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 be-cause 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 de-mand for cooling water. Heat rejected with the cooling system is larger than the heat converted by the steam cycle into use-ful 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 it-self. For estimating this kind of improvement the coefficient Q&od /P [1] is often used. With a reduc-tion 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 cool-ing tower. This has the consequences of lower effi-ciency of the tower ([2] and [6]). The anomalies de-pend on the construction properties of the distribution water system, the heat exchangers in the cool-ing towers or the atmospheric influences on the air velocity distribution entering the cooling tower. Cool-ing-tower efficiency increases with the elimination of local irregularities of the temperature and velocity fields, which consequently increases the overall ef-ficiency 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 charac-teristics of cooling towers that depend on heat and mass transfer on a local basis. Our analysis com-pared 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 Ah1 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 * M ^ h s I kJ/fcgK ab s i fcjßgK. 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, vB, 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 d iz hladilnega stolpa; krajevni toplotni tok Qlok, ki se prenese iz vode na hladilni zrak; temperaturo okolice t k; tlak okolice p k; 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 QR, local heat transfer at the vertical segment Ql , ambient temperature t, ambient pressure p0, relative humidity of ambient