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Laboratory testing of a fabric air dispersion system.

INTRODUCTION

This paper presents pressure loss data for a 368 mm (14.5 in.) diameter non-porous polyester fabric duct with an acrylic/urethane coating. The presence of the coating ensures that air leakage through the fabric is negligible when the system is pressurized within the limits of manufacturer's specifications. The measurements were performed in accordance with ASHRAE Standard 120 (2008). Previous pressure loss tests performed on a similar fabric duct were reported in Idem et al. (2011). They concluded that the friction factor data were dependent on the particular type of connection used to join the fabric ducts to the 356 mm (14.0 in.) diameter rigid steel ducts at the terminal ends of the test section. That test arrangement was mandated by requirements in ASHRAE Standard 120, which stipulate that static wall pressure taps (arranged to form piezometric rings) be located upstream and downstream of a flexible/fabric duct test section, in order to measure the resulting pressure loss. Because of concerns about the disparity in the fabric duct/steel duct diameter at the terminal connections, it was suggested that additional pressure loss tests be performed on fabric ducts using Pitot-static tubes mounted at the duct centerline, at axial locations prescribed by ASHRAE Standard 120. The results of the revised test program based on that recommendation are reported herein.

Fabric ducts are frequently used to supply and disperse air in open ceiling architecture. Common applications include factories, warehouses, and gymnasiums, etc. Fabric ducts are made from specific blends of fabrics rather than from metal or plastic. In order to ensure safety, the material may be treated to be both heat-resistant and flame-retardant. Air passing through the fabric walls eliminates the risk of condensation, and minimizes dust accumulation on the duct surfaces. Compared to sheet metal duct and diffuser systems, fabric air dispersion systems are lighter and less expensive. Simple suspension systems reduce installation time. Hence fabric duct systems are cost effective, and can be an aesthetically attractive alternative to metal ductwork. However, there is a lack of published performance data for fabric duct system components available to design engineers through such references as the ASHRAE Duct Fitting Database (2008) and the Duct Design chapter of the ASHRAE Handbook of Fundamentals (2009). Hence this project will contribute to the improved designs of fabric duct systems.

EXPERIMENTAL PROGRAM

The test apparatus shown in Figure 1, which depicts the measurement planes employed in this study, was in compliance with ASHRAE Standard 120. The test duct was comprised of a single piece of fabric, i.e., there were no transverse joints, and one longitudinal seam was present running down the entire length of the specimen. From plane 1 to plane 2, the duct had an overall length of 30.5 m (100 ft). It was suspended from the laboratory ceiling by means of a hangar system per the manufacturer's recommendations; refer to Figure 2. Two configurations were tested. In one instance there was no internal frame to maintain a round cross section when no static air pressure was in the system. In order to support the structure of the fabric section in that case, the minimum internal static pressure maintained in the experiments was 125 Pa (0.5 in. wg). For other tests a skeletal metal frame was inserted into the duct to maintain the duct shape in the absence of static air pressure. A schematic diagram of the frame is provided in Figure 3. The ring and spoke components of the frame consisted of 6.4 mm (0.25 in.) diameter steel rod, and the diameter of central aluminum tube was 20.3 mm (0.8 in.). The separation distance L' between the rings equaled 1.88 m (74 in). There were six equally-spaced spokes mounted to the terminal rings of the skeletal metal frame, whereas the interior rings had four spokes. The outer diameter of the ring elements closely matched the inner duct diameter. Hence the maximum reduction of the air flow cross section due to the presence of the skeletal frame was 13.5%.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The test setup included a 20 hp centrifugal fan, followed by a cylindrical nozzle chamber which was used for flow measurement. Primary control of air flow through the test duct was accomplished by means of a variable frequency drive, which was used to control the fan speed. Additional control of air flow through the test duct was achieved using a porous fabric orifice mounted at the downstream metal test duct outlet; refer to Figure 4. The open area of the orifice was adjustable. Screens mounted upstream and downstream of the nozzle board inside the chamber were used to settle the flow. The system was blow-through in nature. The nozzle board contained three long-radius spun aluminum flow nozzles having throat diameters of 89 mm (3.5 in.), 152 mm (6 in.) and 254 mm (10 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. Unused nozzles 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 single manometer to measure differential pressure.

