AN IMPROVED CORRELATION FOR TWO-PHASE PRESSURE DROP OF R-22 AND R-410A IN 180 RETURN BENDS

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1 Proceedings of the th Braziian Congress of Therma Sciences and Engineering -- ENCIT 006 Braz. Soc. of Mechanica Sciences and Engineering -- ABCM, Curitiba, Brazi,- Dec. 5-8, 006 Paper CIT06-5 AN IMPROVED CORRELATION FOR TWO-PHASE PRESSURE DROP OF R- AND R-4A IN 80 RETURN BENDS Piotr A. Domanski Nationa Institute of Standards and Technoogy Bureau Drive Stop 863, Gaithersburg, MD, USA 0899 Phone: , e-mai: piotr.domanski@nist.gov Christian J. L. Hermes * POLO Research Laboratories for Emerging Technoogies in Cooing and Thermophysics Department of Mechanica Engineering, Federa University of Santa Catarina P.O. Box 476, Forianópois, SC, BRAZIL Phone: , e-mai: hermes@poo.ufsc.br * Corresponding Author Abstract. A new correation for two-phase fow pressure drop in 80 return bends is proposed based on a tota of 4 experimenta data points for R- and R-4A from two independent studies. The data span smooth tubes with inner diameters (D) from 3.3 mm to.6 mm, bend radiuses (R) from 6.4 mm to 37.3 mm, and curvature ratios (R/D) from.3 to 8.. The correation consists of a two-phase pressure drop for straight tubes and a mutipier that accounts for the bend curvature. The Buckinham-PI Theorem was used to formuate the curvature mutipier in terms of refrigerant properties, fow characteristics, and bend geometry. The correation predicts a data with a mean deviation of 5.7 %, and 75 % of the data fa within ± 5 % error bands. Keywords. short return bends, two-phase pressure drop, curvature mutipier, Buckinham-PI theorem. Introduction Return bends are curved pipe fittings which connect parae straight tubes in finned-tube heat exchangers, such as evaporators and condensers used in air conditioning and refrigeration systems. In such heat exchangers, the air fows outside through the finned region whie refrigerant fows inside tubes. Athough singe-phase refrigerant fow may occur in the form of subcooed iquid refrigerant in the condenser or superheated vapour in the condenser and evaporator, the two-phase fow region occupies the major part of these cois. The proper design of compact heat exchangers requires the cacuation of heat transfer rates and pressure drops. The heat transfer in return bends are insignificant, so the bends are usuay considered as adiabatic. On the other hand, the pressure drops in the return bends may be of the same magnitude of those observed for straight tubes and must be taken into account. Figure shows a sketch of a 80 return bend connecting two parae straight tubes. The upstream refrigerant fow foows the pattern of a typica two-phase fow in a straight-tube, whose characteristics depend on the refrigerant properties, mass fux, vapour quaity, pressure, and tube diameter and inner surface. According to Hoang & Davis (984), the two-phase pressure drop in the bend is affected not ony by the secondary fow effects observed in singephase fows, but aso by the separation of the phases due to centrifuga forces which concentrates the iquid toward the concave (outside) portion, whie the vapour fows toward the convex portion. This increases the reative motion between the phases and pressure drop. At the bend outet, significant pressure drop is aso caused by the remixing process, which extends to about 9 diameters downstream. The pressure drop in bends is significanty higher for twophase than for singe-phase fows. Figure. Schematic of a 80 return bend. Severa studies were conducted in order to quantify the pressure drops in 80 return bends, athough most of them have considered ony singe-phase water fows (Ito 960, Ideshik 986, Wojtkowiak & Popie 000, Chen et a. 003). The first study on two-phase pressure drops in return bends is attributed to Pierre (964), who proposed a correation based on experiments carried out with R- and R-. Pierre (964) assumed that the tota pressure oss is divided into two major effects: friction and turning. The first was cacuated considering the bend as a straight tube, whie the second was obtained by subtracting the straight-tube pressure drop from the overa pressure drop. For the range of centre-to-centre distances he did not observe this parameter to be of a major infuence and did not incude it in his pressure drop correation. The subsequent study by Geary (975) with R- using various bend geometries pointed to

