THE IMPORTANCE OF INDOOR AND OUTDOOR AIR-FILM COEFFICIENT MEASUREMENT TO SOLAR CALORIMETERY

SESCI 2004 Conference University of Waterloo Waterloo, Ontario, Canada August 21 st -25 th, 2004 THE IMPORTANCE OF INDOOR AND OUTDOOR AIR-FILM COEFFICIENT MEASUREMENT TO SOLAR CALORIMETERY M. Collins Dept. of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada ABSTRACT In advance of a new hotbox standard that deals specifically with solar calorimetry, the present analysis addresses the potential calculation errors associated with inaccurate and improper correction of the interior and exterior air-film coefficients. That standard, ASTM C16.30.410 - Standard Test Method for Measuring the Solar Heat Gain Coefficient of Fenestration Systems using Calorimetry Hot Box Methods, has adopted the use of a Calibration Transfer Standard to determine the combine radiative and convective heat transfer coefficient on the indoor side of a test window, and a sol-air film coefficient meter on the outdoor side. The adaptation of these methods is discussed. Generally, the accepted hotbox calibration procedure is applicable with modification. The errors associated with improper calibration are also examined with respect to the standard test procedure. It is shown that in most cases, large errors in the thermal transmission (U-factor result in small errors in the calculated Solar Heat Gain Coefficient (SHGC. It was discovered, however, that incorrect calibration procedure could introduce significant errors in both the SHGC and thermal transmission (U-factor. Of note, tests conducted in still conditions, or those conducted when glass and air temperatures are similar, could produce errant results. NOMENCLATURE A = Area, m 2 F = View Factor, dimensionless G = Solar Radiation, W/m 2 h = Heat Transfer Coefficient, W/m 2 K k = Thermal Conductivity, W/mK N = Inward-Flowing Fraction, dimensionless Q = Energy Flow, W SHGC = Solar Heat Gain Coefficient, dimensionless T = Temperature, o C or K ΔT = Temperature Difference, o C or K U = Thermal Transmission, W/m 2 K α = Absorptivity, dimensionless ε = Emissivity, dimensionless η = Instantaneous Efficiency, dimensionless θ = Tilt Angle, degrees τ = Transmissivity, dimensionless Subscripts 30_8 = Case where h o = 30 and h i = 8 W/m 2 K abs = Absorber Panel 1

act = Actual aux = Calorimeter Auxiliary Power c = Glazing Cavity conv = Convective cor = CTS Core CTS = Calibration Transfer Standard error = Percent Error error,oper = Percent Error due to Operator error,test = Percent Error due to Off-Standard Test error,total = Total Percent Error g1 = Outdoor Glass g2 = Indoor Glass i = Indoor flow = Calorimeter Flow Loop mask = Calorimeter Mask Wall meas = Measured net = Net Gain o = Outdoor p = Plate (Sol-Air Heat Coefficient Meter sky = Sky surr = Surroundings walls = Calorimeter Walls x = Variable INTRODUCTION In recent years, responsible and sustainable energy use has been an important motivating factor in the design of new building products. Of particular note, the thermal and solar performance of windows will likely play a substantial role in energy efficient construction of the future [1]. Gas fills, spectrally selective coatings, a variety of shading devices, and so-called switchable glazings (electrochromic, thermochromic, or photochromic windows either currently provide, or show great promise, in providing substantial energy savings. The complex and varied nature of advanced window technologies also makes it difficult to assess the performance of these products. With the exception of gas fills and spectrally selective coatings, industry standard window analysis software [2,3] cannot analyze the thermal or solar performance of shaded or switchable glazings. Consequently, experimental methods (i.e., calorimetry stand to play an important role in the development and rating of new products. Window performance is evaluated using both hotbox testing (thermal, and solar calorimetry (solar and thermal. While hotbox methods are standardized and well documented [4,5,6], a standard test method for performing solar calorimetric testing, ASTM C16.30.410 [7], is only now being produced. One problem in developing this standard is that North American operators of solar calorimeters have each developed their own calorimeters, methods of calibration, and calorimetric test procedures. Inconsistencies exist not only in the quality of calorimeters and their calibration, but also in the applicability of a calibration or test procedure when applied to a specific calorimetric design. A further difficulty results from the transient nature of test conditions. To test the solar performance of a window, it is necessary to use the sun 1. Tracking the sun's position in the sky will result in a differing view of the foreground and incident direction of the wind as the calorimeter tracks, and over the course of a test day, changing air mass and spectrum. Furthermore, as the calorimeter is outdoors, changing wind speed, turbidity, and direction, outdoor temperature, and sky conditions can all introduce 1 With the exception of Solar Simulators. 2

