1、AN-04-6-4 Estimating the Solar Heat and Thermal Gain from a Window with an Interior Venetian Blind Michael R. Collins, Ph.D. Associate Member ASHRAE ABSTRACT This study gives correlations useful in predicting heat transfer from the indoor glazing surface of a window with an adjacent interior venetia
2、n blind. Data were produced using a steady-state, laminal; two-dimensional, conjugate conduc- tion/convection/ radiation jnite element model of a vertical isothermal surface with heated, horizontal, and rotatable louvers. Using that model, the radiative and convective heat transferfrom thesurface e.
3、, the indoorglass) has been exam- ined with respect to six variables: blind to glass spacing, blind slat angle, irradiation level, glass temperature, and blind and glass emissivity. Data have beenpresented in two forms: as the best statisticaljt for use in software applications and in table format.
4、An example of how these correlations could be used to predict solar heat gain and U-factor has been included with a comparison to calorimetrically obtained data. Results corre- late well with calorimetric data. INTRODUCTION One of the remaining difficulties in the examination of energy transmission
5、in buildings is quantification of the effects of various shading devices. While it is common for a louvered shading device, such as a venetian blind, to be mounted on the indoor surface of a window to provide privacy and to control daylighting, the presence of these shading devices will affect natur
6、al convection and radiant heat transfer from the window. As a result, there will be a change in the heat conduction and solar heat gain constant of the window. In recent times, the solar heai gain coefficient (SHGC) has been used to determine the solar heat gain (SHG) for typical fenestration. The p
7、opularity of this method can be traced to the fact that it can take advantage of both the spectral and angular Stephen J. Harrison, Ph.D., P.Eng. characteristics of incident irradiation. For the majority of systems, detailed analysis of this sort is not difficult to perform, and the results are easi
8、ly presented in a convenient form. Spectral properties are generally well known, and the angular characteristics are accounted for by the solar inci- dence angle. Problems arise, however, when a spatially nonho- mogeneous layer (i.e., a venetian blind) is included in the analysis. For these situatio
9、ns, the louver angle, placement, and radiative properties become additional variables, and the inci- dent angle must be replaced by the solar altitude and relative azimuth angles. The complexity involved is clearly demon- strated in a recent publication by Klems (2002). The analysis is further compl
10、icated by the fact that the inward-flowing frac- tion (N) of absorbed solar energy cannot be determined by conventional methods. Traditionally, N could be determined by considering the combined convective and radiative film coefficients between adjacent layers in the fenestration system (Figure la).
11、 With a shade, however, radiative and convective paths exist at the inner glass that “miss” the shade layer (Figure lb), making it difficult to determine the inward-flowing frac- tion directly. Furthermore, an experimental study of the inward-flowing fraction for a shade layer showed that Ncould var
12、y significantly with changing environmental conditions (Collins and Harrison 1999a). It is possible that the “tradi- tional” method of determining solar gain may not be suitable for use on shaded windows, and alternative methodologies may need to be developed. This study is an exploration of one pos
13、sible alternative methodology for determining SHG and thermal transmission for shaded windows. Specifically, numerically obtained radi- ative and convective heat transfer from the interior surface of a window were obtained with respect to six variables: blind to glass spacing, blind slat angle, irra
14、diation level, glass temper- M.R. Collins is an assistant professor in the Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada. S.J. Harrison is an associate professor and director of the Solar Calorimetry Laboratory, Department of Mechanical Engineering, Queens U
15、niver- sity, Kingston, Ontario, Canada. 486 02004 ASHRAE. Glass i Glass 2 + -1 nb 5 5- z m m 0- a 0 K 8 -5 - 7 10 ; 0 .;E 5- 2 45 I m m 0- 3 25 1 35 AJ ti 16 26 36 15 3 -5- a o I s -i i -lo 1 5- .E s - mr m “ - 2 -60 -40 -20 m -5 - -15 J 20 40 60 15 10 s is0 E( - s5 a Positive Values Are Toward Room
16、; Blind and Glass Emissivity Is 0.76 and 0.84, Respectively; Values Determined at Ti= 297 K; If b 40 mm, Then Use b = 40 mm 19.4 25.7 25.3 17.3 26.0 28.0 54.0 61.5 62.3 52.5 62.4 65.5 $1 -45O 1450 O0 I -1 5 -1 o -5 -1 13.9 -109.5 -111.9 -1 19.4 -1 12.7 -1 12.8 -85.6 -80.0 -8 1.2 -90.5 -82.6 -81.5 -5
17、5.6 -48.8 48.8 -60.0 -50.9 -48.5 O 5 5 I 29.4 I 32.9 I 29.6 I 28.5 I 34.4 I 33.5 I -23.9 -16.0 -14.8 -27.8 -17.4 -13.9 9.4 18.5 20.9 6.1 17.7 22.4 -1 5 I -102.41 -1 00.9 1 -106.2 1 -106.8 1 -102.9 1 -105.81 01 -13.61 -8.4 I -10.1 I -16.21 -8.7 1 -8.01 15 I 90.3 I 99.0 I 100.9 I 89.4 I 100.5 I 104.8
18、I 10 I 44.3 1 54.7 i 58.3 i 41.71 54.4 1 60.4 1 15 80.9 92.5 97.3 78.9 92.8 100.0 -1 5 -125.3 -118.1 -1 17.7 -132.1 -122.5 -1 19.7 -10 I -96.7 I -88.3 I -86.6 I -102.8 I -92.1 I -88.1 I ASHRAE Transactions: Symposia Table 6. (continued) Total Heat Transfer at Indoor Window Surface; Positive Values A
19、re Toward Room; Blind and Glass Emissivity Is 0.76 and 0.84, Respectively; Values Determined at Ti = 297 K; If b 40 mm, Then Use b = 40 mm Table 7. Comparison of Measured and Predicted Solar Heat Gain Coefficients 0.90 0.90 0.90 0.90 Io 10.23 10.45 10.68 10.6610.02 1 O 45 2.82 0.06 0.57 0.63 NAS 45
