© Strojni{ki vestnik 49(2003)6,322-345 © Journal of Mechanical Engineering 49(2003)6,322-345 ISSN 0039-2480 ISSN 0039-2480 UDK 621.18:665.72:536.24 UDC 621.18:665.72:536.24 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Termohidravli~na analiza obratovanja uparjalnika za ukapljeni naftni plin A Thermohydraulic Analysis of a Liquefied-Petroleum-Gas Revaporizer Sanib Ba{i~ - Leopold Škerget - Matja` Hriber{ek Prispevek obravnava analizo obratovanja električnega uparjalnika za ukapljeni naftni plin. Na začetku je podan opis naprave in delovanje v ustaljenih obratovalnih razmerah. Nato je definiran cilj analize in vpeljan navidez osnosimetrični prerez uparjalnika. Podane so vodilne enačbe toka newtonske tekočine v območju sekundarne kapljevine za prenos toplote in toka skozi porozni grelnik. Definirani so robni pogoji na mejah računskega območja. Ločeno so podane osnovne kriterialne enačbe za vrednotenje prenosnih pojavov v posameznih delih uparjalnika. Poseben poudarek je namenjen razmeram konvektivnega uparjanja binarne zmesi v cevni vijačni spirali. Opisan je iterativni računski postopek, s katerim je doseženo končno obratovalno stanje naprave. Na koncu so predstavljeni dobljeni rezultati s komentarjem in sklepi. Za izbrane parametre je obratovalna točka uparjalnika znotraj predpisanih temperaturnih mej. © 2003 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: prenos toplote, uparjalniki, analize termohidravlične, plini naftni ukapljeni) This paper deals with the thermohydraulic characteristics of an electrical liquefied-petroleum-gas (LPG) revaporizer. To begin with both the revaporizer’s description and its working performances are presented. The main goals of the analysis are defined and the quasi-axisymmetrical revaporizer section is introduced. The governing equations for Newtonian fluid flow in the region of the secondary liquid and for flow through a porous heater are presented. The boundary conditions on the computational region boundaries are prescribed. Further, basic empirical corelations for the evaluation of the transport phenomena within the individual revaporizer zones are presented. Special attention is devoted to the convective boiling process of the binary mixture in helically coiled tubes. The iterative calculating procedure with which we finally reached the working state of the device is explained. At the end the achieved results are discussed with comments and conclusions included. The operating point of the revaporizer was to lie inside the prescribed temperature range for the selected combination of process parameters. © 2003 Journal of Mechanical Engineering. All rights reserved. (Keywords: heat transfer, vaporizers, thermohydraulic analysis, liquified petroleum gas) 0 UVOD Ukapljeni naftni plin (UNP) se uporablja kot natančnejše ime za nekaj vrst ogljikovodikov, kakor so propan (C H), butan (CH) in zmesi propana in butana v različnih sestavinskih razmerjih. UNP je na temperaturi okolice in pri atmosferskem tlaku v plinastem agregatnem stanju in se v tej obliki uporablja kot vir energije oz. gorivo. Že pri manjših nadtlakih ob nespremenjeni temperaturi (nekaj barov - odvisno od deleža sestavnih komponent) UNP preide v kapljevito agregatno stanje in se v tej obliki preprosto prevaža in skladišči. Odvisno od potreb po UNP-u se ta porabnikom v večini primerov dostavlja v prenosnih jeklenkah, hramih ali cisternah. V vseh hranilnikih je največji del polnitve v kapljevitem agregatnem stanju, le manjši del nad gladino zaseda plinasta faza. Pri polnjenju hranilnikov je takšno prostorninsko 0 INTRODUCTION Liquefied petroleum gas (LPG) is the name used for several kinds of hydrocarbons, such as propane (C3H8), butane (C4H10) and various propane-butane mixtures. At atmospheric pressure and room temperature LPG has a liquid aggregate state, and in this state it is used as an energy source. At lower gauge pressures (a few bar – depending on the component contents) and temperatures LPG can be easily converted into a liquid aggregate state. This is an important characteristic of LPG, and is used for its economic transport. With regards to requirements, LPG is normally delivered to consumers in gas bottles, containers and cisterns. In all types of storage most of the volume is occupied by the liquid phase, and only a small part above the liquid surface is filled by the gas phas. The appropriate volume ratio between the phases during VH^tTPsDDIK stran 322 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis razmerje med fazama odvisno od visoke vrednosti prostorninskega temperaturnega raztezka kapljevite faze UNP-a [15]. Odvzem plinaste faze neposredno iz shrambnega prostora, ki ga pogosto imenujemo naravno uparjanje UNP-a je povezan s celo vrsto pomanjkljivosti (majhni masni pretoki, uparjanje po frakcijah, usedanje težjih primesi, nevarnost podhladitve UNP-a pri večjih odvzemih). Tem pomanjkljivostim se lahko izognemo z uvedbo prisilnega oz. pospešenega uparjanja, ki temelji na odvzemu kapljevite faze UNP-a iz skladiščnih prostorov. Sprememba agregatnega stanja UNP-a v tem primeru poteka zunaj plinskih hranilnikov, v zato posebej skonstruiranih uparjalnikih, ki jih kot dodatne komponente uvajamo v plinska omrežja. Uparjalniki UNP-a so posebno skonstruirani dvofazni prenosniki toplote, ki izrabljajo toplotno energijo določenih zunanjih virov za pospešeno uparjanje UNP-a. Najbolj uveljavljena razdelitev uparjalnikov za UNP je glede na vir toplote, ki ga ti uporabljajo za pospešeno uparjanje UNP-a. Tako poznamo električne uparjalnike, uparjalnike z vodno paro, toplovodne uparjalnike ter uparjalnike, ki izkoriščajo vrele ostanke zgorevanja UNP-a [17]. V središču pozornosti pričujočega prispevka je električni uparjalnik za UNP s posredno kapljevino za prenos toplote. 1OPIS IN DELOVANJE UPARJALNIKA Uparjalnik (slika 1) ima obliko pokončne valjaste posode [18], [19], ki jo sestavljajo valjni plašč (1) ter pokrov (2) in dno plašča (3). Na pokrovu posode sta dovodni (4) (sl. 2) in odvodni cevovod (5) ter spremljajoča krmilna in varnostna oprema. Znotraj posode uparjalnika je navpično nameščen cevni snop, ki se prilega obliki plašča in je na svojih koncih povezan z vstopnim (6) oz. izstopnim (7) priključkom na pokrovu uparjalnika. Cevni snop sestoji iz dveh sosrednih in simetričnih vijačnih cevnih spiral, zunanje (8) in notranje (9). Cevni snop dodatno sestavljajo še trije navpično nameščeni pomožni cevni vodniki (10, 11 in 12). Skozi ustrezno odprtino je v notranjost plašča v smeri njegove navpične osi vstavljen električni grelnik (13) nespremenljive moči in je pritrjen za dno posode. Uporovni električni grelnik sestavljajo grelna telesa U, obdana z zaščitnim plaščem, ki so pritrjena na skupno krožno nosilo grelnika (14). Na pokrovu uparjalnika so po njegovem obodu pritrjeni trije tovarniško zapečateni kapilarni termostati (15a, 15b in 15c) s pasivnimi stikali, industrijski živosrebrni termometer (16) in mehanski merilnik ravni sekundarne kapljevine za prenos toplote (17). V središču pokrova je nameščen še avtomatski merilnik ravni (električno ravensko stikalo) sekundarne kapljevine v plašču uparjalnika (18). Vsi omenjeni instrumenti s svojimi reservoir loading is a consequence of the high-temperature dilatation coefficient of the LPG’s liquid phase [15]. Gas-phase discharging directly from a gasholder, which is often referred to as natural LPG revaporization, is accompanied by some imperfections (low mass-flow rate, fractional vaporisation, heavy fractions sedimentation, a risk of bottle subcooling at high discharging rates). To avoid these problems forced or promoted vaporisation is frequently used. In this case the LPG’s liquid phase is taken out directly from the gas reservoir and the phase transition occurs outside gasholder in specially designed evaporators, which are introduced into the gas network as additional system components. LPG revaporizers are two-phase heat exchangers that use heat energy from some external sources to promote the evaporation of LPG. The best known classification of LPG revaporizers is in terms of the heat source to be used for the forced revaporization of the LPG. There are electrical revaporizers, revaporizers with hot water or water steam as the heat source, and revaporizers that use the hot combustion products of LPG [17]. This article deals with an electrical LPG revaporizer with a secondary liquid for the heat transfer. 1 DESCRIPTION OF THE REVAPORIZER AND ITS WORKING CHARACTERISTICS The revaporizer (Figure 1), which is designed as a vertical cylindrical vessel, consists of a cylindrical shell (1), a cover (2) and a vessel bottom (3). On the cover there are supply (4) (Figure 2) and discharging (5) pipelines and auxiliary control and safety equipment. Within the vessel there is a vertically placed tube bundle. At its terminations the tube bundle is connected with inlet (6) and outlet (7) connections on the revaporizer cover. The tube bundle consists of two concentric and symmetric helically coiled tubes, outer (8) and inner (9). The tube bundle also includes three vertically placed auxiliary connecting tubes (10, 11 and 12). Through a suitable opening in the vessel bottom in the direction of the vertical axis a constant-power electrical heater is inserted (13). The electrical resistance heater consists of heating U-elements covered with copper sheaths and linked together with a circular heater holder (14). On the revaporizer cover three capillary thermostats (15a, 15b and 15c) with passive contactors, an industrial mercury thermometer (16) and a mechanical secondary-liquid-level gauge (17) are mounted. In addition, in the centre of the revaporizer cover, an automatic secondary-liquid-level gauge (18) is installed. The sensors of all this equipment are immersed in the | lgfinHi(S)bJ][M]lfi[j;?n 03-6_____ stran 323 I^BSSIfTMlGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 6 15a 18 15c 16 15b 11 10 7 2 17 12 1 3 13 14 Sl.1. Prikaz notranjosti uparjalnika z osnosimetričnim prerezom cevnega snopa in grelnika Fig. 1. Revaporizer interior and axisymmetric sections of the tube bundle and heater tipali segajo v notranjost posode (sl. 9) in so do določene globine potopljeni v sekundarno kapljevino za prenos toplote. Pred vstopnim priključkom sta na dovodni cevovod (4) pritrjena elektromagnetni ventil (19) in manometer vstopne strani (20). Za izstopnim priključkom so na odvodnem cevovodu (5) nameščeni glavni zaporni ventil (21), manometer izstopne strani (22) ter tlačni varnostni ventil (23). Dovodni (4) in odvodni cevovod (5) uparjalnika sta povezana z zunanjo povratno cevjo (24), ki ima na mestu prehoda v glavni zaporni ventil (21) pritrjen dodatni zaporni ventil za plinske napeljave (25). Zunanja povratna cev (24) in zaporni ventil (25) sta