Heat Transfer Analysis of Refrigerant Flow in an Evaporator Tube

Transcription

1 Internationa OPEN ACCESS Journa Of Modern Engineering Research (IJMER) Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube C. Rajasekhar 1, S. Suresh, R. T. Sarathbabu 3 1, Department of Mechanica Engineering, SIETK Coege, Puttur, Chittoor Dist, Andhra Pradesh, INDIA 3 Department of Mechanica Engineering, Trumaai Engineering Coege, Kiambi, Kanchipuram Dist, Tami Nadu, INDIA Abstract: the paper aim is to presenting the heat transfer anaysis of refrigerant fow in an evaporator tube is done. The main objective of this paper is to find the ength of the evaporator tube for a pre-defined refrigerant inet state such that the refrigerant at the tube outet is superheated. The probem invoves refrigerant fowing inside a straight, horizonta copper tube over which water is in cross fow. Inet condition of the both fuids and evaporator tube detai except its ength are specified. here pressure and enthapy at discrete points aong the tube are cacuated by using two-phase frictiona pressure drop mode. Predicted vaues were compared using another different pressure drop mode. A computer-code using Turbo C has been deveoped for performing the entire cacuation. Keywords: heat transfer, refrigerant fow, evaporator tube, pressure drop mode, copper tube, Turbo C I. Introduction Two phase fow of gases and iquids or vapors and iquids in pipes, channes, equipment, etc. is frequenty encountered in industry and has been studied intensivey for many years. Exact prediction of pressure gradients an d boiing heat transfer phenomenon during the fow of two phase mixtures is an essentia step in the design of a great variety of industria equipment in the power and process industries. Knowedge of boiing heat transfer phenomenon, fow patterns and heat transfer correations can reduce the cost and avoid the drastic resuts due to over design and under design of evaporators, boiers and other two-phase process equipments. 1.1 Fow boiing In the iterature, two types of boiing of a saturated fuid are described, poo boiing and fow boiing. In poo boiing, heat is transferred to a stagnant fuid, a poo. During fow boiing, heat is transferred to a fuid having a veocity reative to the surface from where the heat is suppied. In saturated fow boiing heat is transferred by two different mechanisms, nuceate boiing and convective evaporation. Convective evaporation resembes ordinary convective heat transfer in singe phase heat transfer; i.e. the main resistance to heat transfer is at the heated wa. This part of the heat transfer is often modeed using heat transfer correations simiar to singe phase heat transfer correations. In nuceate boiing, heat is mainy transferred into the buk of the gas/ iquid by means of bubbes nuceating on the surface, growing and finay detaching from the surface. This part of the heat transfer is simiar to poo boiing and is often modeed as poo boiing. The tota heat transfer coefficient is then cacuated accounting (by weighing) for both mechanisms. The weighing is carried out differenty, as may be found in the iterature. In the most cases, a correction factor is introduced into the pure convective and nuceate parts. The convective part is often said to be enhanced due to the presence of bubbes. In a simiar way, the nuceate part is often said to be suppressed due to the fact that the fow of the iquid may suppress bubbe nuceation. The combined effect of these two mechanisms is not yet we understood and severa different approaches may be found in the iterature Fow boiing heat transfer correations Numerous fow boiing correations exist in the iterature. In this section, some of the better known correations are isted Chen (1966) correation Chen (1966) pubished his cassica paper on fow boiing, where the evaporating heat transfer coefficient was a sum of macro and micro mechanisms. (1.1) mic mac The micro evaporation, nuceate boiing, was cacuated as IJMER ISSN: Vo. 4 Iss.8 Aug

