Comparison between ASHRAE and ISO thermal transmittance calculation methods

Comparison between ASHRAE and ISO thermal transmittance ]. The two approaches, called the ASHRAE and ISO methods, are different 1. Introduction Energy and Buildings 39 (2007 The ability to be able to accurately to predict the energy performance of windows is of great importance to the overall energy performance of buildings. Svendsen et al. [1] showed * Corresponding author. E-mail address: [email protected] (P. Blanusa). 0378-7788/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.enbuild.2006.09.007 region 63.5 mm (2.5 in.) from the glazing/frame sight line. The ISO method assumes that the additional heat transfer due to the existence of the spacer is proportional to the glazing/frame sightline distance that is also proportional to the total glazing spacer length. An example calculation of the overall heat transfer and thermal transmittance (U-value or U-factor) using the two methods for a thermally broken, aluminum framed slider window is presented. The fenestration thermal transmittance calculations analyses presented in this paper show that small differences exist between the calculated thermal transmittance values produced by the ISO and ASHRAE methods. The results also show that the overall thermal transmittance difference between the two methodologies decreases as the total window area (glazing plus frame) increases. Thus, the resulting difference in thermal transmittance values for the two methods is negligible for larger windows. This paper also shows algebraically that the differences between the ISO and ASHRAE methods turn out to be due to the way the corner regions of the window frame and glazing are treated in the assembly of the overall thermal transmittance for a three-dimensional window from the two-dimensional calculations. Three-dimensional heat transfer calculations can be made and correction factors can be applied to both the ASHRAE and ISO two-dimensional results to bring them into agreement with the three-dimensional results. Published by Elsevier B.V. Keywords: ASHRAE; ISO; Frame; Thermal transmittance in the way they treat the effect of the glazing spacer on the heat transf method assumes that the spacer effects both the heat transfer through t er through the frame and the glazing unit near the frame. The ASHRAE he frame and the heat transfer through the glazing in an ‘‘edge-of glass’’ in Europe [ISO 10077-2. Thermal Performance of Windows, Doors a Method for Frames, International Standards Organization, Geneva, 2003 calculation methods Petar Blanusa a,*, William P. Goss b, Hartwig Roth c, Peter Weitzmannn d, Claus F. Jensen e, Svend Svendsen f, Hakim Elmahdy g aCommunity Redevelopment Agency for the City of Los Angeles, 5200 N. Lankershim Blvd, Suite 750, North Hollywood, CA 91601, United States bMechanical and Industrial Engineering Department, University of Massachusetts, Amherst, MA 01003, United States cEngine Development, DaimlerChrysler AG, Stuttgart, Germany dDepartment of Civil Engineering, Technical University of Denmark, Building 118, DK-2800 Kgs. Lyngby, Denmark eBuildDesk International, Hovedgaden 584, DK-2640, Hedehusene, Denmark fDepartment of Civil Engineering, Technical University of Denmark, Lyngby 2800, Denmark g Institute for Research in Construction, National Research Council of Canada, Ottawa, Ontario, Canada K1A OR6 Received 29 April 2006; received in revised form 4 September 2006; accepted 6 September 2006 Abstract The intent of this paper is to describe and compare the two different two-dimensional frame/spacer heat transfer calculation methodologies used in North America (FRAME [EEL. The FRAMEplus Toolkit for Heat Transfer Assessment of Building Components, Version 3.0, Enermodal Engineering, Kichener, Ontario, Canada, 1995], THERM [LBNL. THERM 2: PC Program for Analyzing Two-Dimensional Heat Transfer Through Building Products, LBL-37371, Windows and Delighting Group, Lawrence Berkeley National Laboratory, Berkeley, CA, 1998], ASHRAE SPC 142P [ASHRAE. Standard Method for Determining and Expressing the Heat Transfer and Total Optical Properties of Fenestration Products, Public Review Draft of Standard 142P, American Society of Heating, Refrigerating and Air Conditioning Engineers, Atlanta, 1998]) and nd Shutters–Calculation of Thermal Transmittance—Part 2: Numerical www.elsevier.com/locate/enbuild ) 374–384 d B that for residential buildings in Denmark typical windows have a net energy loss �50 kWh/m2 of unit window area in the heating season. (The energy loss is the net between the window heat loss and the solar heat gain.) The typical window area is about 30% of the residential building floor area in Denmark, this means that 0.30 � �50 kWh/m2 = �15 kWh/m2 energy loss per unit floor area is the extra heating load due to the windows. Since new buildings in Denmark are supposed to have heating loads lower than �50 kWh/m2, windows are already taking up 30% of the allocated overall heat loss. The window thermal performance calculation methods discussed in this paper have the potential of looking at a wide variety of window designs and material properties. Improving the energy performance of windows to the potentially possible range of zero to +15 kWh/m2 (heat gain per unit floor area) has the potential of significantly reducing the overall heating energy loads of residential buildings. Similar comments may apply to windows operating in the cooling season where the solar heat gain through the windows can be significant. ISO 15099 [2] also shows how to evaluate the solar heat gain for fenestration systems, including those with