namenjena odpravljanju posledic poplavljanja cevnega snopa (nezgodne razmere [18] in [19]). V posodo je do določene višine nad cevnim snopom nalita sekundarna kapljevina za prenos toplote (transformatorsko olje ali raztopina monoetilenglikola in vode). Dovodni cevovod uparjalnika je priklopljen na hranilnik UNP-a. Hranilniki za UNP so običajno izdelani iz jeklene pločevine brez toplotne izolacije in je UNP, ki je v njih, v termodinamičnem ravnotežju z okolico [15]. Odvodni cevovod uparjalnika je povezan s porabnikom plina oz. gorilnikom, pred katerim je krmilnik tlaka oz. krmilnik pretoka [16]. secondary liquid for heat transfer in the revaporizer vessel. In front of the inlet connection, an electromagnetic valve (19) and an inlet side manometer (20) are mounted on the supply pipeline (4). Behind the outlet connection, the main block valve (21), the outlet side manometer (22), and the pressure safety valve (23) are assembled on the discharging pipeline (5). The supply (4) and discharging (5) pipelines are additionally connected together by the external recurrent tube (24). On recurrent tube at the joint situ with main block valve (21), additional block gas valve is mounted (25). External recurrent tube (24) and block valve (25) serve as auxiliary system for elimination of tube bundle flooding consequences (incident circumstances [18] and [19]). Up to the prescribed level over the tube bundle, revaporizer vessel is filled up with secondary liquid for heat transfer (mineral oil or solution of mono-ethylene-glycol and water). The supply pipeline of the revaporizer is connected to the LPG reservoir. They are usually manufactured from steel plate without heat insulation, and the LPG within the reservoir is in thermodynamic equilibrium with the surroundings [15]. On the opposite side, the discharging pipeline of the revaporizer is connected with the gas consumer. Normally, it is a burner. In front of the burner a pressure or mass-flow rate regulator is placed [16]. VBgfFMK stran 324 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 5 15b 20 18 Sl.2. Pokrov uparjalnika s krmilno in varnostno opremo Fig. 2. Revaporizer cover with control and safety equipment Parna faza, ki je nad prosto gladino v shrambni posodi za UNP, potiska kapljevito fazo po navpični sifonski cevi skozi izstopni ventil hranilnika v dovodni cevovod (4) električnega uparjalnika. Po vklopu električnega grelnika (13), zaradi naravne konvekcije v sekundarni kapljevini in predvsem zaradi slabega odvoda toplote (ni pretoka UNP-a skozi cevni snop, ker je elektromagnetni ventil (19) na začetku zaprt), slednja akumulira sproščeno toplotno energijo grelnika in se hitro segreva. Ko temperatura kapljevine v točki namestitve tipala termostata, ki krmili delovanje elektromagnetnega ventila (15a), doseže temperaturo 65 oC se elektromagnetni ventil (19) odpre in v cevni snop priteče kapljevita faza UNP-a. Ker kapljevita faza, ki priteka iz hranilnika, ustreza točki na vrelni krivulji UNP-a ob podanem sistemskem tlaku, se uparjanje začne takoj po vstopu kapljevite faze v uparjalnik. V primeru, da temperatura sekundarne kapljevine v točki namestitve tipala termostata, ki krmili delovanje električnega grelnika (15c), doseže temperaturo 80 oC, se grelnik (13) avtomatsko izklopi. Na pokrovu uparjalnika je nameščen tretji termostat (15b), ki je namenjen za krmiljenje električnega grelnika, in sicer v primeru, da iz določenih razlogov prvi termostat (15a) odpove, njegov električni stik pa je sklenjen pod 85 oC. Med temperaturama merilnih točk 65 oC in 80(85) oC je delovno območje uparjalnika. V tem temperaturnem območju uparjalnik deluje ustaljeno, morebitna sprememba parametrov postopka (poglavje 2) pa lahko povzroči premik delovne točke iz ene v drugo lego. 2 DEFINICIJA PROBLEMA Prispevek sega na področje konstruiranja dvofaznih prenosnikov toplote. Izvirna konstrukcijska Due to the pressure head the gas phase in the LPG gasholder pushes the liquid phase out through a vertical siphon tube and the outlet valve to the supply pipeline (4) of the electrical revaporizer. After the electrical heater (13) start-up, the free convection and the low-heat transfer rate (LPG does not flow through the tube bundle because at the start the electromagnetic valve (19) is closed) cause the secondary liquid to accumulate the heat energy of the heater and warm up very fast. When liquid temperature at the point where the thermostat sensor for the electromagnetic valve control is placed reaches 65 oC the valve is opened and the liquid phase of the LPG starts to flow into the tube bundle. Due to fact that the state of the liquid phase entering the tube bundle corresponds to the dew point of LPG for the defined system pressure the evaporation starts immediately after liquid phase enters the revaporizer. In the case when the secondary liquid temperature at the point where the thermostat sensor for the electric heater working control is placed reaches 80 oC, the electric heaters (13) are automatically turned off. On the revaporizer cover the third thermostat (15b) is placed. It also serves for electrical heater control in case the first thermostat breaks down. It is switched on at 85 oC. As a result the operating region of the revaporizer has to be found between the temperatures measured by the two control thermostat sensors. These temperatures are 65 and 80(85) o C. In this temperature region the revaporizer operates normally and steady-state conditions are usually achieved. Changes to the process parameters governing the revaporizer’s thermohydraulic behaviour (Chapter 2) may cause the operating point to be moved to another position. 2 PROBLEM DEFINITION This paper deals with heat excanger that have a two-phase-flow design. The original construction gfin^OtJJlMlSCSD 03-6 stran 325 |^BSSITIMIGC 4 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis izvedba električnega uparjalnika je razvita v podjetju Nafta Lendava d.o.o. (konstruiranje na novo), na kar so sledile postopne izkustvene spremembe sedanjih izvedb (optimizacija). Po več ko dveh desetletjih so razvili izvedbo, za katero smo z namenom nadaljnjih izboljšav izvedli numerično analizo obratovanja, ki jo podajamo v pričujočem prispevku. Sedanji električni uparjalnik za UNP je namenjen obratovanju v širokem območju parametrov postopka. Temperatura okolice (T ), sestava plinske zmesi (ŠCH ), zračni tokovi okrog uparjalnika (v ), vrsta sekundarnega sredstva in višina, do katere ta sega s svojo prosto gladino (Hl) (sl. 3b), ter masni pretok UNP-a (mUNP), so veličine postopka, ki definirajo obratovalne značilnosti uparjalnika. Večina prenosnikov toplote je namenjena delovanju pri točno določeni kombinaciji parametrov postopka, pri čemer so dovoljena le manjša odstopanja od predpisane delovne točke. V tukaj podanem primeru se parametri postopka lahko močno spreminjajo, uparjalnik pa mora nemoteno delovati v čim širšem območju spreminjajočih se vplivnih veličin (delovanje v novih razmerah). Mogoče je torej veliko število obratovalnih točk, ki skupaj dajejo obratovalni diagram uparjalnika. Izdelava obratovalnega diagrama uparjalnika za UNP je končni cilj raziskave. Glede na dejstvo, da obstaja zelo veliko število kombinacij parametrov postopka, ki določajo delovno točko uparjalnika, smo se v prispevku omejili na eno samo delovno točko oz. na eno izbrano kombinacijo parametrov postopka (preglednica 1). Razviti algoritem je mogoče uporabiti za določitev celotnega delovnega območja obravnavanega uparjalnika. Namen je ugotoviti, ali uparjalnik ob izbrani kombinaciji parametrov postopka deluje in koliko daleč je tako definirana delovna točka od meje neobratovanja. Če so temperature sekundarne kapljevine v točkah namestitve tipal krmilnih termostatov v predpisanem območju (60 do 85 oC), potem uparjalnik nemoteno deluje. Namen smo dosegli tako, da smo s postopnim spreminjanjem robnih pogojev na mejah računskega območja izpolnili delne (uparjanje, pregretje in izgube v okolico) in s tem celotno toplotno bilanco uparjalnika. Preverili smo velikost grelne površine sedanjega cevnega snopa za dosego predpisanih izhodnih veličin pregrete parne faze UNP-a. Parametri postopka, ki of the electrical LPG revaporizer was developed by Nafta Lendava d.o.o. (new design). Some empirical modifications to the existing construction followed (optimization). After more than two decades a new construction has been developed for which, with the aim of additional improvements, we performed a numerical analysis of the working conditions presented in this contribution. The existing LPG revaporizer is designed to work within a wide region of process parameters. The surrounding temperature (Tsur), the gas-mixture composition ( xC3H8 ), the air flow around the revaporizer (vw), the secondary liquid type and its filling level in the revaporizer vessel (Hsl), and the mass-flow rate of the LPG ( m&UNP ) are the process parameters that define the operating conditions of the revaporizer. The vast majority of heat exchangers are designed to work for an exactly defined combination of process parameters. Usually, only small deviations from the defined working point are allowed. In the case analysed here the process parameters change significantly and the revaporizer must operate without interruption in as wide as possible region of the affecting parameters (working under the conditions of the new process parameters). A large number of operating points defines the revaporizer’s operational diagram. The development of an LPG revaporizer operational diagram is the final goal of this analysis. Due to the fact that there are many combinations of process parameters defining the revaporizer’s operational points, we limited ourselves to one selected combination of process parameters (Table 1.) The developed algorithm may then be used to determine the entire working region of the revaporizer. The main goal of our research was to find out whether the revaporizer works for a chosen combination of process parameters, and how far away from the limits of the working region is the defined working point. If the temperatures of the secondary liquid at the control thermostat sensor points are in the prescribed range (60-85 oC), the revaporizer works without interruption. The goal can be reached with a numerical analysis by changing the boundary conditions on the boundary of computational domain and by satisfying the partial (evaporation, superheating and heat loses to surroundings) and the global heat balances of the revaporizer. The size of the tube bundle’s surface available for heat transfer was controlled at the Preglednica 1. Parametri postopka delovnega stanja, za katero je izveden nadzor obratovanja uparjalnika Table 1. The process parameters defining the working state of the revaporizer for which the numerical analysis is performed parametri postopka process parameters Tsur [o C] W%] mlpg [ kg/h ] vw [m/s] sekundarna kapljevina secondary liquid Hsl [m] + 20,0 0,6 1, 0-m LPG,opt 10,0 transformatorsko olje mineral oil Hsl,max maimskixmmm ^BSfirTMlliC I stran 326 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis definirajo izbrano delovno točko, so podani v preglednici 1. V uparjalniku potekajo postopki odvisnega prenosa toplote: (a) naravna konvekcija sekundarne kapljevine v posodi uparjalnika, (b) dvofazni (konvektivno uparjanje) in enofazni (pregretje parne faze) diabatni tok UNP-a skozi vijačni cevni snop ter (c) prenos toplote v okolico (toplotne izgube). Zapletena geometrijska oblika cevnega snopa ter notranja zanka naravne konvekcije v plašču uparjalnika ne omogočata izrabe uveljavljenih metod in izkustvenih izrazov za termohidravlični preračun preprostejših izvedb uparjalnikov [24]. Uporaba metod računalniške dinamike tekočin omogoča zanesljivo vrednotenje poteka naravne konvekcije v plašču ([5] in [7]). Po drugi strani te metode za zdaj še ne dajejo zadovoljivih rezultatov na področju numerične simulacije konvektivnega uparjanja pri gospodarskih industrijskih napravah ([5] in [10]). Na pokrovu uparjalnika so krmilni instrumenti, katerih merilne veličine je mogoče uporabiti za spremljanje integralnih kazalnikov obratovanja uparjalnika. Kombinacija uveljavljenih izkustvenih zvez, računalniška dinamika tekočin in fizikalne meritve (krmilni instrumenti na pokrovu uparjalnika) zagotavljajo želene rezultate. 