2 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube k c p g mic t p S (1.) h fg g Kandikar (1990, 003) correation The correation is TP C C5 C C Co Fro C Bo Ff The correation is cacuated twice using each set of constants and the greater of the two vaues is used as the heat transfer coefficient. The Froude number is cacuated with the entire fow as iquid. Fr o g d Pressure drop correations There are numerous correations on pressure drop in two-phase fows in the iterature. The purpose of the present thesis is not to cover them a; merey the most important contributions wi briefy be discussed. A good introduction of adiabatic two-phase fow pressure drop may be found in Chishom (1983) and in Coier and Thome (1996). Lockhart and Martenei (1949) presented their cassica paper where they introduced a new parameter, ater denoted the Lockhart- Martenei parameter, defined as p (1.6) X pg They graphicay correated the two phase mutipier with the Lockhart- Martenei parameter. The two-phase mutipier was defined as p TP (1.7) p Baker (1954) presented a paper investigating pressure drop of simutaneous fow of oi and gas. The data does not correate we with the Lockhart- Martenei correation. He observed a distinct change in sope when potting the data in the Lockhart- Martenei chart. He concudes that something radica changed the fow. He suggests different correations for different fow regimes and stresses the importance of taking into account the actua fow pattern when correating the pressure drop. Chishom and Laird (1958) revisited the work by Lockhart and Martenei (1949) and suggested that the twophase frictiona data coud be correated with reasonabe accuracy as ptp m (1.8) p 1 C / Xˆ m For rough tubes. The vaue of C and m depends on the tube surface and iquid fow rate. The variabe differs from the definition by Lockhart and Martenei. Later, Chishom (1967) conducted a more refined anaysis. However, at the end of the paper he states that the derived equations are too compicated for practica cacuations and suggests 1 C / X C / X (1.9) Where he now used the definition of X according to Lockhart- Martenei. He aso incuded the cassica vaues for the Chishom parameter, C. II. Probem Description.1. Probem The probem invoves refrigerant fowing through a straight, horizonta copper tube over which water is in cross fow. Inet conditions of both the fuids and evaporator tube detai except its ength are specified. The Xˆ IJMER ISSN: Vo. 4 Iss.8 Aug

3 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube main objective is to find the ength of the evaporator tube for a pre defined inet refrigerant state such that the refrigerant at the tube outet is super heated. Fig..1. eometry of evaporator tube Fig... Probem Visuaization.. Input parameters to be specified 1. Refrigerant inet pressure. Refrigerant inet enthapy 3. Name of the refrigerant 4. Mass fow rate of the refrigerant 5. Water veocity 6. Water temperature 7. Inner diameter of the tube 8. Outer diameter of the tube 9. Space between two nodes.3. Soution approach We require two properties to fix the state of the refrigerant i.e., pressure and enthapy. In this anaysis pressure and enthapy can be found at discrete points aong the ength of the tube. For cacuating enthapy one ordinary differentia equation is required. This can be obtained by baancing energy, which fows through an eementary strip as shown beow. Energy baance can be defined as The amount of energy entering into the strip is equa to the energy eaving from that strip. dq h z h z+ OD Fig..3. Energy baance through strip of ength Energy baance for a strip of ength Energy input = Energy output m h dq m h (.1) f z f z wherem f is the mass fow rate of the refrigerant. After simpification equation.1 becomes h z h z Twat Tref r o n 1 ri 1 m f iri k oro d IJMER ISSN: Vo. 4 Iss.8 Aug (.)

4 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube In equation (.) α i and α o are inside and outside heat transfer coefficients. The inside heat transfer coefficients can be found from boiing heat transfer correations by Kimenko and outside heat transfer coefficient is cacuated from the correations of fow over bodies. Then enthapy at next node can be found by using equation For cacuating the pressure we require another differentia equation is required which gives the pressure drop between two nodes. Pressure drop incudes both frictiona pressure drop as we as acceeration pressure drop. Frictiona pressure drop can be obtained from Chishom s mode. Acceeration pressure drop can be obtained from momentum equation aong axia direction. By using pressure and enthapy state of the refrigerant can be fixed at next node. Length of the tube can be found by marching from one node to another unti the state of the refrigerant is super heated. III. Boiing Heat Transfer Boiing process occurs when the temperature of a iquid at a specified pressure is raised to saturated temperature at that pressure. It is considered to be one form of convection heat transfer as it invoves fuid motion (such as rise of bubbes to the top). It differs from other forms of convection in that it depend on atent heat of vaporization of the fuid and surface tension at the iquid-vapor interface, in addition to properties of the fuid in each phase. The heat transfer coefficients associated with boiing are typicay much higher than those encountered in other forms of convection processes that invove singe phase Introduction Many famiiar engineering appications invove boiing and condensation heat transfer. In the househod refrigerator, for exampe, the refrigerant absorbs heat from the refrigerated space by boiing in the evaporator section and rejects heat to air by condensing in the condenser section. Some eectronic components are cooed by boiing by immersing them in a fuid with an appropriate boiing temperature. Boiing is a iquidto-vapor change process just ike evaporation, but there significant differences between the two. 3.. Types of boiing Based on the presence of buk fuid motion boiing is cassified into two types. They are I. Poo boiing II. Fow boiing Boiing is caed poo boiing in the absence of buk fuid motion and fow boiing or forced convection boiing in presence of it. In poo boiing, fuid is stationary, and any motion of fuid is due to natura convection currents and motion of bubbes under the infuence of buoyancy. In fow boiing the fuid is forced to move in a heated pipe or over a surface by externa means such as pump. Poo and fow boiing are further cassified into two types depending on the buk iquid temperature. They are Sub cooed boiing Saturated boiing IV. Pressure Drop 4.1. Introduction During two phase fow in a non horizonta channe, the pressure drop is made up of contributions due to geodetic changes in position, acceeration and friction. Because of very compicated phenomena occurring in two phase fow empirica or semi empirica reationships or physica modes are used for cacuating pressure drop. These physica modes are correated with the experimenta resuts. They are broady cassified into three categories Homogeneous fow mode Heterogeneous fow mode Hybrid fow mode Out of a, homogeneous mode is the simpest. This assumes that the iquid and the gas or vapor are uniformy distributed over the fow cross section and in the fow direction, so that the mixture can be regarded as a singe phase fow with suitaby defined mean vaues of the thermodynamic and hydrodynamic properties of the two phases. It is frequenty used as a reference mode because of its ease of manipuation. In the heterogeneous mode or sip mode it is assumed that the gas or vapor and the iquid fow separatey as continuous phases with distinct mean veocities within different parts of the fow cross section or fow channe. IJMER ISSN: Vo. 4 Iss.8 Aug