shading devices. The International Organization for Standardization (ISO) has been working on developing fenestration (windows, doors, skylights) thermal transmittance (often called U-factor in North America and U-value in Western Europe) calculation methods since the early 1980s. The initial result was a tabular, hand calculation method that recently became an international standard under the designation ISO 10077-1 [3]. While work on this standard was completed a number of years ago, it was recognized that a tabular listing of all of the possible fenestration product frame, glazing and spacer configurations would be quite extensive to satisfy the wide variety of windows and doors available around the world. Under the leadership of the European Community, CEN (European Committee for Standardization) undertook the documentation of a two- dimensional fenestration product heat transfer calculation procedure for frames/spacers and the glazing region near the frame that could be used in conjunction with ISO 10077-1 [3] to produce the overall thermal transmittance of specific fenestra- tion products. This work resulted in ISO 10077-2 [4]. In North America, during the 1980s and early 1990s, two one-dimensional fenestration glazing thermal transmittance calculation programs, WINDOW [5] in the United States and VISION [6] in Canada were developed. Curcija et al. [7] described and compared the results of the European (which ultimately became ISO 10077-1 [3]) and the North American one-dimensional calculation methods. Subsequently, Canada (FRAME, [8]) and the United States (THERM (LBL, 1998)) developed frame/spacer and nearby glazing region two- dimensional fenestration product heat transfer calculational programs that could be used along with the one-dimensional thermal transmittance calculational programs to determine the overall thermal transmittance of specific fenestration products. In the 1990s first ASHRAE, then ISO, started the development of more general fenestration thermal transmittance calculational standards to document the combined one-dimensional and two- P. Blanusa et al. / Energy an dimensional methods mentioned above. The ISO work was initiated after the ASHRAE work, and as a result, started from an earlier draft of the ASHRAE standard developed by ASHRAE Special Project Committee (SPC) 142 [9]. ISO Technical Committee (TC) 163, Working Group (WG) 2, under the convenorship of Elmahdy [10], with significant input from the CEN member nations, has developed a comprehensive fenestration thermal transmittance and solar heat gain interna- tional standard, ISO 15099 [2]. This standard includes both the one-dimensional thermal calculation methodologies used in the WINDOW [5] and VISION [6] programs and in ISO 10077-1 [3] and the two-dimensional frame/spacer heat transfer calculation methodologies used in the FRAME [8] and THERM [11] programs and in ISO 10077-2 [4]. In addition, more recent work on shading device thermal calculation methods has been included in the ISO 15099 [2] standard. Since many of the North American participants are also active in the ASHRAE SPC 142 work, it is anticipated that the final ASHRAE standard will be quite similar to the ISO standard. The intent of this paper is to describe and compare the two different two-dimensional frame/spacer heat transfer calcula- tion methodologies used in North America (FRAME [8], THERM [11], ASHRAE SPC 142P [9]) and in Europe (ISO 10077-2 [4]). The two approaches, hereafter called the ASHRAE and ISO methods, are different in the way they treat the effect of the glazing spacer on the heat transfer through the frame and the glazing unit near the frame. The ASHRAE method assumes that the spacer effects both the heat transfer through the frame and the heat transfer through the glazing in an ‘‘edge-of glass’’ region 63.5 mm (2.5 in.) from the glazing/frame sight line. This so-called edge-of-glass region is based on a short article [12] that appeared in Glass Digest with little technical substantiation. It should be noted that subsequent research by Carpenter and McGowan [13] and Carpenter and Elmahdy [14] put the ASHRAE method on a firmer technical foundation. More recently, Elmahdy [15], in a study that compared experimental results for 10 different glazing systems showed that 63.5 mm (2.5 in.) gave good results. However, the use of the same edge-of glass region of 63.5 mm (2.5 in.) for all window frame/space designs is questionable. It was shown in Curcija and Goss [16], for a wood framed window, that 100 mm (approximately 4 in.) was more appropriate to include all of the frame/spacer two-dimensional heat transfer effects in the glazing. Example frame/spacer profile calculations in ISO 10077-2 [4] use 190 mm to insure that all of these frame/spacer glazing unit heat transfer effects are captured. The ISO method assumes that the additional heat transfer due to the existence of the spacer is proportional to the glazing/ frame sightline distance that is also proportional to the total glazing spacer length. As a consequence of this assumption, the spacer heat transfer effects are linear based as compared to the area based ASHRAE method. The ISO method is technically based on the ISO building envelope thermal bridge standards [17,21] that recognized the technical elegance of treating two- dimensional building envelope thermal bridges (like floor slabs) as linear heat transfer effects to be added to one- uildings 39 (2007) 374–384 375 dimensional building envelope heat transfer results. The ISO overall thermal transmittance for both the ASHRAE and ISO methods. Blanusa [20] studied in detail a number of frame profiles for an aluminum framed slider window. Using the same range of overall window dimensions specified in Roth [18], Blanusa [20] also showed, for the same boundary conditions and thermal conductivity properties, that the ASHRAE and ISO methods gave different results. The differences ranged from 1.4% for the smaller windows to 0.6% for the larger windows. Blanusa [20] also carried out an analytical comparison of the ASHRAE and ISO overall thermal transmittance calculation assembly methods that will be presented later in this paper. 