A New Correlation for Single and Two- Phase Flow Pressure Drop in Round Tubes with Twisted-Tape Inserts

Transcription

1 A New Correlation or Single and Two-Pase Flow Pressure Drop in Round Tubes wit Twisted-Tape Inserts Fabio T. Kanizawa nan S. Hernandes Anderson A. U. de Moraes Gerardt Ribatski Escola de Engenaria de São Carlos USP Mecanical Engineering Department São Carlos, SP, Brazil A New Correlation or Single and Two- Pase Flow Pressure Drop in Round Tubes wit Twisted-Tape Inserts Twisted-tape inserts are requently used in eat excangers as a passive and inexpensive eat transer enancement metod. However, teir use results not only eat transer coeicient increments, but also pressure drop penalties. Te present study analyses te literature on single and two-pase rictional pressure drop inside tubes wit twisted-tape inserts ocusing on te pysical mecanism and te eects o te use o twisted-tape in comparison to plain tubes. Experimental data were gatered rom te open literature and compared against te available correlations developed in order to predict two-pase rictional pressure drop in tubes containing twisted-tape inserts. It was ound tat none o te correlations was able to predict suc a database accurately. A new correlation to estimate te riction actor or two-pase lows inside tubes wit twisted-tape is also proposed. Contrarily to previous studies, te proposed correlation presents reasonable predictions under single and two-pase low conditions and obeys te trends wen te twisted-tape ratio tends to zero and ininite. Keywords: twisted-tape, pressure drop, riction actor, swirl low, low boiling Introduction Te limited availability and rising costs o energy sources ave motivated researcers to ocus on minimizing energy consumption. In tis scenario, great eorts ave been made to develop more eicient and compact eat excangers, according to Akavan-Beabadi et al. (009). In terms o eat excanger eiciency, studies ave concentrated on improving te global eat transer coeicient and minimizing te pumping power. By minimizing te eat excanger size, bot te rerigerant inventory and te material used in its manuacture are reduced resulting in lower initial and operational costs. Moreover, te environmental impact during te system s lietime is also reduced, since, as pointed out by Ribatski (008), decreasing te rerigerant inventory implies tat te amount o rerigerant leakage decreases in bot relative and absolute values. For compact eat excangers te external eat transer coeicient (generally air-side) is usually te predominant termal resistance. However, according to id et al. (1991), tis is not always te case, and any increase in te in-tube eat transer coeicient may lead to a considerable improvement in te global coeicient. Several passive eat transer enancement metods ave been proposed, and most o tem are based solely on modiications o te internal tube surace. According to Satto and Peterson (1996), te tube surace is altered in order to increase its eective eat transer area and/or to disturb te low troug te generation o secondary lows and vortices. Te available alternatives to increase te eat transer coeicient troug te generation o low disruption include te use o microinned tubes, coils, bends and twisted-tape inserts. Figure 1. Scematic view o twisted-tape insert inside a tube, Akavan- Beabadi et al. (009). Twisted-tapes are caracterized by te twist ratio, deined according to Eq. (1), given by te ratio between te tape turn lengt o 180 o along its axis and te tube diameter, Akavan-Beabadi et al. (009), Figure 1. H y d i Twisted-tape inserts ave been used as a eat transer enancement tecnique or over a century, dating back to 1896, according to Manglik and Bergles (1993a). Tis tecnique was initially called "retarders" due to te increase in te pressure drop tat te insert imposes on te low, Manglik and Bergles (1993b). Twisted-tape inserts can be ound in steam generators, eat recovers rom lue gas, domestic eaters, according to Manglik and Bergles (1993b), desalination, according to Satto and Peterson (1996), and industrial processes in general. Te use o twisted-tapes as te ollowing advantages over te oter enancement metods: low abrication and installation costs, easy maintenance, Akavan- Beabadi et al. (009), and te possibility o being installed in eat excangers already in operation, Tome and Ribatski (005). As mentioned above, and similarly to most eat transer enancement tecniques, te eat transer coeicient enancement acieved by twisted-tape inserts is accompanied by a drastic increase in te pressure drop. Tereore, to determine te conditions under wic te use o tis metod is avorable, eat transer and pressure drop databases covering broad ranges o experimental conditions and a reasonable understanding o te penomena involved are necessary. Based on bot, accurate correlations can be developed and te eat excangers perormance estimated, Manglik and Bergles (1993a). At tis point, it sould be igligted tat, or a given eat excanger capacity, te pressure drop augmentation can be potentially overturned by te possibility o reducing te eat excanger size due to te improvement in te eat transer coeicient, wic may imply a decrease in te rerigerant pumping power, Satto and Peterson (1996). Te pressure drop penalty and eat transer enancement provided by twisted-tape inserts are usually evaluated based on te pressure drop and eat transer coeicient or a plain tube under similar operational conditions (vapor quality, mass velocity, luid temperature, rerigerant and internal diameter) as ollows: (1) J. o te Braz. Soc. o Mec. Sci. & Eng. Copyrigt 011 by ABCM Special Issue 011, ol. XXXIII / 43

2 Kanizawa et al. p s p () p p s q (3) p To evaluate te global eectiveness o using twisted-tapes inserts, Akavan-Beabadi et al. (009) suggested te ratio between eat transer enancement and pressure drop penalty parameters as ollows: q (4) p Alternatively to te use o twisted-tapes along te entire eat excanger lengt, researcers ave proposed twisted-tape segments regularly spaced inside te tubes, Eiamsa-Ard et al. (006) and Cang et al. (009), or only along te initial portion o te low entry, Eiamsa-Ard et al. (009). opina and Bergles (1973) developed an experimental study o water low boiling inside tubes wit twisted-tape inserts, and ound tat te eect o te eat lux on te eat transer coeicient is negligible under conditions o low bubble generation requency. Agrawal et al. (198) and Agrawal and arma (1991) perormed an experimental study o pressure drop or convective boiling o R1 in orizontal pipes under constant eat lux conditions. Jensen et al. (1985) developed a study o pressure drop or two-pase vertical low o R113 inside tubes wit twisted tapes. id et al. (1991) compared te perormance o microinned tubes and tubes wit twisted-tape inserts and observed tat better eat transer perormance is acieved by using microinned tubes. Manglik and Bergles (1993a, 1993b) presented an extensive review on orizontal single-pase laminar and turbulent lows inside tubes wit twisted tapes and described some experimental data or water and etylene glycol. Satto and Peterson (1996) also presented a general review on tis subject, ocusing on two-pase lows. Cakroun and Al- Faed (1996) studied eat transer and pressure drop or singlepase laminar low o oil in tubes wit twisted-tape inserts. Eiamsa- Ard et al. (006) analyzed te single-pase water low or eat excangers containing tubes wit ull lengt and regularly spaced twisted-tapes. Tey veriied tat under certain conditions te distance between te twisted-tape segments may promote a pressure drop reduction witout considerable eat transer coeicient penalties. Akavan-Beabadi et al. (009a) and Akavan-Beabadi et al. (009b) investigated te inluence o te twisted-tape ratio on te low boiling eat transer coeicient and pressure drop or R134a. In te present study, a literature review on te pysical mecanisms responsible or te increment o pressure drop and eat transer coeicient in te presence o twisted-tape inserts inside round tubes is presented. Predictive metods rom te literature or pressure drop inside tubes containing twisted-tape inserts are reviewed and critically compared against experimental data rom te literature. Additionally, based on te analysis o te literature and databases rom independent laboratories, a new correlation to predict low boiling and single-pase pressure drop inside tubes wit twisted tapes is proposed. Nomenclature A = coeicient or Müller-Steinagen and Heck correlation, Pa/m B = coeicient or Müller-Steinagen and Heck correlation, Pa/m C = correlation coeicient, dimensionless C i = constants or correlation being developed, i = 1, and 3, dimensionless C MS = coeicient o Müller-Steinagen and