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Laboratory testing of saddle-tap tees to determine loss coefficients.

INTRODUCTION

This paper presents a method of correlating main and branch loss coefficients for saddle-tap tees operating in the diverging and converging flow modes. The project was sponsored by the Spiral Duct Manufacturers Association (SPIDA), who desires to contribute to the enhancement of the ASHRAE Duct Fitting Database (DFDB) (ASHRAE 2010) by assessing loss coefficients for saddle-tap tee junctions. This type of fitting has become available through the advancement of round fitting production by the pressed or drawn manufacturing process. The goal of the test program was to determine if the saddle-tap tee is an efficient air-moving junction, and if so, to include the resulting loss coefficient data in the ASHRAE Duct Fitting Database. It is believed that an increase in efficiency is created by the increased area inlet that is formed by the radius of the bend at the intersection of the body (see Figure 1).

[FIGURE 1 OMITTED]

Loss coefficient data for a variety of heating, ventilating, and air-conditioning (HVAC) duct system fittings have been reported extensively in the literature. A representative survey of more recent work is herein presented. Research performed by Townsend et al. (1996a) and Kulkarni et al. (2009a, 2009b) yielded flat oval elbow loss coefficient data for easy bend, hard bend, and mitered elbows that were incorporated into the DFDB. Main and branch loss coefficient data for diverging flow flat oval tees and laterals have been presented in Townsend et al. (1996b), and Idem (2003). Idem and Khodabakhsh (1999) and Gibbs and Idem (2011) used a power law model to correlate diverging flow branch loss coefficient data for flat oval tees and laterals as a function of branch-to-common flow rate and area ratio. Kulkarni et al. (2011) employed a logarithmic model to correlate branch and main loss coefficients as functions of branch-to-common and main-to-common flow rate ratio, respectively, and pertinent geometry characteristics of converging flow flat oval tees and laterals.

EXPERIMENTAL PROGRAM

Pressure loss tests were performed on the saddle-tap tees listed in Table 1. A line sketch of the fittings is provided in Figure 1. The tee branch and common section diameters, D1 and D2, respectively, were chosen so as to obtain a wide range of branch-to-common area ratios. The dimensionless branch throat radius in the common section flow direction is likewise provided in Table 1. It is noted that the throat radius of the branch was not constant around its circumference. The duct fitting pressure loss tests were conducted in accordance with ASHRAE Standard 120 (ASHRAE 2008), which dictated test setup dimensions, measurement locations, and test procedures. The duct sections were connected by slip couplings, and all joints were thoroughly sealed by cloth-backed duct tape with a natural latex-rubber adhesive. Although such tape is not approved for permanent metal-to-metal connections, its use was deemed to be suitable for the relatively brief duration of each experiment.
Table 1. Saddle-Tap Tee Sizes Tested

D2 (Common)  D1 (Branch)    Area Ratio     Throat Radius
mm (in.)       mm (in.)   [(D1/D2).sup.2]      (R/D1)

356 (14)         102 (4)            0.082          0.099

                 152 (6)            0.184          0.131

                 203 (8)            0.327          0.096

                254 (10)            0.510          0.100

                305 (12)            0.735          0.083

305 (12)         102 (4)            0.111          0.099

                 152 (6)            0.250          0.131

                305 (12)            1.000          0.083

203 (8)          102 (4)            0.250          0.099

                 203 (8)            1.000          0.096


The fittings were tested both for converging and diverging flows. For diverging flow fittings, the test setup conformed to Figure 18 of Standard 120 (ASHRAE 2008), and for converging flow fittings the test apparatus corresponded to Figure 19 of Standard 120. Flow-measuring nozzle chambers were employed in the main (or common) and branch sections of each setup. In each instance, the airflow-measuring chambers were in compliance with Figure 8 of Standard 120. Bellmouths were used to mount the nozzle chambers to the ductwork upstream of any fitting, per Standard 120. Adjustable dampers were inserted in the main and branch sections of a diverging flow fitting, and in the common and branch sections of a converging flow fitting to control the flow rate ratio through the respective sections. The ductwork and fitting construction met or exceeded the requirements provided in the SMACNA HVAC Duct Construction Standards (SMACNA 2005). Duct lengths upstream/downstream of the fitting were in accordance with Standard 120 (ASHRAE 2008). The fitting pressure loss experiments were preceded by a series of tests designed to evaluate the duct tare pressure loss per unit length, so as to permit calculation of the zero-length fitting loss coefficient. Each time a new setup was completed, a leak test was performed per Standard 120 to verify that duct leakage was within acceptable limits, and that the pressure taps and tubing were leak free.

