Measured and predicted pressure loss in corrugated spiral duct.
Corrugated spiral ducts are increasingly being used in aboveground HVAC systems. The presence of corrugations increases the rigidity and structural strength of the duct, so that lighter gauges can be employed in many applications. Under those circumstances corrugated ducts may be less expensive and easier to install than conventional spiral seam ducts. Furthermore their enhanced resistance to permanent deformation allows them to be stacked higher for transportation and storage.
In the present research the roughness characteristics of corrugated galvanized spiral ducts having a somewhat different corrugation profile from that examined by Kulkarni et al. (2009). The objective of this research was to verify whether minor corrugation profile and seam pitch variations have a significant impact on the resulting absolute roughness and roughness category. The test procedure was validated by measuring pressure loss characteristics of a standard conventional spiral seam duct per ASHRAE Standard 120. Those results were then compared to data presented previously in the literature.
Pressure loss characteristics of conventional galvanized steel ducts with continuously rolled spiral seams have been described in Griggs et al. (1987). Similarly, roughness factors for galvanized steel spiral seam ducts with varying numbers of ribs have been reported in Griggs et al. (1987). In these instances the data were not obtained by tests conducted in accordance with ASHRAE Standard 120. Until recently there has been a lack of corrugated galvanized spiral round duct information available to the designers of duct systems. However Kulkarni et al. (2009) used ASHRAE Standard 120 to obtain pressure loss data for one particular corrugation configuration.
Three round, spiral, 24 gauge, galvanized steel ducts with four corrugations between helical seams were tested in this project. The geometric details of the corrugations and seams are shown in Figure 1; in the present study the depth and configuration of the corrugations differed from those tested in Kulkarni et al. (2009). The duct diameters were 203 mm (8 in.), 356 mm (14 in.), and 508 mm (20 in.). In each case the duct sections were 3.05 m (10 ft) in length, and were connected by beaded slip couplings possessing integral scaling gaskets. Each joint was further wrapped by commercial duct tape. The 356 mm (14 in.) diameter non-corrugated galvanized steel ducts tested in this project possessed a standard spiral seam (RL-1 seam per SMACNA (2005)) having a pitch of 121 mm (4.75 in.). The 3.05 m (10 ft) duct sections were connected by beaded slip couplings and sealed using duct tape.
8.5 INCH PIPE CORRUGATION HEIGHT DEPENDS ON PIPE DIAMETER PIPE DIAMETER RANGE CORRUGATION HEIGHT RANGE 6 INCH TO 11 INCH (H) = 1.0mm TO 1.3mm 12 INCH TO 18 INCH (H) = 1.4mm TO 1.8mm 20 INCH TO 50 INCH (H) = 1.6mm TO 2.0mm 52 INCH AND UP (H) = 2.4mm TO 3.0mm Figure 1 Geometric details of round corrugated duct
[FIGURE 1 OMITTED]
The test apparatus shown in Figure 2 (excerpted from ASHRAE Standard 120) was used to measure the pressure loss characteristics of the corrugated and standard spiral duct. In every instance the duct test apparatus consisted of an entrance duct section to achieve fully developed flow (upstream length), the test section, and a tail portion (downstream length). All tests were conducted with a plenum chamber and bellmouth combination situated between the upstream nozzle chamber and the downstream test section, per ASHRAE Standard 120. The plenum chamber had one settling screen with a 46.8% open area. The dimensions for each test setup are listed in Table 1. The duct diameters were measured in three planes and averaged. The apparatus, dimensions, and test procedures were in compliance with ASHRAE Standard 120.
Table 1. Test Setup Dimensions Round Corrugated and Standard Spiral Duct Tests Nominal Duct Measured Duct [L.sub.[z-1]] [L.sub.[1-2]] Tail Duct Diameter mm Diameter m (ft) m (ft) Length (in.) mm (in.) m (ft) 203 (8) 203.2 (8.0) 2.8 (9.2) 5.3 (17.3) 1.1 (3.5) 356 (14) 358.1 (14.0) 4.6 (15.0) 9.1 (30.0) 1.5 (5.0) 508 (20) 508.0 (20.0) 6.1 (21.0) 12.8 (42.0) 2.1 (7.0)
For tests conducted on corrugated ducts and conventional spiral ducts the pressure loss was measured using the static pressure ports of Pitot-static tubes mounted at the duct center-line at axial locations as prescribed by ASHRAE Standard 120. The standard spiral duct tests were also repeated using static wall pressure taps soldered onto the duct surface (at precisely the same locations as the Pitot-static tubes) in order to measure the pressure loss; the Pitot-static tubes were withdrawn from the test section for these tests. The pressure taps were fashioned into a piezometric ring using flexible plastic tubing. The piezometer rings were connected to a single micromanometer by means of flexible tubing so as to measure the pressure drop across the test section. For all pressure loss tests static gage pressure was measured at each location by inserting tees into the pressure tubing. This procedure allowed for the determination of whether the use of Pitot-static tubes to measure pressure loss would yield similar results to measurements performed using wall static pressure taps.
