AN IMPROVED TWO-PHASE PRESSURE DROP CORRELATION FOR 180° RETURN BENDS
Piotr A. Domanski and Christian J. L. Hermes
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National Institute of Standards and Technology
100 Bureau Drive Stop 8631
Gaithersburg, MD, USA 20899-8631
ABSTRACT
A new correlation for two-pha flow pressure drop in 180° return bends is propod bad on a total of 241 experimental data points for R-22 and R-410A. The data span smooth tubes with inner diameters (D) from 3.25 mm to 11.63 mm, bend radii (R) from 6.35 mm to 37.25 mm, and curvature ratios (2R/D) from 2.32 to 8.15. The correlation predicts all data with a mean deviation of 15.7 %, and 75 % of the data fall within ± 25 % error bands.
NOMENCLATURE
a0 …a4constants in equation 7 Greek letters
B straight-tube length between neighboring tubes Λ curvature multiplier
d p/d l pressur
e gradient: in equations [Pa m-1] μ absolute viscosity [Pa s]
: in figures [kPa m-1] ρ density [kg m-3]
D inner diameter [m] σsurface tension [N m-1]
f friction factor Subscripts
G refrigerant mass flux [kg s-1 m-2] k liquid pha or vapour pha
L bend length [m] l liquid pha
p pressure [Pa] r-b return bend
R bend radius [m] s-t straight tube
Re Reynolds number v vapour pha
We Weber
number
x vapour quality
INTRODUCTION
Return bends are curved pipe fittings which connect parallel straight tubes in finned-tube heat exchangers, such as evaporators and condenrs ud in air-conditioning and refrigeration systems. The two-pha flow region occupies the major part of the coils. The pressure drops in the return bends may be of the same magnitude as tho obrved for straight tubes. Figure 1 shows a schematic of a return bend.
Fig. 1 Schematic of a 180° return bend
The first study on two-pha pressure drop in return bends is attributed to Pierre [1] who propod a correlation bad on experiments carried out with R-12 and R-22. Geary [2] studied pressure drop of R-22 using various bend geometries and indicated the importance of the centre-to-centre distance. Chisholm [3] and Paliwoda [4] propod correlations for two-pha pressure drops in return bends although they did not provide validation of their correlations against experimental data. Recently, Chen et al. [5] and Chen et al. [6] studied flows involving water-air mixtures and R-410A, respectively, through different bend geometries.
In the prent work, a t of 241 experimental data points obtained from Geary [2] and Chen et al. [6] was ud to derive a new, improved correlation that can be applied within the whole two-pha region for smooth-tube return bends. All refrigerant property calculations were bad on REFPROP [7].
AVAILABLE EXPERIMENTAL DATA AND CORRELATIONS
Geary’s [2] Databa and Correlation
Geary [2] conducted experiments with two-pha, adiabatic flows of R-22 at 4.5 o C for bends with inner diameters of 11.38 mm to 11.63 mm, curvature ratios from 2.32 to 6.55, vapour-quality range from 0.2 to 0.8, and mass fluxes from 100 kg s -1m -2 to 500 kg s -1m -2, for a total of 145 data points. He tested two bends asmbled in ries and parated by a 190D length tube. He correlated the two-pha pressure drop by using a single-pha pressure drop equation for vapour flow only:
v
x G D L f p ρ22
2=Δ
(1)
where the dimensionless friction factor f is given by:
25.15
.02215.0exp Re a x
D R f v
⎟⎠⎞⎜⎝
⎛
=
(2) In the above equation, a =8.03x10-4, and Re v =xGD/μv is the vapour Reynolds number. (Note that Geary’s paper us
a =5.58x10-6 [ft 2 in -2] to compensate for the British units he lected to u in Eq. (1). Conquently, Geary’s friction factor is not dimensionless).