2 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 the importance of the centre-to-centre distance. His correation is based on a friction factor for the vapour fow and is appicabe for quaities higher than 0. and ower than 0.8. Figure presents vaidation of the Geary correation with his data. The paper reports the prediction of 87 % of the experimenta data within ±5 %. Later, Chishom (983) and Paiwoda (99) proposed correations for two-phase pressure drops in return bends athough did not provide vaidation of their correations against experimenta evidence. Recenty, Chen et a. (004a) and Chen et a. (004b) studied water-air mixture and R-4A fows, respectivey, through different bend geometries. Chen et a. (004b) proposed a correation with which they predicted both Geary s (975) and their own experimenta data within ±50 % error bands and a mean deviation of 9. %. In the present work, a dataset of 4 experimenta points obtained from Geary (975) and Chen et a. (004b) was used to derive a new, improved correation that can be appied within the whoe two-phase region for smooth-tube return bends. This study was partiay reported in Domanski & Hermes (006). A refrigerant property cacuations were based on REFPROP (Lemmon et a. 00).. Avaiabe Experimenta Data and Correations.. Geary s (975) Database and Correation Geary (975) carried out experiments with two-phase, adiabatic fows of R- at 4.5 C for bends with inner diameters of.4 mm to.6 mm, curvature ratios from.3 to 6.6, mass fuxes from kg s - m to 500 kg s - m, and vapour-quaity range from 0. to 0.8, in a tota of 45 experimenta points. He tested two bends assembed in series and separated by a 90D ength tube. Our anaysis of the two-phase fow pattern using the map proposed by Thome (005) showed that the annuar fow was present in amost 70 % of the experiments ( points), the stratified/wavy fow was present in 0 % of the experiments (30 points), and the intermittent fow occurred in the remaining % of the data points (4 points). Geary (975) correated the two-phase pressure drop in return bends by using a singe-phase pressure drop equation for vapor fow ony, as foows: L G x Δ p = f () D ρ v where ρ v is the density of vapour phase [kg m -3 ], L=πR is the bend ength [m], R is the curvature radius [m], D is tube diameter [m], G is refrigerant mass fux [kg m - s - ], x is the vapour quaity, and f is a dimensioness friction factor given by: f 0.5 arev = R exp0.5 x D.5 () where a=8.03-4, and Re v =GxD/μ v is the vapour Reynods number. Note that Geary s paper uses a= [ft in - ] to compensate for the British units he seected to use in equation (). Consequenty, Geary s friction factor is not dimensioness. Predicted /d [kpa/m] +5% -5% Measured /d [kpa/m] Figure. Comparisons between Geary s (975) experimenta data and predictions using his correation.

3 .. Chen s et a. (004b) Database and Correation Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 Chen et a. (004b) carried out experiments with two-phase, adiabatic fows of R-4A at C and 5 C saturation temperatures spanning the vapour quaity range from iquid to vapour. The inner diameters varied from 3.5 mm to 5. mm, the curvature ratios were from 3.9 to 8., and the mass fuxes were from kg s - m to 900 kg s - m, The test section comprised nine bends ocated in one pane, connected in series in a serpentine-type fashion. The neighbouring bends were connected by straight tubes. The measurements incuded both the pressure drop in the upstream straight tube and the overa pressure drop in the whoe test section. The first measurement was used to estimate the pressure drop in the straight tubes connecting neighbouring bends, which then was subtracted from the overa pressure drop yieding the pressure osses in the bends aone. A tota of 3 tests points were made avaiabe from the authors for three out of four geometries tested (Chen 004). Tabe presents detais of these three bend arrangements. Tabe. Bend geometries tested by Chen et a. (004b) Bend # Bend # Bend #3 D, mm R, mm B, mm R/D B/D # data points The two-phase fow pattern anaysis of Chen et a. (004b) data showed that annuar fow was present in 5 % (67 points), whie stratified/wavy fow and intermittent fow took pace in 9 % ( points) and 40 % (53 points) experiments, respectivey. Figure 3 summarises the distribution of fow patterns for both the 45 points for R- and 3 points for R-4A. Most of the 77 points (60 %, 68 points) have shown annuar fow pattern, 5 % (67 points) intermittent and 5 % (4 points) stratified/wavy R-4A (Chen et a. 004b) R- (Geary 975) Tota Number of Data Points Stratified/Wavy Intermittent Annuar Tota Fow Pattern Figure 3. Fow pattern distribution for R and R4A data according to Thome s (005) criteria. Based on Geary s (975) and their own data, Chen et a. (004b) proposed a correation which uses the formuation presented by Geary (975) with a modifications in the friction factor equation. They incuded the Weber number, We=G D/ρvσ, to account for the effects of iquid surface tension and gas inertia, and repaced the vapour Reynods number by a combined vapour and iquid Reynods number, Re m =Re v +Re (Re v =xgd/µ v, Re =xgd/µ ), which yieded: f = We Rem R exp0.94 x D.6 (3) Figure 4 compares the predictions by the Chen et a. (004b) correation with a experimenta data. The mean deviation of predictions is 9. % with most of the data ocated within the ±50 % error bands. Figure 5 shows a comparison of Geary s correation and a data, where it may be seen some R-4A points were underpredicted.