transients into the analysis. In general, calorimeter operators aim to achieve quasi-stead-state conditions, and accept the aforementioned errors within reason. The desire of rating organizations to standardize those procedures, however, is the impetus for the current discussion. The present discussion will focus on one aspect of this calibration that is of critical importance to current solar calorimeter test procedures. Specifically, the use of a Calibration Transfer Standard (CTS and sol-air heat coefficient meter in determining the indoor and outdoor combined convective and radiative heat transfer (air-film coefficients respectively. The errors inherent in the misapplication of those devices are discussed and quantified as it applies to the accepted test procedures. CALORIMETRY Construction Existing calorimeters are unique in design and operating procedure. For the purposes of this discussion, however, only those calorimeters that attempt to achieve quasi-steady conditions will be discussed (i.e., tracking calorimeters. Such calorimeters are particularly useful for rating purposes. To facilitate solar tracking, and to increase calorimeter response time, tracking calorimeters are usually more compact designs (then those utilized by hot box facilities. By reducing size, the thermal mass is reduced, thereby reducing the response time of the calorimeter. As an added benefit, it is easier and cheaper to build a solar tracker if the calorimeter is small. Omitted are stationary test cells such as MoWitt [8] and the European PASSYS cells [9]. While those calorimeters can measure the solar performance of a window, they are better suited to investigations of overall day-to-day performance of test samples. Some examples of tracking calorimeters are shown in Figure 1. Both tracking and stationary calorimeters all have several common elements. In general, they consist of an insulated or guarded wall structure and an insulated surround panel, an absorber panel / flow loop system to remove thermal energy, and associated instrumentation. To measure net heat gain through a glazing system, a test window is first mounted in the surround panel (also called a mask wall. This wall covers the calorimeter aperture and serves as the interface between the interior and exterior environment. The mask wall is generally constructed of a thick homogenous slab of insulation, with an inner and outer protective skin that is painted flat white in order to reduce radiant loading. The wall construction of the solar calorimeter is designed to reduce heat loss either by adding insulation or through the use of a guard. By eliminating the temperature gradient across the wall using a guard (ΔT walls 0, it should be possible to eliminate heat flux. The interior walls are painted black for high emissivity (ε 0.90. The absorber plate is the primary energy absorption device within the calorimeter. It is a plate heat exchanger placed within the calorimeter to intercept solar radiation. It is painted matte black to increase absorptivity, and is oriented to intercept and absorb all solar Figure 1: Queen's Solar Calorimeter, Queen's University, Kingston, Ontario, Canada. radiation incident in the chamber. The temperature of the fluid in the absorber serves to regulate the interior temperature of the calorimeter. Heat extraction (or addition, and interior temperature control is primarily accomplished through the calorimeter flow loop. Within the calorimeter, conditioned fluid is added to the internal circulating loop. This loop consists of an air-to-fluid heat exchanger, the solar absorber plate, and a circulation pump. 3

Test Procedure The instantaneous energy flow rate through the window, Q net, is known to be the difference between the gain due to incident solar radiation, G, and the heat loss due to the air-to-air temperature difference, ΔT = (T i T o (Figure 2. Therefore Q net = SHGC G A U ΔT A (1 Here, U represents the windows overall heat transfer coefficient or U-factor at the time of testing, and A is the projected area of the window. SHGC is the Solar Heat Gain Coefficient, and is given by the equation SHGC = τ + Nα (2 where τ and α are the transmissivity and absorptivity of the window, and N is the Inward-flowing fraction of absorbed solar radiation. For a particular test, G and ΔT will be measured, while Q net is determined through careful metering of the input and output energy flows in the calorimeter Q net = Q flow Qaux + Qwalls + Q (3 mask Q flow, Q aux, Q walls, and Q mask denote: the energy removed by the calorimeter flow loop, the auxiliary electrical power supplied to the calorimeter s internal fans and/or pumps, and heat lost through the walls and mask, respectively. G Solar (Short-Wave Radiation Thermal (Long-Wave Radiation / Convection Gρ g1 Gτ g1 T o 1/h r,o T g1 1/h r,g1_g2 1/h r,i T g2 T i G τ g1 ρ g2 Gτ g1 τ g2 1/h c,o 1/h c,s 1/h i Gα g1 Gα g2 Gα g Gα g Figure 2: Solar and thermal energy transfer in a shaded and unshaded window. Inter-reflection has been omitted for clarity. Terminology is presented in the nomenclature. The SHGC can be determined from a single calorimetric test, performed in the following manner: A calorimetric test is run to determine Q net from Eqn. (2 at a measured environmental condition of G and ΔT. Generally, the indoor air temperature, T i, is controlled to standard NFRC or ASHRAE indoor temperature (21 o C [10], while the outdoor air temperature, T o, is determined by the outdoor temperature at the time of testing. With a value of U predicted via external means, SHGC can be found using Eqn. (1. Of paramount importance to this procedure, is accuracy of