1、484 1 The Effect of Elbows on the Accuracy of Liquid Flow Measurement with an Insertion Flowmeter Seongwoo Woo, PhD Dennis L. ONeal, PhD, PE Fellow ASHRAE AB ST RACT The measurement error of an insertion flowmeter located downstream of a 90-degree elbow was quant$ed for water flowing in 4 in. (O. 1
2、O m) and 6 in. (O. I5 m) diameter pipes. The flowmeter location was varied between 2 and 9 diameters downstream of the elbow. Three metering angle orientations relative to the outside horizontalplane of the elbow were eval- uated: O, 90, and 180 degrees. Three radii ofcurvature were also evaluated:
3、2.5 in. (O. 06 m), 4.5 in. (O. I I m), and 6.5 in. (0.1 7 m). For a 4 in. (0.10 m) diameter pipe with a radius of curvature of2.5 in. (0.06 m), the largest measurement error was 28% at 2 diameters downstream of the elbow and 180- degree orientation. For a 4 in. (O. I O m) diameter pipe with a radius
4、 of curvature of4.5 in. (O. 11 m), the largest measurement error was 15% at 2 diameters downstream and 180-degree orientation. For a 6 in. (0.15 m) diameter pipe with a radius ofcurvature of 2.5 in. (O. 06 in), the largest measurement error was 45% at 2 diameters downstream and 180-degree orienta- t
5、ion. The length requiredfor measurement error to be less than 5%for 4 in. (O. I O m) and 6 in. (O. I5 m) diameter pipes ranged from 6 to 10 diameters downstream of the elbow. INTRODUCTION Monitoring energy use in buildings often requires measurement of thermal energy such as chilled or hot water. Ac
6、curate metering is critical to the verification of retrofit savings or the billing of energy use. Monitoring thermal energy typically requires a flowmeter, two temperature sensors, and a data logger (or energy management system) that can convert the flow and temperature data to thermal energy. Thus,
7、 thermal energy measurement is dependent on accurate measurement of flow and temperature. However, it is difficult to obtain accurate flow data in some buildings because complex piping systems contain numerous devices such as valves, elbows, and tees. These systems offer few locations where flow mea
8、surement will not be affected by such devices. Installation of a flowmeter at a short distance downstream of an elbow or obstruction may produce large errors in flow measurement. Distortions of the velocity and helical swirls (or vortices) can affect the accuracy of the flow measurement. To ensure a
9、ccurate flow measurement, the fluid should have a fully developed velocity profile without swirls or vortices. Such a condition is achieved when flowmeters are installed with adequate lengths of straight pipe after the elbow or tee. Because a long section of straight pipe after an elbow is required
10、to achieve a fully developed flow field, flowmeters should be installed with at least 10 diameters of straight pipe downstream of an elbow (ASME 1971). However, in build- ings, flowmeters are often installed within 5 diameters down- stream of an elbow because of the limited lengths of straight pipe
11、in equipment rooms (Corley 1998). Installation of a flow- meter this close to an elbow could result in a large measure- ment error in flow and, consequently, thermal energy. Dean (1927,1928) conducted some of the first studies of flow through curved pipes. He found that the secondary flow field had
12、two vortices in the cross section of pipe. Patankar et al. (1974) used a numerical model to predict the distorted velocity profile for laminar flows through 180-degree pipe bends. Patankar et al. (1975) also extended their previous work into the turbulent flow region with the k (kinetic equation) an