3. ASHRAE and ISO two-dimensional thermal transmittance calculation methods To show how the two methods calculate the thermal transmittance of a window, Uw, the window schematic shown in Fig. 1, will be used to illustrate the ISO lineal/area weighted method and the ASHRAE area weighted method. The window overall heat transfer will be determined using one of the d Buildings 39 (2007) 374–384 frame/spacer heat transfer calculation method, as developed by CEN in ISO 10077-2 [4] recognized that window spacers were similar to thermal bridge building envelope components. 2. Literature review Roth [18] first recognized that there were differences in the overall window thermal transmittances (U-factors or U-values) obtained using the ASHRAE and ISO methods. Roth [18] studied three different window frame profiles (thermal broken aluminum frame, PVC frame with steel reinforcement, wood frame) specified in ISO 10077-2 [4] with the same insulated glazing unit (IGU). Ten different overall window dimensions were chosen to cover a wide range of possible residential and commercial window sizes for North America and Western Europe. Roth’s [18] calculations gave the unexpected result that the two different methods with the same conditions (cold and warm side temperatures, surface heat transfer coefficients, glazing cavity equivalent thermal conductivity, frame profile thermal conductivities; frame cavity convective and radiative heat transfer coefficients and edge of glass region of 190 mm to capture all of the spacer two-dimensional effects), gave different overall thermal transmittance values. The differences for larger windows were quite small (less than 0.04%) and were greater (3.5% for the aluminum framed window, 3% for the PVC framed window, 2.3% for the wood framed window) for the smaller windows that may exist in true divided light double- hung windows used in North America. Roth [18] also developed the overall radiative heat transfer coefficient for rectangular frame cavities with isothermal ends and re- radiating sides that is currently used in ISO 15099 [2]. Weitzmann et al. [19] subsequently carried out two- and three-dimensional heat transfer calculations for determining overall thermal transmittances of a typical Danish wood window with different overall sizes. Their results also showed that the ASHRAE and ISO methods gave different overall heat transfer and thermal transmittance results with the largest difference (2.2%) occurring for the smallest size (500 mm � 500 mm) window they studied. Weitzmann et al. [19] also showed that for the wood window they studied, the ASHRAE edge of glass region needed to be 150 mm to capture all of the two-dimensional frame/spacer heat transfer effects in the glazing. It should be noted that the above 2.2% difference between the two methods was for the 150 mm edge of glass distance. The 63.5 mm edge of glass distance will normally give a larger percent difference since it usually does not capture all of the two-dimensional frame/spacer heat transfer effects. Weitzmann et al. [19] also showed that by performing three-dimensional frame/spacer corner region heat transfer calculations, point heat loss corrections [the difference between the two-dimensional and three-dimen- sional calculations, (see [17,21] for further details) for the two (ISO and ASHRAE) methods could be determined. These ‘‘point heat loss corrections’’ are the difference between the two-dimensional and three-dimensional heat transfer calcula- tions for a corner region and can be applied as corrections to P. Blanusa et al. / Energy an376 the two-dimensional heat transfer results to give the same thermally broken aluminum framed slider window profiles as described in Blanusa [20]. 4. Defining lengths for the frame and glazing unit In order to simplify the calculations, the projected length, lf, of the frame on the left, right, top, and bottom sides will be assumed to be the same frame profile for both the ASHRAE and ISO method calculations (see Fig. 1). However, the glazing unit is handled differently. In the ISO method the glazing length is lg (see Fig. 1). In the ASHRAE method the glazing length is divided up into center of glass length, lcog, and edge of glass length, leg, (see Fig. 1). Fig. 1. Schematic of analyzed window. Boundary conditions The ISO and ASHRAE winter boundary conditions were both used in the calculations. The boundary conditions consist of: (a) Indoor and outdoor air temperatures (Tin and Tout). (b) Indoor and outdoor overall heat transfer coefficients (hin and hout). ISO boundary conditions The ISO method uses the following boundary conditions (see Tables 1 and 2) on the inside and outside surfaces of the fenestration product. interaction between the frame and the glazing unit (IGU). 