the predicted U-factor. One option is to perform a second test at night. By this approach, the term SHGC G = 0 in Eqn. (1, and the window U- factor can be solved directly. In following this method, it is customary to "correct" the measured U-factor to account for differences in the indoor and outdoor air-film coefficients that occurred between tests. This correction does not account for changes in the cavity air-film coefficient due to differences in glass temperatures. Assuming that the air-film coefficients are measured on both the exterior and interior sides of the window, the correction is made using the equation 1 1 1 1 1 U = U ( 1 adj = U x + hi, act hi, x + ho, act h (4 o, x Here, h i and h o are the indoor and outdoor air-film coefficients, respectively. The subscript adj refers to the approximation to actual conditions experienced during the daytime test, while the subscript x refers to the conditions during the nighttime test. An alternative option is to find U using window analysis software [2, 3]. The calorimeter operator can model the window; including the measured test conditions. 4

Alternatively, the operator can use standard test conditions in the model, and correct the results after the calorimetric test using Eqn. (4, where the subscript x would denote the standard air-film coefficients. The use of a modeled U-factor is preferred because it is far easier to implement. The operator, however, runs the risk that the model, for whatever reason, may not accurately represent the actual window. As was already noted, the main benefit of this method is that a single test is sufficient to determine the SHGC, thereby allowing the calorimeter operator to run several tests over the course of a test day. Since test days are only available when the weather permits, the method could offer a serious potential advantage when time is a consideration. The method is limited, however, by its dependence on an external means of calculating U. Incorrect measurement of the indoor and/or outdoor air-film coefficients, or even the failure to correct the U-factor, provides a significant opportunity to introduce error into the data analysis. It is the ultimate purpose of this paper to discuss the proper measurement and correction procedures, and to quantify the effects of errors introduced into the experimental method via the indoor and outdoor air-film coefficients. METHODOLOGY Calorimeter designs, test specimens, and the conditions under which a test occurs all contribute to making each situation unique. Real results are highly dependent on the situation at hand. As such, it would be difficult to quantify calculation error in an all-inclusive way. It is more useful, rather, to pick a limited number of realistic test situations and demonstrate the progression and impact of error. This investigation is based on a typical calorimeter, operating on a typical test day, testing a typical specimen. Additionally, the intent is not to perform an uncertainty analysis of calorimetric data. Those uncertainties are well documented for specific calorimeters and calorimetric procedures. The intent is only to examine the potential errors caused due to poor or inaccurate measurement of the indoor and outdoor air-film coefficients. The impact of errors in the air-film coefficients on the calculated U-factor and SHGC is examined, followed by a discussion of the ways in which those errors are likely to be introduced. The center-of-glass region of a double glazed window will be examined for two representative test situations. The sample window is composed of two 3.05 mm clear lites (ε = 0.84, τ = 0.83, k = 0.9 W/m K separated by a 12.7 mm air gap. The test situations are indicative of both a warm weather (T o = 35 o C and cold weather (T o = 5 o C calorimetric test conducted in full sunlight (G = 500 W/m 2. The inside condition in both cases is T i = 21 o C. Table 1 presents the test conditions encountered during the two typical test periods, for a range of indoor and outdoor air-film coefficients. Results were produced using the window analysis software VISION [3], which allows the user to manipulate window properties and construction, temperature and air-film coefficients, and irradiation levels. It is assumed that VISION produces accurate results, and a calorimetric test performed under identical conditions would result in the same U-factor and SHGC results. The actual U-value and SHGC are denoted and SHGC act for the given set of conditions. g1 and g2 refer to the outdoor and indoor glass, respectively. A few points are noted concerning Table 1. The U-factor changes largely due to changes in the indoor and outdoor air-film coefficients. However, as the indoor and outdoor glass temperatures also change, so does the air-film coefficient for the glazing cavity. It is this difference in temperatures that accounts for the differing U-factors between Cases 1 and 2. It is further noted that the absorbed solar energy in each glazing (Gα does not change. G is constant and the radiative properties of the glass are assumed constant for the range of conditions examined. Therefore, the change in the SHGC is not due to the level of transmitted solar radiation, but rather due to the absorbed solar radiation that enters the room by convection and thermal radiation (i.e., the inward-flowing fraction, N. 5