The system was blow-through. Airflow was generated by a 30-hp centrifugal fan. A cylindrical nozzle chamber was used for flow measurement, and a variable frequency drive was used to control air flow through the system. Screens mounted upstream and downstream of the nozzle board inside the chamber were used to settle the flow. The nozzle board contained four long-radius spun aluminum flow nozzles having throat diameters of 51-mm (2-in.), 102-mm (4-in.), 152-mm (6-in.) and 203-mm (8-in.). The nozzles were mounted on a 25-mm (1-in.) thick plywood board. Various combinations of flow nozzles were employed, depending on the desired flow rate. Nozzles that were not used were blocked using smooth vinyl balls. The pressure drop was measured by two piezometer rings located 38-mm (1.5-in.) on each side of the nozzle board, with both sides connected to a manometer.
In every case pressure drop measurements over the test section and across the nozzle board were performed using liquid-filled micro manometers having a measurement accuracy of [+ or -]0.025-mm (0.001 -in.). Likewise, the pressure upstream and downstream of the test section was measured by means of inclined liquid-filled manometers having a readability of [+ or -]0.25-mm (0.01-in.). Static pressure in the nozzle chamber was measured using an electronic manometer having the scale readability of [+ or -]0.25-mm (0.01-in.). However, because of observed pressure fluctuations associated with static pressure measurements in the nozzle chamber and test section, these measurements were presumed to exhibit an accuracy of [+ or -]0.63 mm (0.025-in.). The air temperature in the nozzle chamber was measured using a mercury thermometer having a scale readability of [+ or -]0.5[degrees]C (1.0[degrees]F). The dry-bulb and wet-bulb temperatures of the ambient air were measured using an aspirated psychrometer, with an accuracy of [+ or -]0.5[degrees]C (1.0[degrees]F). The test section temperature was not measured directly, but was assumed to be the same as the temperature of the air inside the nozzle chamber. Ambient pressure was measured with a Fortin-type barometer, with an accuracy of [+ or -]0.25-mm (0.01-in.) of mercury. All measurements of temperature and pressure in this project were in compliance with ASHRAE Standard 120. All dimensional measurements in these experiments were assumed to have an accuracy of [+ or -]1%.
In this study all data reduction complied strictly with ASHRAE Standard 120. The Darcy friction factor was calculated by Equation 1; the plane locations are depicted in Figure 2.
[FIGURE 2 OMITTED]
f = [[[DELTA][p.sub.[f,1-2]]/[L.sub.[1-2]]]/[[1/2][[rho].sub.1][V.sub.1.sup.2](D/1000)]] (1 SI)
f = [[[DELTA][p.sub.[f,1-2]]/[L.sub.[1-2]]]/[[[rho].sub.1][([V.sub.1]/1097).sup.2]/(D/12)]](1 I-P)
The flow rate for each test point was calculated by Equation 2, where 5 denotes the section upstream of the nozzle and 6 indicates the nozzle throat.
Q = 1000 [Y.sub.n][square root of [[2[DELTA][p.sub.[s,5-6]]]/[[rho].sub.5]]][SIGMA]([C.sub.n][A.sub.n]) (2 SI)
Q = 1098 [Y.sub.n] [square root of [[[DELTA][p.sub.[s,5-6]]]/[[rho].sub.5]]][SIGMA]([C.sub.n][A.sub.n]) (2 I-P)
Additional equations necessary to support the flow calculation per Equation 2 can be found in ASHRAE Standard 120. The Reynolds number in the test section was determined by Equation 3.