Heck correlation, dimensionless C R = coeicient or ddy correlation, dimensionless d = diameter, m = riction actor, dimensionless Fr = Froude number, dimensionless g = gravity acceleration, m/s² G = mass velocity, kg/m²-s = eat transer coeicient, W/m²-K H = tape turn lengt o 180, m = tube lengt, m n = correlation coeicient, dimensionless p = absolute pressure, Pa = ynolds number, dimensionless x = vapor quality, dimensionless y = twist ratio, dimensionless Greek Symbol = void raction, dimensionless = coeicient in te Müller-Steinagen and Heck correlation, Pa/m p = pressure drop, Pa = global eiciency increment, dimensionless p = pressure drop penalty, dimensionless q = eat transer enancement, dimensionless o = ddy two-pase multiplier, dimensionless = viscosity, Pa.s = density, Kg/m³ = surace tension, N/m = tube inclination relative to vertical, deg Subscripts acc = accelerational pressure drop Cr = critical property = rictional pressure drop g = gravitational pressure drop H = omogeneous model = ydraulic i = internal = liquid-pase p = plain tube s = swirl low tp = two-pase = vapor-pase 44 / ol. XXXIII, Special Issue 011 ABCM

3 A New Correlation or Single and Two-Pase Flow Pressure Drop in Round Tubes wit Twisted-Tape Inserts Heat Transer and Pressure Drop Pysical Mecanism Manglik and Bergles (1993a) presented an analysis o te mecanisms responsible or te eat transer and pressure drop enancements in te presence o twisted-tape inserts or singlepase low. From tis analysis tey pointed out te ollowing mecanisms: Partial obstruction o te cross-section wit consequent increase o te luid velocity; Hydraulic diameter reduction: te low is divided into two ydrodinamically independent lows wit smaller ydraulic diameters, but iger wetted perimeter, promoting an increase in bot eat transer coeicient and pressure drop; Increase in te low eective lengt: te lengt traversed by te luid particles is longer tan tat in a smoot tube, as te luid is orced to ollow te tape proile; Swirl Flows: te motion imposed by te tape sape on te luid particle causes te superposition o centripetal acceleration and longitudinal low, generating swirl lows. As a result, te luid velocity near te wall or tubes wit twisted-tape inserts is iger tan tat or a plain tube. Tis mecanism promotes an increase in bot eat transer coeicient and pressure drop; Fin eect: i te contact between te tape and te pipe surace is tigt, eat is transerred by conduction troug te tape and ten to te luid in suc a way tat te tape acts as a in increasing te overall eat transer area. According to Satto and Peterson (1996), in te case o lows under eating conditions, te centripetal acceleration promotes te movement o te colder luid (wit a iger density) rom te center o te tube to its peripery replacing te warmer luid o lower density. Tome and Ribatski (005) stated tat suc eect, coupled wit te increase in te luid velocity near te tube wall, avors te detacment o bubbles, intensiying te eat transer coeicient during convective boiling under nucleate boiling dominated conditions. In te case o cooling applications, te centripetal acceleration acts to segregate te colder and warmer parcels o te luid near te wall and near te center o te tube, respectively. Tereore, te twisted-tape inserts promote a decrease in te convective eects and are not recommended. Figure rom Manglik and Bergles (1993a) sows scematics o te tree single-pase swirl low modes in te presence o twisted-tape inserts according to ynolds number and te twistedtape ratio. Te sceme presented in Figure (a) corresponds to a condition o low ynolds number or ig twist-ratio, Figure (b) corresponds to a condition o ig ynolds number or small twistratio, and Figure (c) corresponds to a condition o plain tape. Based on tis study, Satto and Peterson (1996) speculated tat similar penomena sould be expected during in-tube two-pase lows. Figure. Single-pase low modes induced by twisted-tape inserts according to Manglik and Bergles (1993a). (a) ow ynolds number and/or ig twist ratio, (b) ig ynolds numbers and/or low twist ratio, (c) ininite twist ratio (lat tape). For in-tube orizontal low boiling, swirl generators are advantageous especially under conditions o intermediate vapor qualities and low mass velocities, since or plain tubes and under tese circumstances stratiied lows are generally observed, according to Satto