Table 1: Window performance as predicted by the VISION software [3] for various values of the air-film coefficient. Case 1: T i = 21 C, T o = 5 C, G = 500 W/m 2 h o h i T g1 T g2 (W/m 2 K (W/m 2 K (C (C (W/m 2 K (W/m 2 (W/m 2 (W/m 2 K SHGC act 5_8 5 8 19.6 23.0 6.23 52.9 35.8 2.03 0.79 8_8 8 8 15.7 21.4 6.10 52.9 35.8 2.38 0.78 10_8 10 8 14.1 20.7 6.05 52.9 35.8 2.52 0.77 15_8 15 8 11.6 19.7 5.97 52.9 35.8 2.73 0.76 20_8 20 8 10.2 19.1 5.93 52.9 35.8 2.85 0.76 25_8 25 8 9.3 18.8 5.89 52.9 35.8 2.93 0.75 30_8 30 8 8.6 18.5 5.87 52.9 35.8 2.98 0.75 35_8 35 8 8.1 18.3 5.86 52.9 35.8 3.02 0.75 40_8 40 8 7.8 18.2 5.85 52.9 35.8 3.05 0.75 30_5 30 5 8.5 17.8 5.86 52.9 35.8 2.43 0.74 30_8 30 8 8.6 18.5 5.87 52.9 35.8 2.98 0.75 30_10 30 10 8.7 18.8 5.88 52.9 35.8 3.23 0.75 30_15 30 15 8.8 19.4 5.91 52.9 35.8 3.62 0.76 30_20 30 20 8.8 19.7 5.91 52.9 35.8 3.86 0.77 30_25 30 25 8.9 19.9 5.92 52.9 35.8 4.02 0.77 30_30 30 30 8.9 20.1 5.92 52.9 35.8 4.13 0.77 30_35 30 35 8.9 20.2 5.93 52.9 35.8 4.21 0.77 30_40 30 40 8.9 20.3 5.94 52.9 35.8 4.28 0.77 h o h i h c Gα g1 Case 2: T i = 21 C, T o = 30 C, G = 500 W/m 2 T g1 T g2 (W/m 2 K (W/m 2 K (C (C (W/m 2 K (W/m 2 (W/m 2 (W/m 2 K SHGC act 5_8 5 8 34.3 29.4 6.76 52.9 35.8 2.09 0.79 8_8 8 8 33.2 28.9 6.73 52.9 35.8 2.47 0.78 10_8 10 8 32.7 28.7 6.70 52.9 35.8 2.63 0.77 15_8 15 8 32.0 28.4 6.68 52.9 35.8 2.87 0.76 20_8 20 8 31.6 28.2 6.66 52.9 35.8 3.01 0.76 25_8 25 8 31.3 28.1 6.65 52.9 35.8 3.10 0.75 30_8 30 8 31.1 28.0 6.75 52.9 35.8 3.17 0.75 35_8 35 8 31.0 27.9 6.64 52.9 35.8 3.22 0.75 40_8 40 8 30.8 27.9 6.63 52.9 35.8 3.25 0.75 30_5 30 5 31.5 30.0 6.70 52.9 35.8 2.57 0.74 30_8 30 8 31.1 28.0 6.75 52.9 35.8 3.17 0.75 30_10 30 10 30.9 27.1 6.61 52.9 35.8 3.43 0.75 30_15 30 15 30.7 25.5 6.57 52.9 35.8 3.86 0.76 30_20 30 20 30.5 24.6 6.55 52.9 35.8 4.12 0.77 30_25 30 25 30.4 24.0 6.52 52.9 35.8 4.29 0.77 30_30 30 30 30.4 23.6 6.51 52.9 35.8 4.41 0.77 30_35 30 35 30.3 23.3 6.51 52.9 35.8 4.50 0.77 30_40 30 40 30.3 23.0 6.50 52.9 35.8 4.57 0.77 ANALYSIS AND DISCUSSION An examination of the errors in U and SHGC resulting from errors between the actual and expected air-film coefficients is performed. In performing this examination, the calorimeter operator has assumed that the indoor and outdoor air-film coefficients are 8 and 30 W/m 2 K, respectively. Under those circumstances, the U-values expected by the operator, U 30_8, would be 2.98 and 3.17 W/m 2 K for Cases 1 and 2, respectively. i.e., U 30_8 = at h o = 30 W/m 2 K and h i =8 W/m 2 K. For the time being, a discussion of the situations under which those film coefficients may be in error is omitted. It is easy to examine the error in the U-factor resulting from incorrect air-film coefficients. The percent error in the U-value used, U error, would be U 30 _ 8 U act U error = *100 (5 U act h c Gα g1 Gα g2 Gα g2 6

where is the actual U-factor that would have occurred at the time of testing, and U 30_8 is the U-factor for the conditions assumed by the operator. The error in the calculated SHGC cannot be determined in the same manner as U error. Referring to Figure 3 and Table 1, the actual heat flux measured by the calorimeter operator during a test would be Qnet = SHGC act G U act ( Ti To (6 A The operator, however, would have been using this value of Q net with the assumed value of U 30_8 to determine the SHGC. Therefore Qnet + U 30 _ 8 ( Ti To SHGC A meas = (7 G Here, SHGC meas is the SHGC resulting from the operators analysis for a particular test. Three errors can now be presented based on this result. The error between the calculated and actual SHGC, directly resulting from the operators assumption, is given by SHGCmeas SHGCact SHGCerror, oper = *100 (8 SHGCact The second and third errors are due to the fact that SHGCs should be presented at standard conditions. Referring again to Table 1, h o = 30 W/m 2 K and h i = 8 W/m 2 K are close to the standard conditions, and therefore the correct SHGC is approximately 0.75 for both cases. The error inherent in testing "offstandard", for this window, can be defined as SHGC act 0.75 SHGC error, test = *100 (9 0.75 Similarly, the error between the calculated SHGC and standard value is given by SHGC meas 0.75 SHGC = *100 (10 error, total 0.75 The results of this analysis can been seen in Table 2. Figure 3 presents the error in the U-factor calculation as a function of changing air-film coefficient. Considering the outdoor air-film coefficients, the greatest potential for error is when h o is small. On a windless day. h o may drop to between 5 and 10 W/m 2 K. For this window, that results in a U error approaching 50%. Conversely, strong winds, and higher air-film coefficients, do not significantly change the outdoor air-film coefficient or the resultant U-factor. For a windy condition, 30 W/m 2 K corresponds to a wind speed of approximately 6 m/s (21.6 km/h. To reach 40 W/m 2 K, the wind speed would have to increase to 9 m/s (32.4 km/h. In fact, by inspection of Table 2, if the actual air-film coefficient was 10 W/m 2 K larger than the value of 30 W/m 2 K used assumed by the operator, s/he would still be within 3% of the actual U-factor. As the indoor environment of the calorimeter is relatively still, small variations between the expected and actual air-film coefficient will result in serious inaccuracies in data results. In reality, h i is strongly affected not only by air motion, but also by calorimeter