3 NUMERIČNI MODEL Poskusi s 3D numeričnim modelom uparjalnika so pokazali, da je ta način prezahteven, tako z vidika velikosti problema kakor tudi zaradi svoje zapletenosti in potrebe po velikem številu poenostavitev. Računalniški program FIDAP 8.5, s katerim smo izvedli izračune, ne omogoča modeliranja pojavov, ki nastopajo pri spremembi agregatnega stanja v sistemu kapljevina - para [7]. Popolno uparjanje zmesi propana in butana, ki poteka od vrednosti masnega deleža parne faze 0 do vrednosti 1, prehaja skozi vse načine dvofaznega toka ([3] in [20]) (od mehurčastega prek obročastega do disperzno-kapljičastega) in je izredno zahtevno za numerično modeliranje. Zato smo vpeljali navidez osnosimetrični prerez uparjalnika (sl. 3). V nadaljevanju utemeljujemo vpeljavo te poenostavitve: (a) Problem naravne konvekcije v posodi uparjalnika s sredinsko nameščenim grelnikom je osnosimetričen, torej so učinki obodnega deleža toka zanemarljivi. (b) Vpliv »plazečih tokov«, ki se pojavljajo vzdolž vijačnih lokov cevnega snopa, je zaradi lokalnega pomena slednjih in njihove nizke intenzitete zanemarljiv. (c) Odseki pomožnih povezovalnih cevi so zelo kratki v primerjavi z razvito dolžino cevnega snopa in bistveno ne vplivajo na termohidravlično dogajanje v plašču uparjalnika (kolena in podobni odmiki od enoličnosti pretočne poti - sl. 1 - poz. prescribed outlet temperature of the superheated LPG gas phase. The process parameters defining the selected working point are presented in Table 1. Within the revaporizer, conjugate heat-transfer processes occur: (a) natural convection of the secondary liquid in the revaporizer vessel, (b) two-phase (convective boiling) and single-phase (superheating of the gas phase) non-adiabatic LPG flow through the helically formed tube bundle and (c) heat transfer to the surroundings (heat loses). The complex geometry of the tube bundle and the internal loop of natural convection in the revaporizer vessel do not allow the use of well-established methods and empirical correlations for the thermohydraulic analysis for a simple design of the evaporators. The methods of computational fluid dynamics enable a reliable evaluation of the natural covection in the shell ([5] and [7]). However, these methods have so far not given satisfactory results in the area of the numerical simulation of convective boiling processes in industrial vaporisers ([5] and [10]). On the revaporizer cover there are control instruments that may be used to give us values of the integral working parameters. Therefore, the combination of known empirical corelations, computational fluid dynamics and measurements (control instrument on the revaporizer cover) is used to obtain the desired results. 3 NUMERICAL MODEL The modelling work on the construction of a 3D numerical model of the revaporizer showed the complexity of the 3D approach and the need for many simplifications in order to obtain results. The FIDAP 8.5 program package was used to solve the governing equations of fluid flow. Physical phenomena occurring during the phase transformation in the liquid–gas system could not be modelled by the program capabilities [7]. The total evaporation of the propane–butane mixtures, ranging from vapour quality 0 to 1, passes through all the regimes of the two-phase flow ([3] and [20]) (from bubbly, through annular, to the dispersed-flow regime) and is very complex for the numerical modelling. These reasons led us to the introduction of a quasi-axisymmetric section of the revaporizer (Figure 3). Explanations for these simplifications are given below: (a) The natural convection phenomenon in the revaporizer vessel with the heater in its central part may be considered as an axisymmetrical one as the effects of the tangential velocity component can be neglected. (b) The creeping flows occurring along the tube bends are only important on a local scale because of its low intensity. Therefore, we can also neglect its influence on the flow field. (c) The length of the auxiliary connecting tubes is very short compared with the total length of the tube bundle, and its effect on the thermohydraulic conditions of the revaporizer is not important (bends and similar curved flow paths (Figure 1 – | lgfinHi(s)bJ][M]lfi[j;?n 03-6_____ stran 327 I^BSSIfTMlGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 10, 11 in 12) imajo lahko pomemben vpliv na režim dvofaznega toka v področju uparjanja [6]). (d) Pojavi mehurčastega vrenja in konvektivnega izparevanja, ki potekajo v dvojni vijačni cevni spirali, so zaradi majhnih vrednosti sistemskih parametrov (p,q,G) in nizke intenzitete sredobežnih sil razširjeni vzdolž večjega dela cevnega snopa. Zato je mogoče dvofazni tokovni režim v področju uparjanja, ki poteka vzdolž posameznega cevnega loka, preslikati v en sam pripadajoči mu krožni prerez v osnosimetrijski ravnini. Enaka analogija velja v področju pregretja parne faze UNP-a. (e) Nagib cevnih lokov je zelo majhen in ga z vpeljavo osnosimetričnega modela zanemarimo. S tem so spiralni cevni loki nadomeščeni z dvema vrstama sosrednjih zvitkov. (f) Zračni prostor nad gladino pomeni dodaten upor toplotnim izgubam v okolico. Vpliv naravne konvekcije v tem delu posode smo v tej fazi dela zanemarili. Ta poenostavitev ni imela bistvenega vpliva na rezultat izračuna. (g) Električni grelnik je stisnjene izvedbe (velika površina za prenos toplote na enoto prostornine) in ga je mogoče numerično modelirati s porozno snovjo z ustrezno predpisanimi snovnimi lastnostmi (poroznost in prepustnost). ra m KMJ Is o« pos. 10, 11 and 12) but may play an important role in the two-phase flow regime when convective boiling occurs [6]). (d) Because of the low values of the system parameters (p, q& , G) and low centrifugal forces, the processes of bubbly boiling flow and convective evaporation are spread over a large part of the tube bundle. Because of this, the two-phase flow regime that occurs within one tube turn could be represented by a corresponding circular section in the axisymmetric plane. The same analogy is valid in the region of superheating of the LPG gas phase. (e) The slope of the tube turn has a very low value and can be neglected when the axisymmetrical section is introduced. Thus, helically coiled turns in the 3D presentation are substituted by two rows of concentric rings. (f) The air space above the free surface represents an additional thermal factor. Natural convection in this part of the vessel was neglected as its impact on heat loses was assumed to be negligible. (g) The electrical heater has a compact form (large heat-transfer surface per unit volume) and can be numerically modelled as a heated porous region with suitably selected physical and transport properties (porosity and permeability). Hsl Hsl,min Hsl,max hc dout Ds Doc O O 6 %- O (T O O O O O O o o> -o o -o o o o -o o o o D O O -e- Dic Dht,out Dht,in E (a) (b) Sl.3. Navidez osnosimetrični prerez uparjalnika: (a) področji reševanja vodilnih enačb toka, (b) geometrijske veličine prereza Fig. 3. Quasi-axisymmetrical section of revaporizer: (a) regions where governing equations are solved (b) geometrical dimensions VH^tTPsDDIK stran 328 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 4 VODILNE ENAČBE Numerična simulacija tokovnih in toplotnih razmer je izvedena za področje naravne konvekcije sekundarne kapljevine v uparjalniku. Naravno konvekcijo v zračnem prostoru nad prosto gladino smo zanemarili. Področje sekundarne kapljevine je razdeljeno na področje naravne konvekcije in področje toka skozi porozni grelnik. V nadaljevanju so podane vodilne enačbe za področje toka v sekundarni kapljevini in poroznem grelniku [7]. 4.1 Naravna konvekcija v plašču uparjalnika Splošna oblika zakona ohranitve mase se glasi: 4 GOVERNING EQUATION The numerical calculation of the velocity and temperature fields is performed in the region of natural convection of the secondary liquid in the revaporizer shell and in the region of the porous heater. The natural convection within the air space over the free surface was neglected. The governing equations describing the physics of the problem can be written separately for natural convection in a pure fluid and for flow in a porous region [7]. 4.1 Natural convection in the revaporizer vessel The general form of the continuity equation is written as: dr dt + ( rui ) i =0 (1), kjer sta r gostota, u pa vektor hitrosti. Ohranitev gibalne količine, i pri kateri je upoštevan Boussinesqueov približek temperaturne spremenljivosti gostote le pri masnih silah, je podana z enačbo: where r is the fluid density and ui is the velocity vector. The momentum equation with Boussinesq’s approximation, where the temperature’s influence on the fluid mass density is considered only within the body force term, is written as: r0 [iui + ujui, j J = -p,i + [m(ui, j + uj,i)]j + ( r - r 0 ) (2). V enačbi (2) so r0 gostota pri primerljivi temperaturi T0, p termodinamični tlak, m dinamična viskoznost in gi težnostni pospešek. Ob tem velja povezava (r-r0)/r0 = -bT(T-T0), ki pomeni normalizirano funkcijsko odvisnost gostote od temperature. Z bT je označen prostorninski temperaturni raztezek. Energijska enačba za temperaturo kot neodvisno spremenljivko se glasi: In equation (2), r0 represents the fluid density at the reference temperature T0, p is the thermodynamic pressure, m is the dynamic viscosity and gi is the gravity vector. The term (r - r0 )/r0 = -bT (T-T0) represents a normalized density temperature variation function, where bT is the thermal volume expansion coefficient. The energy equation with temperature as an independent variable is written as: rcp dT dt uT i ,i ( l T , i ) , i (3), kjer so c specifična izobarna toplota, T temperatura, l toplotna prevodnost in I intenziteta toplotnega vira oz. ponora. 