[FIGURE 4 OMITTED]

Tests were performed with the fabric duct connected to 356 mm (14 in.) diameter steel ducts located upstream and downstream of the fabric duct test section. The terminal ends of the fabric duct were attached to the rigid steel ducts with minimum overlaps of 50 mm (2 in.), and clamped tightly using straps in order to make an airtight connection. Pitotstatic tubes aligned precisely with the air flow were mounted upstream and downstream of the fabric duct test section to measure the pressure loss per unit length. The Pitotstatic tube measurement locations in the fabric duct provided an entrance duct section to achieve fully developed turbulent flow (upstream length), the test section, and a tail portion (down-stream length). The dimensions conformed to the requirements of ASHRAE Standard 120. Pressure taps arrayed in a piezometric ring were mounted on the rigid steel ducts in order to obtain an auxiliary measure of the pressure loss across the entire length of the fabric duct. When an internal support was inserted into the test apparatus, the pressure loss over the length of the frame was measured using the static pressure ports of the Pitotstatic tubes. Under those circumstances the pressure taps mounted on the rigid steel ducts were not used to measure the pressure loss. Pertinent test section dimensions are provided in Table 1. The downstream Pitotstatic tube was situated after the end of the support structure, so that wake effects impacting that sensor were minimized. As outlined subsequently, the tare pressure loss of the fabric duct was subtracted from the pressure drop measured using the Pitotstatic tubes in order to evaluate pressure loss per unit length over the internal metal frame, i.e., from plane C to plane D.
Table 1. Test Set-Up Dimensions

[L.sub.Z-1]/D  [L.sub.  [L.sub.  [L.sub.  [L.sub.  [L.sub.  [L.sub.
               1-A]/D   A-C]/D   C-D]/D   Z-1]/D   D-B]/D   B-2]/D

12.9              18.0      3.3     35.2     12.9     11.2     15.0


Pressure drop measurements over the pressure taps mounted on the rigid steel ducts and across the nozzle board were performed using liquid-filled micromanometers having a measurement accuracy of + or -0.025 mm (0.001 in.). Like-wise, the static pressure upstream and downstream of the test section and the pressure loss indicated by the Pitot-static tubes was measured by means of electronic manometers having a readability of + or -0.25 mm (0.01 in.). Similarly static pressure in the nozzle chamber was measured using an electronic manometer having the scale readability of + or -0.25 mm (0.01 in.). The air temperature in the nozzle chamber was measured using a mercury thermometer having a scale read-ability 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 pres-sure in this project were in compliance with ASHRAE Standard 120.

DATA REDUCTION

Referring to Figure 1, when the internal support frame was not present the pressure loss [[DELTA]p.sub.s,1-2] was measured directly by means of the pressure taps mounted on the rigid steel ducts. Likewise the pressure loss [[DELTA]p.sub.s,A-B] was evaluated using the static pressure ports of the Pitotstatic tubes. However, when the internal frame was inserted into the apparatus the pressure loss was calculated by Equation 1:

[[DELTA]p.sub.s,C-D] = [[DELTA]p.sub.s,A-B] - ([L.sub.A-C] + [L.sub.D-B] ([[DELTA]p.sub.f]/L) (1)

The terms [L.sub.A-C] and [L.sub.D-B] represent the separation distance between the upstream Pitot tube static pressure ports and the entrance plane of the frame, and the exit plane of the frame and the downstream Pitot tube static pressure ports, respectively. The friction loss per unit length [[DELTA]p.sub.f] / L is the duct tare pressure loss per unit length, as calculated by Equation 2:

[[DELTA]p.sub.f] / L = a[V.sup.b] (2)

The coefficients 'a' and 'b' were determined by a least squares curve fit, based on Pitot tube pressure loss data obtained in the absence of the support frame.