[Re.sub.1] = [[[[rho].sub.1][V.sub.1]([D.sub.1]/1000)]/[[mu].sub.1]] (3 SI)
[Re.sub.1] = [[[[rho].sub.1]([V.sub.1]/60)([D.sub.1]/12)]/[[mu].sub.1]] (3 I-P)
The average air velocity in the duct 'V' was defined by the continuity equation using Equation 4.
[V.sub.1] = ([[Q.sub.1]/1000/A]) (4 SI)
[V.sub.1] = ([[Q.sub.1]/A]) (4 I-P)
The measured pressure loss data were plotted on a Moody diagram in terms of friction factor 'f' as a function of relative roughness '[epsilon]/D' and Reynolds number. These quantities are related by the Colebrook equation.
[1/[square root of f]] = -2 log [[[[epsilon]/[D.sub.1]]/3.7] + [2.51/[Re.sub.1][square root of f]]] (5 SI)
[1/[square root of f]] = -2 log [[[12[epsilon]/[D.sub.1]]/3.7] + [2.51/[Re.sub.1][square root of f]]] (5 I-P)
The relative roughness was determined iteratively by fitting the experimentally determined friction factors to the Colebrook equation using the least squares method; this approach is described in more detail in Kulkarni et al. (2009).
The measurements were subjected to an uncertainty analysis based on the method of Kline and McClintock (1953), as prescribed by ASHRAE Standard 120 for random variations of the measured quantities. In every instance the measurement uncertainty estimates were performed with a 95% confidence level.
The friction factor data for tests performed on the corrugated ducts are plotted as Moody diagrams in Figures 3 through 5. The horizontal bars through the data points represent the range of expected uncertainty in the measured Reynolds numbers, with a 95% confidence limit. Similarly the vertical bars through each point depict the range of expected uncertainty in the measured friction factor, with a confidence limit of 95%. The absolute roughness data for the corrugated galvanized spiral ducts tested in this study are summarized in Table 2. The average absolute roughness value for corrugated ducts was 0.85 mm (0.0028 ft). These results compare closely to an absolute roughness value of 0.74 mm (0.0024 ft) reported in Kulkarni et al. (2009) for a similar corrugation profile. Likewise standard spiral duct pressure loss data obtained using either Pitot-static tubes or wall static pressure taps with piezometer rings are depicted in Figure 6. Absolute roughness values for standard galvanized steel spiral ducts obtained are also provided in Table 2. The average absolute roughness for standard spiral ducts was 0.12 mm (0.0004 ft). Griggs et al. (1987) reported an absolute roughness for 254 mm (10 in) diameter unribbed standard spiral ducts having a nominal joint spacing of 3.66 m (12 ft) equal to 0.06 mm (0.0002 ft).
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Table 2. Test Results for Galvanized Spiral Ducts Nominal Size (D) mm (in.) Relative Roughness Absolute Roughness ([epsilon]/D) ([epsilon]) nun (ft) Corrugated Duct Data 203 (8) 0.0025 0.52 (0.0017) 356 (14) 0.0025 0.88 (0.0029) 508 (20) 0.0022 1.13 (0.0037) Average 0.85 (0.0028) Standard Spiral Duct Data Using Pitot-Static Tube 356 (14) 0.0035 0.12 (0.0004) Standard Spiral Duct Data Using Wall Static Pressure Tap 356 (14) 0.0040 0.15 (0.0005) Average 0.14 (0.0005)
PREDICTED DUCT PRESSURE LOSS
Equation 1 can be rearranged such so as to obtain the Darcy equation.
[DELTA][p.sub.f] = [1000fL/D][[rho][V.sup.2]/2] (6 SI)
[DELTA][p.sub.f] = [12fL/D][rho][([V/1097]).sup.2] (6 I-P)
In order to assess the influence of relative roughness on duct pressure loss, a parametric study was performed over a range of typical duct diameters, lengths, and volumetric flow rates. For corrugated ducts an absolute roughness of 0.85 mm (0.0028 ft) was employed. Based on the measurements performed in the present study, an absolute roughness of 0.12 mm (0.0004 ft) was assumed for standard spiral ducts; it is noted that the Friction Chart in the Duct Design chapter of the ASHRAE Handbook (2009) assumes a "medium smooth" roughness of 0.09 mm (0.0003 ft) based on data reported in Griggs et al. (1987). The Colebrook equation was used to solve iteratively for the friction factor by means of a standard root-solving procedure. In every instance standard conditions of temperature and pressure were assumed when calculating air thermal properties. The resulting predicted pressure loses are presented in Tables 3 through 5, where the quantity '[DELTA][p.sub.c]' represents the friction pressure loss for corrugated ducts, and '[DELTA]p' indicates the friction pressure loss for standard spiral ducts. The label '-' denotes a pressure loss that is smaller than 0.25 Pa (0.001 in. wg). Referring to the Darcy equation, the pressure loss in the duct is proportional to length. Hence at a given flow rate and duct diameter, the pressure results presented in Tables 3 through 5 can readily be extended to other duct lengths by means of straightforward proportioning.