tilt and the temperature of the absorber panel, and is not likely to be 8 W/m 2 K even if the air is still. In both of the example cases presented in Table 2, underestimating the indoor air-film coefficient by as few as 2 W/m 2 K has resulted in a value of U error of almost 10%. It is noted that ASTM C16.30.410 [7] will require calorimeter operators to measure the indoor air-film coefficient for a particular calorimeter. Neither of these results is surprising. It is well understood that changes in the air-film coefficients have the greatest affect on the U-factor when the air-film coefficients are small (Figure 4. This effect has long been recognized by calorimeter operators when considering the outdoor air-film coefficient. In the authors experience, calorimeter operators are not likely to operate on still days. The errors introduced into the data are simply too difficult to correct with any certainty. In light of this statement, it is ironic that many laboratories do not correct for the indoor air-film coefficient. In fact, many laboratories operate on 7

the premise that h i = 8 W/m 2 K (i.e., natural convection. While the measures introduced in ASTM C16.30.410 [7] will provide a better indication of the actual air-film coefficient, they cannot correct for the large variability inherent in the test situation. A far better solution, in the authors opinion, is to introduce and account for significant air motion inside the calorimeter, thereby moving to a more stable test situation. Table 2: Error in SHGC due to inaccurate U-factor calculation and testing off-standard conditions. The conditions of each case have been presented in Table 1. Case 1: T i = 21 C, T o = 5 C, G = 500 W/m 2 U 30_8 (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.03 2.98 46.8% 0.79 0.82 3.8% 5.3% 9.4% 8_8 2.38 2.98 25.2% 0.78 0.80 2.5% 4.0% 6.6% 10_8 2.52 2.98 18.3% 0.77 0.78 1.9% 2.7% 4.6% 15_8 2.73 2.98 9.2% 0.76 0.77 1.1% 1.3% 2.4% 20_8 2.85 2.98 4.6% 0.76 0.76 0.5% 1.3% 1.9% 25_8 2.93 2.98 1.7% 0.75 0.75 0.2% 0.0% 0.2% 30_8 2.98 2.98 0.0% 0.75 0.75 0.0% 0.0% 0.0% 35_8 3.02 2.98-1.3% 0.75 0.75-0.2% 0.0% -0.2% 40_8 3.05 2.98-2.3% 0.75 0.75-0.3% 0.0% -0.3% 30_5 2.43 2.98 22.6% 0.74 0.76 2.4% -1.3% 1.0% 30_8 2.98 2.98 0.0% 0.75 0.75 0.0% 0.0% 0.0% 30_10 3.23 2.98-7.7% 0.75 0.74-1.1% 0.0% -1.1% 30_15 3.62 2.98-17.7% 0.76 0.74-2.7% 1.3% -1.4% 30_20 3.86 2.98-22.8% 0.77 0.74-3.7% 2.7% -1.1% 30_25 4.02 2.98-25.9% 0.77 0.74-4.3% 2.7% -1.8% 30_30 4.13 2.98-27.8% 0.77 0.73-4.8% 2.7% -2.2% 30_35 4.21 2.98-29.2% 0.77 0.73-5.1% 2.7% -2.6% 30_40 4.28 2.98-30.4% 0.77 0.73-5.4% 2.7% -2.9% U 30_8 Case 2: T i = 21 C, T o = 30 C, G = 500 W/m 2 (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.09 3.17 51.7% 0.79 0.77-2.5% 5.3% 2.7% 8_8 2.47 3.17 28.3% 0.78 0.77-1.6% 4.0% 2.3% 10_8 2.63 3.17 20.5% 0.77 0.76-1.3% 2.7% 1.4% 15_8 2.87 3.17 10.5% 0.76 0.75-0.7% 1.3% 0.6% 20_8 3.01 3.17 5.3% 0.76 0.76-0.4% 1.3% 0.9% 25_8 3.10 3.17 2.3% 0.75 0.75-0.2% 0.0% -0.2% 30_8 3.17 3.17 0.0% 0.75 0.75 0.0% 0.0% 0.0% 35_8 3.22 3.17-1.6% 0.75 0.75 0.1% 0.0% 0.1% 40_8 3.25 3.17-2.5% 0.75 0.75 0.2% 0.0% 0.2% 30_5 2.57 3.17 23.3% 0.74 0.73-1.5% -1.3% -2.8% 30_8 3.17 3.17 0.0% 0.75 0.75 0.0% 0.0% 0.0% 30_10 3.43 3.17-7.6% 0.75 0.75 0.6% 0.0% 0.6% 30_15 3.86 3.17-17.9% 0.76 0.77 1.6% 1.3% 3.0% 30_20 4.12 3.17-23.1% 0.77 0.79 2.2% 2.7% 4.9% 30_25 4.29 3.17-26.1% 0.77 0.79 2.6% 2.7% 5.4% 30_30 4.41 3.17-28.1% 0.77 0.79 2.9% 2.7% 5.6% 30_35 4.50 3.17-29.6% 0.77 0.79 3.1% 2.7% 5.9% 30_40 4.57 3.17-30.6% 0.77 0.80 3.3% 2.7% 6.0% 8

60.0% 50.0% 40.0% 30.0% 20.0% U error (% 10.0% 0.0% 0 5 10 15 20 25 30 35 40 45-10.0% -20.0% -30.0% -40.0% Case 1: ho = hact Case 1: hi = hact Case 2: ho = hact Case 2: hi = hact h act (W/m 2 K Figure 3: U error as a function of differences between the actual and expected air-film coefficient for the given test cases. How U error translates to error in the calculated SHGC is also given in Table 2. An important characteristic of the results is that the errors associated with inaccurate measurement of the air-film coefficient are of the same magnitude as those caused by measuring off-standard conditions. Unfortunately, testing off-standard is not something that is easily corrected by the calorimeter operator. As was previously stated, a better solution is to simply avoid extreme situations where the errors are largest. For the given test cases, avoiding these extremes will reduce calculation errors to less than 3% in all cases. An unexpected result is how the errors offset one another in a predictable way. For Case 1, when T i > T o, errors due to h i offset off-standard measurement error. Similarly, for Case 2, T o > T i and errors due to h o offset off-standard measurement error. On one hand, a reduction in the indoor air-film coefficient, or increase in the outdoor air-film coefficient result in a reduction of the inward-flowing fraction and the SHGC. The effect that these changes have on the air-film coefficient, combined with the direction of heat flow, are similarly predictable. The operator is cautioned, however, against using this to reduce errors. It is uncertain if the relative errors will evenly offset for a different window. Many calorimeter operators do attempt to correct the measured values to account for differences in the air-film coefficient using Eqn. (4, and the measured or estimated air-film coefficients