6. ASHRAE area weighted method In the ASHRAE method, the glazing unit heat transfer accounts for both one-dimensional center-of-glass and a two- dimensional edge-of-glass contribution. The frame U-value, Uf, ASHRAE includes a contribution that due to the two-dimensional heat transfer effects from having the spacer portion of the IGU inserted in the frame. In contrast to the ISO method, the ASHRAE method does not require two separate calculations. The overall thermal transmittance is obtained directly from the two-dimensional numerical heat transfer calculations similar to P. Blanusa et al. / Energy and B 20 7.69 Table 2 ISO boundary conditions on the outside surface Tout (8C) hout (W/m 2 8C) 0 where kg is the glazing thermal conductivity and keffcav is the gas fill overall (including convection and radiation) thermal con- ductivity. For the frame thermal transmittance, Uf, the insulation panel is inserted into the frame in place of the insulating glazing unit (IGU). Two-dimensional heat-transfer calculations using the THERM [11] program were made to determine the overall Table 1 ISO boundary conditions on the inside surface Tin (8C) hin (W/m 2 8C) ASHRAE boundary conditions Different boundary conditions (see Table 3) are applied to the frame section and glazing sections for the inside surfaces of the fenestration product. The outside surface boundary condition (see Table 4) is the same for both the frame section and glazing section of the fenestration product. 5. ISO lineal/area weighted calculation procedure In order to calculate the overall thermal transmittance (Ut, ISO) for a window with the ISO lineal/area weighted calculation procedure, thermal transmittance values of an insulation panel (Up), the glazing unit (Ug) and the frame (Uf), have to be obtained. The low thermal conductivity panel’s thermal transmittance, Up, is determined from Eq. (1), where the thermal conductivity, lp, of the low thermal conductivity panel is assumed to be 0.04 (W/m K). 1 Up ¼ 1 hC þ tp lp þ 1 hH (1) The glazing unit thermal transmittance, Ug, is obtained from the WINDOW [5] program as shown in Eq. (2). 1 Ug ¼ 1 hC þ 2lg kg þ lcav keffcav þ 1 hH (2) 25 heat-transfer, q, through the panel and frame as shown in Fig. 2. Both ISO and ASHRAE boundary conditions were used in the calculations. The frame thermal transmittance, Uf, can then be determined from Eq. (3) below. Uf ¼ ðq=DTÞ � Uplp lf (3) where DT = Tin � Tout. Next, the two-dimensional heat transfer calculations are repeated with the IGU inserted into the frame. The heat transfer calculations with the IGU in the frame were made using the THERM [11] program. The results, qtotal, ISO, are used to determine the linear thermal transmittance, (cg), which characterizes the additional window heat transfer due to the spacer region of the IGU. The linear thermal transmittance, cg, is determined from Eq. (4): cg ¼ qtotal; ISO DT � Ufðlf � 1Þ � Ugðlg � 1Þ (4) Finally, the total fenestration product thermal transmittance Ut, ISO, is then given by Eq. (5): Ut;ISO ¼ PðAgUgÞ þ PðAfUfÞ þ PðlccgÞ At (5) where Ag and Af are the projected vision and frame areas, respectively, At the total projected window area and lc is the length of the vision area perimeter (often called sightline). The linear thermal transmittance, cg, accounts for the heat transfer Table 3 ASHRAE boundary conditions on the inside surface Aluminum frame Glazing sections Tin (8C) hin (W/m 2 8C) Tin (8C) hin (W/m 2 8C) 21.11 8.29 21.11 7.602 Table 4 ASHRAE boundary conditions on the outside surface Tout (8C) hout (W/m 2 8C) �17.769 28.656 uildings 39 (2007) 374–384 377 those used in the ISO method to determine the linear thermal d B P. Blanusa et al. / Energy an378 transmittance, cg. No heat transfer calculations with an insulation panel in place of the glazing unit (IGU) are required. In the ASHRAE method, the total heat transfer is determined by calculating the separate heat transfer contributions of the center-of-glass, edge-of-glass and frame areas. The center of glass thermal transmittance, Ucog, is the same as Ug in the ISO method if the same boundary conditions are used. The heat transfer, qt, ASHRAE, through the fenestration product is obtained from Eq. (6). qtotal;ASHRAE ¼ Ucogðlcog � 1ÞDT þ Ufðlf � 1ÞDT þ Uegðleg � 1ÞDT (6) After applying both the ASHRAE and ISO boundary conditions, Ucog was calculated by the WINDOW [5] program Fig. 2. Two-dimensional heat transfer isotherm results with an insulation panel. using THERM [11] program output. This is achieved by performing the two-dimensional heat transfer calculations in THERM and then exporting selected files into WINDOW for analysis. The overall thermal transmittance (Ut, ASHRAE) is then calculated by adding the area-weighted U-factors for each contribution: Ut;ASHRAE ¼ P UcogAcog þ P UegAeg þ P UfAf Apf (7) where the subscripts cog, eg, and f refer to the center of glass, edge of glass, and frame, respectively. Apf is the area of the fenestration product’s rough opening in the wall or roof less installation clearances and is assumed to be the same as the ISO method At in Eq. (5). 7. Window area calculations 7.1. ISO area calculations A square window (i.e., W = H B L) was divided up into top (header), bottom (sill) and side (jambs) portions. In order to minimize the algebra, the assumption was made that all the frame lengths are equal (lf,S = lf,T = lf,B B lf). The areas are calculated as follows: Top: Af;T �Wlf;T � 212lf;Slf;T ¼ Wlf � l2f ¼ lfðL� lfÞ (8) Bottom: Af;B �Wlf;B � 212lf;Slf;B ¼ Wlf � l2f ¼ lfðL� lfÞ (9) Side: Af;S �Hlf;S � 12lf;Slf;T � 12lf;Slf;B ¼ Hlf � l2f ¼ lfðL� lfÞ (10) Total frame area: Af �Af;T þ Af;B þ 2Af;S ¼ 4lfðL� lfÞ (11) The area of the visible glazing is given by (see Fig. 1): Ag �ðW � 2lf;SÞðH � lf;T � lf;BÞ ¼ ðW � 2lfÞðH � 2lfÞ ¼ ðL� 2lfÞ2 (12) For the ISO calculation procedure, the perimeter length at the sight line lc is calculated as follows: lc� 2ðW þ HÞ � 8lf ¼ 4ðL� 2lfÞ (13) 7.2. ASHRAE area