and Peterson (1996). Te advantage arises rom te act tat te twisted-tape insert promotes te transition rom stratiied to annular low at low mass velocities. In te case o annular lows, te entire internal tube perimeter is wet; tereore, te eective eat transer area is muc iger tan tat o stratiied lows or wic more tan al o te tube perimeter is dry. According to Bergles et al. (1971), swirl generators can also be beneicial under mist low conditions, since te radial acceleration avors te deposition o liquid droplets on te wall increasing te wetted surace lengt. Based on tis beavior, Jensen (1985) suggested te use o twisted-tape segments along te region o ig vapor qualities. Considering only te riction actor beavior wit ynolds number, Manglik and Bergles (1993a) deined our regimes or single-pase low inside tubes wit twisted-tape inserts. Te regimes were identiied according to te contribution to te pressure drop o viscous, inertial and centriugal orces, as well as turbulence orces related to te luid velocity luctuations. Te regimes were described as ollows: gime I iscous low: caracterized by te predominance o inertial and viscous orces. Te pressure drop increment is mainly due to te cross-section partial blockage and te increase in te low eective lengt; gime II Axial and swirl low: te balance among inertial, viscous and centriugal orces caracterizes te low beavior. Te riction actor increases due to te partial blockage o te cross-section, iger eective low lengt, and swirl lows induced by tape; gime III Swirl-turbulent transition: caracterized by te beginning o velocity luctuations by turbulence and te predominance o swirl low eects and suppression o turbulent luctuations due to centriugal orces. Te inluence o velocity luctuations on te pressure drop is smaller tan or plain tubes witout twisted tapes; gime I Turbulent swirl-low: te velocity ield is aected by bot velocity luctuations and centriugal orces. Crosssection partial blockage and low mixing by secondary lows are responsible or te pressure drop increment wen compared to plain tubes witout twisted-tape; Te transition rom laminar to turbulent low is caracterized by velocity luctuations and low instabilities. According to Manglik and Bergles (1993b), te twisted-tape insert dampens te velocity luctuations due to te promotion o centriugal orces; tereore, te transition to turbulent regime is delayed. A low map based on te Nusselt number as a unction o ynolds number and containing our low regimes was also presented by Manglik and Bergles (1993a). Manglik and Bergles (1993b) proposed a generalized correlation or single-pase low pressure drop in tubes wit twisted-tape inserts, valid or bot laminar and turbulent low regimes, witout discontinuities in te laminar-to-turbulent transitional region. Pressure Drop Correlations or Two-Pase Flow Inside Tubes Containing Twisted-Tape Inserts Te total pressure drop is given by te sum o te rictional, gravitational and accelerational pressure drop contributions. In te case o two-pase low inside tubes, te last two are estimated based on analytical models tat include te variations o vapor quality and void raction as ollows: J. o te Braz. Soc. o Mec. Sci. & Eng. Copyrigt 011 by ABCM Special Issue 011, ol. XXXIII / 45

4 pg gh sin (1 ) (5) x x (1 ) p acc G (1 ) out (1 x) x (1 ) in In Equations (5) and (6), te outlet and local vapor qualities are calculated rom an energy balance along te eated surace, and an additional correlation (or model) is necessary to estimate te void raction ( ) variation along te tube. To calculate te supericial void raction or plain orizontal tubes witout twisted-tape inserts, Wojtan et al. (005) suggested te modiied correlation o Rouani and Axelsson (1970) given as ollows: x 1 (1 0.1(1 )) x x x (1 x) g ( ) 0.5 G 0.5 Te pressure drop rictional component is usually determined by empirical or semi-empirical correlations based on experimental databases, and includes te eects o transport and termodynamic properties o te gas and liquid pases, vapor quality, mass velocity, geometry and surace caracteristics o te cannel, supericial void raction and low pattern. Te rictional pressure drop predictive metods or two-pase low inside tubes wit twisted-tape inserts are generally based on te product between a twisted-tape multiplier and te pressure drop or a plain tube wit te same diameter. Based