that occurred at the time of testing. This correction, however, does nothing to account for changes in the heat transfer coefficient of the glazing cavity (due to glass temperatures or due to testing off-standard conditions. By adjusting U 30_8 using Eqn. (4, and recalculating the analysis of Eqns (7 thru (12, Table 3 can be reformulated to examine the quality of this correction. After correction, operator error is significantly reduced. As a worst case, a still day, the projected U-factor error is only -1.9%. Of greater importance is the resulting error in the operators calculation. For all the cases presented, the error introduced by the operator is less than 0.2%. Unfortunately, correcting the U-factor does not account for testing at off-standard conditions. In some cases, the total error is actually increased because the offsetting of errors has been eliminated. 9

Table 3: Error in SHGC after standard U-factor correction due to changes in the cavity heat transfer coefficient and testing off-standard conditions. The conditions of each case have been presented in Table 1. Case 1: T i = 21 C, T o = 5 C, G = 500 W/m 2 U adj (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.03 1.99-1.9% 0.79 0.79-0.2% 5.3% 5.2% 8_8 2.38 2.34-1.7% 0.78 0.78-0.2% 4.0% 3.8% 10_8 2.52 2.49-1.3% 0.77 0.77-0.1% 2.7% 2.5% 15_8 2.73 2.71-0.7% 0.76 0.76-0.1% 1.3% 1.3% 20_8 2.85 2.84-0.4% 0.76 0.76 0.0% 1.3% 1.3% 25_8 2.93 2.92-0.3% 0.75 0.75 0.0% 0.0% 0.0% 30_8 2.98 2.98 0.0% 0.75 0.75 0.0% 0.0% 0.0% 35_8 3.02 3.02 0.1% 0.75 0.75 0.0% 0.0% 0.0% 40_8 3.05 3.06 0.2% 0.75 0.75 0.0% 0.0% 0.0% 30_5 2.43 2.44 0.2% 0.74 0.74 0.0% -1.3% -1.3% 30_8 2.98 2.98 0.0% 0.75 0.75 0.0% 0.0% 0.0% 30_10 3.23 3.22-0.3% 0.75 0.75 0.0% 0.0% 0.0% 30_15 3.62 3.61-0.4% 0.76 0.76-0.1% 1.3% 1.3% 30_20 3.86 3.84-0.6% 0.77 0.77-0.1% 2.7% 2.6% 30_25 4.02 3.99-0.7% 0.77 0.77-0.1% 2.7% 2.5% 30_30 4.13 4.10-0.7% 0.77 0.77-0.1% 2.7% 2.5% 30_35 4.21 4.18-0.7% 0.77 0.77-0.1% 2.7% 2.5% 30_40 4.28 4.25-0.8% 0.77 0.77-0.1% 2.7% 2.5% U adj Case 2: T i = 21 C, T o = 30 C, G = 500 W/m 2 (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.09 2.07-0.8% 0.79 0.79 0.0% 5.3% 5.4% 8_8 2.47 2.46-0.6% 0.78 0.78 0.0% 4.0% 4.0% 10_8 2.63 2.62-0.5% 0.77 0.77 0.0% 2.7% 2.7% 15_8 2.87 2.87-0.1% 0.76 0.76 0.0% 1.3% 1.3% 20_8 3.01 3.01 0.0% 0.76 0.76 0.0% 1.3% 1.3% 25_8 3.10 3.10 0.1% 0.75 0.75 0.0% 0.0% 0.0% 30_8 3.17 3.17 0.0% 0.75 0.75 0.0% 0.0% 0.0% 35_8 3.22 3.22 0.0% 0.75 0.75 0.0% 0.0% 0.0% 40_8 3.25 3.26 0.2% 0.75 0.75 0.0% 0.0% 0.0% 30_5 2.57 2.56-0.3% 0.74 0.74 0.0% -1.3% -1.3% 30_8 3.17 3.17 0.0% 0.75 0.75 0.0% 0.0% 0.0% 30_10 3.43 3.44 0.4% 0.75 0.75 0.0% 0.0% 0.0% 30_15 3.86 3.89 0.8% 0.76 0.76-0.1% 1.3% 1.3% 30_20 4.12 4.16 0.9% 0.77 0.77-0.1% 2.7% 2.6% 30_25 4.29 4.34 1.1% 0.77 0.77-0.1% 2.7% 2.5% 30_30 4.41 4.47 1.3% 0.77 0.77-0.1% 2.7% 2.5% 30_35 4.50 4.57 1.5% 0.77 0.77-0.2% 2.7% 2.5% 30_40 4.57 4.64 1.6% 0.77 0.77-0.2% 2.7% 2.5% It has also been mentioned that it is common for calorimeter operators to determine the U-factor by a second night time test. Assuming that air motion and temperature conditions do not change, the only difference would be the lack of absorbed solar radiation in each glazing of the window. To examine the effects of this, each of the situations presented in Table 1 have been remodeled using VISION [3] with G set to 0 W/m 2. Using the resulting U-factors, Table 3 has been reproduced and presented as Table 4. Using the night time U-factor does not introduce any significant error by virtue of differences in the level of irradiation. At worst, only -1.9% error exists between the actual and night time value. This small difference has a negligible effect on the resulting SHGC calculation. Night time determination of the U- factor, however, still does not account for testing at off-standard conditions. Further, it is rare that both temperature and air motion characteristics will remain constant between the day time and night time tests. This analysis does not attempt to gage those compounding factors. It is expected that while the night time measurement of U-factor can be corrected for differences in the air-film coefficients, the same cannot be 10

easily done for changes in temperature. Examination of Table 4, however, shows there is less than a 1% increase in the actual U-factors between Cases 1 and 2, despite a 25 o C increase in the ambient temperature. Since it has already been established that 1% error in the actual and expected U-factors translate to a negligible error in the calculated SHGC, and a 25 o C change in temperature is extreme, then slight changes in temperature are likely not a significant problem. The operator is cautioned, however, that there is no easy way to gage the magnitude of this error for other windows without performing some models. This being the case, s/he is better off resorting to a modeled U-factor, and not bothering with a night time test at all. Table 4: Error in SHGC using night time test to determine the U-factor. The conditions of each case have been presented in Table 1. Case 1: T i = 21 C, T o = 5 C, G = 500 W/m 2 U night (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.03 1.99-2.0% 0.79 0.79-0.2% 5.3% 5.2% 8_8 2.38 2.34-1.7% 0.78 0.78-0.2% 4.0% 3.8% 10_8 2.52 2.48-1.6% 0.77 0.77-0.2% 2.7% 2.5% 15_8 2.73 2.69-1.5% 0.76 0.76-0.2% 1.3% 1.2% 20_8 2.85 2.81-1.4% 0.76 0.76-0.2% 1.3% 1.2% 