calculations The ASHRAE method requires dividing the window into top, bottom, side, center of glass, and edge-of-glass areas uildings 39 (2007) 374–384 (see Fig. 1). These areas are calculated as follows using the same assumptions of a square window and equal frame length. Top: Af;T �Wlf;T � 2 12 lf;Slf;T ¼ Wlf � l2f ¼ lfðL� lfÞ (14) Aeog;T �ðW � 2lf;SÞleg � l2eg ¼ ðW � 2lfÞleg � l2eg ¼ legðL� 2lf � legÞ (15) Bottom: Af;B �Wlf;B � 2 12 lf;Slf;B ¼ Wlf;B � l2f ¼ lfðL� lfÞ (16) Aeog;B �ðW � 2lf;SÞleg � l2eg ¼ ðW � 2lfÞleg � l2eg ¼ legðL� 2lf � legÞ (17) Side: Af;S �Hlf;S � 12lf;Slf;T � 12lf;Slf;B ¼ Hlf � l2f ¼ lfðL� lfÞ (18) Aeog;S �ðH � lf;T � lf;BÞleg � l2eg ¼ ðH � 2lfÞleg � l2eg ¼ legðL� 2lf � legÞ (19) Center of glass: Acog �ðW � 2lf;S � 2legÞðH � lf;T � lf;B � 2legÞ ¼ ðL� 2lf � 2legÞ2 (20) Edge of glass: 7.3. Window area calculation results In order to study the influence of the size of windows on the overall thermal transmittance assembly techniques in the ASHRAE and ISO methods, 10 different windows were chosen in order to cover the wide range of possible window designs. The selection of windows was based on the sizes used by Roth [18], and is given in Table 5. The area formulas given previously, before the assumption (H = W B L) was introduced, were in these calculations. 8. Thermal transmittance calculations Calculations were made to determine center of glass thermal transmittance Ucog or Ug. Results are presented in Table 6 for the ISO boundary conditions and in Table 7 for the ASHRAE boundary conditions. The ISO method calculated heat transfer (qtotal, ISO) is equal to the ASHRAE method calculated heat transfer (qtotal, ASHRAE) through the same window section. A summary representing all the necessary input data in order to obtain the overall thermal transmittance (U-factor) is given in Table 8. 9. Comparison of overall U-factor results Using the data in Table 8, the ASHRAE and ISO overall U- factors for the different calculational methods are given in (m) 2 P. Blanusa et al. / Energy and Buildings 39 (2007) 374–384 379 Aeg � 2Aeog;S þ Aeog;T þ Aeog;B ¼ 4legðL� 2lf � legÞ (21) Table 5 Area calculation results for both ISO and ASHRAE methods Number Height (H, mm) Width (W, mm) Aw (m 2) 1 500 500 0.25 2 600 800 0.48 3 1000 800 0.8 4 900 1000 0.9 5 1220 1720 2.1 6 1500 2000 3 7 1500 2500 3.75 8 1500 3000 4.5 9 2000 5000 10 10 3000 7000 21 Table 6 ISO boundary conditions; Ug calculation hout (W/m 2 K) hin (W/m 2 K) Tout (8C) Tin (8C) H (m) W 20 3.6 0 20 0.5 0.5 20 3.6 0 20 0.6 0.8 20 3.6 0 20 1 0.8 20 3.6 0 20 0.9 1 20 3.6 0 20 1.22 1.7 20 3.6 0 20 1.5 2 20 3.6 0 20 1.5 2.5 20 3.6 0 20 1.5 3 20 3.6 0 20 2 5 20 3.6 0 20 3 7 Table 9 for ASHRAE B.C. and Table 10 for ISO B.C. rounded Af (m 2) Ag (m 2) lc (m) Aeg (m 2) Acog (m 2) 0.12 0.13 1.44 0.08 0.05 0.18 0.30 2.24 0.13 0.18 0.23 0.57 3.04 0.18 0.39 0.25 0.65 3.24 0.20 0.46 0.39 1.71 5.32 0.33 1.39 0.47 2.53 6.44 0.40 2.14 0.54 3.21 7.44 0.46 2.75 0.61 3.89 8.44 0.53 3.37 0.96 9.04 13.44 0.85 8.20 1.38 19.62 119.44 1.23 18.40 Aw (m 2) l (cavity) (W/m K) l (glass) (W/m K) c (W/m K) Ug (W/m 2 K) 0.25 0.03 0.9 0.073 1.236 0.48 0.03 0.9 0.155 1.236 0.8 0.03 0.9 0.233 1.236 0.9 0.03 0.9 0.269 1.236 2.0984 0.03 0.9 0.579 1.236 3 0.03 0.9 0.782 1.236 3.75 0.03 0.9 0.970 1.236 4.5 0.03 0.9 1.162 1.236 10 0.03 0.9 2.364 1.236 21 0.03 0.9 4.531 1.236 Table 7 ASHRAE boundary conditions; Ucog calculation hout (W/m 2 K) hin (W/m 2 K) Tout (8C) Tin (8C) H (m) W (m) Aw (m 2) l (cavity) (W/m K) l (glass) (W/m K) c (W/m K) Ucog (W/m 2 K) 28.656 8.29 �17.8 21.1 0.5 0.5 0.25 0.03 0.9 0.051 1.532 28.656 8.29 �17.8 21.1 0.6 0.8 0.48 0.03 0.9 0.124 1.532 28.656 8.29 �17.8 21.1 1 0.8 0.8 0.03 0.9 0.187 1.532 28.656 8.29 �17.8 21.1 0.9 1 0.9 0.03 0.9 0.221 1.532 28.656 8.29 �17.8 21.1 1.22 1.72 2.0984 0.03 0.9 0.497 1.532 28.656 8.29 �17.8 21.1 1.5 2 3 0.03 0.9 0.676 1.532 28.656 8.29 �17.8 21.1 1.5 2.5 3.75 0.03 0.9 0.847 1.532 28.656 8.29 �17.8 21.1 1.5 3 4.5 0.03 0.9 1.021 1.532 28.656 8.29 �17.8 21.1 2 5 10 0.03 0.9 2.103 1.532 28.656 8.29 �17.8 21.1 3 7 21 0.03 0.9 4.053 1.532 ons P. Blanusa et al. / Energy and Buildings 39 (2007) 374–384380 off to four significant figures for comparison purposes. The overall thermal transmittance results given the last two columns in both tables show that there is a difference between the ASHRAE and ISO methods for the set of windows studied here. The ISO overall thermal transmittance, Ut, ISO, gives larger overall U-factor values for both sets of boundary calculations. There is also a difference in the results presented in Tables 9 and 10 when using different boundary conditions with the same calculation method. For example, compare the Ut, ASHRAE column in Table 9 with Ut, ASHRAE column in Table 10. The values in Table 9 for the ASHRAE B.C. give higher U-values than those in Table 10 for the ISO B.C.’s. Similar differences Table 8 Calculated component U-factors for both ISO and ASHRAE boundary conditi Uf, ISO (W/m 2 K) Uf, ASHRAE (W/m 2 K) ASHRAE B.C. 9.1417 9.0610 ISO B.C. 8.4745 8.4400 exist for the Ut, ISO values in the two tables (for the same window number). Both of the above-described differences were first shown by Roth [18]. This difference is to be expected since the ASHRAE overall outside heat transfer coefficient is larger due to the larger outside wind velocity and the ASHRAE overall outside air temperature is lower then the ISO value of Table 9 Overall U-factor using ASHRAE boundary conditions Window number H (m) W (m) Overall U-factors Ut, ASHRAE (W/m2 K) Ut, ISO (W/m2 K) 1 0.5 0.5 5.435 5.492 2 0.6 0.8 4.515 4.567 3 1.0 0.8 3.894 3.937 4 0.9 1.0 3.758 3.800 5 1.22 1.72 3.050 