Table 3. Pressure Loss for Corrugated vs. Non-Corrugated Spiral Ducts L = 3.05 m (10 ft.) Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 472 (1000) 1416 (3000) [DELTA] [DELTA]p [DELTA] [DELTA]p [P.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 17.4 (0.070) 12.0 (0.048) 153.7 (0.617) 99.1 (0.398) 508 (20) 0.48 (0.002) 0.39 (0.002) 4.09 (0.016) 2.99 (0.012) 762 (30) - - 0.51 (0.002) 0.40 (0.002) 1016 (40) - - - - Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 2340 (5000) 3304 (7000) [DELTA] [DELTA]p [DELTA] [DELTA]p [p.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 425.0 (1.707) 269.2 (1.081) 831.9 (3.341) 521.9 (2.096) 508 (20) 11.2 (0.045) 7.97 (0.032) 21.8 (0.088) 14.9 (0.060) 762 (30) 1.37 (0.005) 1.04 (0.004) 2.64 (0.011) 1.96 (0.008) 1016 (40) 0.31 (0.001) 0.25 (0.001) 0.60 (0.002) 0.47 (0.002) Table 4. Pressure Loss for Corrugated vs, Non-Corrugated Spiral Ducts L = 7.62 m (25 ft.) Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 472 (1000) 1416 (3000) [DELTA] [DELTA]p [DELTA] [DELTA]p [P.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 43.5 (0.175) 30.0 (0.120) 384.1 (1.543) 247.6 (0.995) 508 (20) 1.21 (0.005) 0.98 (0.004) 10.2 (0.041) 7.48 (0.030) 762 (30) - - 1.26 (0.005) 1.01 (0.004) 1016 (40) - - 0.29 (0.001) 0.25 (0.001) Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 2340 (5000) 3304 (7000) [DELTA] [DELTA]p [DELTA] [DELTA]p [p.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 1063 (4.268) 672.7 (2.701) 2080 (8.352) 1305 (5.240) 508 (20) 28.0 (0.112) 19.7 (0.079) 54.5 (0.219) 37.5 (0.151) 762 (30) 3.41 (0.014) 2.61 (0.010) 6.60 (0.027) 4.91 (0.020) 1016 (40) 0.78 (0.003) 0.63 (0.003) 1.50 (0.006) 1.18 (0.005) Table 5. Pressure Loss for Corrugated vs. Non-Corrugated Spiral Ducts L = 15.2 m (50 ft.) Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 472 (1000) 1416 (3000) [DELTA] [DELTA]p [DELTA] [DELTA]p [p.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 87.0 (0.349) 60.0 (0.241) 768.3 (3.085) 495.3 (1.989) 508 (20) 2.41 (0.010) 1.96 (0.008) 20.4 (0.082) 15.0 (0.060) 762 (30) 0.31 (0.001) 0.27 (0.001) 2.53 (0.010) 2.02 (0.008) 1016 (40) - - 0.58 (0.002) 0.50 (0.002) Flow Rate L/s ([ft.sup.3]/min) D mm (in.) 2340 (5000) 3304 (7000) [DELTA] [DELTA]p [DELTA] [DELTA]p [p.sub.c] Pa (in. wg) [p.sub.c] Pa (in. wg) Pa (in. wg) Pa (in. wg) 254 (10) 2126 (8.537) 1345 (5.403) 4159 (16.70) 2610 (10.48) 508 (20) 56.0 (0.225) 39.4 (0.158) 109.0 (0.438) 75.1 (0.301) 762 (30) 6.83 (0.27) 5.22 (0.21) 13.2 (0.053) 9.82 (0.039) 1016 (40) 1.56 (0.006) 1.27 (0.005) 2.99 (0.012) 2.37 (0.009)
In this research, pressure drop tests were performed in compliance with ASHRAE Standard 120 on three round corrugated galvanized spiral ducts to determine their absolute roughness values. The joint spacing was 3.05 m (10 ft) in length, and the duct sections were connected by beaded slip couplings which had integral scaling gaskets, thereby minimizing leakage under pressure. Darcy friction factors were calculated at each test point and plotted on Moody diagrams. The relative roughness values were determined by least squares curve fitting. The friction factor data closely followed a single relative roughness curve for each duct cross section tested. The average absolute roughness value for round corrugated spiral galvanized steel ducts was 0.85 mm (0.0028 ft), which is categorized as "medium rough" in the Duct Design chapter of the Handbook of Fundamentals (2009). These results compared closely to an absolute roughness value of 0.74 mm (0.0024 ft) reported in Kulkarni et al. (2009) for a similar corrugation profile. This implies that minor differences in corrugation profiles and seam pitches do not have a significant impact on the resulting pressure loss, as the two absolute roughness values differ by less than 15%.