The Darcy friction factor was calculated by Equation 3.

f = ([[DELTA]p.sub.s,i-j]/[L.sub.i-j]) / (1/2 [[rho].sub.1] [V.sub.1.sup.2]/(D/1000)) (SI) (3)

f = ([[DELTA]p.sub.s,i-j]/[L.sub.i-j]) / (1/2 [[rho].sub.1] [([V.sub.1][disjunction]1097).sup.2]/(D/12)) (I-P) (3)

In Equation 3 the evaluation planes i-j refer to 1-2, A-B, or C-D, depending on the particular circumstances of the measurement. The flow rate for each test point was calculated by Equation 4, where 5 denotes the section upstream of the nozzle and 6 indicates the nozzle throat.

[Q.sub.1] = 1000 [Y.sub.n] [square root of 2([p.sub.2,5] - [p.sub.2,6]) / [[rho].sub.5]] [SIGMA]([C.sub.n] [A.sub.n]) (SI) (4)

[Q.sub.1] = 1098 [Y.sub.n] [square root of 2([p.sub.2,5] - [p.sub.2,6]) / [[rho].sub.5]] [SIGMA]([C.sub.n] [A.sub.n]) (I-P) (4)

Additional equations necessary to support the flow calculation per Equation 4 can be found in ASHRAE Standard 120. Determination of the flow rate required the measurement of the pressure drop across the nozzle board, the static pressure of the chamber, and the temperature inside the chamber. The density of air in the test section was calculated by means of the correlations presented in ASHRAE Standard 120, based on measurements of the ambient dry-bulb and wet-bulb temperatures, barometric pressure, test section temperature, and aver-age static pressure.

The Reynolds number in the test section was determined by Equation 5.

[Re.sub.1] = ([[rho].sub.1][V.sub.1]/([D.sub.1]/1000))/[[mu].sub.1] (SI) (5)

[Re.sub.1] = ([[rho].sub.1]([V.sub.1]/60)/([D.sub.1]/12))/[[mu].sub.1] (I-P) (5)

The average velocity in the test section 'V' was defined by the continuity equation as

[V.sub.1] = (([Q.sub.1]/1000)/A) (SI) (6)

[V.sub.1] = ([Q.sub.1]/A) (I-P) (6)

The measured pressure loss data were plotted on a Moody diagram in terms of friction factor 'f' as a function of relative roughness 'H/D' and Reynolds number. These quantities are related by the Colebrook equation

1/[square root of f] = -2log[([epsilon]/[D.sub.1])/3.7 + 2.51/([Re.sub.1][square root of f])] (SI) (7)

1/[square root of f] = -2log[(12[epsilon]/[D.sub.1])/3.7 + 2.51/([Re.sub.1][square root of f])] (I-P) (7)

The relative roughness was determined iteratively by fitting the experimentally determined friction factors to the Colebrook equation, using the least squares method. Guessed relative roughness values were substituted successively into the Colebrook equation until the square of the difference of the calculated and experimentally determined friction factors approached zero.

All dimensional measurements were assumed to have an accuracy of [+ or -]1%. In some instances, the measurement uncertainty of a parameter exceeded the basic scale readability of a particular instrument. For example, that occurred when random fluctuations in the system static pressure were present, and those fluctuations exceeded the scale readability of the manometer. Estimates of the measurement uncertainty of several quantities are presented in Table 2, for the conditions typically encountered in the experiments. The friction factor 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 measurands. In every instance the measurement uncertainty estimates were performed with a 95% confidence level.
Table 2.Uncertainties in Measured Parameters