For each pressure drop test, the blower motor was allowed to run for several minutes in order to obtain stable conditions. Flow rates were varied over a range by adjusting motor speed and changing the combination of nozzles and damper settings. Two nozzle chambers, in compliance with Standard 120, were used to measure the flow rate through the fitting. For each chamber, the nozzle boards and flow settling screens were housed inside a large chamber. Screens located upstream of the nozzle boards were used to make the flow more uniform before entering the flow nozzles. Any unused nozzles were blocked by vinyl balls. The pressure drop across the nozzles was measured by two piezometric rings located 38 mm (1.5 in.) on either side of the nozzle board. Both sides were connected to a micromanometer which read the pressure drop with a scale readability of 0.025 mm (0.001 in.). The upstream piezometric ring was also connected through a "T" to a digital manometer, which measured the nozzle chamber static pressure with a scale readability of 0.25 mm (0.01 in.). The ambient wet-bulb and dry-bulb temperatures were measured using a compact lab pyschrometer with a scale readability of 0.6 [degrees] C (1 [degrees] F). The atmospheric pressure was measured using a mercury barometer with a scale readability of 0.25 mm (0.01 in.) of mercury. All temperature and pressure measurements were performed in compliance with Standard 120.

DATA REDUCTION

The main and branch total pressure loss coefficients for diverging and converging flow tees were calculated per ASHRAE Standard 120. In every instance, the measured fitting dimensions did not equal the nominal values. However, all data reduction equations employed actual fitting dimensions. In the following data reduction equations, the cross sections (subscripts) refer to Figures 18 and 19 of Standard 120, for diverging and converging flow fittings, respectively. For both diverging and converging flows, the main pressure loss was evaluated as follows:

[[increment of p].sub.t,1-2] = [[increment of p].sub.s,7-8]+([p.sub.v7]-[p.sub.v8])-([L.sub.7-1][[increment of p].sub.f,7-1]+[L.sub.2-8][[increment of p].sub.f,2-8]) (1)

For diverging flow fittings, the pressure loss in the branch was determined by:

[[increment of p].sub.t,1-3] = [[increment of p].sub.s,7-9]+([p.sub.v7]-[p.sub.v9])-([L.sub.7-1][[increment of p].sub.f,7-1]+[L.sub.3-9][[increment of p].sub.f,3-9]) (2)

The term [L.sub.7-1] represents the separation distance between the upstream taps and the entrance plane of the fitting. Likewise, the quantity [L.sub.2-8] is the length between the main exit plane of the fitting and the main section pressure taps. Similarly, [L.sub.3-9] is the distance between the exit plane of the fitting and the branch section pressure taps. For converging flow fittings, the pressure loss in the branch was deter-mined by:

[[increment of p].sub.t,3-2] = [[increment of p].sub.s,9-8]+([p.sub.v9]-[p.sub.v8])-([L.sub.9-3][[increment of p].sub.f,9-3]+[L.sub.2-8][[increment of p].sub.f,2-8]) (3)

The dimension [L.sub.9-3] is the length between branch section taps and the exit plane of the fitting. The velocity pressure at any test plane x was calculated based on the airflow and cross sectional area. Thus:

[p.sub.vx] = 1/2[rho][([Q.sub.x]/1000/[A.sub.cs,x]).sup.2] = 1/2[rho][V.sub.x.sup.2] (4 SI)

[p.sub.vx] = [rho][([Q.sub.x]/ [A.sub.cs,x]/1097).sup.2] = [rho][([V.sub.x]/1097).sup.2] (4 I-P)

The tare pressure losses per unit length, i.e., ['p.sub.f,7-1,] ['p.sub.f,2-8], ['p.sub.f,3-9], and ['p.sub.f,9-3], were calculated from the initial straight duct tests by:

[[increment of p].sub.f] = a[V.sub.b] (5)

where the coefficients a and b were determined by least squares curve fit.