25_8 2.93 2.89-1.4% 0.75 0.75-0.2% 0.0% -0.2% 30_8 2.98 2.95-1.0% 0.75 0.75-0.1% 0.0% -0.1% 35_8 3.02 2.99-1.0% 0.75 0.75-0.1% 0.0% -0.1% 40_8 3.05 3.02-1.0% 0.75 0.75-0.1% 0.0% -0.1% 30_5 2.43 2.40-1.2% 0.74 0.74-0.1% -1.3% -1.5% 30_8 2.98 2.95-1.0% 0.75 0.75-0.1% 0.0% -0.1% 30_10 3.23 3.19-1.2% 0.75 0.75-0.2% 0.0% -0.2% 30_15 3.62 3.58-1.1% 0.76 0.76-0.2% 1.3% 1.2% 30_20 3.86 3.82-1.0% 0.77 0.77-0.2% 2.7% 2.5% 30_25 4.02 3.98-1.0% 0.77 0.77-0.2% 2.7% 2.5% 30_30 4.13 4.10-0.7% 0.77 0.77-0.1% 2.7% 2.5% 30_35 4.21 4.18-0.7% 0.77 0.77-0.1% 2.7% 2.5% 30_40 4.28 4.25-0.7% 0.77 0.77-0.1% 2.7% 2.5% U night Case 2: T i = 21 C, T o = 30 C, G = 500 W/m 2 (W/m 2 K (W/m 2 K U error SHGC act SHGC meas SHGC error,oper SHGC error,test SHGC error,total 5_8 2.09 2.05-1.9% 0.79 0.79 0.1% 5.3% 5.4% 8_8 2.47 2.43-1.6% 0.78 0.78 0.1% 4.0% 4.1% 10_8 2.63 2.59-1.5% 0.77 0.77 0.1% 2.7% 2.8% 15_8 2.87 2.83-1.4% 0.76 0.76 0.1% 1.3% 1.4% 20_8 3.01 2.98-1.0% 0.76 0.76 0.1% 1.3% 1.4% 25_8 3.10 3.07-1.0% 0.75 0.75 0.1% 0.0% 0.1% 30_8 3.17 3.14-0.9% 0.75 0.75 0.1% 0.0% 0.1% 35_8 3.22 3.18-1.2% 0.75 0.75 0.1% 0.0% 0.1% 40_8 3.25 3.22-0.9% 0.75 0.75 0.1% 0.0% 0.1% 30_5 2.57 2.54-1.2% 0.74 0.74 0.1% -1.3% -1.3% 30_8 3.17 3.14-0.9% 0.75 0.75 0.1% 0.0% 0.1% 30_10 3.43 3.40-0.9% 0.75 0.75 0.1% 0.0% 0.1% 30_15 3.86 3.83-0.8% 0.76 0.76 0.1% 1.3% 1.4% 30_20 4.12 4.08-1.0% 0.77 0.77 0.1% 2.7% 2.8% 30_25 4.29 4.25-0.9% 0.77 0.77 0.1% 2.7% 2.8% 30_30 4.41 4.37-0.9% 0.77 0.77 0.1% 2.7% 2.8% 30_35 4.50 4.46-0.9% 0.77 0.77 0.1% 2.7% 2.8% 30_40 4.57 4.53-0.9% 0.77 0.77 0.1% 2.7% 2.8% 11

Two approaches are suggested to mitigate errors caused by testing at off-standard conditions. First, avoid testing at extreme conditions. No tests should be performed, for example, on a still day. For the given test gases, this would result in a maximum error of about 3% in the SHGC. Second, the operator should acknowledge the conditions of the test, and model the window using both standard and test conditions to gage the error. As long as the window model, performed using air-film coefficients measured during the test, agrees with test results, a reliable approximation of standard SHGC can be presented. Both of these measures assume that the operator performs a correction of the U-factor used in his/her data reduction. Air-Film Coefficient Measurement Having examined the progression of error from the air-film coefficients to the calculated values of U-factor and SHGC, it is now useful to focus on the methods of measuring these air-film coefficients. The preceding discussion has assumed that that both the indoor and outdoor coefficients can be measured, and corrections made. In the case of the outdoor air-film coefficient, h o, ASTM Standard 16.30.410 [7] suggests that calorimeter operators install a sol-air heat coefficient meter. The meter is simply a blackened plate with an insulated back that sits in the plane of the window specimen. Measurement of the plate temperature, air temperature and irradiation, allows the sol-air heat transfer coefficient to be estimated using 4 4 Gα p ( Tp Tsurr ho, p = = hconv, o + ε pσ (11 ( Tp To ( Tp To where T p and T surr are the plate and surroundings temperatures, respectively. α p and ε p are the plate absorptivity and emissivity: both approximately 0.9. h conv,o is the convective part of the outdoor air-film coefficient. Potential problems may arise due to the application of this data. As per ASTM Standard 16.30.410 [7], it is assumed that ε g ε p and T g1 T p, and therefore, h o,p h o,g1. While the assumption of similar emissivities is likely good, the outdoor glass and plate temperatures will be significantly different. In reality, the heat coefficient at the window would be different. However, it is suggested that the following correction factor be applied to the sol-air heat meter measurement. 4 4 4 4 ( Tp Tsurr ( Tg1 Tsurr ho, g1 = ho, p ε pσ + ε g1σ (15 ( Tp To ( Tg1 To Where the operator should estimate the surrounding temperature using an equation similar to that presented by Swinbank [11]. The determination of the indoor air-film coefficients is accomplished using a Calibration Transfer Standard (CTS [12]. This consists of a window specimen constructed using foam insulation as a core. Thermocouple sensors are placed in coincident locations on either side of the core, under the glass, to measure the temperature drop across the foam core. With knowledge of the foam core s thermal conductivity, and by inducing a temperature gradient across it, interior and exterior heat transfer coefficients, and heat flux, Q CTS, through the core can be determined from Q CTS = ACTS Ccor ( T g 2 T g1 (16 where C cor is the conductance of the polystyrene core and A CTS is the profile area of the calibration specimen. T' g2, T' g1 are the interior and exterior surface temperatures of the specimen core, respectively. The surface temperatures of the glass is then determined by Ccor T g 2 = T g 2 + ( T g 2 T g1 (17 C g 2 Ccor T g1 = T g1 ( T g 2 T g1 (18 C g1 Finally, the indoor air-film coefficient is found using 12