5 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube eneray, the actua fow behavior of a two phase mixture ies between these two imiting cases. Ony at very sma mass fractions of vapor does the condition occur in which the veocities of the two phases are the same. As a resut, a series of mixed or hybrid modes have been deveoped such as variabe density mode, driftveocity mode. Tota pressure drop constitutes 1. Pressure drop due to change in eve. Acceeration pressure drop 3. Frictiona pressure drop The first two components describe a reversibe change of pressure, since a part of the energy or momentum of the fow ony appears in another form and can be converted back again without oss. On the other hand, the frictiona pressure drop is an irreversibe change of pressure resuting from the energy dissipated in the fow by friction, eddying, etc. In the fow of a two phase mixture through a pipe with a constant fow cross section, there is aways an increase in the voumetric fow due to the reduction in pressure caused by friction, and in a singe-component mixture aso due to fash evaporation. This resuts in an increase in the veocity of both phases. The resuting momentum changes make themseves fet as a pressure drop due to acceeration. When vaporizing mixtures are heated, there is an increase of the vapor fraction resuting in further increase in the voumetric fow and an additiona pressure drop due to acceeration. In genera, frictiona pressure drop contributes most significanty to the tota pressure drop. However, even today its cacuation is sti quite imprecise. Experimenta resuts show that under comparabe conditions, frictiona pressure drop in two phase fow may be consideraby arger than in singe fow. The ratio of two pressure drops indicates how many times arger the frictiona pressure drop in two phase fow is than in singe phase fow. It is usuay referred to as the two phase friction mutipier. The determination of frictiona pressure drop or friction mutipier is not possibe by theoretica means aone, since the individua phenomena occurring such as in momentum transfer between two phases, wa friction or shear at the phase interface, can sti not be specified quantitativey. In practice, using of reationships based on different frictiona pressure drop modes, which are corrected or correated by measurements Pressure drop due to change in eve The pressure drop as a resut of changes in geodetic position is given by the reationship dp 1 g sin g h (4.) Where φ denotes the ange between the pipe axis and the horizonta. The pressure drop disappears for a horizonta pipe since sin φ = 0. At sma mean void fractions of gas or vapor and arge density ratios this component may form the argest contribution to the overa pressure drop in a non horizonta fow. In the more usua case, in which the geodetic pressure drop is very sma, cacuations with the homogeneous fow mode are sufficient, i.e., with the voumetric fow quaity instead of with the mean void fraction Acceeration pressure drop An exact cacuation of the pressure drop due to acceeration in two phase fow is not possibe, since this requires a knowedge of oca phase veocities or mass fow rates, which can be ony incompetey approximated by the mean phase veocities. If homogeneous fow of the two phases is assumed, the pressure drop due to acceeration can be cacuated from d x x dpacc 1 (4.3) g 1 Compared to the equation for the pressure drop due to acceeration when heterogeneous fow is assumed: d x x dp acc g 1 (4.4) 1 1 The first equation eads in most cases to a more accurate conservative form. The assumption of a homogeneous fow is vaid for ony for specia fow conditions. Acceeration pressure drop can be cacuated by soving momentum equation. In unheated two phase fows the pressure drop due to acceeration can often be f IJMER ISSN: Vo. 4 Iss.8 Aug