The main and branch loss coefficients were calculated per Standard 120. For both diverging and converging flow tees, the main loss coefficient was calculated by:

[C.sub.s] = [[increment of p].sub.t,1-2]/[p.sub.v8] (6)

The diverging flow branch loss coefficient was determined using:

[C.sub.b] = [[increment of p].sub.t,1-3]/[p.sub.v9] (7)

Similarly for converging flows, the branch loss coefficient was evaluated using:

[C.sub.b] = [[increment of p].sub.t,3-2]/[p.sub.v9] (8)

In order to evaluate the local velocity pressure, the fitting dimensions were carefully measured in three planes using a tape measure and then averaged. 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 loss coefficient 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)


DATA CORRELATION

Diverging Tees

The resulting branch and main loss coefficient data for diverging flow tees are summarized in Figures 2 through 7. Corresponding branch and main loss coefficient data for converging flow tees are not shown for brevity, but are avail-able in Idem and Nalla (2011). In these graphs, the branch and main loss coefficients are plotted for each value of main duct cross section considered in this study, as a function of either branch-to-common flow rate ratio ([Q.sub.b]/[Q.sub.c]) or main-to-common flow rate ratio ([Q.sub.s]/[Q.sub.c]), and the branch-to-common area ratio. In Table 1, the branch-to-common area ratio values are presented in terms of the square of the diameter ratio(i.e., [[D1 / D2].sup.2]). The horizontal bars through the data points represent the range of expected uncertainty in the measured flow rate ratio, with a 95% confidence limit, and the vertical bars through each point depict the range of expected uncertainty in the measured loss coefficient.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

It was noted that for each ratio of branch-to-common cross section, the diverging flow branch loss coefficient data tended to follow a straight-line curve when plotted as a function of branch-to-common flow rate ratio on log-log axes, implying a power law relationship exists. Hence, in this study it was proposed to correlate the diverging flow branch loss coefficient data by means of the following expression:

[C.sub.b] = [alpha][([Q.sub.b]/[Q.sub.c]).sup.[beta]][([A.sub.b]/[A.sub.c]).sup.[gamma]](9)

A similar approach was used to successfully correlate diverging flow branch loss coefficient data for flat oval tees and laterals in Idem and Khodabakhsh (1999) and Gibbs and Idem (2011). The constant parameters [alpha], [beta], and [gamma] in Equation 9 were evaluated by log-linearizing the data and performing a least-squares curve-fit. The resulting power law correlation for diverging flow saddle-tap tee branch loss coefficients is depicted in Figure 8. The family of curves corresponding to different area ratios evidently collapsed to a single straight line by plotting the quantity [C.sub.b]/[([A.sub.b]/[A.sub.c]).sup.n] as a function of ([Q.sub.b]/[Q.sub.c]).

[FIGURE 8 OMITTED]

The measured main loss coefficients for diverging flow tees were not significantly influenced by the branch-to-common area ratio, and displayed a monotonic decrease in magnitude as the straight-to-common flow rate ratio increased. Hence, it was deemed that the data depended primarily on ([Q.sub.s]/[Q.sub.c]), and it was proposed to correlate diverging flow tee main loss coefficients using the following equation:

[C.sub.s] = [alpha]+[beta]/([Q.sub.s]/[Q.sub.c])(10)

Equation 10 is a linear function of the inverse of the straight-to-common flow rate ratio, hence the constant coefficients [alpha] and [beta] were obtained by fitting a first-order polynomial to the data by means of a least-square curve-fit. The resulting linear correlation for diverging flow saddle-tap tee main loss coefficients is depicted in Figure 9. The family of curves corresponding to different area ratios successfully collapsed to a single curve by plotting [C.sub.s] as a function of [([Q.sub.s]/[Q.sub.c]).sup.-1].