4 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT R-4A (3 points) R- (45 points) +50% Predicted /d [kpa/m] -50% Measured /d [kpa/m] Figure 4. Comparison of a data with predictions by the Chen s (004b) correation. 0 R-4A (3 points) R- (45 points) +50% -50% Predicted /d [kpa/m] Chishom / Ideshik Method 0. 0 Measured /d [kpa/m] Figure 5. Comparison of a data with predictions by the Geary s (975) correation. Chishom (983) proposed a two-phase mutipier Φ to cacuate the pressure drop in return bends based on the pressure drop cacuated for the singe-phase, a iquid fow in a return bend, Δp sp. Δ p = ΦΔp sp (4) where Φ is given by Φ = + ρ x[ b( x) + x] (5) ρv

5 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 where x is the vapour quaity, ρ and ρ v are the densities of the iquid and vapour phases [kg m -3 ], and b is given by b = + K. R + D sp (6) K sp is the oca pressure drop coefficient obtained for singe-phase, a iquid fows. Ideshik (986) suggested the foowing expression to estimate the K sp parameter in 80 o bends: K sp = f L D R D (7) where f is the singe-phase friction factor, cacuated as a function of the Reynods number, Re =GD/μ, as foows: f = Re (8) 0. 5 Equation (7) assumes the pressure drop has two terms. The first term accounts for the pressure drop as if the bend was a straight tube, whie the second term provides a correction for the bend curvature. The singe-phase pressure drop is then obtained as foows: G Δ psp = K (9) sp ρ Figure 6 compares pressure drops predicted using the Chishom/Ideshik method with the R and R4A experimenta data. The mean deviation between the measurements and predictions is 44.4 %, and approximatey 37 % of the points fa outside the ±50 % error bands. The fow pattern anaysis using Thome s method (005) indicated that the points whose fow pattern is annuar are concentrated at the 50 % ine, whie the points with intermittent fow pattern are centered on the +50 % ine. 0 R-4A (3 points) R- (45 points) +50% Predicted /d [kpa/m] -50% Measured /d [kpa/m] Figure 6. Comparison of R- and R-4A measurements with predictions by the Chishom/Ideshik method. 3. Improved Correation We propose a new correation based on the two-phase pressure drop correation for straight tubes by Muer- Steinhagen & Heck (986) and a mutipier which accounts for the bend curvature. This approach differs from that proposed by Chishom (983), where a two-phase mutipier was appied to a singe-phase correation for a return bend.

