toka in diskretnih kavitacij, ki jih razberemo iz meritev, je v DPKM modelih (sl. 5 in 6) popisana približno. Zrušitev velike kavitacije pri ventilu in diskretnih kavitacij vzdolž cevovoda vzbudi strma tlačna valovna čela, ki potujejo vzdolž cevi. Primerjava rezultatov izračuna in meritev (sl. 5 in 6) jasno pokaže, da DPKM+KM+VPF bolje popiše fizikalni pojav pri večjem številu cevnih odsekov. V splošnem amplituda in časovni potek glavnih tlačnih utripov, določenih z upoštevanjem navidezno stalnega in nestalnega trenja, konvergirata s povečanjem števila cevnih odsekov (vsak model konvergira k nekoliko različnemu rezultatu). DPKMne vzbudi visokih fizikalno nerealnih tlačnih utripov v primerjavi z diskretnim parnim kavitacijskim modelom (DPAKM) ([7] in [13]). Računska modela pa ne napovesta nekaterih visokofrekvenčnih utripov, razbranih v meritvah. Dosedanje preizkusne raziskave so pokazale, da prehodne kavitacije vzdolž cevi niso homogene ([23] in [24]), zato nekateri visokofrekvenčni pulzi niso ponovljivi in tudi ne vplivajo na glavne tlačne utripe. Podoben pojav lahko izluščimo v rezultatih izračuna z DPKM, pri katerih so nekateri visokofrekvenčni tlačni utripi vplivani s številom cevnih odsekov. Ta pojav zaznamo v področjih z blago kavitacijo vzdolž cevovoda (nepretrgani parni kavitacijski tok, diskretne kavitacije) kot posledico popisa kavitacije z različnim številom cevnih odsekov. Ta vpliv pa je zanemarljiv v primerjavi z odzivom na veliki skali. 5 SKLEP Podana je primerjava med rezultati izračuna in meritev za primer hitrega zapiranja navzdolnjega ventila v preprostem cevnem sistemu. Primerjana sta diskretni plinski kavitacijski model z upoštevanjem navidezno stalnega kapljevinskega trenja (DPKM+NST) in nestalnega trenja z uporabo konvolucijega modela (DPKM+KM+VPF). Primerjalna analiza obsega primer z blago in primer z intenzivno kavitacijo. Konvolucijski model nestalnega trenja bolj natančno popiše nestalno kapljevinsko trenje v primerjavi z navidezno stalnim približkom. Upoštevanje nestalnega trenja v DPKM da zato bolj natančne računske rezultate. Raziskali smo tudi vpliv izbire števila cevnih odsekov. Računska analiza pokaže, da je DPKM+KM+VPF grob s povečanjem števila cevnih vaporous cavitation zones and intermediate cavities that have been recorded by measurements and only approximately accounted for in the DGCMs (Figs. 5 and 6). The collapse of a large cavity at the valve and intermediate cavities along the pipe create steep pressure wave fronts that travel along the pipe. Comparisons between the measured and computed results clearly showed (Figs. 5 and 6) that the DGCM+CBM+MCF better represents the real flow situation as the number of computational reaches is increased. Generally, the magnitude and timing of the main pressure pulses predicted by the DGCM model using either the quasi-steady or the convolution-based model converge as the number of reaches is increased (although each method converges to a slightly different solution). The DGCM model does not generate large, unrealistic pressure spikes in comparison to the discrete vapour-cavity model (DVCM) ( [7] and [13]) . However, there still remain some high-frequency peaks in the experimental measurements that are not reproduced by either numerical model. Previous experimental studies clearly showed that transient cavities along the pipeline are not distributed homogeneously ([23] and [24]); therefore, some high-frequency peaks are not repeatable and do not affect the main pressure pulses significantly. A similar behaviour is revealed in the DGCM computational results in that some high-frequency peaks vary with the different numbers of reaches. This behaviour occurs in regions with distributed vaporous cavitation and intermediate cavities where small-scale cavitation takes place in slightly different ways for different numbers of computational reaches. However, typically this behaviour is small compared to the bulk transient response. 