Pressure loss data for a 305 mm (14 in.) diameter conventional spiral duct were also obtained by two methods that were compatible with ASHRAE Standard 120. In one instance the pressure loss was measured using Pitot-static tubes mounted at the duct centerline, at axial locations prescribed by ASHRAE Standard 120. For comparison purposes these tests were repeated using static wall pressure taps mounted on the duct surface at identical axial locations. The taps were arranged so as to form a piezometric ring. The absolute roughness values obtained by these two approaches were indistinguishable (to within the presumed accuracy of such measurements), thereby lending confidence to the corrugated duct/fitting data obtained in this study using Pitot-static tubes. The average absolute roughness for standard spiral ducts was 0.12 mm (0.0004 ft), which places them in a category midway between 'medium smooth' and 'average' according to Chapter 21 of the ASHRAE Handbook of Fundamentals (2009). By comparison, Griggs et al. (1987) reported an absolute roughness of 0.06 mm (0.0002 ft) for 254 mm (10 in) diameter unribbed standard spiral ducts having a nominal joint spacing of 3.66 m (12 ft); these data were not obtained in strict accordance with ASHRAE Standard 120.
A = cross-sectional duct area, [m.sup.2] ([ft.sup.2])
[A.sub.n] = nozzle throat area, [m.sup.2] ([ft.sup.2])
[C.sub.n] = nozzle discharge coefficient, dimensionless
D = diameter, mm (in.)
[D.sub.h] = hydraulic diameter, mm (in.)
f = friction factor, dimensionless
L = length, m (ft)
Q = flow rate, L/s ([ft.sup.3]/min)
V = velocity, m/s (ft/min)
[Y.sub.n] = nozzle expansion coefficient, dimensionless
[DELTA]p = pressure loss, Pa (in. wg)
[epsilon] = absolute roughness, mm (ft)
[rho] =air density, kg/[m.sup.3] (lbm/[ft.sup.3])
[mu] = dynamic viscosity, Nxs/[m.sup.2] (lbm/ftxs)
1 = plane 1
2 = plane 2
5 = plane 5
6 = plane 6
c = corrugated
f = friction
s = static
ASHRAE. 2008. ANSI/ASHRAE Standard 120-2008, Method of Testing to Determine Flow Resistance of HVAC Ducts and Fittings. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
ASHRAE. 2009. Duct Fitting Database, Version 5.00.08. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
Griggs, E.I.. W.B. Swim, and G.H. Henderson. 1987. Resistance to Flow of Round Galvanized Ducts. ASHRAE Transactions, 93(1):3-16.
Kline, S.J. and F.A. McClintock. 1953. Uncertainty in Single Sample Experiments. Mechanical Engineering 75:3-8.
Kulkarni, D., S. Khaire, and S. Idem. 2009. Pressure Loss of Corrugated Spiral Duct. ASHRAE Transactions, 115(1):28-34.
SMACNA. 2005. HVAC Duct Construction Standards - Metal and Flexible, 3rd Edition. Chantilly, VA: Sheet Metal and Air-Conditioning Contractors' National Association.
D.C. Gibbs is a mechanical engineer with BWSC, Inc., in Nashville, TN. S. Idem is a professor in the Department of Mechanical Engineering at Tennessee Tech University. Cookeville, TN.
Associate Member ASHRAE
S. Idem, PhD
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|Author:||Gibbs, D.C.; Idem, S.|
|Date:||Jul 1, 2010|
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