20、30 2.78 0.05 0.60 0.65 0.64k0.02 45 45 2.78 0.04 0.58 0.63 0.6410.02 blind layer optical properties needs to be developed. No data were available for comparison of predicted U-factors. The shade layer reduced the SHGC for all cases. Consid- ering the blind with the lower absorptivity, the SHGC was r
21、educed by 26% to 42% between O“ and 45“ slat angles at 45“ solar incidence. In this case, the reduction was due to the inter- ception of directly transmitted solar radiation. Even so, the average reduction was 32%. When considering the more absorbing blind, however, the benefits are less pronounced
22、than with the less absorbing blind. In ail cases, the SHGC was only reduced between 7% and 15%, where again, the lower reductions are due to better alignment of the solar incident and slat angles. While a highly absorbing shade layer does have some benefit, it does not efficiently limit the transmis
23、sion of solar heat to the space. Calorimetric data provided window U-factors, but in the absence of data needed to predict the U-factor ofthe frame and edge of glazing, the center-of-glass U-factors could not be determined. In relation to the glazing U-factor, however, the predicted glazing and shad
24、e U-factor is only slightly lower. While a reduction in U-factor is beneficial in both a heating and cooling situation, the reduction observed here was small. This result agrees with the results presented by Machin et al. (1 997) and Ye et al. (1 999). ASHME Transactions: Symposia 495 The implicatio
25、ns of these results for shade design and placement are dependent on the designers intentions. TO reduce solar heat gain successfully, a design must meet two criteria: it must intercept the majority of incident solar radia- tion without absorbing it, i.e., the blind should be closed and reflective. M
26、ost importantly, if a shade is to be effective, the majority of solar radiation has to be intercepted by the shade layer. To increase solar heat gains, it is best not to use a blind, as the shade layer will reduce SHG. If we factor in other concerns, however (Le., privacy and aesthetics), a highly a
27、bsorbing blind would be preferable. Improvements in U- factor are not significant enough to be important. CONCLUSIONS Equations for predicting the radiative, convective, and total heat transfer from the interior surface of a window with an attached venetian blind have been obtained. While the result
28、ing equations are complex, qualitative and quantitative indicators show that the data fit is very good. Based on a number of assumptions, an equation and table of flux from the interior glazing has been presented for simplified calculation purposes. A method has also been presented for predicting SH
29、GC and U-factor in a window and shade combination. Predicted versus experimental data show excellent agreement. More cases need to be compared, however, to provide full vali- dation of the method. Additionally, a reliable estimator of blind layer optical properties needs to be developed in order to
30、facilitate this comparison. A more theory-based final product would most likely be more practical for use in software routines. While it was understood that the mechanisms of heat transfer in this system can be described in traditional terms and may not demonstrate a second order response, the prese
31、nt approach prevents their use. An attempt to predict heat transfer at the interior glass surface has been made instead of determining the heat transfer relations between the glass and shade layers. Use of the full resistance network, such as the one presented in Figure 1, would provide increased mo
32、del versatility and information. Radiative exchange between surfaces could be easily deter- mined based on well-established theory. An examination of convection from the glass and both sides of the shade as a func- tion of blind temperature and geometry is all that is required. ACKNOWLEDGMENTS The a
33、uthors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council (NSERC) for providing the financial support for this research. NOMENCLATURE b h I = solar irradiation, W/m2 k = conductivity,W/m.K 1 = plate height, mm = nominal louver spacing, mm = heat transfer coef
34、ficient, W/m2.K MSE MSR n N = mean square error, dimensionless = mean square regression, dimensionless = louver tip to plate spacing, m = inward-flowing fraction, dimensionless, or number of points in data fit = number of parameters in data fit P ps = louverpitch, mm 4 = heat flux, W/m2 R = Rcoeffic
35、ient rc SHGC = solar heat gain coefficient, dimensionless = louver radius of curvature, mm t T TSS U W X Y Y louver thickness, mm temperature, K total sum squares, dimensionless thermal transmission, W/m2.K louver width, mm variable (matrix form) response, W/m2 response (matrix form) Symbols a = abs
36、orptivity, dimensionless , = parameter estimate E = emissivity, dimensionless = louver angle, deg. y = solar altitude, deg. p = reflectivity, dimensionless CT = standard deviation, W/m2 z = transmissivity, dimensionless Subscripts b = blind/louver d = difise D = direct f = fenestration g = glass i =
37、 indoor o = outdoor p = plate s = glazing airspace sys = system Superscripts T = transpose REFERENCES ASHRAE. 2001. 2001 ASHRAE Hundbook-Fundumen- tuls. Atlanta: American Society of Heating, Refrigerat- ing and Air-conditioning Engineers, Inc. 496 ASHRAE Transactions: Symposia Collins, M.R. 2001, Nu
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