3.081 6 1.5 2.0 2.809 2.835 7 1.5 2.5 2.705 2.730 8 1.5 3.0 2.636 2.660 9 2.0 5.0 2.314 2.332 10 3.0 7.0 2.068 2.080 0 8C. This results in different thermophysical property values on both the outside air stream and the glazing cavities. When the overall U-factor results are rounded off to more realistic two significant figures as shown in Table 11, the difference between the two calculation methods is actually relatively small. The difference also decreases with the increase of the window sizes as the effect of the frame/edge region on the overall U-factor diminishes. The relative percentage difference DU (see Table 12) summarizes the differences in the boundary conditions and shows that using the ISO boundary conditions gives larger differences when compared to using ASHRAE boundary Ucog = Ug (W/m 2 K) Ueg (W/m 2 K) leg (m) lf (m) 1.532 2.2150 0.0635 0.0700 1.23 2.2120 0.0635 0.0700 conditions. The relative difference (DU) in the thermal transmittance calculated as shown in Eq. (22). DUð%Þ ¼ Ut;ASHRAE � Ut;ISO Ut;ASHRAE � 100 (22) Table 10 Overall U-factor using a ISO boundary conditions Window number H (m) W (m) Overall U-factors Ut, ASHRAE (W/m2 K) Ut, ISO (W/m2 K) 1 0.5 0.5 5.070 5.140 2 0.6 0.8 4.175 4.234 3 1.0 0.8 3.566 3.613 4 0.9 1.0 3.432 3.477 5 1.22 1.72 2.735 2.767 6 1.5 2.0 2.496 2.523 7 1.5 2.5 2.394 2.419 8 1.5 3.0 2.326 2.350 9 2.0 5.0 2.007 2.024 10 3.0 7.0 1.762 1.774 bou E d B Table 11 Rounded overall U-factors showing the difference between ASHRAE and ISO Window number H (m) W (m) ASHRAE Ut, ASHRA (W/m2 K) 1 0.5 0.5 5.4 2 0.6 0.8 4.5 3 1 0.8 3.9 4 0.9 1 3.8 5 1.22 1.72 3.1 6 1.5 2 2.8 7 1.5 2.5 2.7 8 1.5 3 2.6 9 2 5 2.3 10 3 7 2.1 Table 12 Relative U-factor for the two calculational methods Window number Aw (m 2) ASHRAE B.C., relative DU (%) ISO B.C., relative DU (%) 1 0.25 1.25 1.48 2 0.48 1.14 1.39 P. Blanusa et al. / Energy an 9.1. Analytical comparison of ASHRAE and ISO overall thermal transmittance calculation methods In order to explain the above differences an analytical comparison of the ASHRAE and ISO overall thermal transmittance calculations will be made. 10. Frame/glazing section calculation procedure For a section (frame plus IGU of length lp, see Fig. 1) of a window, the ISO method divides the section heat transfer as follows: q˙ISOðW=mÞ ¼ Ufilf þ Uglp þ c (23) For the same section of the window, the ASHRAE method divides the section heat transfer as follows: q˙ASHRAEðW=mÞ ¼ Ufalf þ Ugðlp � legÞ þ Uegleg (24) Since the heat transfer for the section is the same in both methods: q˙ISO ¼ q˙ASHRAE (25) 3 0.80 1.09 1.30 4 0.90 1.09 1.30 5 2.10 0.99 1.15 6 3.00 0.93 1.08 7 3.75 0.91 1.05 8 4.50 0.89 1.03 9 10.00 0.74 0.85 10 21.00 0.57 0.67 Substituting Eqs. (23) and (24) into Eq. (25) and solving for c yields: c ¼ ðUfa � UfiÞlf þ ðUeg � UgÞleg (26) 11. Window calculation procedure Because the overall calculated window thermal transmit- tances by the two methodologies (ASHRAE and ISO) do not agree as shown previously, it is not possible to equate the total window heat transfer for each method. The ASHRAE total window heat transfer, Q˙ASHRAE, is: Q˙ASHRAEðWÞ ¼ UASHRAEAtðT in � ToutÞ ¼ ½UfaAf þ UcogAcog þ UegAeg�ðT in � ToutÞ (27) The ISO total window heat transfer, Q˙ISO is: Q˙ISOðWÞ ¼ UISOAtðT in � ToutÞ ¼ ½UfiAf þ UgAg þ clc�ðT in � ToutÞ (28) where ndary conditions ISO boundary conditions Ut, ISO (W/m2 K) Ut, ASHRAE (W/m2 K) Ut, ISO (W/m2 K) 5.5 5.1 5.1 4.6 4.2 4.2 3.9 3.6 3.6 3.8 3.4 3.5 3.1 2.7 2.8 2.8 2.5 2.5 2.7 2.4 2.4 2.7 2.3 2.3 2.3 2.0 2.0 2.1 1.8 1.8 uildings 39 (2007) 374–384 381 Q˙ISO 6¼ Q˙ASHRAE (29) Substituting the ISO area calculations (Eqs. (8)–(13)) into Eq. (28) and the ASHRAE area calculation (Eqs. (14)–(21)) into Eq. (27) yields: Q˙ASHRAE DT ¼ Ufa4½Llf � l2f � þ Ug½L� 2lf � 2leg�2 þ Ueg4leg½L� 2lf � leg� (30) Q˙ISO DT ¼ Ufi4½Llf � l2f � þ Ug½L� 2lf �2 þ c½4L� 8lf � (31) Substituting Eq. (26) into Eq. (31) to eliminate c, gives the following: Q˙ISO DT ¼ Ufi½4l2f � þ Ufa4lf ½L� 2lf � þ Ug½ðL� 2lfÞ � ðL� 2lf � 4legÞ� þ Ueg4leg½L� 2lf � (32) edge of glass areas, respectively. Finally, substituting the first parts of Eqs. (27) and (28) into Eq. (33) and solving for the difference between the ASHRAE and ISO thermal transmit- tances yields the following: Ut;ASHRAE � Ut;ISO ¼ ½Ufa � Ufi�4l2f � ½Ug � Ueg�4l2eg L2 (34) where At = H � W � L2 has been used. Thus, the difference between Ut, ASHRAE and Ut, ISO is represented by the difference between the ASHRAE and ISO frame U-factors multiplied by the four frame corner areas plus the difference between the ISO glazing U-factor and the P. Blanusa et al. / Energy and Buildings 39 (2007) 374–384382 The difference between ASHRAE and ISO total window heat transfer is obtained by subtracting Eq. (32) from Eq. (30). The result after algebraic rearrangements and cancellations is: Fig. 3. Geometric interpretation of corner areas. Q˙ASHRAE � Q˙ISO DT ¼ ½Ufa � Ufi�4l2f � ½Ueg � Ug�4l2eg (33) where DT ¼ T in � Tout 12. Geometric interpretation Fig. 3 presents a geometric interpretation of the two areas l2f and l2eg which are two-dimensional corner areas in the frame and edge of glass areas. Since there are 4 corners in each area, 4l2f and 4l2eg representing the total corner areas for the frame and the Table 13 Comparison between the calculated and analytical differences in the overall U-fac Boundary conditions Aw (m 2) Uf, ASHRAE (W/m2 K) Uf, ISO (W/m2 K) Ue (W Roth [18] ASHRAE 0.25 9.061 9.1417 2.2 ISO 0.25 8.440 8.4745 2.2 Weitzmann et al. [19] ISO 0.25 4.221 3.593 2.8 Blanusa [20] ASHRAE 0.25 4.441 3.817 3.2 ISO 0.25 2.003 1.644 1.4 Note: All the results are given for windows 0.5 m � 0.5 m. ASHRAE edge of glazing U-factor multiplied by the four edge of glazing corner areas. 