[FIGURE 9 OMITTED]

Converging Tees

Converging flow branch loss coefficient data exhibited negative values at low branch-to-common flow rate ratios. In the limit as [Q.sub.b]/[Q.sub.c] [right arrow] or [vector] 0, measured branch loss coefficient data became indeterminate, i.e., [C.sub.b] [right arrow] or [vector] - [infinity]. As the branch-to-common flow rate ratio increased, the branch loss coefficients rose monotonically, until they achieved a constant value in the limit as [Q.sub.b]/[Q.sub.c] [right arrow] or [vector] 1. For converging flow branch loss coefficients, the following functional form was proposed:

[C.sub.b] = [alpha]ln([Q.sub.b]/[Q.sub.c]+m[[A.sub.b]/[A.sub.c]]+[beta])(11)

An analogous correlation approach was employed in Kulkarni and Idem (2011) to characterize flat oval tee branch loss coefficient data for converging flows. Equation 11 is a linear function of the logarithm of the branch-to-common flow rate ratio. The constant coefficients [alpha] and [beta] were obtained by fitting a first-order polynomial to the log-linearized data by means of least-square curve-fitting. The coefficients m and n were chosen by a trial and error procedure designed to maximize the goodness of fit, as outlined subsequently. The resulting linear correlation for converging flow saddle-tap tee branch loss coefficients is depicted in Figure 10. The family of curves corresponding to different area ratios collapsed to a single curve by plotting [C.sub.s] as a function of [([Q.sub.s]/[Q.sub.c]).sup.-1]. Measured main loss coefficients for converging flow tees were also not strongly affected by the branch-to-common area ratio. Moreover, they likewise displayed a monotonic decrease in magnitude as the straight-to-common flow rate ratio increased. Therefore, it was reasoned that Equation 10 was also an appropriate means to characterize converging flow main loss coefficient data for saddle-tap tees. The resulting correlation is shown in Figure 11.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

Coefficient of Determination

In order to evaluate the adequacy of the regression analyses, coefficients of determination were calculated for each set of loss coefficient data. The coefficient of determination (which equals the square of the linear correlation coefficient) was evaluated using:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

In reference to Equations 9 and 12 for diverging flow branch loss coefficient tests, the log-linearized variables [x.sub.i] and [y.sub.i] were defined as follows:

[x.sub.i] = ln[([Q.sub.b]/[Q.sub.c]).sub.i](13)

and:

[y.sub.i] = ln[([C.sub.b]/[[[A.sub.b]/[A.sub.c]].sup.[gamma]]).sub.i](14)

Likewise, for converging flow branch loss coefficient tests by Equations 11 and 12, the log-linearized variable [x.sub.i] was given by:

[x.sub.i] = [(ln[Q.sub.b]/[Q.sub.c]+m[[[A.sub.b]/[A.sub.c]].sup.n]).sub.i] (15)

and:

[y.sub.i] = [C.sub.s,i] (16)

In order to calculate the coefficient of determination for diverging or converging flow main loss coefficient tests by Equations 10 and 12, the variables [x.sub.i] and [y.sub.i] were defined as:

[x.sub.i] = [([Q.sub.s]/[Q.sub.c]).sub.i] (17)

and:

[y.sub.i] = [C.sub.s,i] (18)

In every instance, the quantities x and y were mean values of the experimentally determined values of [x.sub.i] and [y.sub.i], and hence were defined by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Regarding the development of Equation 11 for converging flow branch loss coefficients, the coefficients m and n were systematically varied over a prescribed range of values. Therein, the coefficients [alpha] and [beta] were determined by performing a least squares curve-fit in terms of the log-linearized variables. For every combination of m and n, a coefficient of determination [R.sup.2] was calculated. Those values of m and/or n that yielded the highest coefficient of determination were then used to develop the loss coefficient correlations.

RESULTS

The curve-fit equations obtained by the least squares method for the main and branch loss coefficients are depicted in Figures 8 through 11. This approach yielded the following empirical correlations for diverging and converging saddle-tap tees, along with the corresponding coefficients of determination as calculated using Equation 12.