Dry Bulb Temperature                 0.6[degrees]C (1[degrees]F)
Wet Bulb Temperature                 0.6[degrees]C (1[degrees]F)
Plenum Chamber Temperature           0.6[degrees]C (1[degrees]F)
Test Section Temperature             0.6[degrees]C (1[degrees]F)
Plenum Chamber Static Pressure                25 Pa (0.1 in. wg)
Pressure Drop Across Nozzle Chamber           5 Pa (0.02 in. wg)
Test Section Static Pressure                2.5 Pa (0.01 in. wg)
Barometric Pressure                     0.25 mm Hg (0.01 in. Hg)


RESULTS

Friction factors for a 368 mm (14.5 in.) diameter nonporous fabric duct were measured over the Reynolds number range 2 x [10.sup.5] to 6 x [10.sup.5]. The results are plotted in Figure 5. Two configurations were tested. In one instance an internal frame to maintain a round cross section when no static air pressure was in the system was absent. Under these circumstances the measured duct relative roughness based on Pitot tube pressure loss data equaled 0.0003. Likewise, the relative roughness determined using pressure taps mounted on the rigid steel ducts located at each end of the fabric duct yielded a relative roughness of 0.0005. For the case where a skeletal metal frame was inserted into the fabric duct, the pressure loss measurements over the test section performed using Pitotstatic tubes yielded a relative roughness of 0.0046. In every instance when plotted on a Moody diagram, the data closely followed a single relative roughness curve. The horizontal bars through the data points represent the range of expected uncertainty in the measured Reynolds number, with a 95% confidence limit, and the vertical bars through each point depict the range of expected uncertainty in the measured friction factor.

[FIGURE 5 OMITTED]

The absolute roughness values are summarized in Table 3 in terms of the terminal fabric duct/steel duct connection, and the presence/absence of an internal skeletal metal support frame. For cases where an internal support frame was absent the absolute roughness of the ducts based on test data obtained using Pitot-static tubes was 0.11 mm (0.0004 ft). This value lies within the duct roughness range described as "MEDIUM SMOOTH" in the Duct Design chapter of the Handbook. When an internal support frame was present the absolute roughness of the ducts based on Pitot tube test data was 1.69 mm (0.0056 ft). This conforms closely to the category of "MEDIUM ROUGH" in the Duct Design chapter of the Handbook.
Table 3. Test Results for Fabric Ducts

                 Internal                  Internal
               Frame Absent                 Frame
                                           Present

Pressure Loss    Relative     Absolute     Relative    Absolute
Measurement      Roughness    Roughness   Roughness   Roughness
Method         [epsilon]/D   [epsilon],  [epsilon]/D  [epsilon],
                               mm (ft)                   mm (ft)

Pitot-Static         0.0003        0.11       0.0046        1.69
Tubes                          (0.0004)                 (0.0056)

Pressure Taps        0.0005        0.18           --          --
                               (0.0006)


PREDICTED DUCT PRESSURE LOSS

A parametric study was performed to predict the pressure loss performance of 368 mm (14.5 in.) diameter fabric ducts over a range of typical volumetric flow rates. Two cases were considered, namely (i) the internal frame was absent and (ii) the internal frame was present. In the former case the absolute roughness was assumed to equal 0.11 mm (0.0004 ft), whereas in the latter case the absolute roughness was taken to be 1.69 mm (0.0056 ft). The pressure loss for a prescribed duct length was obtained by means of Equation 8, which is referred to as the Darcy equation.

[[DELTA]p.sub.f] = 1000fL/D [rho][V.sup.2]/2 (SI) (8)

[[DELTA]p.sub.f] = 12fL/D [rho][(V/1097).sup.2] (I-P) (8)

The pressure loss was calculated in units of Pa/m (in. of water per 100 feet of duct length) for flow rates ranging from 236 L/s (500 [ft.sup.3]/min) to 1180 L/s (2500 [ft.sup.3]/min). 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 Table 4. For the specified duct diameter the flow rates correspond to air velocities ranging from 2.21 m/s (436 ft/min) to 11.1 m/s (2180 ft/min). Current fabric air dispersion system design guidelines dictate that maximum airflow velocities should be limited to approximately 8.13 m/s (1600 ft/min), in order to reduce stress and noise, and to obtain a better balanced system. When the fabric air dispersion system has an internal skeletal metal frame that tensions the walls of the system, the maximum can rise to 12.7 m/s (2500 ft/min) or higher, depending on the internal static air pressure of the system. The system design guidelines also show that increased duct roughness and pressure losses assist in providing uniform air dispersion from the inlet to the extremities of the system.
Table 4.   Predicted Pressure Loss Pa/m (in. water/100 ft) for Fabric
Ducts