Q CTS i ( T T A i g 2 For solar calorimetric testing, determining h i is important. With the CTS installed in place of the window, ASTM Standard 16.30.410 [7] specifies that h i be determined at three unspecified tilt angles at T i = 24 o C and T o = 32 o C. This procedure, however, cannot fully account for the air-film coefficients that may exist at the time of testing. The calibration test is performed in the absence of solar radiation, and therefore, very little energy enters the calorimeter when compared to an actual test situation. Because the absorber panel is used to control the interior temperature, it will almost certainly be run at warmer temperatures than those used during the CTS calibration test, and therefore, the radiative portion of the air-film coefficient will be affected. From the authors experience, the absorber temperature may be anywhere from 15 to 20 o C, depending on the calorimeter, specimen, and test conditions. The effect of calorimeter tilt is specific to the calorimeter, and cannot be quantified here. By inspection, however, increasing tilt is known to cause a reduction in the convective portion of the internal air-film coefficient. In the past, calorimeter operators have recognized this problem, and generally do not tilt test specimens more than 60 o from vertical [13]. Performing the calibration at 3 tilt angles, from 0 to 60 o, is likely sufficient. CONCLUSIONS It has been demonstrated that in addition to the careful and accurate correction of indoor and outdoor air-film coefficients, a knowledgeable calorimeter operator is important. In the preceding analysis, common test situations have been introduced that could significantly impact the accuracy of the test results. Of importance: Only large errors between the actual and expected U-factors result in significant error in the resulting SHGC calculation. e.g.,u error on the order of 20% or greater will result in SHGC error,oper of 4% and greater, depending on the situation. Large errors in the U-factor are incurred when testing under still-air conditions. It is recommended that tests never be run when the outdoor condition is still, and that precautions be taken so that air motion is induced in the calorimeter interior. If the operator corrects the results for the air-film coefficients that occurred at the time of testing, the SHGC results can be very accurate. However, it is noted that testing off-standard conditions may not result in the same SHGC that would be found during testing on-standard conditions. Determining U from software, is far better than using a separate night time test. The night time test takes more time, and will likely introduce it's own inaccuracies to the data analysis. By keeping these points in mind, the calorimeter operator should be capable of avoiding test situations that would result in errant results. The sol-air heat coefficient meter, specified in ASTM Standard 16.30.410 [7], does a good job of measuring the exterior air-film coefficient. However, a more detailed correction equation was presented that would further improve its usefulness. A CTS is specified in ASTM Standard 16.30.410 [7] to characterize the interior air-film coefficient during the commissioning of the calorimeter. A potential flaw was noted in this procedure in that the absorber plate would be much colder during an actual test, than it would be during the CTS calibration. As such, radiative heat transfer may have an unexpected impact on the data reduction. REFERENCES [1] Apte, J., Arasteh, D., and Huang, J., "Future Advanced Windows for Zero-Energy Homes", ASHRAE Transactions, Vol. 109 (2, 2003 [2] "Window 4.1, A PC Program for Analyzing Window Thermal Performance", Windows and Daylighting Group, Lawrence Berkeley Laboratory, University of California, 1988. CTS = h (19 13

[3] Wright, J.L., "Glazing System Thermal Analysis", CANMET, Advanced Glazing System Laboratory, VISION3, Minister of Supply and Services Canada, University of Waterloo, 1992. [4] ASTM C 1363-97, Standard Test Method for the Thermal Performance of Building Assemblies by Means of a Hot Box. Annual Book of ASTM Standards, 2003 [5] National Fenestration Rating Council, "Procedure for Determining Fenestration Product Solar Heat Gain Coefficients at Normal Incidence" NFRC 200-92, Silver Spring, MD, 1992. [6] ASTM C 236-89, Standard Test Method for Steady-State Thermal Performance of Building Assemblies by Means of a Guarded Hot Box. Annual Book of ASTM Standards, 2003. [7] ASTM C 16.30.410, Standard Test Method for Measuring the Solar Heat Gain Coefficient of Fenestration Systems using Calorimetry Hot Box Methods. ASTM Draft Standard, 2004. [8] Klems, J.H., "Measurement of Fenestration Net Energy Performance: Considerations Leading to Development of the Mobile Window Thermal Test (MoWitt Facility", Transactions of the ASME, Vol. 110, pp. 208-216, 1988. [9] Wouters, P., Vandaele, L., Voit, P. and Fisch, N., "The Use of Outdoor Test Cells for Thermal and Solar Building Research within the PASSYS Project", Building and the Environment, Vol. 28 (2, pp. 107-113, 1993. [10] ASHRAE: Handbook of Fundamentals, American Society of Heating, Refrigeration, and Air Conditioning Engineers, Atlanta, GA, 2001. [11] Swinbank, W.C., "Long-Wave Radiation from Clear Skies", Quarterly Journal of the Royal Meteorological Society, Vol. 89, 1963. [12] Bowen, R. P. "DBR s Approach for Determining the Heat Transmission Characteristics of Windows", Division of Building Research, National Research Council Canada, 1985. [13] Collins, M.R., and Harrison, S.J., "Test of Measured Solar Heat Gain Variation with Respect to Test Specimen Tilt", ASHRAE Transactions, Vol. 107 (1, pp. 691-699, 2001. 14