13. Comparison between ASHRAE and ISO calculated and analytical results As mentioned previously, Roth [18] first indicated the differences in the ASHRAE and ISO Methods for determining the overall thermal transmittance of fenestration systems. In the work of Roth [18] for a wood framed window the ASHRAE method overall thermal transmittance was larger then the ISO method for both sets of boundary conditions. This differs from the results in this paper for an aluminum-framed window and in the paper by Weitzmann et al. [19] for a wood framed window where the ASHRAE Method overall U-factor is less than the ISO Method result. Weitzmann et al. [19] also showed that an edge region of 63.5 mm was too small for all of the frame/edge two-dimensional effects to be taken into account. They showed that if the edge of glass region was increased to 150 mm, the two-dimensional effects were captured. In addition to two- dimensional calculations presented in Weitzmann et al. [19], they also present the results of three-dimensional heat transfer calculations for the window corner region and point correction factors (see ISO, 10211) were determined that could be applied to the ASHRAE and ISO calculated two-dimensional overall U-values to have them agree with the more accurate three- dimensional results. However, it is probably not practical to perform three-dimensional heat transfer calculations on all windows that are analyzed using conventional two-dimensional tor calculated by the ASHRAE and ISO methods g /m2 K) Ug = Ucg (W/m2 K) lf (m) leg (m) Ut, ASHRAE–Ut, ISO Calculated results Analytical Eq. (34) 15 1.532 0.07 0.0635 �0.06 �0.05 12 1.23 0.07 0.0635 �0.07 �0.07 74 2.674 0.11 0.0635 0.11 0.11 04 2.776 0.11 0.0635 0.09 0.09 19 1.163 0.095 0.15 �0.04 �0.04 d B U-value programs. Blanusa’s [20] analysis of an aluminum- framed slider window with the same range of overall window dimensions used by Roth [18] showed that the differences ranged from 1.4% for the smaller windows to 0.6% for the larger windows. The results presented in Table 12 give a comparison of the difference in the ASHRAE and ISO methods overall calculated U-factors from Roth [18], Weitzmann et al. [19] and Blanusa [20] for the ISO and ASHRAE Methods and the analytical Eq. (34) predicted difference for windows where H = W = L = 0.5 m. The results show that Eq. (34) gives the same difference as the overall calculated U-factor for the ASHRAE and ISO methods (Table 13). 14. Conclusions and recommendations The fenestration thermal transmittance calculations analysis presented in this paper has shown that small discrepancies exist between the calculated thermal transmittance (U-value or U- factor) values produced by the ISO and ASHRAE methods. The overall thermal transmittance values calculated independently by three researchers [18–20] comparing the two different methods indicated a maximum difference of 3% or less. The analyses also showed that the overall thermal transmittance difference between the two methodologies decreases as the window area (glazing plus frame) increases. Thus, the resulting difference in thermal transmittance values for the two methods is negligible for larger windows. However, in some special cases, like true divided-lite windows the range of 500 mm � 500 mm and smaller that exist in many older homes in North America, the thermal transmittance calculation methods may have differences that may have to be taken into account when analyzing the thermal performance of buildings with a significant number of true divided-lite windows and doors. Blanusa [20] showed algebraically (see Eq. (34)) that the differences between the ISO and ASHRAE methods turn out to be due the way the corner regions of the window frame and glazing are treated by the assembly of the overall thermal transmittance for a three-dimensional window from the two- dimensional calculations. Weitzmann et al. [19] showed that neither the ISO or ASHRAE two-dimensional calculation methods are able to reproduce three-dimensional thermal transmittance values obtained from more sophisticated com- puter (finite element or finite difference) heat transfer analysis programs. This indicates that future research work should focus on developing window corner correction factors that could be used to correct the ISO and/or ASHRAE two-dimensional thermal transmittance values to more nearly agree with what three-dimensional values would produce. These correction factors could be in the form of simple formulas or tabulated values for a wide variety of window frame and glazing combinations. At the present time, the convective heat transfer conditions on the inside and outside surfaces of a fenestration product are treated as boundary conditions and the convective heat transfer within glazing and frame cavities are treated as P. Blanusa et al. / Energy an equivalent thermal conductivities in the ISO and ASHRAE two-dimensional thermal transmittance calculations. In the future, as personal computer (PC) calculation speeds and storage increase, these thermal transmittance calculation methods can be made more accurate by incorporating the convective heat transfer on the inside and outside surfaces window surfaces as well as in the glazing and frame cavities. Most of this can now be done with supercomputers, and if past trends in PC development continue into the future, overall fenestration thermal transmittance values could be produced in a single three-dimensional calculation that would include all of the conductive, convective and radiative heat