Diverging Flow Branch Loss Coefficients:

[C.sub.b] = 0.809[([Q.sub.b]/[Q.sub.c]).sup.-2.044][([A.sub.b]/[A.sub.c]).sup.2.147]; [R.sup.2] = 0.852 (20)

Diverging Flow Main Loss Coefficients:

[C.sub.s] = 0.802/([Q.sub.s]/[Q.sub.c])-1.048; [R.sup.2] = 0.712 (21)

Converging Flow Branch Loss Coefficients:

[C.sub.b] = 0.530ln([[Q.sub.s]/[Q.sub.c]]-0.323[[[A.sub.b]/[A.sub.c]].sup.0.718])+1.539; [R.sup.2] = 0.543 (22)

Converging Flow Main Loss Coefficients:

[C.sub.s] = 1.056/([Q.sub.s]/[Q.sub.c])-1.128; [R.sup.2] = 0.927 (23)

Collectively, the correlations presented in Equations 20 through 23 model branch and main loss coefficients for saddle-tap tees operated in the diverging and converging flow modes. The goodness of fit is expressed in terms of coefficients of determination. Those values ranged from 0.543 to 0.927, indicating a suitable degree of correlation.

CONCLUSIONS

Saddle-tap field-fabricated tees are commonly employed for supply duct systems. Therein, it is useful to compare diverging flow branch loss coefficients obtained in the present study to values for a geometrically similar factory (shop) fabricated fitting. Referring to Figure 1, the increased area inlet that is formed by the radius of the bend at the intersection of the body for a saddle-tap tee implies that an analogous fitting in the ASHRAE Duct Fitting Database (DFDB) is a tee with a conical branch tapered into the body (SD5-10). Table 3 presents diverging flow branch loss coefficients for a saddle-tap tee as predicted by Equation 20. Likewise, Table 4 exhibits diverging flow branch loss coefficients for SD5-10 tees from the DFDB. It is apparent over a wide range of branch-to-common flow rate and area ratios that branch loss coefficients for saddle-tap tees are closely comparable to those for the SD5-10 fitting. Hence, saddle-tap tees might be attractive options for supply duct systems, since their branch pressure loss performance is nearly equivalent to that for a SD5-10 tee. Sheet metal contractors may elect to incorporate saddle-tap field-fabricated tees into their duct systems as an alternative to factory (shop)-fabricated tees with a conical branch tapered into the body, due to their ease of fabrication and consequent lower initial costs.
Table 3. Diverging Flow Branch Loss Coefficients for Saddle
Tap Tees

[A.sub.b]/[A.sub.c]           [Q.sub.b]/[Q.sub.c]

                        0.01    0.1    0.2   0.3   0.4   0.5

0.01                    0.50   0.00   0.00  0.00  0.00  0.00
0.1                    70.62   0.64   0.15  0.07  0.04  0.02
0.2                   312.80   2.83   0.69  0.30  0.17  0.11
0.3                   747.01   6.75   1.64  0.71  0.40  0.25
0.4                  1385.39  12.52   3.04  1.33  0.74  0.47
0.5                  2236.85  20.21   4.90  2.14  1.19  0.75
0.6                  3308.56  29.90   7.25  3.17  1.76  1.11
0.7                  4606.53  41.63  10.09  4.41  2.45  1.55
0.8                  6135.96  55.45  13.45  5.87  3.26  2.07
0.9                  7901.46  71.40  17.31  7.56  4.20  2.66
1                    9907.15  89.53  21.71  9.48  5.26  3.34

[A.sub.b]/[A.sub.c]
                      0.6   0.7   0.8   0.9     1

0.01                 0.00  0.00  0.00  0.00  0.00
0.1                  0.02  0.01  0.01  0.01  0.01
0.2                  0.07  0.05  0.04  0.03  0.03
0.3                  0.17  0.13  0.10  0.08  0.06
0.4                  0.32  0.23  0.18  0.14  0.11
0.5                  0.52  0.38  0.29  0.23  0.18
0.6                  0.77  0.56  0.43  0.34  0.27
0.7                  1.07  0.78  0.59  0.47  0.38
0.8                  1.42  1.04  0.79  0.62  0.50
0.9                  1.83  1.34  1.02  0.80  0.65
1                    2.30  1.68  1.28  1.00  0.81

Table 4. Diverging Flow Branch Loss Coefficients for Tees with a
Conical Branch Tapered into the Body (SD5-10)

[A.sub.b]/[A.sub.c]           [Q.sub.b]/[Q.sub.c]