5 CONCLUSION Results from the discrete gas-cavity model with the quasi-steady friction approximation (DGCM+QSF) and with the convolution-based unsteady-friction model (DGCM+CBM+MCF) are compared with the results of measurements for a fast-downstream end-valve closure in a simple reservoir-pipeline-valve laboratory apparatus. A comparative analysis includes experimental tests for two different flow conditions with moderate and severe cavitation. The convolution-based unsteady-friction model better captures the behaviour of unsteady fluid friction than the quasi-steady friction approximation. The results clearly show that the inclusion of unsteady friction into the DGCM significantly improves the numerical results. The influence of the different numbers of reaches is also investigated. The examination of the computational results reveals the numerically robust 706 Bergant A. - Karadžič U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 odsekov. Obravnavani model zaradi dobrega ujemanja rezultatov izračuna z meritvami in računske grobosti priporočamo za inženirsko uporabo. Zahvala Ta prispevek je bil napisan med obiskom gospoda Karadžiča v Litostroju E.I. d.o.o. od 5. januarja do 28. februarja 2005. Avtorji se toplo zahvaljujejo Litostroju in CMEPIUSu (Center za mobilnost in evropske programe izobraževanja in usposabljanja) za podporo tega obiska. Za podporo raziskav se toplo zahvaljujejo tudi ARRSu (Agencija za raziskovalno dejavnost Republike Slovenije). behaviour of the DGCM+CBM+MCF as the number of reaches increases. Due to the excellent matches with experimental data and the robust numerical algorithm this model is recommended for engineering practice. Acknowlegments This paper was written during Mr Karadzic’s visit to Litostroj E.I. d.o.o. from January 5 to February 28, 2005. The authors wish to thanks Litostroj and CMEPIUS (Centre of the Republic of Slovenia for Mobility and European Programmes for Education and Training) who supported this visit. The support of the research by ARRS (Slovenian Research Agency) is gratefully acknowledged as well. prečni prerez hitrost širjenja udarnih (tlačnih) valov premer cevi Darcy-Weisbachov koeficient trenja zemeljski pospešek piezometrična višina (višina) parna tlačna višina dolžina cevi koeficienti eksponentne vrste število cevnih odsekov pretok navzdolnji pretok navzgornji pretok Reynoldsovo število = VD/n čas čas zapiranja ventila merilna negotovost povprečna pretočna hitrost pretočna hitrost utežna funkcija kordinata vzdolž cevi člen utežne funkcije geodetska višina plinski kavitacijski razmernik vztrajnostni korekcijski koeficient časovni korak dolžina cevnega odseka brezrazsežni časovni korak strmina cevovoda kinematična viskoznost brezrazsežni čas utežni koeficient diskretna prostornina kavitacije 6 OZNAČBE 6 SYMBOLS A a D f g H Hv L mk, nk N Q Qd Qu Re t, t* t c Ux V v W x yk z ag b Dt Dx Dt q n t y " pipe area water-hammer (pressure) wave speed pipe diameter Darcy-Weisbach friction factor gravitational acceleration piezometric head (head) gauge vapour pressure head pipe length exponential sum coefficients number of computational reaches discharge node downstream end discharge node upstream end discharge Reynolds number = VD/n time valve closure time uncertainty in a measurement average flow velocity flow velocity weighting function distance along the pipe component of the weighting function pipeline elevation gas void fraction momentum correction factor time step reach length dimensionless time step pipe slope kinematic viscosity dimensionless time weighting factor discrete cavity volume Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 707 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 Indeksi: Subscripts: približen app approximate plin g gas računska točka i node number polovica dolžine cevovoda mp midpoint navidezno stalni del q quasi-steady part hram T tank (reservoir) t time nestalni del u unsteady part ventil v valve stalen (začeten) ali referenčen 0 steady state (initial) or reference Okrajšave: Abbreviations: diskretni plinski kavitacijski model DPKM/DGCM discrete gas-cavity model diskretni plinski kavitacijski model z DPKM+NST/ discrete gas-cavity model with navidezno stalnim trenjem DGCM+QSF quasi-steady friction diskretni plinski kavitacijski model s DPKM+KM+ discrete gas-cavity model with konvolucijskim modelom in +VPF/DGCM+ convolution-based model and momentum vztrajnostnim popravnim faktorjem +CBM+MCF correction factor diskretni parni kavitacijski model DPAKM/DVCM discrete vapour-cavity model metoda karakteristik MK/MOC method of characteristics 7 LITERATURA 7 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] Chaudhry, M.H. 