transfer phenomena. It is recommended that the ASHRAE method adopt the same criteria as the ISO method with regards to the portion of the glazing that is analyzed in the two-dimensional heat transfer calculations. For many fenestration products, 63.5 mm ‘‘edge of glass’’ distance does not capture all of the two-dimensional heat transfer that occurs in the glazing. In some cases since 100–150 mm may be necessary, the ISO method requires that the distance be increased until no further changes in the overall thermal transmittance occurs. Once complete modeling of fenestration products becomes possible, the need for testing will be diminished. Over time, fenestration product testing, as we know it today, may become obsolete. The only need for fenestration product testing would then be for new innovative products and/or periodic validation of the calculation programs being used. References [1] S. Svendsen, J. Kragh, J.B. Lausten, Energy performance of windows based on net energy gain, in: Nordic Symposium on Building Physics, Reykjavik, Iceland, June 13–15, 2005. [2] ISO 15099, Thermal Performance of Windows, Doors and Shading Devices-Detailed Calculations, International Standards Organization, Geneva, 2003. [3] ISO 10077-1, Thermal Performance of Windows, Doors and Shutters- Calculation of Thermal Transmittance—Part 1: Simplified Method, International Standards Organization, Geneva, 2000. [4] ISO 10077-2, Thermal Performance of Windows, Doors and Shutters– Calculation of Thermal Transmittance—Part 2: Numerical Method for Frames, International Standards Organization, Geneva, 2003. [5] LBNL, WINDOW 4.1: PC Program for Analyzing Window Thermal Performance, LBL-35298, Windows and Delighting Group, Lawrence Berkeley National Laboratory, Berkeley, CA, 1994. [6] J.L. Wright, VISION4, Glazing System Thermal Analysis: User and Reference Manuals, Advanced Glazing System Laboratory, University of Waterloo, Ontario, Canada, 1995. [7] D. Curcija, L.L. Ambs, W.P. Goss, A comparison to European and North American window U-value calculation procedures, ASHRAE Transac- tions 95 (Pt. 1) (1989) 575–591. [8] EEL. The FRAMEplus Toolkit for Heat Transfer Assessment of Building Components, Version 3.0, Enermodal Engineering, Kichener, Ontario, Canada, 1995. [9] ASHRAE, Standard Method for Determining and Expressing the Heat Transfer and Total Optical Properties of Fenestration Products, Public Review Draft of Standard 142P, American Society of Heating, Refrig- erating and Air Conditioning Engineers, Atlanta, 1998. [10] A.H. Elmahdy. Report of Properties of Windows, ISO/TC 163/WG2- Thermal Transmission Properties of Windows, ISO Technical Committee 163, Document No. 343E, International Standards Organization, Geneva, uildings 39 (2007) 374–384 383 August 3, 2001. [11] LBNL, THERM 2: PC Program for Analyzing Two-Dimensional Heat Transfer Through Building Products, LBL-37371, Windows and Delighting Group, Lawrence Berkeley National Laboratory, Berkeley, CA, 1998 . [12] C.O. Peterson, How is low-E performance criteria determined? Glass Digest 1 (1987) 70–76. [13] S. Carpenter, A. McGowan, Effect of framing systems on the thermal performance of windows, ASHRAE Transactions 99 (1) (1993) 907– 914. [14] S. Carpenter, A.H. Elmahdy, Thermal performance of complex fenestra- tion systems, ASHRAE Transactions 100 (1994). [15] A.H. Elmahdy, Effects of Improved Spacer Bar Design on Window Performance, Construction Technology Update No. 58, Institute for Research in Construction, National Research Council of Canada, Ottawa, Ontario, Canada, 2004, K1A. [16] D. Curcija, W.P. Goss, Two-dimensional finite element model of heat transfer in complete fenestration systems, ASHRAE Transactions 100 (Pt. 2) (1994) 1207–1221. [17] ISO 10211-1, Thermal Bridges in Building Construction-Heat Flow and Surface Temperatures-Part 1: General Calculation Methods, International Standards Organization, Geneva, 1995. [18] H. Roth. Comparison of thermal transmittance calculation methods based on ASHRAE and CEN/ISO standards, Master of Science Thesis, Depart- ment of Mechanical and Industrial Engineering, University of Massachu- setts, Amherst, 1998. [19] P. Weitzmann, C.F. Jensen, S. Svendsen, Comparison of calculations of thermal transmittance of windows using two- and three-dimensional models, in: Proceedings of the EuroSun Conference, Copenhagen, Den- mark, June 19–22, 2000. [20] P. Blanusa. A comparison of different heat transfer calculation methods for fenestration systems, Master of Science Thesis, Department of Mechan- ical and Industrial Engineering, University of Massachusetts, Amherst, 2001. [21] ISO 10211-2, Thermal Bridges in Building Construction–Calculation of Heat Flows and Surface Temperatures—Part 2: Linear Thermal Bridges, International Standards Organization, Geneva, 2001. P. Blanusa et al. / Energy and Buildings 39 (2007) 374–384384 Comparison between ASHRAE and ISO thermal transmittance �calculation methods Introduction Literature review ASHRAE and ISO two-dimensional thermal transmittance calculation methods Defining lengths for the frame and glazing unit ISO lineal/area weighted calculation procedure ASHRAE area weighted method Window area calculations ISO area calculations ASHRAE area calculations Window area calculation results Thermal transmittance calculations Comparison of overall U-factor results Analytical comparison of ASHRAE and ISO overall thermal transmittance calculation methods Frame/glazing section calculation procedure Window calculation procedure Geometric interpretation Comparison between ASHRAE and ISO calculated and analytical results Conclusions and recommendations References