                         0.01    0.1    0.2   0.3   0.4   0.5   0.6

0.01                     0.65   0.04   0.02  0.01  0.01  0.01  0.01
0.1                     95.04   0.65   0.24  0.15  0.11  0.09  0.07
0.2                    393.00   2.98   0.65  0.33  0.24  0.18  0.15
0.3                    895.00   7.36   1.56  0.65  0.39  0.29  0.24
0.4                   1600.00  13.78   2.98  1.20  0.65  0.43  0.33
0.5                   2508.00  22.24   4.92  1.98  1.04  0.65  0.47
0.6                   3620.00  32.73   7.36  2.98  1.56  0.96  0.65
0.7                   4935.00  45.26  10.32  4.21  2.21  1.34  0.90
0.8                   6453.00  59.82  13.78  5.67  2.98  1.80  1.20
0.9                   8175.00  76.41  17.75  7.36  3.88  2.35  1.56
1                    10100.00  95.04  22.24  9.27  4.92  2.98  1.98

[A.sub.b]/[A.sub.c]

                      0.7   0.8   0.9     1

0.01                 0.01  0.00  0.00  0.00
0.1                  0.06  0.05  0.05  0.04
0.2                  0.13  0.11  0.10  0.09
0.3                  0.20  0.17  0.15  0.13
0.4                  0.27  0.24  0.21  0.18
0.5                  0.36  0.31  0.27  0.24
0.6                  0.49  0.39  0.33  0.29
0.7                  0.65  0.51  0.42  0.35
0.8                  0.86  0.65  0.52  0.43
0.9                  1.11  0.83  0.65  0.53
1                    1.40  1.04  0.81  0.65


It is likewise instructive to compare diverging flow main loss coefficients measured in this study to those available in the DFDB for an analogous fitting, e.g., a tee with a conical branch tapered into the body (SD5-10). The straight-to-common area ratio of the saddle-tap tees tested in this project was unity in every instance. Therein, Table 5 displays diverging flow main loss coefficients for a saddle-tap tee as predicted using Equation 21. These are in turn compared to tabular values taken from the DFDB for the SD5-10 fitting for values of [A.sub.s]/[A.sub.c] = 1. Referring to Table 5, it is observed that Equation 21 apparently does not represent the main loss coefficient data well over the straight-to-common flow rate range [Q.sub.s]/[Q.sub.c] [greater than or equal to] 0.8, as evidenced by the degree of "undershoot" of the correlation. In contrast, main loss coefficients predicted using Equation 21 for saddle-tap tees are significantly lower than those taken from the DFDB for the SD5-10 fitting in the limit as [Q.sub.s]/[Q.sub.c] [right arrow] or [vector] 0. However, there is significant scatter in the saddle-tap tee main loss coefficient data for low straight-to-common flow rate ratios; refer to Figure 9. It is concluded that a comparison of main loss coefficients for saddle-tap tees and analogous fittings cited in the DFDB is rather inconclusive, and further study is suggested.
Table 5. Comparison of Diverging Flow Main Loss Coefficient Values
for Saddle Tap Tees and SD5-10 Tees

Fitting           [Q.sub.s]/[Q.sub.c]

            0.01    0.1   0.2   0.3   0.4   0.5   0.6   0.7    0.8

Saddle     79.15   6.97  2.96  1.63  0.96  0.56  0.29  0.10  -0.05
Tap Tee

SD5-10   8500.00  45.00  6.25  1.44  0.38  0.20  0.17  0.12   0.13
Tee
Fitting

           0.9      1

Saddle   -0.16  -0.25
Tap Tee

SD5-10    0.14   0.13
Tee


The ASHRAE Duct Fitting Database cites main and branch loss coefficient values only for straight-body converging flow tees. Since such fittings are not geometrically similar to saddle-tap tees, it was deemed to be inappropriate to compare loss coefficient data obtained in this study to those available in DFDB for exhaust duct systems.

NOMENCLATURE

[A.sub.cs] = duct cross-sectional area, [m.sup.2] (f[t.sup.2])

[alpha], [beta], [gamma] = curve-fitting coefficients

C = loss coefficients

D1 = branch diameter, mm (in.)

D2 = main diameter, mm (in.)

L = length, m (ft.)

m, n = constant parameters

N = number of data points

[p.sub.s] = static pressure, Pa (in. wg)

[p.sub.v] = velocity pressure, Pa (in. wg)

[[increment of p].sub.f] = duct pressure loss per unit length, Pa/m (in. wg/ft.)