13、d E (dissipation equation) turbulence model. Using a Laser- Doppler anemometer, Enayet et al. (1 982) measured the lami- nar and turbulent flows through a 90-degree elbow. Results showed the development of strong pressure-driven secondary Seongwoo Woo is a group manager in the System Appliances Divi
14、sion at Samsung Electronics Co., Gwangju-City, Korea. Dennis L. ONeal is the Holdrede/Paul Professor and head of the Department of Mechanical Engineering, Texas Aj L .CI 5 10- o, OL 20,.,.,.,.,.,. 0.0 2.0 4.0 6.0 8.0 10.0 Average Flow Velocity (ftk) -5 . L 2 li 4- c -10- o Figure 5 Measurement error
15、 in a 4 in. (0.10 m) diameter pipe for three radii of curvature, O-degree meter orientation, and flowmeter located 2 diameters downstream of the elbow. O-“ “ - Average Flow Velocity (rnls) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 20“ “ “ “ “ “ “ Downstream Location: 5.5 D Pipe Diameter: 4 in. (0.10 m) Meter Orie
16、ntation: O degrees 10 1 -I0 1 0.0 2.0 4.0 6.0 8.0 10.0 Average Flow Velocity (Ws) Figure 7 Measurement error in a 4 in. (0.10 m) diameter pipe for three radii of curvature, 0-degree meter orientation, and flowmeter located 5.5 diameters downstream of the elbow. RESULTS Figures 5 and 6 show the measu
17、rement errors in the 4 in. (O. 1 Om) diameter pipe for O- and 180-degree flowmeter orien- tations, respectively. For both figures, the flowmeter was located 2 diameters downstream of the elbow. Data are shown for all three radii of curvature for velocities ranging from 0.5 to 2.7 m/s (1.6 to 8.9 fts
18、). Both figures show that radius of curvature plays an important role in measurement error. The smaller radius of curvature provided the largest measurement error for both orientations. For the case of O-degree orienta- Average Flow Velocity (mls) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 O -1 o L L i;j -20 +8 C
19、o, Q) 0, -30 n -40 -50 Downstream Location: 2 D Pipe Diameter: 4 in. (0.10 m) Meter Orientation: 180 degrees 0.0 2.0 4.0 6.0 8.0 10.0 Average Flow Velocity (Ws) Figure 6 Measurement error in a 4 in. (0.10 m) diameter pipe for three radii of curvature, 180-degree meter orientation, and jlowmeter loca
20、ted 2 diameters downstream of the elbow. Meter Orientation: 180 degrees -20 0.0 2.0 4.0 6.0 8.0 10.0 Average Flow Velocity (Ws) Figure 8 Measurement error in a 4 in. (0.10 m) diameter pipe for three radii of curvature, 180-degree meter orientation, and flowmeter located 5.5 diameters downstream of t
21、he elbow. tion, the flowmeter overestimated the flow rate by approxi- mately 17%, while for 180-degree orientation, it underestimated the flow by approximately 29%. One surpris- ing result, seen in both figures, was that the flowmeter measurement error was relatively insensitive to velocity; we had
22、anticipated significant differences in measurement error as a function of water velocity in the pipe. Figures 7 and 8 illustrate the same trend of relatively constant measurement error as a function of average water velocity at measurement locations between 4.6 and 5.5 diam- eters downstream ofthe e
23、lbows in 4 in. (O. 10 m) diameter pipe. 198 ASHRAE Transactions: Research Similar results were also found for the 6 in. (O. 15 m) diameter pipe. The relatively constant measurement error would mean that testing at one velocity could be used to provide reliable estimates of measurement errors for oth
24、er water velocities in the pipe. Because of the trends in measurement error with respect to velocity, the data for different velocities were aver- aged to determine a single value that, for most orientations, locations downstream of the elbow, pipe diameters, and radii of curvature, will provide rel