4.2 Tok sekundarne kapljevine skozi porozni grelnik Zakon ohranitve mase je podan z enačbo (1). Zakon ohranitve gibalne količine se glasi [7]: where c is sthe pecific isobaric heat, T stands for the temperature, l is the heat conductivity and I is the heat source. 4.2 Secondary liquid flow through the porous region The continuity equation is presented with expression (1). The momentum equation for the porous region can be written as [7]: roui f dt rv m u + — ki -pi+lm(ui, j+uji)] +rgi (4), kjer so f poroznost, v koeficient vztrajnosti, ki prepustnost porozne snovi, |u| absolutna vrednost hitrostnega vektorja in m dejanska dinamična viskoznost. Energijsko enačbo zapišemo v obliki: where f is the porosity, v is the inertia coefficient, ki is the permeability of the porous matter, IuI is the magnitude of the velocity and m is an effective dynamics viscosity. The energy equation is written as: 8T ( rcp ) eä+rcpujTj = ( l e T , j )j + I (5), kjer indeks e velja za primerjalne lastnosti, ki where subscript e indicates an effective property whose | IgfinHŽslbJlIMlIgiCšD I stran 329 glTMDDC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis povezujejo posamezne lastnosti tekočine in trdne faze, in so predpisane z naslednjimi izrazi: (rcp)e=frc +(1-f)(rc )s in le=fl + (1-f)ls. V teh izrazih se indeks s nanaša na lastnosti trdnine, lastnosti brez indeksa pa veljajo za kapljevino. Zgoraj podani sistem enačb predstavlja znani Forchheimer-Brinkmanov model porozne snovi. 5 ROBNI POGOJI V nadaljevanju so podani robni pogoji na mejah računskega območja W navidezno osnosimetričnega prereza uparjalnika. Predpisani so hitrostni in toplotni robni pogoji. Hitrostni robni pogoj podamo v naslednji splošni obliki value needs to be prescribed on the basis of the average properties of the liquid and solid phases. These properties are defined by the next expressions: (rcp)e = frcp + (1-f)(rcp)s and le = fl + (1 -f) ls . Here, the subscript s refers to solid matrix properties, and the properties without subscripts are those of the liquid phase. The equation system presented above is sometimes referred to as the Forchheimer-Brinkman model. 5 BOUNDARY CONDITIONS The boundary conditions on the boundaries of the computational domain W of the quasi-axisymmetrical revaporizer section are presented. The velocity and hea-transfer boundary conditions are prescribed. The velocity boundary conditions are written as: ui = ui(l,t) (6), kjer je / koordinatna razdalja vzdolž ustreznega roba. Vzdolž vseh robov so vrednosti hitrostnega vektorja nič. Na simetrijski osi je normalna komponenta hitrosti nič, medtem ko je vzdolž simetrijske osi predpisan pogoj »proste« vrednosti vzdolžne komponente hitrosti [7]. Mešani (Cauchyjev) toplotni robni pogoj se glasi: where l is the coordinate distance along the appropriate boundary. The zero-velocity boundary condition is prescribed along all the solid boundaries. On the symmetry axis of the revaporizer the free-slip boundary condition is set. The momentum flux has to be zero in the direction normal to the symmetry axis [7]. The general form of the mixed boundary condition is given by the expression: q& =a(T -Tref ) (7), kjer so q gostota toplotnega toka, a toplotna prestopnost in T f temperatura okolice. Mešani robni pogoji so predpisani vzdolž dna, plašča in pokrova uparjalnika ter v področju konvektivnega uparjanja in pregretja parne faze UNP-a (cevni loki). Za vsak izmed teh robov določimo vrednost toplotne prestopnosti in vrednost primerljive temperature. Neumannov robni pogoj (gostota toplotnega toka) se glasi: where q& is the heat flux, a is the convective heat-transfer coefficient and Tref is a reference temperature (surroundings temperature). The mixed (Cauchy) boundary conditions for heat transfer are prescribed along all the boundaries of the computational domain. These boundaries are the bottom, the shell, the revaporizer cover and the circular sections of the helical tube where the convective boiling and superheating of the LPG take place. The Neumann boundary condition (constant heat flux): q = kons t (8), in je predpisan vzdolž robov poroznega grelnika. is prescribed along the boundaries of the porous heater. 5.1 Toplotni robni pogoji Na robovih računskega območja predpišemo prilagojeno toplotno prestopnost, s katero upoštevamo tudi prevod toplote skozi trdne stene. Pri vijačnih spiralnih ceveh je opazna določena trajna deformacija prečnega prereza, ki je posledica postopka izdelave. Neenakomernost debeline cevne stene zato vpliva na značilnosti prevoda toplote skozi steno cevi. Jensen [9] je podal analitično rešitev tega problema. V našem primeru smo ta vpliv zanemarili in upoštevali dejansko debelino cevne stene pred izdelavo (imenska debelina). Prilagojeno toplotno prestopnost določimo s splošno veljavnim izrazom, 5.1 Temperature boundary conditions On the boundaries of the computational domain a modified heat-transfer coefficient way prescribed. In this way the heat conduction through the solid walls of the computational region was also taken into consideration. As result of the manufacturing process the helically coiled tubes have some permanent deformation of the transverse section. Accordingly, the non-uniformity of tube-wall thickness affects the heat transfer through the tube walls. Jensen [9] presented an analytical solution of this problem. Here, we have neglected this effect and taken the actual tube-wall thickness before the manufacturing process. Thus, the next expression VBgfFMK stran 330 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis ki se glasi: for the modified heat-transfer coefficient is obtained: a* =1(R + 1a) (9), kjer je R upor prevoda toplote. Vrednost upora prevoda toplote je določena z izrazom R = 8/A za ravno steno (dno in pokrov plašča) in z izrazom R = 1(2nA) ¦ ln (dt Idin ) za krožno steno (plašč, cev cevnega snopa). Z d je označena debelina prevodne stene, z d zunanji in z d notranji premer krožne stene. Za vsako izmed področij določimo vrednost toplotne prestopnosti, izrazi, ki veljajo za vsako izmed teh področij pa so podani v nadaljnjih oddelkih. Temperaturni robni pogoj v območju obtekanja posode zapišemo z enakostjo: where R represents the heat conduction resistance. The heat conduction resistance is defined by the expression R = 8/A for the plain wall (bottom and revaporizer cover) and by the expression R = 1(2nA)-ln(doutldin) for the circular wall (revaporizer shell, tubes of tube bundle). The d stands for the thickness of the conducting walls, d is the outer and din the inner diameter of the circular wall. The temperature boundary condition in the region of the air flow around the revaporizer shell is written as T =T ref sur (10), kjer je T temperatura okolice (preglednica 1). V primeru uparjanja dvokomponentne zmesi UNP-a obstaja temperaturno območje uparjanja. Domnevamo, da se temperatura zvišuje linearno v področju uparjanja. Zaradi osnosimetrične ponazoritve uparjalnika je treba podati ločene vrednosti temperature za vsak izmed cevnih lokov. Temperaturni robni pogoj se tako v področju uparjanja glasi: where Tsur is the temperature of the surroundings (Table 1). In the case of an LPG binary mixture a temperature range of evaporation exists. We have supposed that the temperature in this region increases linearly. Due to the axisymmetrical approximation an individual value for the temperature has to be prescribed separately for each of the tube turns. The temperature boundary conditions in the region of the convective boiling of the binary mixture of propane and butane are written as: Tref =Tbub+( ncb-1)DTcb (11), kjer so: Tb btemperatura vrelišča binarne zmesi propana in butana, n b - število cevnih lokov, znotraj katerih poteka konvektivno uparjanje UNP-a, DTb pa je temperaturno območje med dvema sosednjima lokoma v področju uparjanja in je podano z izrazom: where Tb b is the bubble-point temperature of the propane-butane mixture, n b is the number of tube turns in the region of convective boiling and DTb is the temperature difference between adjacent turns of the helically coiled tube in the region of convective boiling, defined by the expression DTcb (Tdew Tbub) ncb (12). Tde je temperatura rosišča binarne zmesi propana in butana. Tudi v področju pregrevanja parne faze UNP-a domnevamo linearno naraščanje temperaturnega poteka. Primerljiva temperatura je podana z izrazom: T =T ref dew Tdew is the dew-point temperature of the butane– propane mixture. In the superheating region the reference temperature is defined by the expression ( nsup-1)DTsu (13), kjer sta n število cevnih lokov znotraj katerih poteka pregrevanje parne faze UNP-a, DTs pa temperaturna razlika med sosednjima lokoma v področju pregrevanja in je podana z enačbo: DT where n represents the number of tube turns in the region of the superheating of the propane-butane mixture, DTs is the temperature difference between adjacent tube turns in the superheating region defined by the expression: T de w )ln su (14). S T je označena temperatura pregrete parne faze UNP-a na izstopu iz uparjalnika. where Tout is the outlet temperature of the propan–-butane vapour phase. Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 5.2 Enofazni tok v vijačni cevni spirali Zaradi vijačne oblike pretočne poti so delci tekočine med pretokom izpostavljeni delovanju sredobežnih sil, kot posledica delovanja teh sil pa je prostorska struktura toka bistveno drugačna od tiste, ki jo poznamo pri ravnih ceveh. Tekočinski delci v bližini aksialne osi cevi se gibljejo z največjimi hitrostmi in so izpostavljeni večjim sredobežnim silam od počasneje se gibajočih delcev v neposredni bližini cevne stene. Posledica tega je struktura toka, v kateri se tekočina v središčnem področju cevi premika stran od krivinskega središča vijačnice, tekočina ob cevni steni pa prav nasprotno v smeri simetrijske osi vijačnice. Pojav je znan kot sekundarno gibanje v ukrivljenih vodih, ki se superponira na glavno vzdolžno smer toka. Tok se tako sestoji iz para spiralnih vijačnih vrtincev [26]. Odstopanja hidrodinamičnih in toplotnih karakteristik vijačnih cevi v primerjavi z ravnimi cevmi je mogoče pripisati prav pojavu sekundarnega gibanja. V splošnem je, v primerjavi z ravnimi cevmi ob enakih pogojih toka, prenos toplote izboljšan, tlačne izgube pa so nekoliko večje. Za prehod iz laminarnega v turbulentni režim toka v vijačnih cevnih spiralah velja Schmidtova odvisnost [22], ki podaja kritično vrednost Re števila in se glasi: 5.2 Single-phase flow in helically coiled tubes Because of the helical flow path the fluid particles are subjected to centrifugal forces. Because of this, the spatial flow structure is significantly different from the one which occurs in straight tubes. Fluid particles flowing close to the tube’s longitudinal axis have the maximum velocity values and they are subjected to the maximum centrifugal forces in contrast to slowly moving particles in the vicinity of the tube walls. Liquid in the central part of the tube section moves away from the symmetry axis of helical tube. In contrast, liquid in the vicinity of the tube walls moves towards the helical tube symmetry axis. This phenomenon is known as secondary flow in curved pipes and it is superimposed on the main axial flow direction. Thus the flow consists of a pair of helical spiral vortices [26]. The hydrodynamic and heat-transfer characteristics are different in comparison with straight tubes and they can be attributed exclusively to the occurence of secondary flow. Normally, heat transfer and pressure losses in comparison with straight tubes under the same flow conditions are increased in helically coiled tubes. For the laminar-to-turbulent flow transition in helically coiled tubes the Schmidt correlation [22] is used, which represents the critical value of the Re number as Recr 2300 1 + 8,6 0,45 d in D (15). Reynoldsovo število je defirano kot Re = vdin n, z d pa je označen notranji premer cevi vijačne cevne spirale. D označuje prilagojeni premer vijačnice, ki upošteva c vzpon vijačnice glede na vodoravno ravnino [25] in je podan z izrazom: Dmc=Dc 1 + Z Dc je označen premer vijačnice, s h pa korak vzpona vijačnice. Schmidt [22] je ugotovil, da med laminarnim in popolnoma razvitim turbulentnim območjem obstaja prehodno območje toka, za katero velja Re < Re < 2.2x104. Za določitev toplotne prestopnosti v področju turbulentnega toka podajamo odvisnost Gnielinskega [8], ki se glasi: The Reynolds number is defined as Re = vdin n , where di is the inner tube diameter of the helically coiled tube. D represents the diameter of the modified coil, including the slope of the helical tube with respect to the horizontal plane [25], and is written as: pD (16). The helical coil diameter is D and h is the helical tube pitch. Schmidt [22] found that between the laminar and the turbulent flow region a transition region exists, where Re < Re < 2.2x104. An estimation of the heat-transfer coefficient in the turbulent region can be made by means of the Gnielinski correlation [8], written as: Nu =----- Re Pr kjer je x količnik trenja in je podan z izrazom: x 1 + 12,7x/8 ( P r 2/3 - 1 ) where x is the friction factor defined as 0.3164 Re025 Pr je Prandtlovo število, ki je definirano s Pr = m-c /l. Nusseltovo število je definirano z izrazom Nu = a-din/l. Območje veljavnosti podanega izraza za določitev Nu števila ter tekočine, na katere se izraz nanaša, so podani v + 0,0 3 (17), (18). Pr is the Prandtl number defined as Pr = m ¦ cp Il and the Nusselt number is defined as Nu = a-din/l. The ranges within which the presented expression for the Nu number can be used and the fluids for which this correlation was derived are presented in [9] and [22]. VBgfFMK stran 332 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis [9] in [22]. Domnevamo, da ekstrapolacija tega izraza na območje parametrov postopkov, ki veljajo v našem primeru, ne povzroča večje napake izračuna. 5.3 Konvektivno uparjanje v vijačni cevni spirali Sistematično obdelanih podatkov o konvektivnem uparjanju zmesi propana in butana ni v dostopni literaturi. Enako velja za raziskave konvektivnega uparjanja binarnih zmesi v vijačnih cevnih spiralah ([3], [12] do [14] in [25]) . Zato smo omejeni na uporabo izrazov, ki veljajo za uparjanje najpogosteje raziskovanih binarnih zmesi (hladiva) v ravnih ceveh. Pri konvektivnem uparjanju binarnih zmesi je konvektivno izparevanje prevladujoč mehanizem spremembe agregatnega stanja. Področje mehurčastega vrenja je premaknjeno proti večjim vrednostim pregretja cevne stene ali pa se sploh ne pojavlja. Prispevek mehurčastega vrenja je pri konvektivnem uparjanju binarnih zmesi zadušen z učinki difuzije na medfaznih površinah rastočih mehurčkov. Glede na intenzivnost zadušitve mehurčastega vrenja je Kandlikar [14] podal tri področja, za katera je predpisal različne izraze za določitev toplotne prestopnosti. Področja so definirana na podlagi vrednosti hlapljivosti V1 in vrelnega števila Bo. Hlapljivost je definirana z izrazom: V1 p,l kjer so: c l specifična toplota kapljevite faze, hlv specifična uparjalna entalpija UNP-a, a toplotna difuzivnost, D12 snovska difuzivnost, x1 molski delež komponente 1 v kapljeviti fazi in y1 molski delež komponente 1 v parni fazi. Odvod dT/dx1 določa strmino vrelne krivulje v diagramu T-x1 ob določeni sestavi. Vrelno število Bo je definirano z izrazom: Bo = We suppose that the extrapolation of the presented expression over the range of process parameters encountered in our computations will not significantly affect the results of the numerical analysis. 5.3 Convective boiling in helically coiled tubes Systematically assembled data on the convective flow boiling of prop-ne-butane mixtures cannot be found in the open literature. The same statement holds for convective flow boiling investigations of binary mixtures in helically coiled tubes ([3], [12] to [14] and [25]). Because of this we are restricted to using correlations derived for the boiling of frequently explored binary mixtures (refrigerants) in straight tubes. For binary mixtures boiling convective evaporation is the dominant mechanism of phase transformation. The nucleate boiling mechanism occurs at higher values of tube-wall superheating or it is not present at all. The contribution of nucleate boiling during the convective boiling of binary mixtures is suppressed by diffusion effects at the interfaces of growing bubbles. With regard to the intensity of the suppression of the nucleation boiling process, Kandlikar [14] defined three regions where different expressions for the heat-transfer coefficient estimation can be used. The regions have been defined on the basis of volatility, V1, and boiling number values, Bo. The volatility is written as dT dx1 ( x 1 - y 1 ) (19), where cp,l is the specific isobaric heat of the liquid phase, hlv is the specific vaporisation enthalpy of LPG, a the heat diffusivity, D12 the molecular diffusivity, x1 the mole fraction of component 1 in the liquid phase and y1 the mole fraction of component 1 in the vapour phase. The derivative dT/dx1 defines the slope of the bubble curve on the T-x1 diagram for the selected mixture composition. The boiling number is defined as: G-h (20), kjer je G gostota masnega toka. Snovske lastnosti zmesi propana in butana v primeru kapljevitega in plinastega agregatnega stanja so določene na podlagi izrazov iz [21] in [25]. Za izbrane parametre uparjanje poteka v področju zmerne zadušitve mehurčastega vrenja, povzročene z učinki difuzije (0,03 < V 1 < 0,2 in Bo > 1E-4). Področje prevladujočega mehurčastega vrenja ni več opazno. Konvektivno izparevanje je osnovni mehanizem prenosa toplote. Z difuzijo povzročena zadušitev je zmerna, vendar ne vpliva na člen mehurčastega vrenja v področju prevladujočega konvektivnega izparevanja. Dvofazna toplotna prestopnost v tem področju je podana z izrazom: where G stands for the mass flux. The physical properties of the propane-butane mixtures in the liquid and gas states are calculated on the basis of expressions from references [21] and [25]. For selected process parameters the boiling occurs in the region of moderate suppression of nucleate boiling caused by diffusion (0.03 < V1 < 0.2 in Bo > 1E-4). The region where nucleate boiling is the dominant mechanism does not exist. The governing heat-transfer mechanism is convective evaporation. Suppression caused by diffusion still exists, but its moderate contribution does not affect the nucleate boiling term in the region where convective evaporation dominates. The two-phase heat-transfer coefficient in this region is written as Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis a a (1 -x)0.8 [1, 136• Co-0.9 ¦ f2 (Frlo) + 667,2• B o 0 7 ¦ F fl m] (21). V enačbi (21) so: a, enofazna toplotna prestopnost, za primer, da o celoten tok zaseda kapljevita faza, x masni delež parne faze, Co konvektivno število, f2(Frlo ) množitelj Froudovega števila in Ffl parameter, ki je odvisen od lastnosti tekočine in površine cevne stene. Konvektivno število je definirano z izrazom: Co = {v kjer sta rv gostota parne faze in rl gostota kapljevite faze. Množitelj Froudovega števila ima vrednost 1 za pokončne in vodoravne cevi z vrednostjo Frlo > 0,4. Za Frlo < 0,4 pri vodoravnih ceveh je vrednost f2(Fr lo) definirana z izrazom (25Frlo)0,3. Froudovo število za primer, da celoten tok zaseda kapljevita faza, je definirano z izrazom: Frlo= In expression (21), alo is the single-phase all-liquid heat-transfer coefficient, x is the mass fraction of the vapour phase or the quality, Co is the convection number, Frlo is the Froude number with all flow as liquid and f2 (Frlo) is the Froude number multiplier. Ffl, is a fluid-surface parameter that depends on the fluid and the heater surface characteristics. The convective number is defined as: (1-x) (22), where rv and rl are the density of the vapour and the liquid phases, respectively. The Froude number multiplier is 1 for vertical tubes and for horizontal tubes with Fr, > 0.4. For Frlo < 0.4 at horizontal tubes the value of o f2(Frlo) is (25Frlo)0.3. The Fr number with all flow as the liquid is defined as rl -g- (23). Parameter učinkov stične površine [14] je določen z vzvodnim pravilom in se glasi: Fluid-surface parameters [14] are defined by the mixing rule as F fl,m xF + x F 1 fl,1 2 fl,2 (24). Podani izrazi veljajo za področje popolne omočenosti cevne stene. V področju izsuševanja cevne stene se razmere spremenijo zaradi postopnega razširjanja neomočenega dela cevnega oboda. Parametri, ki najbolj vplivajo na razmere v področju izsuševanja, so sistemski tlak p, premer vijačnice D , gostota toplotnega toka q in gostota masnega toka G. Berthoud in Jayanti [4] sta na podlagi vpliva sistemskih parametrov določila tri karakteristična področja, v katerih prevladuje eden izmed vodilnih mehanizmov izsuševanja, in sicer: (a) področje prevladujočega disperznega razprševanja, (b) področje prevladujočega usedanja razpršenih kapljic