on suc an approac, Agrawal et al. (198) proposed te ollowing correlation: p s p p C n y were y is te twist ratio, p s is te rictional pressure drop or te tube wit twisted-tape inserts, and p p is te pressure drop or plain tube given by Martinelli and Nelson, apud Tome (004), keeping te same mass velocity and internal diameter. Te empirical values o C and n are 5.10 and 0.509, respectively, and were itted according to teir database described in Table 1. Similarly, Akavan-Beabadi et al. (009) compared teir twopase low pressure drop data inside plain tubes witout twisted-tape inserts against predictive metods. According to teir data, te Friedel (1979) metod was quoted as te best. Tereore, in teir predictive metod also given by Eq. (8), p p is provided by Friedel (1979) and new values o C and n equal to 5.1 and 0.8, respectively, are adjusted to teir database also described in Table 1. According to te state-o-te-art review by Satto and Peterson (1996), Blatt obtained values o C and n o 7.36 and 3/5, respectively, based on R11 experimental data. Jensen et al. (1985) perormed an extensive study o two-pase pressure drop inside tubes wit twisted-tape inserts using R113 as working luid. Tey obtained diabatic and adiabatic pressure drop data (6) (7) (8) Kanizawa et al. or tubes wit and witout twisted-tape inserts. Te experimental conditions are presented in Table 1. Teir metod to predict two-pase pressure drop or low inside tubes wit twisted-tape inserts consists o two steps: Step one: to determine te riction actor or two-pase low inside plain tubes, as ollows: were p H d tp p (9) G p p o p (10) wit te two-pase multiplier calculated as proposed by ddy, apud Jensen et al. (1985): were C R o 1 x 1 CR (11) C R 1.17x (1 10 p / p Cr G ) x G 0.45 p / p Cr p / p Cr (1) Step two: to calculate te two-pase pressure drop or te tube wit twisted-tape insert wit riction actor given by te ollowing equation: s tp s tp y y 3 or y y or y 11.5 (13) Table 1. Database descriptions and pressure drop plain tube correlations adopted by te autors in order to develop teir two-pase pressure drop correlations or tubes containing twisted-tape inserts. Autor Agrawal et al. (198) Akavan- Beabadi et al. (009) Jensen et al. (1985) Fluid No. o Points R1 10 Twist-Ratios 3.76,5.58,7.37 and G[kg/m -s] d i[mm] p P Metod Martinelli and Nelson, apud Tome (004) R134a 160 3,6,9 and Friedel (1979) R ,8.94 and ddy, apud Jensen et al. (1985) For te caracteristic lengt o te low, Jensen et al. (1985) adopted te ydraulic diameter calculated assuming te presence o te tape and given by: d i 4 d / 4 d d d i i i (14) 46 / ol. XXXIII, Special Issue 011 ABCM

5 A New Correlation or Single and Two-Pase Flow Pressure Drop in Round Tubes wit Twisted-Tape Inserts At tis point it is interesting to observe tat te values o te constants and exponents presented by Akavan-Beabadi et al. (009), Blatt, apud Satto and Peterson (1996), and Agrawal and arma (1991) are quite similar, indicating consistency between tese works. A New Pressure Drop Correlation In general, te low boiling eat transer coeicient and pressure drop increase wit decreasing o te twisted-tape ratio, Jensen et al. (1985). However, to date tere as been no generalized correlation or model or teir prediction. Modeling te low boiling mecanisms inside plain tubes witout twisted tapes is still callenging to several researcers over te world, since its solution combines te knowledge o nucleate boiling mecanisms, turbulence, interacial penomena, two-pase low, termal instabilities, and oters. All tese subjects are also not completely understood and ave been temes o several scientiic papers publised every year. Additional diiculties appear in te case o low boiling in tubes containing twisted-tape inserts, due to te presence o two-pase swirl low. Moreover, only a limited amount o experimental data concerning eat transer, pressure drop and low pattern is available. Based on tese aspects, instead o developing a mecanistic model, tis paper proposes a new empirical correlation or te rictional pressure drop during single and two-pase low inside tubes wit twisted-tape inserts. Te correlation was developed based on experimental data or R134a low boiling and air and water single-pase lows gatered in te literature, totalizing 180 data. Te database is described in Table and includes data rom independent