6 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube negected. A simpe rue for estimating the pressure drop in fows of refrigerants consists of comparing the frictiona pressure drop with saturation pressure Frictiona pressure drop In genera, frictiona pressure drop contributes most significanty to the tota pressure drop. However, even today its cacuation is sti quite imprecise. Experimenta resuts show that under comparabe conditions, frictiona pressure drop in two phase fow may be consideraby arger than in singe fow. As a rue the frictiona pressure drop in two- phase is referred to that of pure iquid fow at the same tota mass fow rate. dp dp, ph 1, ph, o The ratio of two pressure drops indicates how many times arger the frictiona pressure drop in two phase fow is than in singe phase fow. It is usuay referred to as the two phase friction mutipier. The determination of frictiona pressure drop or friction mutipier is not possibe by theoretica means aone, since the individua phenomena occurring such as in momentum transfer between two phases, wa friction or shear at the phase interface, can sti not be specified quantitativey. In practice, using of reationships based on different frictiona pressure drop modes, which are corrected or correated by measurements Frictiona pressure drop modes The frictiona pressure drop modes given beow come under heterogeneous mode category. They are cassified as 1. Chishom mode. Friede mode V. Pressure Drop Modes Chishom mode B x 1 x x (5.1) dp go f go D g (5.) 0. 5 Re f (5.3) go g go D Re go (5.4) dp dp go o (5.5) 0. 5 Re f (5.6) o o D Re o (5.7) IJMER ISSN: Vo. 4 Iss.8 Aug

7 dp fric dp (5.8) o Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube dp fo (5.9) o D Friede mode 3.4 F H o E (5.10) Fr We E f go 1 x x (5.11) g fo F x 0 1 x (5.1) H g Fr 0.91 g d g H 0.19 g (5.13) (5.14) d We (5.15) H 1 x x 1 (5.16) H g VI. Procedure Step 1: Specify the inet refrigerant conditions. Step : Cacuation of pressure at node a) Frictiona pressure drop b) Acceeration pressure drop Frictiona pressure drop is cacuated by using Chishom mode. Acceeration pressure drop is cacuated by using the foowing equation. dp acc (6.1) 1 But for that equation we require the density of refrigerant at state. For that one we assume pressure at node as the cacuated pressure by considering frictiona pressure drop ony. Step.1: Cacuation of enthapy at node (Est.) Enthapy is cacuated by using the foowing equation h h 1 Twat Tref r o n 1 ri 1 m f iri k oro (6.) Step.1.1. Cacuation of apho ( o ) is cacuated by using the foowing equation. m Nu C Re D Pr (6.3) IJMER ISSN: Vo. 4 Iss.8 Aug

8 Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube A the reevant properties are cacuated at mean fim temperature by assuming T wo =T ref. Step.1.. Cacuation of aphi ( i ) is cacuated by using the boiing heat transfer equations. T wi is cacuated by using the foowing equation. Twi Tref Twat Tref 1 r n o i i A 1 r 1 i i Ai k c L o A o (6.4) By using the iterative procedure we wi refine the aphi and T wi vaues unti the error (%) shoud be ess than or equa to By using the vaue of ( o ) outside wa temperature (T wo ) is cacuated from the foowing equation. T wo T Twi Tref (6.5) wi r n o 1 ri i Ai k c L Step o is refined from the outside wa temperature (T wo ) by the equation Step At the end of step.1.3., we wi get a refined vaues of i and o. We can fix the estimated state of the refrigerant at next node. Step.: Cacuate the acceeration pressure drop using the equation 6.1. Step.3: Find the pressure at node considering both frictiona and acceeration pressure drops Step 3: Cacuation of enthapy at node by repeating the step..1. Step 4: At the end of step we wi get pressure at node and at the end of step 3 we wi get enthapy at node. By using these two vaues we can fix the exact state of refrigerant at node. Step5: Repeat the steps from 1 to 4 unti the condition of the refrigerant reaches superheated condition Step6: Finay check for aw of conservation of energy. VII. Resuts and Discussion Length of the evaporator tube was determined for a pre-defined refrigerant inet state and finay checked for aw of conservation of Energy. Energy is conserved for a refrigerant inet states and for a combination of pressure drop, boiing heat transfer modes. This chapter is divided into two sections. In the first section, variation of parameters aong the ength for same mass fow rate of 60 kg/hr and different combination of pressure drop and boiing heat transfer correations are discussed. In the second section, comparison of ength of the evaporator tube at different mass fow rates and two different combinations of modes is compared. Variation of different parameters aong ength of the tube for different mass fow rates, for different initia states of the refrigerant for the two different combinations were observed. Those investigations are not producing here. As shown in Fig.7.1. For the same mass fow rate of 60 kg/hr of R-, pressure drop for Kimenko- Chishom combination is high for a given ength. Pressure drop depends on the state of the refrigerant. Twophase fow mutipier is arge for Chishom s mode when compared to Friede s mode. Therefore frictiona pressure drop is arge, in Chishom s mode. Sope of the Kimenko-Chishom curve is arger than Dembi- Friede curve, so pressure drop is arge for Kimenko-Chishom curve. As shown in Fig.7.. Enthapy variation is more or ess constant through out ength of the tube for the same mass fow rate of R- and for both combinations. Both curves merge one over other as. Stricty speaking enthapy difference is a itte bit high for Dembi- Friede curve. As shown in Fig.7.3. Saturated temperature variation is arge in Kimenko- Chishom combination, since the saturated pressure difference is arge for that combination. Sope of the curve is arger for that combination. As shown in Fig.7.4. For the same mass fow rate dryness fraction varies ineary for both types of combinations and both the curves overap one over other. And their sopes are more or ess constant. As shown in Fig.7.5. Inside heat transfer coefficient increases aong the ength of the tube for both types of combination. But their range is different. In Kimenko s mode singe phase forced convection heat transfer is incorporated and convective boiing number is used to distinguish between nuceate boiing and forced convection boiing. As the fow progresses singe phase forced convection heat transfer coefficient IJMER ISSN: Vo. 4 Iss.8 Aug