6 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 According to Muer-Steinhagen & Heck (986), the two-phase pressure drop in a straight tube is predicted considering the pressure drops of iquid and vapour phases, which are cacuated separatey. d k f k G = () D ρ k where k stands for or v, and f k is given by equation (8) using vapour or iquid properties, as appropriate. The pressure drops computed for each phase are combined by the foowing equation: d s t = d + x d v d d 3 3 ( x) + x v () where the index s-t denotes the straight-tube pressure drop. The pressure drop in the return bend, denoted by the index r-b, is then obtained by appying a curvature mutipier, Λ, to the straight-tube correation: d r b = Λ d s t () We derived the mutipier Λ via the Buckinham-PI Theorem with the foowing dimensioness groups: (i) GxD/μ v ; (ii) /x-; (iii) ρ /ρ v ; and (iv) R/D. The first group is the vapour-ony Reynods number to take into account the infuence of vapour veocity, Gx/ρ v, whie the second and the third terms are reated to mass distribution for each phase. The ast term regards the effects of the bend curvature. The resuting PI-equation is given by: Λ = a 0 GxD μv a a a 3 a4 ρ R x ρ v D () where the coefficients, fitted through the Least Squares Method, are given in Tabe in coumn (A). Figure 7 pots the pressure drop predictions for a the experimenta data. Whie the agreement between the measurements and correation is good in genera, the correation underpredicts severa points for bend #3 from the Chen et a. (004b) database. The fourteen most underpredicted data points for bend #3 have a stratified-wavy fow. This, however, coud not be the ony reason for the underprediction since Geary s stratified-wavy data are predicted we. 0 R-4A (96 points, bends # & #) R-4A (36 points, bend #3) R- (45 points) +5% Predicted /d [kpa/m] -5% Measured /d [kpa/m] Figure 7. Comparison of a measurements with predictions by the new correation (A). Looking further for the reason for underpredictions, we note that in #3 experimenta arrangement the straight tubes connecting the subsequent bends had the straight ength of approximatey four tube diameters, whie Hoang & Davis

7 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 (984) suggested that the ength equa to nine tube diameters is required to compete the remixing process of the phases after eaving a return bend. It can be then specuated that the connection tubes were too short in #3 configuration to aow the fow to re-estabish the straight-tube fow pattern, and this resuted in a arger return-bend pressure drop than woud be measured otherwise. The straight-tube engths for # and # test arrangements corresponded to approximatey eight tube diameters. Since the heat exchangers used in air conditioning and refrigeration have ong tubes (much onger than 9 tube diameters) that aow the refrigerant to re-estabish its straight-tube fow pattern after eaving the return bend, we removed bend #3 data from the database and refitted the constants in equation. Tabe incudes the new constants in coumn (B). Tabe. Fitted coefficients for equation (). Coefficient (A) 77 points - a points (B) 4 points - a points except bend #3 a a a a a Figure 8 pots the pressure drop predictions against the reduced 4-point database that incudes a R- data and the R-4A data for bends # and #. The mean deviation of predictions is 5.7 %, and 75 % of the predictions are within ±5 % error bands. Tabe 3 provides the statistica information on the goodness of predictions of the reduced 4-point dataset by the four correations considered in this study. 0 R-4A (96 points, bends # & #) R- (45 points) +5% Predicted /d [kpa/m] -5% Measured /d [kpa/m] Figure 8. Comparison of 4-point database measurements with predictions by the new correation (B). Tabe 3. Statistica evauation of predictions for the 4-point database for four studied correations. Geary (975) Chen et a. (004b) Chishom (983) Proposed (B) Mean deviation (%) Points within % Points within 5 % Points within 50 % Points outside 50 % Figure 9 compares the four correations for the entire vapour quaity range from the saturated iquid to saturated vapour. Starting with the saturated iquid, a correations show an increase of pressure drop with increasing quaity, which can be expained by a decrease of the two-phase density. Whie the Geary correation and the Chen et a. correation continue this trend throughout the two-phase region to the saturated vapor ine, the Chishom/Ideshik predictions fatten at high vapor quaities, and the new correation predicts a decrease in pressure drop when vapor quaity approaches unity. Thus, the predictions by the Chishom/Ideshik correation and the new correation agree with