25、iable estimates within *2% of the measured value at a particular water velocity. Figure 9 shows the average measurement error in the 4 in. (0.10 m) diameter pipe for a radius of curvature of 2.5 in. (0.06 m) for flowmeter locations ranging from 2 to 8.4 diam- eters downstream of the elbow. Pipes wit
26、h this radius of curva- ture are often used in chilled water piping systems. The metering orientation angles were O, 90, and 180 degrees. The magnitude and sign (+) of the error were strongly dependent on orientation of the flowmeter. For the 180-degree orienta- tion, the largest error was approxima
27、tely -28% at 2 diameters downstream and approached 0% by 6 diameters downstream of the elbow. For O-degree orientation, the largest measure- ment error was +16% at 2 diameters downstream and decreased to near zero at 6 diameters downstream. The measurement error at O degrees fluctuated between *5% b
28、ut converged toward zero at 6 diameters downstream. These data would indicate that a flowmeter should be installed at 6 diam- eters or more downstream of an elbow. The 1 80-degree meter orientation produced a large nega- tive error in flow measurement because of the flow pattern immediately downstre
29、am of the elbow. As the water travels around the elbow, a pressure difference between the inside and outside of the pipe is generated by centrifugal forces. The velocity profile is distorted toward the outside of the pipe. 20 - I 30 3 I Flow Velocity Range: 1.6 to 8.9 Ws (0.5 to 2.7 mis) Pipe Diamet
30、er: 4 in. (0.10 m) R = 4.5 in. (0.1 1 m) Flow Velocity Range: 1.6 to 8.9 ftls (0.5 to 2.7 mis) Pipe Diameter: 4 in. (0.10 m) R = 2.5 in. ( 0.06 m) + O Degrees -8- 90 Degrees -A- 180 Degrees 10 ili CO 2 -10 U al -20 -30 _- Diameters Downstream of Elbow Figure 9 Measurement error of4 in. (0.10 m) diam
31、eterpipe at the radius of curvature R = 2.5 in. (0.06 m); metering location L = 2.0, 2.7, 4.2, 4.8, 2.5 in. (0.06 m) and 8.4 diameters downstream; metering angle = 0, 90, and 180 degrees. Thus, when measuring flow at the 180-degree orientation, the flowmeter underestimated the flow rate. Figure 10 s
32、hows the measurement error in the 4 in. (0.10 m) diameter pipe elbow with a radius of curvature of 4.5 in. (O. 1 1 m). The 4.5 in. (O. 1 1 m) radius of curvature elbow produced a much smaller measurement error at the 180-degree orientation and 2 diameters downstream than that of the radius of curvat
33、ure of 2.5 in. (0.06 m). The elbow with the longer radius of curvature provided for a more gradual transition through the 90-degree turn, which apparently has less distor- tion in the flow pattern at 2 diameters downstream. The measurement error at 2 diameters downstream for the O- and 1 80-degree o
34、rientations were nearly equal in magnitude (1 5%) but opposite in sign. Proceeding downstream, the measurement errors for the O- and 1 80-degree orientations generally decreased. Though the measurement error at 2 diam- eters downstream for the 4.5 in. (0.1 1 m) radius of curvature elbow was smaller
35、than that for 2.5 in. (0.06 m) radius of curvature, the flow required a longer length to develop. However, the measurement error at the 90-degree orientation was near zero at 2 diameters, increased to almost 4% at about 5.5 diameters, then decreased to approximately 1% at 7.3 diameters downstream of
36、 the elbow. While data were only shown to 7.3 diameters downstream, Figure 1 O indicates that at least 8 to 9 diameters of pipe would be required to reduce measurement error below 5%. Figure 1 1 shows the measurement error in a 4 in. (O. 1 O m) diameter pipe with a radius of curvature of 6.5 in. (0.