laboratories. It was not possible to gater data rom oter studies since tey were not available or some o teir experimental conditions were missing. Table. Data o pressure drop collected or te development o a new correlation. Autor Akavan- Beabadi et al. (009) Eiamsa-Ard et al. (006) No. o Data Points Fluid Internal Diameter Twist-Ratio Inlet apor Quality Range Mass elocity 116 R134a 7.5 3,6,9 and Water and Figure 3. Comparison between Müller-Steinagen and Heck (1986) correlation and data rom Saiz Jabardo and Bandarra Filo (006), Moreno-Quibén (005) and Colombo et al. (008). According to te Müller-Steinagen and Heck (1986) metod, te two-pase rictional pressure drop is basically given as an empirical interpolation between liquid and vapor rictional pressure drop given by Blasius metod. Tereore, te correlation can also be used under single-pase low conditions. Te Müller-Steinagen and Heck (1986) correlation is given as ollows: were dp d 1/ C MS C MS, tp (1 x) Bx (15) C MS is 3 and is given by A ( B A) x (16) Napon (006) 0 Water and wit Promvonge (008) 10 Air Hernandes (010) perormed a comparison between te leading plain-tube rictional pressure drop predictive metods and a database gatered rom te literature containing experimental results rom independent laboratories. From tis study, e ound tat te predictive metod by Müller-Steinagen and Heck (1986) provided te best agreement wit is database. Figure 3 illustrates a comparison between te experimental data or R134a o Saiz- Jabardo and Bandarra Filo (006), Moreno-Quibén (005) and Colombo et al. (008) wit internal diameters o 8.76, 8.9 and 13.8 mm, respectively, and te predicted data according to Müller- Steinagen and Heck (1986) correlation. Te igure sows tat most o te experimental data are predicted by tis metod witin an error range o 30%. and dp d dp d,, 16, 0.079, 1/ 4 G d A (17) G B (18) d 16, or, , or, 1/ 4 > 1187 J. o te Braz. Soc. o Mec. Sci. & Eng. Copyrigt 011 by ABCM Special Issue 011, ol. XXXIII / 47

6 Kanizawa et al. Gd, Gd Fr G (4) gd H Taking into account tat te metod o Müller-Steinagen and Heck (1986) is simple to be implemented and worked te best according to Hernandes (010) comparisons, tis metod was adopted in te present study to estimate te plain tube riction actor and to develop a correlation or rictional pressure drop inside tubes containing twisted-tape inserts. In our proposed metod, te plain tube riction actor is calculated as ollows: H d p p (19) G tp were G is based on te internal diameter, p p is te plain tube pressure drop given by Müller-Steinagen and Heck (1986) correlation, and H is te omogeneous two-pase density. 1 1 x x H (0) In order not to take into account te tape tickness inluence on te correlation to be developed, a ydraulic diameter neglecting te tape tickness was assumed in Eq. (14) as ollows: d d i (1) Tereore, te riction actors or swirl and plain tube lows are calculated wit te ydraulic diameter given by Eq. (1) and keeping te same mass velocity. Based on tese assumptions, riction actor ratios based on te experimental data or tubes wit twisted-tape inserts and on te Müller-Steinagen and Heck (1986) correlation or plain tubes were calculated. Tese results are displayed in Figure 4, according to wic te riction actor ratio as a strong dependence on te mass velocity, in tis case given troug te Froude number (Eq. (4)). It can be also speculated tat gravitational eects can play a role in te rictional pressure drop since tey are related to te transition rom stratiied to annular low. Tereore, te Froude number was considered in order to capture inertial and gravitational eects. Taking into account tese eects, a relationsip in te orm o Eq. () was considered or te development o te new pressure drop correlation or single and two-pase lows inside tubes wit twisted-tape inserts. Figure 4. Dependence between riction actor ratio and Froude number, or twist ratio rom 4 to 15, considering data rom studies described in Table. In te rigt and-side o Eq. (), te unity was added to predict te ollowing limit cases: (i) plain tape corresponding to an ininity twist ratio wen te riction actor ratio sould be equal to one; (ii) blocked tube, corresponding to a twist ratio equal to zero wen te riction actor ratio sould be ininity. Te act tat bot exponents (o Froude number and twist ratio) are negative in Eq. (3) is in agreement