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(1989) Experimentation and uncertainty analysis for engineers. John Wiley and Sons, New York, ZDA [22] Maudsley, D. (1984) Errors in simulation of pressure transients in a hydraulic system. Proceedings of the Institute of Measurement and Control, 6(1), 7 - 12. [23] Fan, D., Tijsseling, A. (1992) Fluid-structure interaction with cavitation in transient pipe flows. Journal of Fluids Engineering, ASME, 114(2), 268 - 274. [24] Simpson, A.R., Bergant, A. (1996) Interesting lessons from column separation experiments. Proceedings of the 7th International Conference on Pressure Surges, BHR Group, Harrogate, Velika Britanija, 83 - 97. Naslovi avtorjev: doc.dr. Anton Bergant Authors’ Addresses: Doc.Dr. Anton Bergant Litostroj E.I. d.o.o. Litostroj E.I. d.o.o. Litostrojska 50 Litostrojska 50 1000 Ljubljana 1000 Ljubljana, Slovenia anton.bergant@litostroj-ei.si anton.bergant@litostroj-ei.si mag. Uroš Karadzic Mag. Uroš Karadzic Univerzitet Crne Gore University of Montenegro Mašinski fakultet Faculty of Mechanical Engineering Cetinjski put b.b. Cetinjski put n.n. 81000 Podgorica 81000 Podgorica Srbija i Crna Gora Serbia and Montenegro urosk@cg.ac.yu urosk@cg.ac.yu dr. John P. Vitkovsky Dr. John P. Vitkovsky Oddelek za naravne vire in Department of Natural rudarstvo Resources & Mines Indooroopilly, QLD 4068 Indooroopilly, QLD 4068 Avstralija Australia john.vitkovsky@nrm.qld.gov.au john.vitkovsky@nrm.qld.gov.au Diskretni plinski kavitacijski model - A Discrete Gas-Cavity Model 709 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 692-710 dr. Igor Vušanovič Univerzitet Crne Gore Mašinski fakultet Cetinjski put b.b. 81000 Podgorica Srbija i Crna Gora igorvus@cg.ac.yu prof. Angus R. Simpson Šola gradbenega in okoljskega inženirstva Univerza v Adelaidi Adelaide, SA 5005 Avstralija asimpson@civeng.adelaide.edu.au Dr. Igor Vušanovič University of Montenegro Faculty of Mechanical Engineering Cetinjski put n.n. 81000 Podgorica Serbia and Montenegro igorvus@cg.ac.yu Prof. Angus R. Simpson School of Civil & Environmental Engineering University of Adelaide Adelaide, SA 5005 Australia asimpson@civeng.adelaide.edu.au Prejeto: Received: 18.2.2005 Sprejeto: Accepted: 29.6.2005 Odprto za diskusijo: 1 leto Open for discussion: 1 year 710 Bergant A. - Karadzic U. - Vitkovsky J. - Vušanovič I. - Simpson A.R. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 UDK - UDC 621.56:536 Strokovni članek - Speciality paper (1.04) Statistični pristop k analizi hladilnih sistemov s hladilnimi stolpi na naravni vlek A Statistical Approach to the Analysis of Cooling Systems with Natural-Draft Cooling Towers Jure Smrekar - Janez Oman - Brane Širok Povečevanje in zaostrovanje zahtev pri obratovanju termoelektrarn, z namenom da bi pocenili proizvodnjo električne energije in zagotovili čistejše okolje, je pripeljalo do potrebe po optimizaciji celotnega postopka. Leta je v načelu sestavljen iz dovoda toplote v krožni proces, iz samega krožnega postopka in iz odvoda toplote v okolico. Optimizacija vseh treh sklopov energetskega postrojenja zagotavlja najboljše rezultate. Prispevek se nanaša na analizo meritev energijskih parametrov bloka 4 Termoelektrarne Šoštanj in prikazuje vpliv hladilnega sistema na izkoristek termoelektrarne. Analiza obsega statistične pristope analize termoenergetskega postrojenja, ki omogočajo vpogled v medsebojno odvisnost posamičnih parametrov in vplive na povečevanje izkoristka termoelektrarne. V našem primeru je glavni element hladilnega sistema hladilni stolp na naravni vlek, saj pomeni povezavo termoelektrarne z okolico. Približevanje optimalnejšemu obratovanju hladilnega sistema tako prispeva znatne prihranke pri porabi goriva in zmanjšani emisiji dimnih plinov. Prispevek vsebuje potrditev značilne linearne soodvisnosti med prenesenim toplotnim tokom na okolico in močjo na sponkah generatorja. © 2005 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi hladilni, stolpi hladilni, analize sistemov, postopki statistični) Changes to the operating requirements at power plants, with the intention of lowering energy costs and ensuring a cleaner environment, have brought optimization to the whole process. In principle, the process consists of an inlet heat stream to the process, the steam cycle itself and the rejected heat stream to the environment. The optimization of all three parts of the energetic system will ensure the best results. This study relates to an analysis of the measurements of energetic parameters at Block 4 of the Šoštanj power plant and shows the influence of the cooling system on the power plants efficiency. The paper includes a statistical approach to the analysis of a thermo-energetic system that enables an understanding of the relations between