37、17 m). The metering locations ranged from 2 to 7.3 diameters down- stream ofthe elbow. The measurement error had similar trends as those of the 4.5 in. (O. 11 m) radius of curvature. For exam- ple, the largest errors were with the O- and 1 80-degree orien- tations at 2 diameters downstream of the el
38、bow. These errors / I + ODegrees 1 -20 1 -13- 90 Degrees I -A- 180 Degrees 1 -301 “. I I . I, , . O 2 4 6 8 10 Diameters Downstream of El bow Figure 1 O Measurement error of4 in. (O. 1 O m) diameterpipe at radius of curvature R = 4.5 in. (0.11 m); metering location L = 2.0, 3.5, 5.5, and 7.3 diamete
39、rs downstream; metering angle = 0, 90, and 180 degrees. ASHRAE Transactions: Research 1 99 - f Flow Velocity Range: 1.6 to 8.9 ftis I 2o i U -10 Or- -20 i (0.5 to 2.7 mls) Pipe Diameter: 4 in. (0.10 rn) R = 6.5 in. ( 0.17 m) I + O Degrees -6- 90 Degrees -i% 180 Degrees Figure Il Measurement error of
40、 4 in. (0. 1 Om) diameterpipe at radius of curvature R = 6.5 in. (0.17 m); metering location L = 2.0, 3.5, 4.0, 5.5, and 7.3 diameters downstream; metering angle = 0, 90, and 180 degrees. generally decreased as the meter location moved farther down- stream of the elbow. Figure 12 shows the measureme
41、nt error of a 6 in. (O. 15 m) diameter pipe with radius of curvature of 2.5 in. (0.06 m). This elbow type is mainly used for pressure fittings. The metering locations were 2,3,4,5,6,7,8, and 9 diameters downstream. The metering angles were O, 90, and 180 degrees, and the aver- age flow rates were 20
42、0, 300, 450, and 600 gpm (12.6, 18.9, 28.4, and 37.9 L/s). For the 180-degree orientation, the largest measurement error was approximately -45% at 2 diameters downstream and it decreased to -2% at 7 diameters down- stream of the elbow with negative measurement error. On the other hand, for O-degree
43、orientation, the largest measurement error was 22% at 2 diameters downstream. The error decreased to 0% at 7 diameters downstream of the elbow. The length required to reduce the error to less than 5% was approx- imately 7 diameters downstream of the elbow. CONCLUSIONS AND RECOMMENDATIONS The results
44、 from the 4 in. (O. 10 m) and 6 in. (O. 15 m) diam- eter pipes indicate that flow measurement can be severely affected if the flowmeter is installed within 5 diameters of an elbow. Such an installation could result in a significant under- prediction of the energy use if the flowmeter orientation was
45、 180 degrees or overprediction if the flowmeter orientation was O degrees. Given a limited length of straight pipe downstream of an elbow, it appears the best orientation is 90 degrees. For both pipes, this orientation provided the smallest measurement errors on average of the three orientations. To
46、 minimize measurement errors with this type of flow- meter, the data suggest installing the flowmeter at least 6 to 7 diameters downstream of the elbow and preferably 8 diame- “ 2o I Flow Velocity Range: 1.6 to 8.9 ftis (0.5 to 2.7 mis) Pipe Diameter: 6 in. (0.15 m) R = 2.5 in. ( 0.06 m) -E- 90 Degr
47、ees 4 180 Degrees 30 O 2 4 6 8 10 Diameters Downstream of Elbow Figure 12 Measurement error of 6 in. (0. 15 m) diameter pipe at radius of curvature R = 2.5 in. (0.06 m); metering location L = 2, 3, 4, 5, 6, 7, 8, and 9 diameters downstream; metering angle = 0, 90, und 180 degrees. ters downstream of
48、 an elbow. These results were consistent with the commonly used procedures of installing flowmeters at least 10 diameters downstream of an elbow (ASME 1971). For those installations where an insertion flowmeter is already installed near an elbow in either a 4 in. (O. 1 O m) or a 6 in. (0.15 m) diame
49、ter pipe, the data presented here can be used to correct the measured flow rate to obtain a more accu- rate estimate of energy use. This study was limited to two pipe diameters: 4 in. (O. 10 m) and 6 in. (0.15 m). While these sizes are common in chilled and hot water systems in buildings in the US, larger diameter pipes are also used. With larger diameters, it is often more difficult to get adequate lengths of straight runs because of space constraints. Therefore, we recommend a study with larger pipe diameters to provide useful data for evaluat
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