9 Temperature(deg C) Dryness fraction Pressure(bar) Enthapy(kJ/kg) Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube decreases and nuceate boiing heat transfer increases in Kimenko s mode. But in Dembi s mode forced convection heat transfer increases much faster than nuceate boiing. The contribution of forced convection in Dembi s correation is arge when compared to singe phase forced convection in Kimenko s correation. So heat transfer coefficient is high in Dembi s mode. As shown in Fig.7.6. Outside heat transfer coefficient decreases aong the ength of the tube and both the curves are parae to each other.the variation of outside heat transfer coefficient is very ess in these two modes, as it depends on outside wa temperature. In the second section ength of evaporator tube for different mass fow rates and different combinations are compared and finay checked for energy conservation. Energy is conserved for a sets of input data as shown in Tabe.7.1.It was observed that if the mass fow rate increases, ength of the tube was increasing due to arger pressure drop and ess increment in enthapy. S.No Mass fow combination Heat ost by Heat gained by rate(kg/hr) water(w) refrigerant(w) 1 60 Dembi- Friede Kimenko-Chishom Dembi- Friede Kimenko-Chishom Dembi- Friede Kimenko-Chishom Tabe.7.1. Comparison of energy baance and Length of evaporator tube for different mass fow rates and different combination Kimenko-Chishom Dembi-Friede Kimenko-Chishom Dembi-Friede Fig.7.1. Pressure aong ength of tube for same mass Fig.7.. Enthapy variation aong ength of tube for same fow rate and for different combinations mass fow rate and for different combinations Kimenko-Chishom Dembi-Friede Kimenko-Chishom Dembi-Friede Fig.7.3. Temperature aong ength of tube for same mass fow rate and for different combinations Fig.7.4.Dryness fraction aong ength of tube for same mass fow rate and for different combinations IJMER ISSN: Vo. 4 Iss.8 Aug

10 Inside htc(w/sqrm K) Outside htc(w/sqrm K) Heat Transfer Anaysis of Refrigerant Fow in an Evaporator Tube Kimenko-Chishom Dembi-Friede Kimenko-Chishom Dembi-Friede 0 4 Fig.7.5. Inside heat transfer coefficient aong ength Fig.7.6.Outside heat transfer coefficient aong ength of of tube for same mass fow rate and for different tube for same mass fow rate and for different combinations combinations VIII. Concusion The obtained resuts were satisfactory and energy was conserved for a refrigerant inet states. There is good agreement between the two combinations of modes when they compared and yied resuts with minimum deviation. REFERENCES Journa Papers: [1]. A generaized correation for two-phase forced fow heat transfer - V.V.Kimenko, Int.J.Heat and Mass Transfer. Vo.31, pp , []. A genera correation for fow boiing in tubes and annui K.E.ungor and R.H.S.Winterton, Int.J.Heat and Mass Transfer. Vo.9, No.3, pp , [3]. Pressure gradients due to friction during the fow of evaporating two-phase mixtures in smooth tubes and channes D.Chishom, Int.J.Heat and Mass Transfer. Vo.16, pp , [4]. Pressure drop during gas or vapor-iquid fow in pipes L.Friede, Int.J.Chemica Engineering. Vo 0, No.3, pp , IJMER ISSN: Vo. 4 Iss.8 Aug