the parameters and shows guidelines for enlarging the thermo-energetic efficiency. The main part of the cooling system is the natural-draft cooling tower, which represents the interaction between the power plant and the environment. Approaching the optimal operating point of the cooling system contributes to fuel savings and decreasing the amount of exhaust-gas pollution. This paper also includes a verification of the typical linear relation between the heat transferred to the environment and the generation of power. © 2005 Journal of Mechanical Engineering. All rights reserved. (Keywords: cooling systems, cooling towers, systems analysis, statistical approach) 0 UVOD 0 INTRODUCTION Optimalno delovanje hladilnega sistema se izraža v največjem pridobljenem delu iz turbine in tako večjem celotnem izkoristku termoelektrarne zaradi najmanjše odvedene toplote iz sistema. Učinkovitost delovanja hladilnega sistema je eden The optimal operating condition of a cooling system results in the maximum acquired work from the turbine and overall power-plant efficiency because of the minimal amount of heat rejected to the environment. The efficiency of the cooling system 711 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 izmed odločilnih dejavnikov, ki pomembno vplivajo na izkoristek termoenergetskega sistema kot celote. Kakovosten hladilni sistem pomeni manjšo izgubo toplote, kar omogoča manjše hladilne naprave in manj hladilne vode. Količina toplote, odvedene s hladilnim sistemom, je večja od toplote, ki se v parnem krožnem postopku spremeni v delo. V današnjih hladilnih sistemih, novih in starih termoelektrarn, je odvedena toplota od 1,3 do 2,5-krat večja od koristno pridobljenega dela iz termoelektrarne. Pri načrtovanju stolpov je najpomembnejši parameter izkoristek hlajenja hladilnega stolpa. Z zmanjšanjem odvedene toplote se izkoristek krožnega postopka sam po sebi izboljša. Za ocenjevanje omenjenih izboljšav se med drugim uporablja tudi koeficient Q /P [1]. Z zmanjšanjem koeficienta je mogoče izboljšati učinkovitost celotnega termoenergetskega postrojenja, kar pa je odvisno od celovitih in lokalnih karakteristik hladilnega sistema, pri katerem je v analiziranem primeru glavni element hladilni stolp. Večina današnjih hladilnih stolpov je starih 30 do 50 let in njihovo obratovanje ni več optimalno. Naletimo na velike temperaturne in hitrostne neenakosti, ki se kažejo v različnih temperaturnih in hitrostnih stanjih zraka po prečnem prerezu hladilnega stolpa, kar ima za posledico manjšo učinkovitost stolpa ([2] in [6]). Anomalije so odvisne od konstrukcijskih lastnosti delilnih vodnih sistemov, prenosnikov toplote v hladilnih stolpih ali od vplivov okolja na hitrostne razmere zraka, ki vteka v stolp. Z odpravo krajevnih nepravilnosti hitrostnega in temperaturnega polja se izkoristek hladilnega stolpa poveča, kar posledično povečuje izkoristek celotnega termoenergetskega sistema. Dosedanje analize delovanja hladilnih stolpov večinoma temeljijo le na poznavanju parametrov okoliškega zraka ter parametrov vstopne in izstopne hladilne vode. S takšno analizo je mogoče ugotoviti le celotne lastnosti delovanja hladilnega stolpa, ki pa so vsekakor odvisne od učinkovitosti prenosa toplote na krajevni ravni. Analiza obsega proučevanje povezave med učinkovitostjo prenosa toplote na krajevni in celoviti ravni z močjo generatorja. Povezanost parametrov je prikazana z uporabo statističnih orodij. Prispevek vsebuje tudi predloge za izboljšave učinkovitosti prenosa toplote v hladilnih stolpih. is one of the most important parameters that have a large impact on the power plant’s efficiency. A high-quality cooling system represents lower heat losses, which leads to smaller cooling devices and less demand for cooling water. Heat rejected with the cooling system is larger than the heat converted by the steam cycle into useful work. In currently operating systems, old and new, the heat extracted varies from 1.3 to 2.5 times the useful work extracted from the thermodynamic system. When constructing a cooling tower the most important parameter is the tower’s efficiency. With the reduction of heat rejected to the environment, the overall power-plant efficiency improves by itself. For estimating this kind of improvement the coefficient Q&od /P [1] is often used. With a reduction of this coefficient it is possible to increase the efficiency of the power plant, which depends on the local characteristics of the cooling system, which in