Chen et al.’s [6] Databa and Correlation
Chen et al. [6] conducted experiments with two-pha, adiabatic flows of R-410A at 10 o C and 25 o
C saturation temperatures spanning the vapour qualities from saturated liquid to saturated vapour. The inner diameters varied from 3.25 mm to 5.07 mm, the curvature ratios were from 3.91 to 8.15, and the mass fluxes were from 100 kg s -1m -2 to 900 kg s -1m -2. The test ction comprid nine bends located in one plane, connected in ries in a rpentine configuration.
Bad on Geary’s [2] and their own data, Chen et al. [6] propod a correlation which us the formulation prented by Geary (1975) with a modification to the friction factor correlation. They included the Weber number, We =G 2D/ρv σ, to account for the effects of liquid surface tension and gas inertia, and replaced the vapour Reynolds number by a combined vapour and liquid Reynolds number, Re m =Re v +Re l (Re v =xGD/μv , Re l =(1-x)GD/μl ), which yielded:
26.112.035
.022194.0exp We Re 10x
D R f m ⎟⎠⎞⎜⎝
⎛
=
− (3)
A total of 132 tests points from the study by Chen et al. [6] were made available to the authors for three out of
four geometries tested Chen [8]. Table 1 prents details of the three bend arrangements.
Table 1 Bend geometries tested by Chen et al. [6] Bend #1 Bend #2 Bend #3 D , mm 3.3 3.25 5.07 R , mm 13.45 6.35 13.15 B , mm 23.5 24.5 23 2R/D 8.15 3.91 5.19 B/D 7.12 7.54 4.54 # data points 60 36 36
Figure 2 compares Geary’s [2] and Chen et al.’s [6] experimental data with the predictions by the Chen et al. [6] correlation. The mean deviation of predictions is 19.1 % with most of the data located within the ±50 % error bands.
IMPROVED CORRELATION
We propo a new correlation bad on the two-pha pressure drop correlation for straight tubes by Muller-Steinhagen & Heck [9] and a multiplier which accounts for the bend curvature. The Muller-Steinhagen & Heck [9] correlation predicts the two-pha pressure drop in a straight tube bad on t
he pressure drops of liquid and vapour phas, which are calculated parately.
k
k k
G D f l
p ρ22d d =
(4)
where f k =0.079 Re k -0.25, Re k =GD/µk , and k reprents either v or l .
The pressure drops computed for each pha are combined:
()33
1d d 1d d d d 2d d d d x l p x l p l p x l p l
p v l v l
t
s +−⎥⎥⎦a380图片
⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−+=− (5)
We propo that the pressure drop in the return bend to be calculated by applying a “curvature” multiplier, Λ, to the
straight-tube correlation:
t
s b
r l
p l
p −−Λ
=d d d d (6)
We derived the curvature multiplier Λ via the Buckinham-PI Theorem using four dimensionless groups. The first term is the vapour Reynolds number accounts for the influence of vapour velocity, xG/ρv , while the cond and the third terms are related to mass distribution for each pha. The last term accounts for the effects of the bend curvature.
4
3
21
a
a a
a 0211a ⎟⎠
⎞⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛=ΛD R x GxD v l v ρρμ (7)
where the coefficients, determined from the Least Squares Method, are given in Table 2 in column (A).
Figure 3 plots the pressure drop predictions for all available experimental data using the coefficients from column (A). While the agreement between the measurements and correlation is generally good, the correlation underpredicts veral points for bend #3 from the Chen et al. [6] databa. We note that, in the #3 experimental arrangement, the straight tubes connecting the subquent bends had a straight length of approximately four tube diameters, while Hoang & Davis [10] suggested that a length equal to nine tube diameters is required to completely mix the phas after leaving a return bend. We thus speculate that the connection tubes were too short in the #3 configuration to allow the flow to re-establish the straight-tube flow pattern, and thus resulted in a larger return-bend pressure drop than would be measured otherwi. The straight-tube lengths for the #1 and #2 test configurations corresponded to approximately eight tube diameters.