in (c) področje prevladujoče plastitve toka. Na sliki 4 je prikazan diagram, s katerim določimo cono prevladujočih mehanizmov izsuševanja cevne stene v vijačni cevni spirali. Brezrazsežno število x0 = g( rv gDc) podaja vpliv sredobežnih sil, ki delujejo na parno fazo toka in v njej razpršene kapljice. Vpliv tega števila je najbolj pomemben v področju prevladujočega vnovičnega usedanja razpršenih kapljic. Brezrazsežno število y0 =G-din -(d /0,02)12ml je Re število kapljevite faze toka, ki in je spremenimo s popravnim količnikom notranjega cevnega premera. Vpliv tega števila je prevladujoč v področju razprševanja kapljic v parno jedro toka. Za podane sistemske parametre uparjalnika je plastovito izsuševanje cevne stene prevladujoč mehanizem. Izraz za določitev masnega deleža parne faze ob začetni izsušitvi za področje The expressions given above can be used if the tube walls are completely wetted. In the region of tube-wall dryout, the conditions are changed as non-wetted portions of the tube walls are gradually spread. The main system parameters leading to the tube-wall dryout process are the system pressure p, the helical coil diameter Dc and the heat and mass flux, q and G, respectively. By analysing the system parameters Berthoud and Jayanti [4] defined three regions with different governing mechanisms of dryout: (a) region where the dispersed entrainment is dominant, (b) region with the intensified redeposition of dispersed drops and (c) region where the flow-stratification effects dominate. In Figure 4 different zones of governing dryout mechanisms in helically coiled tubes are presented. The nondimensional number x0 = G/( rv^JgDc ) accounts for the centrifugal forces’s influence on vapour phase and the dispersed drops in it. The value of this number is large in the region with the intensified redeposition of dispersed drops. The nondimensional number y0=G-din -( din /0,02 )/ml is the Re number for liquid-phase flow with a modified value of the inside tube diameter. The value of this number is large in the region of the dispersed entrainment in the vapour core of the flow. For selected system parameters the stratification or gravity-dominated dryout of the tube walls is the governing mechanism. The mass quality at the initial stage of dryout for the region in which VBgfFMK stran 334 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 64-10-- 32-10 - 16-10*-- 8-10 + ¦10 - \ \ Zone of entrainment (Intermediate first dryout quality) \ y cona prevladujočega / ^disperznega razprševanja \ / V \ območje prevladujoče^ plastitve Gravity-affected zone (low first dryout quality) \ \ Zone of redeposition (High first dryout quality) območje prevladujočega usedanja razpršenih kapljic 0.5 16 32 X0 Sl.4 Območja prevladujočih mehanizmov izsusevanja v vijačni cevni spirali [4] Fig. 4. Zones of different dryout mechanisms in helically coiled tubes [4] prevladujočega vpliva plastovitosti toka oz. stratification dryout is the governing mechanism can težnostnih sil se glasi [4]: be calculated by the expression [4]: 107 v ml 1,712 rvgDc Gh (25), kjer je ml dinamična viskoznost kapljevite faze. Za praktične namene velja ugotovitev, da se popolna izsušitev cevne stene pojavi za ravnotežni masni delež parne faze z vrednostjo x = 1. Pri plastnem izsuševanju se točka začetne izsušitve pojavi v zgornji točki cevnega oboda, nato pa se izsušitev simetrično razširja po cevnem obodu. Končni izraz za določitev toplotne prestopnosti v vijačni cevni spirali [25] se glasi: where ml is the dynamic viscosity of the liquid phase. For practical purposes the total dryout of the tube walls can be considered to occur at mass quality xtot = 1. When stratification is the governing mechanism of dryout, the initial dryout point appears at the uppermost circumferential tube position. Thereafter, dryout is symmetrically spread along the tube walls. Thus, the final expression for the estimation of heat-transfer coefficient within the helically coiled tube is written as: a = aTP (1 - Q) + aEPQ (26), kjer so: Q trenutni kot omočenja cevne stene v področju uparjanja, aEP toplotna prestopnost v enofaznem področju in aTP toplotna prestopnost v dvofaznem področju (konvektivno uparjanje). 5.4 Obtekanje plašča uparjalnika Uparjalnik je v večini primerov nameščen na odprtem prostoru. Za določitev toplotnih izgub v okolico je treba podati toplotno prestopnost pri obtekanju plašča uparjalnika. Zaradi spremenljivih tokovnih razmer okrog posode uparjalnika je določitev toplotne prestopnosti zelo težavna. Za obtekanje valjaste posode uparjalnika smo uporabili znano odvisnost Churchilla in Bernsteina, ki velja za široko področje Re in Pr števil. Odvisnost velja ob pogoju Re-Pr > 0,2 in se glasi: where Q is the temporary angular position of the dryout propagation front in the convective boiling region, aE is the heat-transfer coefficient in the single-phase region of flow and aTP is the heat-transfer coefficient in the region of two-phase flow. 5.4 Flow around the revaporizer vessel Revaporizers are mainly manufactured without any thermal insulation. The heat-transfer coefficient for air flow around the revaporizer has to be defined if we want to allow for heat loses to the surroundings. Unsteadiness of the flow conditions around the revaporizer’s shell can make such an estimation very difficult. For the flow around the cylindrical shell the well-known correlation of Churchill and Bernstein is used. The correlation is applicable to a wide range of Re and Pr numbers with the only restriction being Re-Pr> 0.2 : | IgfinHŽslbJlIMlIgiCšD I stran 335 glTMDDC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis Nu = 0,3 + 0, 62Re1/2Pr1/3 [1 + (0,4/Pr)2/3]1/4 1+ Re {282000 5/8 4/5 (27). Snovske lastnosti veljajo za suh zrak. Hitrost zračnih tokov je upoštevana s povprečno vrednostjo hitrosti vetra, ki je usmerjena normalno na plašč uparjalnika. Pri obtekanju dna in pokrova posode smo uporabili izraz: In equation (27) the physical properties for the dry air are selected. The velocity of the air flow is included by means of an average value of the wind velocity normal to the revaporizer shell. For flow along the bottom and the cover of the revaporizer a correlation for the turbulent flow region is used: Nu = 0,037-Re 08 Pr ki velja za turbulentno področje in je podan v [1]. 5.5 Električno uporovno gretje [2] Prostornino, ki jo zaseda električni grelnik, smo nadomestili z porozno snovjo. Gostota toplotnega toka, ki je predpisana na robovih porozne snovi, je izračunana iz moči grelnika in njegove površine. Enačba, ki povezuje električne in toplotne veličine grelnika, se glasi: 1/3 (28), I2R rL el w Pri določitvi poroznosti in prepustnosti poroznega grelnika smo upoštevali navodila, ki so podana v [7]. V izrazu (29) so: Pl električna moč grelnika, Qht toplotna moč grelnika, qht gostota toplotnega toka grelnika in Aht njegova površina. 6 RAČUNSKI ALGORITEM Računski algoritem, s katerim smo prišli do rešitve, je podan na sliki 5. 7 REZULTATI Računalniški program FIDAP 8.5 omogoča nastanek nestrukturirane mreže končnih elementov. Uporabljen je algoritem oblaganja za diskretizacijo računskega območja, pri čemer je opravljeno lokalno zgoščevanje mreže ob robovih računskega območja (stene posode in cevni loki). Po testiranju občutljivosti numeričnih rezultatov na gostoto mreže je bila kot primerna izbrana računska mreža s 14.900 elementi v področju toka sekundarne kapljevine in 1900 elementi v področju poroznega grelnika. Hitrosti v polju naravne konvekcije so majhne, tokovni režim je laminaren. Postopek izračuna (slika 5) smo ponovili tolikokrat, da smo dosegli ujemanje toplotnega toka, ki ga cevni snop sprejme v področju uparjanja Q b in uparjalne entalpije UNP-a Qlv . Na koncu je doseženo stanje, v katerem so se rezultati nadaljnje določitve povprečne gostote toplotnega toka v področju uparjanja spreminjali le znotraj območja enega cevnega loka. To je obenem tudi največja mogoča natančnost tukaj vpeljanega postopka. Rezultati, ki so bili doseženi v zadnjem koraku izračuna, so podani v nadaljevanju. VH^tTPsDDIK stran 336 and it has been taken from [1]. 5.5 Electrical resistance heating [2] The revaporizer section where the electrical heater is placed was modelled as a porous region. The heat flux prescribed at boundaries of the porous heater can be calculated from heater’s electric power and its surface area, as given by the expression Q& ht (29). where Pel is the electrical power, Q&ht is the power of the heater, q&ht is the heat flux and Aht its surface area. The instruction given in [7] was taken into consideration when the porosity and the permeability of the porous heater were defined. 6 CALCULATION ALGORITHM The calculation algorithm used to obtain the final solution of the defined problem is presented in Fig. 5. 7 RESULTS Unstructured finite-element grids can be created with the FIDAP 8.5 program package. For the computational-region mesh generation we used the paving algorithm. Local mesh refinement in the vicinity of all the region boundaries was carried out. The study of the influence of the grid density on the numerical results resulted in an optimum mesh density with 14,900 finite elements in the region of the secondary liquid flow and 1900 elements in the region of the porous heater. The flow regime was laminar since the Re number value for the natural convection inside the secondary liquid flow was below the critical value. The calculation procedure (Figure 5) had to be repeated several times before we achieved the final operational stage where the total heat received by the tube bundle in the convective boiling region Q&cb was equal to the vaporisation enthalpy of the LPG Q&lv . The results obtained in the last iteration of the calculation procedure served as the basis for the discussion of the results. Convective boiling occurs inside the 21 turns of the tube bundle. The mass Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis Preglednica 2. Toplotni tokovi vzdolž robov računskega območja ob pogoju nespremenljive vrednosti gostote toplotnega toka (prvi računski korak) Table 2. Heat fluxes through the computational domain boundaries (first calculation step - uniform heat-flux distribution along tube bundle assumed when the boundary conditions are defined) Rob Boundary Toplotni tok [W] Heat flow rate [W] Rob Boundary Toplotni tok [W] Heat flow rate [W] lok1 turn1 30,20 lok17 turn17 352,20 lok2 turn2 42,30 lok18 turn18 341,80 lok3 turn3 51,10 lok19 turn19 338,20 lok4 turn4 62,20 lok20 turn20 334,30 lok5 turn5 70,00 lok21 turn21 332,10 lok6 turn6 79,40 lok22 turn22 281,30 lok7 turn7 89,20 lok23 turn23 242,00 lok8 turn8 92,30 lok24 turn24 212,80 lok9 turn9 101,80 lok25 turn25 171,70 lok10 turn10 111,30 lok26 turn26 114,10 lok11 turn11 118,10 lok27 