our case is the main part of the natural-draft cooling tower. The majority of today’s cooling towers are 30 to 50 years old, and their operation is no longer optimal. We come across large inhomogeneities in the air, which are shown in different temperatures and velocities across the cross-section of the cooling tower. This has the consequences of lower efficiency of the tower ([2] and [6]). The anomalies depend on the construction properties of the distribution water system, the heat exchangers in the cooling towers or the atmospheric influences on the air velocity distribution entering the cooling tower. Cooling-tower efficiency increases with the elimination of local irregularities of the temperature and velocity fields, which consequently increases the overall efficiency of the thermo-energetic system. Previous operation analyses of the cooling towers were mostly based just on measurements of atmospheric quantities and the parameters of the inlet and outlet cooling water. This kind of analysis enables only a determination of the integral characteristics of cooling towers that depend on heat and mass transfer on a local basis. Our analysis compared the research of the correlation between heat-transfer efficiency on a local and integral basis with the power of the generator. The connection between the parameters is shown with the help of statistical tools. The paper also includes proposals for heat-transfer improvement in cooling towers. 712 Smrekar J. - Oman J. - Širok B. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 1 ODVISNOST DELOVANJA HLADILNEGA STOLPA IN GENERATORJA Hladilni stolpi na naravni vlek se pogosto uporabljajo v industriji in kot sestavni del termoelektrarn. Ker je hladilni stolp sestavni del celotnega postrojenja termoelektrarne, njegova učinkovitost delovanja vpliva na toplotni izkoristek celotnega postrojenja. V elektrarnah so energijski tokovi veliki, kar pomeni, da že majhne izboljšave izkoristka na postrojenju pomenijo velik prihranek pri porabi goriva in zmanjšanju emisije dimnih plinov. V hladilnem stolpu poteka hlajenje vode z neposrednim stikom med vodo in hladilnim zrakom [3]. Pri tem se zrak segreje, njegova relativna vlažnost se poveča, zniža pa se temperatura hladilne vode. Za dosego največjega odvoda toplote iz vode na okolico je potrebno optimalno delovanje hladilnega stolpa pri njegovih imenskih karakteristikah. Na sliki 1 si poglejmo vpliv hladilnega sistema na količino pridobljenega dela iz termodinamičnega krožnega procesa. Naloga hladilnega sistema je odvod toplote v okolico pri temperaturah, ki so čim bližje temperaturi okolice. Intenzivnejši odvod toplote na sedanjem hladilnem sistemu se kaže v nižji temperaturi in tlaku v kondenzatorju, kar prinaša večjo entalpijsko razliko, npr. iz Ah na Ah , in s tem dodatno pridobljeno delo Ah iz turbine. Učinkovit hladilni sistem tako omogoča manjše izgube toplote na enoto pare, ta se je na primeru s slike 1 zmanjšala iz površine 4-3-C-B, ki pomeni 1 THE OPERATIONAL DEPENDENCE BETWEEN COOLING TOWER AND GENERATOR Natural-draft cooling towers are usually used in the process industry and are often part of a thermal power plant. Because it is a part of the whole thermo-energetic system, its efficiency has an influence on the overall power-plant efficiency. In power plants we are faced with large energetic flows, which means that little efficiency improvements in the system represent large fuel savings and a reduction in pollution from exhaust gases. In natural-draft cooling towers the heat is transferred by direct contact between the water and the cooling air that flow in opposite directions [3]. The air tem-perature rises and the humidity increases through the cooling-tower packings, where, on the other hand, the water temperature decreases. To achieve the largest heat transfer from the water to the air on a given cooling tower, it has to operate at its optimum point Figure 1 shows the influence of the cooling system on the work extracted from thermodynamic steam cycle. The task of the cooling system is rejecting heat to the environment at temperatures that should be close to atmospheric temperature. More intensive heat rejection for the given cooling system results in a lower water temperature and lower pressure in the condenser, which brings a larger enthalpy difference, for example, from Ah to Ah, and more acquired work, Ah , from the turbine. A more efficient cooling system a enables less heat loss, which is reduced in Figure 1 from the area 4-3-C-B, ! 