wit te ollowing aspects: (i) te swirl eect decreases wit increasing mass velocity approacing te beavior o tubes witout twisted-tape inserts; (ii) by increasing te twist ratio, te eects o te twisted tape on te two-pase low tend to become negligible. Figure 5 sows tat, according to te proposed correlation, te ratio o te riction actors or a tube wit and witout twisted tape inserts tends asymptotically to 1 by increasing te twist ratio. Finally, te two-pase pressure drop or tubes wit twisted tape inserts is given as ollows: H G ps s (5) d s p C C C 3 1 C y Fr 4 1 () Using te least square regression analysis, te database abovementioned was correlated as ollows: s p y Fr wit te Froude number given by: (3) Figure 5. Illustration o correlation trend or cases o twist ratio tending to zero and ininite, or R134a, T sat o 1 C, internal diameter o 7.5 mm, G o 00 kg/m²-s, and vapor quality o / ol. XXXIII, Special Issue 011 ABCM

7 A New Correlation or Single and Two-Pase Flow Pressure Drop in Round Tubes wit Twisted-Tape Inserts Te proposed correlation sows reasonable agreement wit te data points considered in te present study since 81.5% o te results were predicted witin ±30% o te experimental data (see Figure 6). Te best agreement was obtained or te single-pase low, wit 98% o te predictions witin ±30% o te experimental data, wile te two-pase low presented 73.3% witin tis accuracy range. Considering te database o Akavan-Beabadi et al. (009), a comparison between te proposed and prior correlations is displayed in Figure 7. It can be observed tat te proposed correlation presents good agreement wit te experimental data, as well as te correlation o Akavan-Beabadi et al. (009). Agrawal et al. (198) correlation overpredicted te riction actor, and Jensen et al. (1985) and Blatt, apud Satto and Peterson (1996) underpredicted it. Additionally, te correlation obeys te limits wen te twist ratio tends to 0 and ininity. Conclusions Based on te present study, te ollowing conclusions can be drawn: An extensive review o single and two-pase low inside tubes wit twisted tape as been presented, addressing mecanisms and working parameters tat may inluence pressure drop and eat transer coeicient. As a result, correlations or te rictional pressure drop available in te literature or two-pase low inside tubes wit twisted-tape inserts ave been presented and discussed and seem to ave ailed wen predicting independent databases; Te tecnique o twisted tape inside tubes allows enancing te eat transer coeicient wit reduced cost, and its application is possible in eat excangers already in use; A new correlation or te riction actor valid or single and two-pase lows inside tubes wit twisted-tape inserts as been proposed. Acknowledgements Te autors grateully acknowledge te scolarsips under contract numbers 006/ and 008/ given by FAPESP (Te State o São Paulo searc Foundation, Brazil). Te inancial support given by CNPq (Te National Council or Scientiic and Tecnological Development, Brazil) under contract number /008-4 is also deeply recognized. Figure 6. Predicted and experimental riction actor or single and twopase low inside tubes wit twisted-tape inserts. Dotted lines or ±30% deviation, and solid line or null deviation. Figure 7. Calculated and experimental riction actor or Akavan- Beabadi et al. (009) data points. Finally, it must be igligted tat, contrarily to te previous predictive metods, te proposed correlation as te advantages o predicting te riction actor or bot, single and two-pase low. erences Agrawal, K.N., and arma, H.K., 1991, Experimental study o eat transer augmentation versus pumping power in a orizontal evaporator R1, International Journal o rigeration, ol. 14, pp Agrawal, K.N., arma, H.K. and al, S., 198, Pressure Drop During Forced Convection Boiling o R-1 under Swirl Flow, Transactions o te ASME, ol. 104, pp Akavan-Beabadi, M.A., Kumar, R. and Jamali, M., 009, Investigation on eat transer and pressure drop during swirl low boiling o R-134a in a orizontal tube, Int. J. Heat and Mass Transer, ol. 5, pp Akavan-Beabadi, M.A., Kumar, R., Moammadpour, A. and Astiani-Jamali, M., 009, Eect o twisted tape insert on eat transer and pressure drop in orizontal evaporators or te low o R-134a, Int. J. rigeration, ol. 3, pp Bergles, A.E., Fuller, W.D. and Hynek, S.J., 1971, Dispersed low ilm boiling o nitrogen wit swirl