turn27 82,30 lok12 turn12 122,20 lok28 turn28 43,10 lok13 turn13 131,40 pokrov cover 34,10 lok14 turn14 138,60 plašč shell 185,10 lok15 turn15 328,50 dno bottom 25,10 lok16 turn16 341,20 S 5000 Konvektivno uparjanje poteka znotraj 21 cevnih lokov. Masni delež parne faze ob začetni izsušitvi znaša x =0,41. Število cevnih lokov, znotraj katerega je opazna popolna omoČenost cevnega oboda, je 9. Znotraj 12 lokov poteka izsuševanje cevne stene. Od tod naprej poteka pregrevanje parne faze UNP-a. Za podane parametre je to stanje ustaljenega delovanja uparjalnika. V preglednici 2 so podane vrednosti toplotnih tokov, ki jih sprejmejo posamezni loki cevnega snopa ob pogoju stalne vrednosti gostote toplotnega toka, ki prehaja na cevni snop (začetna domneva). V preglednici 3 so podane vrednosti toplotnih tokov po posameznih lokih cevnega snopa v zadnjem računskem koraku, in sicer, ko je upoštevana neenakomerna porazdelitev gostote toplotnega toka po posameznih lokih cevnega snopa (končno stanje). Na sliki 6 je podan potek toplotne prestopnosti in temperature (robni pogoji) po posameznih cevnih lokih cevnega snopa v prvem koraku izračuna quality of the vapour phase at the initial dryout position has a value xini = 0.41. It was found that the total wetting of the tube walls is present inside the first 9 turns of the tube bundle. Dryout of the tube walls takes place inside the next 12 turns of the tube bundle. From that point to the outlet of the tube bundle the superheating of the LPG occurs. For the prescribed working parameters of the revaporizer this is the steady-state operating regime. In Table 2 the heat-flow values received by particular turns of the tube bundle are presented. As an initial assumption the uniform heat flux distribution along the tube bundle was assumed when correlations to estimate boundary conditions were used. In Table 3 the heat-flow values received by the particular turns of the tube bundle in the last calculating step are presented. There is nonuniformity of the heat-flow distribution along the tube bundle, and it was taken into account when defining the boundary conditions gfin^OtJJlMlSCSD 03-6 stran 337 |^BSSITIMIGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis Parametri postopka, Process parameters (Tsur,xCH ,mLPG,v w, sekundarna kapljevina (secondary liquid),H sl j q b,1 =Q htlA b , Q»,1 =0 A b,1 = Q vlq tb,1 out,1 ht lvJ/ LPG p,LPG dew a1robovi (boundaries) enačbe, equations (15, 19, ...) T1 robovi(boundaries) enačbe, equations (11-14) Izračun sistema enačb (1-5) s pomočjo MKE programa FIDAP 8.5 Governing equations (1-5) solved by finite elements program FIDAP 8.5 Rezultati (gostota toplotnega toka vzdolž mej računskega območja) Results (heat fluxes along domain boundaries) Q los,i+1 = J q shell,i+1 dA + J q bottomi +1 dA + J q bottom,i+1 dA A shell A bottom A over q tb,i+1 = (üht - Q los,i+1 )I A b Q lv = \q tb,i+1 dA => A cb,i+1 => n cb,i+1 => n i+1 A cb,i +1 T out,i +1 = Q ht - Q lv - Q losMlllm LPG ¦ c ,LPg) + T dew ai+1 robovi (boundaries) enačbe, equations (15, 19, ...) Ti +1 robovi (boundaries) enačbe, equations (11-14) 3 Izračun sistema enačb (1-5) s pomočjo MKE programa FIDAP 8.5 Governing equations (1-5) solved by finite elements program FIDAP 8.5 Rezultati (gostota toplotnega toka vzdolž mej računskega območja) Results (heat fluxes along domain boundaries) Sl.5 Računski algoritem Fig. 5. Calculating algorithm (nespremenljiva gostota toplotnega toka vzdolž in the next calculating steps. The heat-transfer cevnega snopa). Na sliki 7 je prikazan potek toplotne coefficient and the temperature distribution along tube prestopnosti in temperature v zadnjem računskem turns are presented in Figures 6 and 7, in the first and koraku. last calculating step, respectively. Na sliki 8a) je prikazan izsek hitrostnega polja In Figure 8(a) the velocity field in the vicinity of the v osnosimetričnem prerezu uparjalnika, od koder je upper part of the electrical heater is presented. It is evident grin^SfcflMISDSD ^BSfiTTMlliC | stran 338 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis Preglednica 3. Toplotni tokovi vzdolž robov računskega območja v zadnjem računskem koraku, ko je upoštevana neenakomernost gostote toplotnega toka (končno stanje) Table 3. Heat fluxes through the computational domain boundaries (final calculation step - nonuniform heat-flux distribution along the tube bundle taken into account when the boundary conditions are defined) Rob Boundary Toplotni tok [W] Heat flow rate [W] Rob Boundary Toplotni tok [W] Heat flow rate [W] lok1 turn1 60,00 lok17 turn17 356,00 lok2 turn2 65,50 lok18 turn18 366,00 lok3 turn3 68,50 lok19 turn19 366,50 lok4 turn4 73,00 lok20 turn20 367,00 lok5 turn5 82,50 lok21 turn21 368,50 lok6 turn6 89,00 lok22 turn22 260,00 lok7 turn7 95,50 lok23 turn23 215,50 lok8 turn8 102,50 lok24 turn24 106,00 lok9 turn9 106,00 lok25 turn25 96,00 lok10 turn10 114,50 lok26 turn26 50,50 lok11 turn11 119,50 lok27 turn27 49,50 lok12 turn12 125,50 lok28 turn28 48,50 lok13 turn13 132,00 pokrov cover 32,00 lok14 turn14 139,50 plašč shell 261,50 lok15 turn15 321,50 dno bottom 25,50 lok16 turn16 336,00 S 5000 razvidno, da so največje hitrosti grelne kapljevine največje v središčnih območjih uparjalnika (notranjost grelnika). Najmanjše hitrosti sekundarne kapljevine se pojavijo v bližini plašča uparjalnika. Na sliki 8b) je podan izsek temperaturnega polja v osnosimetričnem prerezu uparjalnika. Področje konvektivnega uparjanja zaseda največji del cevnega snopa. Področje majhne temperaturne razlike med sekundarno kapljevino in cevno steno je vzrok, da je konvektivno izparevanje vodilni mehanizem agregatne spremembe (temnejša področja na sliki 8b). V zgornjem delu električnega grelnika so temperature sekundarne kapljevine največje (slika 8b), vendar pa ne presegajo največje dopustne vrednosti, ki je predpisana s strani proizvajalca (130 oC). Izstopna temperatura pregrete parne faze UNP-a je podatek, ki smo ga uporabili za preverjanje doseženih rezultatov. Polje naravne konvekcije v uparjalniku je uporabljeno za prenos krmilne veličine od izstopnega loka cevnega snopa na zaznavala that the maximum velocities of the secondary liquid arise in the central part of the revaporizer (internal section of electrical heater). In contarast, the minimum velocities occur immediately in the vicinity of the revaporizer shell. In Figure 8(b) the temperature field in the same view as in Figure 8(a) is shown. It is evident that convective boiling occupies the largest part of the tube bundle. The low temperature difference between the secondary liquid and the tube wall is the reason why the convective evaporation – as a mode of the boiling process – is the governing mechanism of the phase transition (dark regions of the plot). In the upper sections of the electrical heater the temperature reaches its maximum (see Figure 9), but its value does not exceed the allowed value prescribed by the manufacturer (130 oC). The outlet temperature of the LPG superheated vapour phase is the parameter used for the verification of the achieved results of the numerical analysis. The natural convection field was used for regulating the value transport between the gfin^OtJJlMlSCSD 03-6 stran 339 |^BSSITIMIGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis 700 600 500 400 300 200 100 0 zaporedje cevnih lokov — toplotna prestopnost (W/m2K) temperatura (K) sequence of tube turns heat trans. coeff.______________temperature cevni loki (površina za prenos toplote) tube turns (heat transfer area) Sl.6. Potek toplotne prestopnosti in temperature po posameznih lokih cevnega snopa v prvem računskem koraku (robni pogoji - začetni računski korak) Fig. 6. Heat-transfer coefficient and temperature distribution along the turns of the tube bundle in the first calculation step (boundary conditions - initial state) 700 600 500 400 300 200 100 0 zaporedje cevnih lokov * toplotna prestopnost (W/m2K) temperatura (K) sequence of tube turns heat trans. coeff.______________temperature cevni loki (površina za prenos toplote) tube turns (heat transfer area) Sl.7. Potek toplotne prestopnosti in temperature po posameznih lokih cevnega snopa, ko je doseženo končno obratovalno stanje (robni pogoji - zadnji računski korak) Fig. 7. Heat-transfer coefficient and temperature distribution along the turns of the tube bundle in the last calculation step (boundary conditions - final state) krmilnih termostatov. Krmiljena veličina je temperatura. Za obratovanje uparjalnika je potrebno, da je temperaturno polje v točki namestitve zaznaval krmilnih termostatov vedno v predpisanem delovnem območju. Delovno območje krmilnih termostatov je od 65 oC do 85 oC. Na podlagi poteka izoterm temperaturnega polja smo ugotovili, da je temperatura v točkah namestitve krmilnih termostatov znotraj predpisanega temperaturnega območja. Temperatura v točki namestitve zaznavala termostata, ki krmili last turn of tube bundle and the sensor of the control thermostats. The controlled value is the temperature. Undisturbed operating of the revaporizer requires that the temperature value at the thermostat sensor position has to be always within the defined temperature range. The working range of the control thermostats is from 65 oC to 85 oC. Using an isotherms plot it was found that the temperature at the location of the control thermostats lies within the defined temperature range. The temperature at the position of the thermostat VBgfFMK stran 340 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis zgornjega dela grelnika Fig. 8. (a) Velocity and (b) temperature field in axisymmetrical section of revaporizer in the region of upper parts of heater delovanje elektromagnetnega ventila, znaša 76 oC. Doseženo stanje velja ob izbranih parametrih postopka (preglednica 1). Krmilni termostati so oprema uparjalnika, ki daje določene podatke o celostnih značilnostih delovanja naprave. Za vpogled v krajevne razmere v posameznih delih uparjalnika so potrebne podrobne meritve izbranih fizikalnih veličin. Na sliki 9 je podan prikaz temperaturnega polja v točkah namestitve tipal krmilnih termostatov. 