2 , i 1 1 ¦ 1 5, n * s I kJ/fcgK a B s i tjyfcgK. c Sl. 1. Povezava med pridobljenim delom in odvodom toplote Fig. 1. Connection between acquired work and rejected heat Statistični pristop k analizi hladilnih sistemov - A Statistical Approach to the Analysis of Cooling Systems 713 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 odvedeno toploto na površino 4'-3'-C-A. Senčena which represents the rejected heat, to area 4'-3'-C-A. ploskev ponazarja razliko toplote, ki se je pri tem The hatched area represents the heat difference that spremenila v koristno pridobljeno delo. was additionally converted to useful work. Odvedeno toploto iz hladilnega sistema lahko The rejected heat from a cooling system can ocenimo po sledeči enačbi [1]: be estimated by the equation [1]: kjer so: Q d odvedena toplota iz hladilnega sistema, P moč generatorja in h izkoristek krožnega postopka. Povezavo med močjo generatorja in hladilnim stolpom lahko utemeljimo tudi s statističnimi orodji na podlagi meritev. Odvisnost pridobljenega dela generatorja s parametri, ki vplivajo na delovanje stolpa, lahko dobimo z matričnim zapisom koeficientov odvisnosti, ki povedo medsebojne odvisnosti posamičnih spremenljivk. Na podlagi matrike koeficientov odvisnosti lahko sistematično določimo parametre, ki pomembno vplivajo na delovanje hladilnega stolpa. S tovrstnimi izračuni se ukvarja regresijska analiza [7]. 2 OPIS MERITEV IN MERILNE OPREME Meritve obsegajo podatke na bloku 4 Termoelektrarne Šoštanj [9] in ustreznem hladilnem stolpu bloka 4 [8]. Celoviti parametri, ki so simultano merjeni po standardu DIN 1947 [5] so: vstopna in izstopna temperatura hladilne vode iz hladilnega stolpa, celotni masni pretok vode, ki je merjen z ultrazvočnim merilnikom pretoka in izhodna moč generatorja. Merilni sistem obsega še naprave za zbiranje merjenih podatkov v hladilnem stolpu. Merilna negotovost temperaturnih zaznaval je bila ocenjena na manj ko 0,25 °C. Meritve so obsegale različne režime obratovanja, tj. pri različnih močeh generatorja ter 34000 m3/h prostorninskem pretoku hladilne vode. Sočasno so potekale meritve parametrov okoliškega zraka, ki so obsegale hitrost okoliškega zraka v štirih točkah (vA, vB, vC, v), temperaturo okolice v bližini hladilnega stolpa (tZ) in gostoto zraka v bližini hladilnega stolpa (r). V preglednici 1 so predstavljene povprečne vrednosti okoliških parametrov, izmerjenih v celotnem času trajanja meritev. Iz preglednice 1 je razvidno, da se parametri okolice niso bistveno spreminjali in zaradi tega tudi niso vplivali na rezultate meritev znotraj hladilnega stolpa. where Q d is the rejected heat from the cooling system, P is the generator power and h is the efficiency of the thermodynamic system. The connection between the generator and the cooling tower can also be shown with statistical tools based on measurements. The dependence of the generated power on parameters that influence the cooling-tower operation can be acquired with a matrix of correlation coefficients that tell us the mutual dependence between two variables. With the help of a correlation matrix we can systematically determine the parameters that have a significant impact on the operation of the cooling tower. This kind of analysis can be described as a regression analysis [7]. 2 DESCRIPTION OF THE EXPERIMENT AND THE MEASUREMENT EQUIPMENT Measurements include data acquired at Block 4 of the Šoštanj power plant [9] and the corresponding cooling tower of Block 4 [8]. The integral parameters that are simultaneously measured by the DIN 1947 standard [5] are as follows: inlet and outlet cooling-water temperature from the cooling tower; the total water-mass flow rate, which is measured with an ultrasonic flow meter and the power on the generator. The measurement system also includes equipment for collecting data in the cooling tower. The measurement uncertainty of the temperature sensors was estimated to be less than 0.25°C. The measurements included different operating points, i.e., from different power outputs on the generator, and were conducted by a constant volumetric water flow of 34000 m3/h Simultaneously, we measured atmospheric parameters, which included the air velocity at four points (vA, v, vC, vD), the ambient temperature near the cooling tower (t0) and the air density near the cooling tower (r). Table 1 shows the average values of the atmospheric parameters measured through the whole duration of the measurement. From the table it is clear that the variations of the parameters were not significant, which means that the measurements in the cooling tower were not influenced by the environmental conditions. 