[[increment of p].sub.s] = static pressure difference, Pa (in. wg)

[[increment of p].sub.t] = total pressure difference, Pa (in. wg)

Q = flow rate, L/s (cfm)

R = throat radius (see Figure 1), mm (in.)

[R.sup.2] = coefficient of determination

V = average velocity, m/s (ft/min)

[rho] = air density, kg/[m.sup.3] (lbm/f[t.sup.3])

Subscripts

1 = plane 1

2 = plane 2

3 = plane 3

7 = plane 7

8 = plane 8

9 = plane 9

b = branch section

c = common section

s = straight (main) section

x = plane number

DISCUSSION

Patrick Brooks, Director, United McGill Corp.: Were both the downstream and upstream pressure tap distances varied to determine the effect or were they maintained at the SPC 120 recommended length of 11 diameters?

Stephen Idem: Neither the downstream nor upstream pressure tap distances were varied to determine the effect on the fitting loss coefficients; in every instance the dimensions of the experimental setups strictly adhered to the lengths required by Standard 120.

Scott Hobbs, Technical Services, McGill Airflow, LLC: Does branch/main ratio affect the 'p of the tap? Does ASHRAE have any recommendations regarding the ratio of branch/main size in regards to optimal pressure drop through the tap and when the tap size can adversely affect pressure drop vs full body fittings?

Idem: The branch-to-common area ratio does affect the pres-sure drop through the tap. At any given branch-to-common flow rate ratio, the magnitude of the branch loss coefficient increases proportionately to the area ratio. ASHRAE does not have any recommendations regarding the ratio of branch-to-common size in regards to optimal pressure drop through the tap, because that is dictated by the particular design requirements of the system.

REFERENCES

ASHRAE. 2008. ANSI/ASHRAE Standard 120-2008, Methods of Testing to Determine Flow Resistance of HVAC Air Ducts and Fittings. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers.

ASHRAE. 2010. ASHRAE Duct Fitting Database, Version 5.00.10. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta.

Gibbs, D.C. and S. Idem. 2011. Measurements of flat oval diverging flow fitting loss coefficients. ASHRAE Transactions, In Press.

Idem, S. and F. Khodabakhsh. 1999. Influence of area ratio on flat oval divided-flow fitting loss coefficients. HVAC&R Research 5(1):19-33.

Idem, S. 2003. Main loss coefficient measurements for flat oval tees and laterals. ASHRAE Transactions 109(1):456-461.

Idem, S. and A. Nalla. 2011. Laboratory testing of saddle tap tees to determine loss coefficients, SPIDA Final Report, Spiral Duct Manufacturers Association, Irmo, SC.

Kline, S.J. and F.A. McClintock. 1953. Describing uncertainties in single-sample experiments." Mechanical Engineering 75:3-8.

Kulkarni, D., S. Khaire, and S. Idem. 2009a. Influence of aspect ratio and hydraulic diameter on flat oval elbow loss coefficients. ASHRAE Transactions 115(1):48-57.

Kulkarni, D., S. Khaire, and S. Idem. 2009b. Measurements of flat oval elbow loss coefficients. ASHRAE Transactions 115(1):35-47.

Kulkarni, D., J. Cui and S. Idem. 2011. Laboratory Testing of Converging Flow Flat Oval Tees and Laterals to Determine Loss Coefficients. HVAC&R Research 17(5):710-25.

SMACNA. 2005. HVAC Duct Construction Standards--Metal and Flexible. Chantilly, VA: Sheet Metal and Air-Conditioning Contractors' National Association.

Townsend, B., F. Khodabakhsh, and S. Idem. 1996a. Loss coefficient measurements for flat oval elbows and transitions. ASHRAE Transactions 102(2):159-169.

Townsend, B., F. Khodabakhsh, and S. Idem. 1996b. Loss coefficient measurements in divided-flow flat oval fit-tings. ASHRAE Transactions 102(2):151-158.

A.N. Nalla

S. Idem, PhD

Member ASHRAE

A.N. Nalla is a graduate student and S. Idem is a professor in the Department of Mechanical Engineering at Tennessee Tech University, Cookeville, TN.
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Author:Nalla, A.N.; Idem, S.
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2012
Words:5164
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