8 SKLEPI Sočasen nastop večjega števila prenosnih pojavov onemogoča natančno obravnavo obnašanja uparjalnika. Zapletena geometrijska oblika cevnega snopa in električnega grelnika omejuje možnosti uporabe znanih metod dimenzioniranja in nadzora dvofaznih prenosnikov toplote. Uporaba standardnih računskih postopkov za dimenzioniranje uparjalnikov je v danem primeru nezadostna. V splošnem je zelo malo empiričnih podatkov o toplotni prestopnosti pri tokovih z naravno konvekcijo v zapletenih geometrijskih oblikah. Vodilni prenosni pojav v električnem uparjalniku je konvektivno uparjanje ukapljenega naftnega plina. Pravilno vrednotenje tega pojava je zahtevna inženirska naloga. Pri izračunu smo domnevali, da se uparjalnik obnaša približno kot sistem z vsiljeno nespremenljivo gostoto toplotnega toka. Čeprav je krajevna porazdelitev gostote toplotnega toka neenakomerna, je povprečna vrednost le-te nespremenljiva in določena z močjo in površino grelnika (sistem s posrednim električnim gretjem). Rezultati so pokazali, da se uparjalnik obnaša kot sistem z vsiljeno temperaturno razliko (zunanje področje cevnega snopa), delno pa kot sistem z vsiljeno gostoto toplotnega toka (notranje področje sensor controlling the electromagnetic valve has a value of 76 oC. This operating state corresponds to the selected process parameters (Table 1). In Figure 9 the temperature field in the uppermost part of the revaporizer axisymmetrical section is presented. To get a better insight into the local conditions in particular parts of the revaporizer more accurate measurements should be performed, and their results compared with the computational results. 8 CONCLUSIONS Due to different transport phenomena occuring in the revaporizer it is impossible to achieve an exact solution of the heat and flow conditions inside the device. The complex tube bundle and the electrical heater geometry restricts the implementation of well-known methods for design and rating calculations of two-phase heat exchangers. In the open literature there are not, in general, empirical data about heat-transfer coefficients due to natural convection in the systems with complex geometry. Likewise, convective boiling of LPG in helically coiled tubes is an unexplored phenomenon. The correct treatment of the latter is a demanding engineering task. In our approach we assumed that the revaporizer operates as a system with a constantly imposed heat flux. Although the local distribution of heat flux exhibits considerable nonuniformity its averaged value is constant, defined by the heat power and the surface area of the electric heater (system with indirect electrical heating). It can be concluded that the revaporizer operates partly as a system with an imposed temperature difference (external region of the tube bundle) and partly as a system with an imposed heat flux (internal region of the tube bundle). gfin^OtJJIMISCSD 03-6 stran 341 |^BSSITIMIGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis cevnega snopa). Uporabo preverjene Kandlikarjeve zveze za ravne cevi pri vrednotenju nasičenega uparjanja znotraj vijačne cevne spirale je mogoče pojasniti z nizko vrednostjo gostote toplotnega in masnega toka ter zanemarljivim vplivom centrifugalnih sil. Ker razpršitev ni prevladujoč pojav v področju obročastega toka, je omenjeno povezanost mogoče kombinirati z zvezo za čisto parno fazo in tako določiti toplotno prestopnost v področju izsuševanja cevne stene. Krajevne razmere so za predpisovanje robnih pogojev na mejah računskega območja odločilnega pomena. Robni pogoji na mejah področja, kjer poteka uparjanje, so zato predpisani na temelju dandanes The implementation of Kandlikar’s correlation for the heat-transfer characteristics’ estimation for saturated boiling in helically coiled tubes can be explained by the low heat and mass flux values and the negligible effects caused by centrifugal forces. Due to the fact that the dispersed entrainment is not a dominant phenomenon in the region where annular flow regime exists, Kandlikar’s correlation can be combined with the correlation for the heat-transfer coefficient’s estimation in the region of the all-vapour phase flow. Thus it is possible to define the heat-transfer coefficient in the dryout region of the tube bundle. Local conditions in the revaporizer are of great importance when boundary conditions have to be TEMPERATURNO POLJE ZA KONČNO STANJE IZRAČUNA, KO SO ZADOVOLJENE DELNE IN CELOTNA TOPLOTNA BILANCA TEMPERATURE FIELD FOR FINAL CALCULATION STEP (PARTIAL AND GLOBAL HEAT BALANCES SATISFIED) 349,00 K SLIKA TEMP. OBRISOV TEMP. CONTOUR PLOT 293,50 K .383E+03 .371E+03 .3S0E+03 .349E+03 .33SE+03 .327E+03 .315E+03 .304E+03 Sl. 9. Potek temperaturnega polja v zgornjem delu uparjalnika (temperatura v točki namestitve tipala krmilnega termostata elektromagnetnega ventila) Fig. 9. Temperature field in the upper part of the revaporizer (temperature is shown at the position where the thermostat sensor of the electromagnetic valve is placed) VH^tTPsDDIK stran 342 Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis najbolj uveljavljenih odvisnosti. Celostni kazalniki obnašanja uparjalnika so po opravljenem toplotnem uravnoteženju pokazali veljavnost vpeljanih hipotez. Za izbrane delovne parametre je temperatura v točki namestitve zaznaval krmilnih termostatov uparjalnika dosegla predpisane vrednosti. Uparjalnik deluje znotraj predpisanega temperaturnega območja v merilnih točkah. Zadovoljene so bile delne in celotna toplotna bilanca. Kolikšen je pomen morebitnih napak, ki izvirajo iz ekstrapolacije uporabljenih odvisnosti na uparjanje UNP-a v vijačni cevni spirali, ni znano. Analiza obratovanja uparjalnika v ekstremnih razmerah oz. na mejah delovnega področja bo pokazala velikost teh napak. prescribed. Boundary conditions on the boundaries where convective boiling takes place are prescribed on the basis of verified correlations. The observed integral characteristics of the revaporizer confirmed the correctness of our assumptions. For the selected combination of process parameters the temperature at the control sensor is within the prescribed temperature range. The local and global heat balances are satisfied. Some deviations can arise from the extrapolation of used correlations outside of the prescribed ranges. An analysis of the revaporizer operating in extreme conditions, that is in the vicinity of the borders of the working diagram can show the magnitude of these deviations. 9 OZNAKE 9 NOMENCLATURE toplotna difuzivnost površina vrelno število konvektivno število specifična izobarna toplota premer premer cevi difuzivnost množitelj Fr števila Froudovo število gostota masnega toka težnostni pospešek specifična entalpija, korak vzpona vijačnice višina jakost električnega toka masni pretok število cevnih lokov Nusseltovo število termodinamični tlak Prandtlovo število gostota toplotnega toka toplotni tok upor prevoda toplote, električna upornost Reynoldsovo število prečni prerez električnega voda čas temperatura hitrost absolutna vrednost hitrostnega vektorja hlapljivost, električna napetost masni delež parne faze, molski delež komponente v kapljeviti fazi molski delež komponente v parni fazi Grški simboli efektivna dinamična viskoznost koeficient vztrajnosti porozne snovi modificirana toplotna prestopnost poroznost debelina cevne stene dinamična viskoznost a thermal diffusivity A area Bo Boiling number Co Convective number c specific heat at constant pressure D diameter d tube diameter D diffusion coefficient f (Fr ) Fr number multiplicator Fr Froude number G mass flux g acceleration due to gravity h specific enthalpy, helix pitch H height I electric flow rate m& mass flow rate n number of tube turns Nu Nusselt number p thermodynamic pressure Pr Prandtl number q& heat flux Q& heat flow rate R thermal resistance, electric resistance Re Reynolds number S transversal section of electrical conductor t time T temperature u, v velocity u absolute value of velocity vector V volatility x quality, mole fraction in liquid phase y mole fraction in vapour phase Greek Symbols m effective dynamic viscosity v porous inertia coefficient a* modified heat-transfer coefficient f porosity d tube-wall thickness m dynamics viscosity gfin^OtJJlMlSCSD 03-6 stran 343 |^BSSITIMIGC Ba{i~ S., [kerget L., Hriber{ek M.: Termohidravli~na analiza - A Thermohydraulic Analysis gostota, specifična električna upornost r density, specific electric resistance kinematična viskoznost n kinematics viscosity koeficient upora, masni delež x friction factor, mass fraction kot omočenja cevne stene v področju uparjanja Q tube-wall wetting angle in the boiling region toplotna prestopnost a heat-transfer coefficient toplotna prevodnost l heat conductivity permeabilnost porozne snovi k porous permeability prostorninski temperaturni raztezek b volumetric temperature dilatation coefficient temperaturna razlika med sosednjima DT temperature difference between adjacent tube cevnima lokoma turns Podpisi Subscripts vrelišče bub bubble point vijačnica c helix propan CH propan konvektivno vrenje cb convective boiling področje prevladujočega konvektivnega izparevanja CBD convective evaporation dominant region rosišče dew dew point električna veličina el electrical value enofazno področje EP single-phase region stična površina fl contact surface grelnik ht heater ic inside helix notranji in interior ini initial value kapljevita faza l liquid phase celoten tok zaseda kapljevita faza lo all-flow liquid toplotne izgube los heat losses kapljevina - para lv liquid–vapour modificirana vijačnica mc modified helix zunanja vijačnica oc outside helix optimalna vrednost veličine opt optimum value zunanji out outer referenčna vrednost ref, 0 reference value plašč s shell sekundarna kapljevina sl secondary liquid pregrevanje sup superheating okolica sur surroundings cevni snop tb tube bundle končna vrednost tot final value dvofazno področje TP two-phase region ukapljeni naftni plin LPG liquified petroleum gas parna faza v vapour phase zračni tokovi okrog plašča, prevodna žica w air flow around vaporizer, conducting wire 10 LITERATURA 10 REFERENCES [1] Alujevič, A., L. 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Mashelkar (1988) Heat transfer equipment design. Hemisphere Publishing Corporation, New York. Smith, RA. (1986) Vaporisers: selection, design and operation. Longman Scientific and Technical, Wiley, New York. VDI Heat Atlas, Verein Deutscher Ingenieure, VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (GCV), VDI Verlag, Düsseldorf (1993). Ward-Smith, A.J. (1980) Internal fluid flow: the fluid dynamics of flow in pipes and ducts. Clarendon Press, Oxford. Avtorji se zahvaljujejo Vladi Republike Slovenije in podjetju Nafta Lendava d.o.o., ki so s finančnimi sredstvi podprli delo na projektu »Revitalizacija električnih in toplovodnih uparjalnikov za ukapljeni naftni plin«. Naslov avtorjev: mag. Sanib Bašič prof.dr. Leopold Škerget doc.dr. Matjaž Hriberšek Univerza v Maribor Fakulteta za strojništvo Smetanova 17 2000 Maribor sanib.basic@uni-mb.si leo@uni-mb.si matjaz.hribersek@uni-mb.si Authors’ Address: Mag. Sanib Bašič Prof.Dr. Leopold Škerget Doc.Dr. Matjaž Hriberšek University of Maribor Faculty of Mechanical Eng. Smetanova 17 2000 Maribor, Slovenia sanib.basic@uni-mb.si leo@uni-mb.si matjaz.hribersek@uni-mb.si Prejeto: Received: 20.6.2002 Sprejeto: Accepted: 12.9.2003 Odprto za diskusijo: 1 leto Open for discussion: 1 year