714 Smrekar J. - Oman J. - Širok B. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 Preglednica 1. Parametri okoliškega zraka Table 1. Parameters of ambient air kvadrant quadrant 1 2 3 4 vA [m/s] 1,8 2,2 2,1 2,3 vB [m/s] 2,2 1,9 2,7 2,4 vC [m/s] 1,6 2,2 1,8 1,9 vD [m/s] 2,2 2 2,1 1,8 tZ [m/s] 21,8 22,8 21,4 20,9 r [kg/m3] 1,17 1,17 1,16 1,16 3 MERITVE LOKALNIH PARAMETROV NA NAVPIČNEM SEGMENTU Za določitev osnovnih karakteristik prenosa toplote in snovi opazovanega hladilnega stolpa so bile izvedene meritve aerodinamičnih in termodinamičnih veličin na navpičnem segmentu, prikazanem na sliki 2. Segment je bil izbran kot primerjalna točka v področju hladilnega stolpa, kjer imamo brezhibne konstrukcijske lastnosti in je obsegal tlorisno površino okoli 9 m2. Namen segmenta je tudi določitev prenosa toplote na lokalni ravni v hladilnem stolpu. V osnovi je izkoristek krajevnega delovanja stolpa moč izračunati samo prek krajevnih meritev parametrov vlažnega zraka ali vode, ki ga popisuje enačba [10]: 3 MEASUREMENT OF THE LOCAL PARAMETERS IN A VERTICAL SEGMENT To determine the basic characteristics of heat and mass transfer in the cooling tower we conducted measurements of the aero- and thermo-energetic quantities in the vertical segment shown in Figure 2. The segment was chosen as a reference point in the cooling tower where the construction characteristics were fault-free and the segment was occupying a ground plane of approximately 9 m2. The purpose of the vertical segment is also to determine the heat transfer on a local base in the cooling tower. In principle, this can be the local efficiency, calculated by measurements of moist air or water parameters, and its definition can be written as [10]: h -h h -h kjer so: h 1 vstopna specifična entalpija vode, h 2 izstopna specifična entalpija vode, h specifična entalpija vode ovrednotena pri temperaturi mokrega termometra okoliškega zraka, ki predstavlja največji temperaturni potencial, do katerega lahko vodo ohladimo. Navpični segment na sliki 2 je sestavljen iz lamelnega prenosnika toplote, ki je v spodnjem področju, razpršilnika vode, ta je v sredini in izločilnikov vodnih kapljic v zgornjem delu segmenta. Na opazovanem delu so bili merjeni naslednji parametri: vstopna temperatura vlažnega zraka t 1, izstopna temperatura nasičenega zraka t 2, vstopna temperatura vode t 1, izstopna temperatura vode t 2, masni pretok vode m w, masni pretok vlažnega zraka Merilna negotovost temperaturnih zaznaval Pt-100 je manjša od 0,25 °C. Hitrost vlažnega zraka (2), where h 1 is the inlet-specific enthalpy of the water, h 2 is the-outlet specific enthalpy of the water, h isWthe specific enthalpy of the water evaluated at the wet-bulb temperature of atmospheric air, which represents the maximum temperature potential to which water can be cooled. The vertical segment in Figure 2 consists of a lamellate heat exchanger, which is at the bottom, spray elements, which are in the middle, and drift eliminators, which are placed at the top of the segment. For the observed segment we conducted measurements of the following parameters: inlet temperature of moist air t1, outlet temperature of saturated air t, inlet water temperature tw1, outlet water temperature tw2, mass flow of water mw, mass flow of air mzr. The measurement uncertainty of the Pt-100 temperature sensors was estimated to be less than 0.25°C. The air velocity was measured with a pre- Statistični pristop k analizi hladilnih sistemov - A Statistical Approach to the Analysis of Cooling Systems 715 Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 Sl. 2. Navpični segment v hladilnem stolpu [4] Fig. 2. Vertical segment in the cooling tower [4] se je merila s predhodno umerjenim anemometrom na vetrnico Perioda vzorčenja je bila 1 min in celotni čas zbiranja podatkov je bil 3 4 dni Vlažnost vstopnega zraka je bila določena s temperaturami suhega in mokrega termometra Relativna vlažnost okolice in prav tako temperatura okolice sta bili dobljeni z meritvami v meteorološki postaji Šoštanj Vse meritve v hladilnem stolpu so bile izvedene v skladu s standardom DIN 1947 [5]. 