8 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 the genera trend of pressure drop known in straight tubes. The decrease in the pressure drop at high vapour quaities can be expained by the reduced interference between the phases once the iquid ayer on the tube thins and the wa becomes occasionay dry. The proposed correation has a smooth transition to Muer-Steinhagen & Heck (986) for quaities ower than 0. and greater than 0.8, athough it is singuar for x=0 and zero for x=. 8 6 Chishom (983) Geary (975) Chen et a. (004) Proposed (B) 4 /d [kpa/m] Fina Remarks Vapour Quaity [-] Figure 9. Comparison of return bend pressure drop predictions by the studied correations (Conditions: refrigerant R-, D=5.0 mm, R=.0 mm, T sat =7 C, and G=00 kg m - s - ) An improved correation for pressure drop in return bends was deveoped using 45 data points for R- and 96 points for R-4A. The correation is based on the Muer-Steinhagen & Heck (986) pressure drop correation for straight tubes and a mutipier that accounts for the bend curvature. The Buckinham-PI Theorem was used to formuate the curvature mutipier in terms of refrigerant properties, fow characteristics, and bend geometry. The new correation predicts 75 % of the experimenta data points within the ±5 % error bands with the mean deviation of 5.7 % for a data. Future experimenta research on refrigerant fow in return bends is recommended to incude the characterization of refrigerant fow pattern and its infuence on refrigerant pressure drop. 5. Acknowedgements The authors are gratefu to Prof. I. Y. Chen, Nationa Yunin University of Science and Technoogy, Taiwan, who kindy provided us with the R-4A pressure drop data. Thanks are aso addressed to Dr. W. Vance Payne, Nationa Institute of Standards and Technoogy, for reviewing the manuscript. Dr. C. J. L. Hermes duy acknowedges CAPES Agency for supporting his one-year sabbatica stay at the Nationa Institute of Standards and Technoogy. 6. References Chen, I.Y., 004, Private Communication, Nationa Yunin University of Science and Technoogy, Yunin, Taiwan Chen, I.Y., Huang, J.C., Wang, C.-C., 004a, Singe-phase and two-phase frictiona characteristics of sma U-type wavy tubes, Int. J. Heat and Mass Transfer, 47, pp Chen, I.Y., Lai, Y.K., Wang, C.C., 003, Frictiona performance of U-type wavy tubes, Transactions of the ASME, 5, pp Chen, I.Y., Wang, C.-C., Lin, S.Y., 004b, Measurements and correations of frictiona singe-phase and two-phase pressure drops of R4A fow in sma U-type return bends, Int. J. Heat and Mass Transfer, 47, pp Chishom, D., 983, Two-phase fow in pipeines and heat exchangers, George Godwin, London, 304p. Domanski, P.A., Hermes, C.J.L., 006, An improved two-phase pressure drop correation for 80 return bends, 3rd Asian Conference on Refrigeration and Air-Conditioning, Gyeongju, Korea, May -3 Geary, D.F., 975, Return bend pressure drop in refrigeration systems, ASHRAE Transactions, 8(), pp

9 Proceedings of ENCIT ABCM, Curitiba, Brazi, Dec. 5-8, 006 Paper CIT06-5 Hoang, K., Davis, M.R., 984, Fow structure and pressure oss for two phase fow in return bends, Transactions of the ASME, 6, pp Idechik, I.E., 986, Handbook of hydrauic resistance, nd edition, Hemisphere, New York, 640p. Ito, H., 960, Pressure osses in smooth pipe bends, Journa of Basic Engineering, 8, pp Lemmon E.W., McLinden M.O., Huber M.L., 00, NIST Reference fuids thermodynamic and transport properties REFPROP 7.0, Standard Reference Database 3, Nationa Institute of Standards and Technoogy, Gaithersburg, MD, USA Muer-Steinhagen, H. & Heck, K., 986, A simpe pressure drop correation for two-phase fow in pipes, Chem. Eng. Process, 0, pp Paiwoda, A., 99, Generaised method of pressure drop cacuation across pipe components containing two-phase fow of refrigerants, Int. J. Refrigeration, 5(), pp. 9-5 Pierre, B., 964, Fow resistance with boiing refrigerants Part II, ASHRAE Journa, October, pp Thome, J.R., 005, Update on advances in fow pattern based two-phase heat transfer modes, Experimenta Therma and Fuid Science, 9(3), pp Wang, C.-C., Chen, I.Y., Shyu, H.-J., 003, Frictiona performance of R- and R-4A inside a 5.0mm wavy diameter tube, Int. J. Heat and Mass Transfer, 46, pp Wojtkowiak, J., Popie, C.O., 000, Effect of cooing on pressure osses in U-type wavy pipe fow, Int. Comm. Heat Mass Transfer, 7(), pp Nomencature Symbos B straight-tube ength between neighboring tubes /d pressure gradient, Pa m - D inner diameter, m f friction factor G refrigerant mass fux, kg s - m - K oca pressure oss coefficient L bend ength, m p pressure, Pa R bend radius, m x vapour quaity Greek etters Φ two-phase mutipier Λ curvature mutipier μ absoute viscosity, Pa s ρ specific mass, kg m -3 σ surface tension, N m - Subscripts iquid phase sp singe phase v vapour phase