low, Int. J. Heat Mass Transer, ol. 14, pp Cakroun, W.M. and Al-Faed, S.F., 1996, Te Eect o Twisted-Tape Widt on Heat Transer and Pressure Drop or Fully Developed aminar Flow, Transactions o te ASME, ol. 118, pp , July. Cang, S.W., Yang, T.., and iou, J.S., 009, Heat transer and pressure drop in tube wit broken twisted tape insert, Experimental Termal and Fluid Science, ol. 3, pp Colombo,., uccini, A., Muzzio, A., Pittoni, P., 008, Experimental sults on Flow Boiling and Convective Condensation o R134a in Microin Tubes", 5t European Termal-Sciences Conerence, te Neterlands. Eiamsa-ard, S., Tianpong, C., and Promvonge, P., 006, Experimental Investigation o eat transer and low riction in a circular tube itted wit regularly spaced twisted tape elements, Int. Commun. Heat and Mass Transer, ol. 33, pp Eiamsa-ard, S., Tianpong, C., Eiamsa-ard, P., and Promvonge, P., 009, Convective eat transer in a circular tube wit sort-lengt twisted tape insert, Int. Comm. Heat and Mass Transer, ol. 36, pp Friedel,., 1979, Improved riction pressure drop correlations or orizontal and vertical two-pase pipe low, European Two-Pase Flow Group Meeting, Paper E, Ispra, Italy. J. o te Braz. Soc. o Mec. Sci. & Eng. Copyrigt 011 by ABCM Special Issue 011, ol. XXXIII / 49

8 Kanizawa et al. Hernandes, R.S., 010, Avaliação do desempeno termo-idráulico da ebulição convectiva de rerigerantes alogenados no interior de tubos com itas retorcidas", port to FAPESP, Grant number 008/ , Marc. Jensen, M.K., 1985, An evaluation o te eect o twisted-tape swirl generators in two-pase low eat excangers, Heat Transer. Eng, ol. 6, pp Jensen, M.K., Pourdasti, M. and Bensler, H., 1985, Two-Pase Pressure Drop wit Twisted Tape Swirl Generators, Int. J. Multipase Flow, ol. 11, No., pp opina, R.F. and Bergles, A.E., 1973, Subcooled Boiling o Water in tapegenerated Swirl Flow, Journal o Heat Transer, ol. 95, pp , May. Manglik, R.M. and Bergles, A.E., 1993a, Heat Transer and Pressure Drop Correlations or Twisted-Tape Inserts in Isotermal Tubes: Part I- aminar Flows, Journal o Heat Transer, ol. 115, pp Manglik, R.M. and Bergles, A.E., 1993b, Heat Transer and Pressure Drop Correlations or Twisted-Tape Inserts in Isotermal Tubes: Part II-Transition and Turbulent Flows, Journal o Heat Transer, ol. 115, pp Moreno-Quibén, J., Experimental and Analytical Study o Two-pase Pressure Drop During Evaporation in Horizontal Tubes, Institut des sciences de l'énergie, École Polytecnique Fédérale de ausanne. p. 159, Grade de Docteur, ausanne, EPF: 005. Müller-Steinagen, H. and Heck, K., 1986, A simple riction pressure drop correlation or two-pase low in pipes, Cem. Process Engineering, ol. 0, pp Napon, P., 006, Heat transer and pressure drop in te orizontal double pipes wit and witout twisted tape insert, Int. Commun. Heat Mass Trans., ol. 33, pp Promvonge, P., 008, Termal augmentation in circular tube wit twisted tape and wire coil turbulators, Energy Conversion and Management, ol. 49, pp id, R.S., Pate, M.B. and Bergles, A.E., 1991, A Comparison o Augmentation Tecniques During In-Tube Evaporation o R-113, Journal o Heat Transer, ol. 113, pp , May. Ribatski, G., 008, Novas Tecnologias em Trocadores de Calor para a dução de Carga de Fluido rigerante, Publicação em Diusão do Uso de rigerantes Alternativos em Sistemas de rigeração e Ar- Condicionado - Publicação Técnica, Ministério do Meio Ambiente MMA. Rouani, S.Z. and Axelsson, E., 1970, Calculation o void volume raction in te subcooled and quality boiling regions, Int. J. Heat Mass Transer, ol. 13, pp Saiz Jabardo, J.M. and Bandarra Filo, E.P., 006, Convective boiling perormance o rerigerant R-134a in erringbone and microin copper tubes, International Journal o rigeration, ol. 9, pp Satto, D.P. and Peterson, G.P., 1996, A view o Flow Boiling Heat Transer wit Twisted Tape Inserts, J. Enanced Heat Transer, ol. 3, No. 4, pp Tome, J.R., 004, Engineering Data Book III, EPF, Switzerland. Tome, J.R. and Ribatski, G., 005, Boiling and evaporation: Augmentation o boiling and evaporation. In: Georey F. Hewit. (Org.). Aeduan Heat Excanger Design Update, 1st ed. Wallingord: Begell House Inc, ol. 1. Wojtan,., Ursenbacer, T. and Tome J.R., 005, Investigation o low boiling in orizontal tubes: Part I A new diabatic two-pase low pattern map, Int. J. Heat Mass Transer, ol. 48, pp / ol. XXXIII, Special Issue 011 ABCM