4 ODVISNOST PARAMETROV POVEZANIH Z OBRATOVANJEM HLADILNEGA STOLPA Pri iskanju povezav med močjo generatorja in hladilnim stolpom smo uporabili statistične postopke pri katerih smo s korelacijskimi koeficienti dobili stopnje odvisnosti med posamičnimi spremenljivkami Povezanost parametrov z delovanjem hladilnega stolpa in posredno z močjo generatorja je prikazana v preglednici 2 kjer smo za izračun koeficientov odvisnosti izbrali naslednje parametre: moč generatorja P; celotni odvedeni toplotni tok Q iz hladilnega stolpa; krajevni toplotni tok Q ki se prenese iz vode na hladilni zrak; temperaturo okolice t ; tlak okolice p ; relativno calibrated vane anemometer. The period of the data sampling was 1 min and the total measurement time was 3 4 days The relative humidity of the inlet air was determined with the help of a dry-bulb and a wet-bulb thermometer The relative humidity and the temperature of the ambient air were acquired from the Šoštanj meteorological station All the measurements in the cooling tower were carried out according to the DIN 1947 standard [5]. 4 DEPENDENCE OF THE PARAMETERS ASSOCIATED WITH THE COOLING TOWER S OPERATION When seeking a connection between the generator and the cooling tower we used statistical methods to determine the degree of correlation between the variables The connections of the parameters to the cooling-tower operation and indirectly to the power generation are shown in Table 2 where for the calculation of the correlation coefficient we used the following parameters: power at the generator P total rejected heat from the cooling tower Q local heat transfer at the vertical segment Q ambient temperature t ambient pressure p relative humidity of ambient outlet temperature of moist air 716 Smrekar J. - Oman J. - Širok B. Strojniški vestnik - Journal of Mechanical Engineering 51(2005)11, 711-723 Preglednica 2. Tabela koeficientov odvisnosti, ki povezujejo moč generatorja s celovitim in krajvenim prenosom toplote v hladilnem stolpu Table 2. Table of correlation coefficients that associate the power on the generator with integral and local heat transfer in the cooling tower P Qod / QR Qlok / Qloc 0,95 0,95 tok / t0 pok / p0 Pok / P0 twv / tw,i twiz / two twizk / twoc Qod/Qr Qlok/Qloc tok/t0 pok/p0 x>y>z)sF tt = RPY(>x> ,t x=arctan Fx ) (5) m =arctan F ) (6). Kadar tipalo drsi po površini, se v sili F izmeri When the tool is sliding over the surface a tudi sila trenja, ki deluje v nasprotni smeri gibanja. frictional force in the opposite direction of the motion Silo trenja je mogoče oceniti v primeru znanega is present. The friction force can be calculated only koeficienta trenja in ravnih površin, kar pa v praksi if the friction coefficients are known and the surface ni najbolj pogosto. V primeru neupoštevanja sile is flat. As in practice this is usually not the case, the trenja se pri drsenju pojavi določen kot napake pri influence of the friction is neglected and nagibu orodja glede na normalo površine. To napako consequently some error is introduced to the zmanjšamo z uporabo orodij z majhnim koeficientom inclination angles. To minimize these errors we use trenja. tools with low friction coefficients. 1.3 Slikovno zaznavalo 1.3 Vision sensor Za sledenje na površini izrisane poti uporabimo na zapestje nameščenno slikovno zaznavalo (kamera). Zajeto sliko je treba obdelati. Da bi sistem omogočal kar najbolj robustno delovanje, je zajem slikovne informacije zastavljen na barvni kameri, v barvnem prostoru “barvni odtenek -nasičenost - vrednost” (HSV). Slika je razčlenjena na podlagi barvne sestavine H in S. V prvi fazi se v področju zanimanja, predstavljenem v pravokotniku s polno črto (sl. 3a), na podlagi barvne informacije določi področje slike, ki pripada orodju. Iz tega področja se izračuna koordinate vrha orodja P. Zaradi znane medsebojne lege orodja, glede na kamero, se pri analizi slike poišče le vrh podajnega orodja, katerega dolžina se v odvisnosti od sile, s katero deluje na podlago, lahko spreminja. Potek krivulje se poišče s Canny-evim postopkom iskanja robov na sestavini barvnega prostora H (sl. 3b). Krivulja na sliki ima dva robova. Za točke krivulje so upoštevane zgolj točke srednjih vrednosti robov. Ob tem se preveri še, ali je odtenek barve med robovoma podoben barvi, ki je v fazi kalibracije določena kot barva krivulje. Na podlagi segmentiranih podatkov se po metodi najmanjših kvadratov približa potek krivulje s kvadratnim polinomom v smeri premika orodja (sl. 3c). V višini vrha orodja j se iz približne krivulje določi tangento in izračuna razdaljo med orodjem in tangento e (sl. 3d). Po tangenti se določi kot