Since the heat exchangers ud in air conditioning and refrigeration have long tubes (much longer than 9 tube diameters) that allow the refrigerant to re-establish its straight-tube flow pattern after leaving the return bend, we removed bend #3 data from the databa and refitted the constants in Eq. (7). Table 2 includes the new constants in column (B), and Figure 3 shows the pressure drop predictions using the constants.
0.101010000.11101001000Measured d p /d l [kPa/m]0.010.11101001000P r e d i c t e d d p /d l [k P a /m ]
Fig. 2 Comparison of all data with predictions by the Chen et al. [6] correlation Fig. 3 Comparison of all measurements with predictions by the new correlation (A)
P r e d i c t e d d p /d l [k P a /m ]
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0.1
1101001000
Measured d p /d l [kPa/m]
Table 2 Fitted coefficients for Eq. (7)
Coefficient
(A) 277 points - all points (B) 241 points - all points except bend #3
a 0 5.2 x ⋅10
-3
6.5 x10-3a 10.59 0.54 a 20.22 0.21 a 30.27 0.34 a 4
-0.69 -0.67
0.1
1
神奇的七色花
10
100
1000
Measured d p /d l [kPa/m]
0.1
1新年贺卡的制作
10
100
1000
P r e d i c t e d d p /d l [k P a /m ]
Fig. 4 Comparison of 241 data points with predictions by the new correlation (B)
CONCLUSIONS
An improved correlation for pressure drop in return bends was developed using 145 data points for R-22 and 96 points for R-410A from two different experiments. The new correlation predicts 75 % of the experimental data points within ±25 % error bands with a mean deviation of 15.7 % for all the data.
ACKNOWLEDGMENTS
中国经济发展The authors are grateful to Prof. I. Y. Chen, National Yunlin University of Science and Technology, Taiwan, who kindly provided us with the R-410A pressure drop data. Thanks are also addresd to Dr. W. V. Payne, National Institute of Standards and Technology, and Prof. S. Brown, Catholic University of America, for reviewing the manuscript. Mr. C. J. L. Hermes duly acknowledges CAPES Agency, Government of Brazil, for supporting his one-year sabbatical stay at the National Institute of Standards and Technology.
REFERENCES
[1] Pierre, B., 1964, Flow resistance with boiling refrigerants – Part II, ASHRAE Journal, October, pp. 73-77
[2] Geary, D.F., 1975, Return bend pressure drop in refrigeration systems, ASHRAE Transactions, 81(1), pp. 250-265 [3] Chisholm, D., 1983, Two-pha flow in pipelines and heat exchangers, George Godwin, London, pp. 154-166
[4] Paliwoda, A., 1992, Generalid method of pressure drop calculation across pipe components containing two-pha flow of refrigerants, Int. J. Refrigeration, 15(2), pp.119-125
[5] Chen, I.Y., Huang, J.C., Wang, C.-C., 2004, Single-pha and two-pha frictional characteristics of small U-type wavy tubes, Int. Comm. Heat and Mass Transfer, 31(3), pp. 303-313
[6] Chen, I.Y., Wang, C.-C., Lin, S.Y., 2004, Measurements and correlations of frictional single-pha and two-pha pressure drops of R410A flow in small U-type return bends, Int. J. Heat and Mass Transfer, 47, pp. 2241-2249
[7] Lemmon, E.W., McLinden, M.O., Huber, M.L., 2002, NIST Reference fluids thermodynamic and transport
properties − REFPROP 7.0, Standard Reference Databa 23, National Institute of Standards and Technology, Gaithersburg, MD, USA
[8] Chen, I.Y., 2004. Private Communication. National Yunlin University of Science and Technology, Yunlin, Taiwan. [9] Muller-Steinhagen, H. & Heck, K., 1986, A simple pressure drop correlation for two-pha flow in pipes, Chem.
家乡美食手抄报
Eng. Process, 20, pp. 297-308
[10] Hoang, K., Davis, M.R., 1984, Flow structure and pressure loss for two pha flow in return bends, Transactions of
the ASME, 106, pp. 30-37