                                    Q, L/s
                             ([ft.sup.3]/min)

Test           236      472        708 (1500)      944     1180
Condition    (500)   (1000)                     (2000)   (2500)

Internal     0.172    0.621     1.323 (0.162)    2.271    3.471
Frame      (0.021)  (0.076)                    (0.278)  (0.425)
Absent

Internal     0.253    0.980     2.181 (0.267)    3.863    6.012
Frame      (0.031)  (0.120)                    (0.473)  (0.736)
Present


CONCLUSIONS

Two trends in the data were readily apparent from the measured pressure loss data for non-porous fabric ducts. The presence of the internal skeletal metal frame increased the measured relative roughness in the duct, relative to the case where no frame was used. In addition, accurate results were critically dependant on where the friction factor data were taken and whether pressure taps mounted on the terminal rigid steel ducts or Pitotstatic tubes were used to measure the pressure loss in the test section. The disparity between the resulting relative roughness values is consistent with test data reported in Idem et al. (2011). They attributed this variation to the presence of transitions in the fabric duct adjacent to the pressure taps mounted on the steel ducts, which were caused by the different diameters of the fabric and steel ducts. It was postulated this affected the measured pressure loss in the test section. It is standard practice in the fabric air dispersion system industry to manufacture the fabric duct larger than the rigid supply duct to which it is attached, in order to facilitate the mounting of the fabric duct. Typical fabric duct installations do not employ a connection to a steel duct at the fabric system outlet. It is suggested that the static pressure ports of Pitot tubes mounted at the centerline of the test duct be employed to measure the pressure loss, provided that other stipulations of ASHRAE Standard 120 are satisfied. Since only one diameter of fabric air dispersion system was studied in this test program, it is suggested that additional pressure loss tests be conducted over a wider range of duct diameters, with and without the skeletal metal frame being present, in order to establish whether the duct roughness is significantly affected by the duct diameter. If duct roughness is a function of duct diameter, it is necessary to determine whether the roughness increases or decreases with increasing duct diameter.

NOMENCLATURE

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.)

f = friction factor, dimensionless

L = length, m (ft)

L' = separation distance, m (ft)

Q = flow rate, L/s ([ft.sup.3]/min)

Re = Reynolds number, dimensionless

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, N * s/[m.sup.2] (lbm/ft * s)

Subscripts

A plane A

B plane B

C plane C

D plane D

Z plane Z

1 plane 1

2 plane 2

5 plane 5

6 plane 6

REFERENCES

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.

ASHRAE, 2009. I-P & SI Handbook-Fundamentals, Table 1, p. 35.7. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Idem, S., A.N. Nalla, and K. Gebke. 2011. Laboratory Testing of Fabric Air Dispersion System Friction Loss, Final Report, DuctSox Corp.

Kline, S.J. and F.A. McClintock. 1953. Uncertainty in Single Sample Experiments. Mechanical Engineering 75:3-8.

D. Kulkarni

Student Member ASHRAE

A.N. Nalla

S. Idem, PhD

Member ASHRAE

K. Gebke

Member ASHRAE

D. Kulkarni is a graduate student and S. Idem is a professor in the Department of Mechanical Engineering, Tennessee Tech University, Cookeville, TN. A.N. Nalla is an aftermarket engineer with Cummins Filtration, Stoughton, WI. K. Gebke is a new product development engineer with DuctSox Corporation, Peosta, IA.
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Author:Kulkarni, D.; Nalla, A.N.; Idem, S.; Gebke, K.
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2012
Words:3771
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