1、 AN-04-6-2 Methods for Calculating the Effective Longwave Radiative Properties of a Venetian Blind Layer Darryl S. Yahoda ABSTRACT Window solar gain can strongly influence building energy consumption, peak loads, and comfort. Shading devices are routinely used to control solar gain. The use of venet
2、ian blinds is particularly common. There is a strong need for models that can accurately simulate this type of device. As a$rst step, this study deals with the mechanisms of longwave radiant exchange. Methods are presented by which spatially averaged optical properties (referred to as “efective” opt
3、ical proper- ties) can be calculated. An enclosure model was formulated to model the interaction of radiation with the slat surfaces. Six enclosure areas, rather than foul; were used to account for the possible overlap of blind slats. This optical model allows the venetian blind to be treated as a p
4、lanal; homogeneous “black- box” layer in a series of glazing layers and, coupled with the appropriate convection model, can be incorporated within a standard one-dimensional center-glass heat transfer analysis. Sample calculations were performed and the resulting efec- tive optical properties discus
5、sed. The model compares favor- ably with expected trends and limits. The efect of slat curvature was also examined. INTRODUCTION One strategy for reducing solar heat gain through windows is the use of a slat-type shading device-in particu- lar, a venetian blind-that can act as an adjustable barrier
6、to solar transmission. The selection ofthe correct shading system requires information on the optical characteristics of the shad- ing system as well as its influence on heat transfer. This selec- tion process is complicated by the myriad available shading products, often with variable geometries, a
7、nd the inability of current evaluation and rating techniques, based on one-dimen- John L. Wright, Ph.D., P.Eng. Member ASHRAE sional center-glass computer analysis, to accurately simulate shading systems. The result is that expensive and time- consuming calorimetric testing is the only alternative f
8、or assessing the thermal performance of shading systems. Typically, the analysis of the center-glass area of glazing systems takes advantage of the fact that there is no appreciable overlap between the band of solar wavelengths (0.3 to 3 pm) and the band of longer wavelengths (3 to 50 pm) by which r
9、adiant transfer occurs. This absence of overlap between the solar and longwave spectra allows the analysis to be carried out in two steps. First, a solar-optical calculation determines how much solar radiation is absorbed at each layer and how much is transmitted to the indoor space. Second, a heat
10、trans- fer analysis is used to perform an energy balance at each layer in which the net heat transfer from a layer must equal the amount of absorbed solar radiation (e.g., Wright 1998, Hollands et al. 2001). The simultaneous solution of the result- ing set of energy balance equations yields the temp
11、erature of each glazing layer as well as the various values ofheat flux and heat flux components at each location within the system. In order to expand the scope of center-glass simulation, the front and back surfaces of the shading layer are assigned spatially averaged optical properties, called “e
12、ffective” optical properties. The use of effective optical properties allows the shading layer to be treated as a homogeneous, planar layer within a glazing system. For example, the entire glazing system can be treated as an n-node array consisting of n-3 glaz- ing layers, one shading layer, togethe
13、r with the indoor (i = 1) and outdoor (i = n) nodes, as shown in Figure 1. A complete energy flow analysis requires the effective optical properties, both solar and longwave, of the shading layer. A number of models for radiation transport through Darryl S. Yahoda is a consultant at DBM Systems, Inc
14、., Cambridge, Ontario, Canada, and John L. Wright is Associate Professor in the Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada. 02004 ASHRAE. 463 planar, Specular Qlating Layer i - Planar, Mon-Specular Shading Layer Outdoor Side (i=n) n-1 i+ 1 i a Figure I La
15、yer representation of glazing system with venetian blind. venetian blinds exist in the literature. Unfortunately, most are strictly concerned with solar radiation (e.g., Klems 1994a, 1994b, 2002). The models that do treat longwave radiant exchange (IS0 2000; Rheault and Bilgen 1989) are based on rad
16、iositylirradiance calculations, similar to the models presented in this paper, but some similarities and differences should be noted. Both earlier models (IS0 2000; Rheault and Bilgen 1989) prescribe a subdivision of the slat surface by re- using the divisions used in the analysis of incident solar
17、radi- ation. Rheault divides the slat according to the extent of direct- beam solar radiation, and the IS0 model uses five slat segments of equal size. The model described here is focused solely on the longwave aspects of the analysis and decisions regarding slat surface subdivision are based only o
18、n the consideration of longwave radiation. Rheault and Bilgen (1989) do not present results in the form of effective optical properties, but a small set of effective transmittance and effec- tive emissivity results is presented in the IS0 (2000) docu- ment. The results presented for opaque venetian
19、blind slats (slats that are not opaque with respect to longwave radiation are felt to be very rare) agree very closely with results produced using the model currently described-a preliminary indication that good results can be obtained for longwave anal- ysis using far fewer than five slat divisions
20、. The purpose of this paper is to describe methods for deter- mining the effective longwave radiative properties of the shad- ing layer, which can be used in the heat transfer analysis of the glazing system. An effort has been made to retain a level of simplicity in these models that is expected to
21、translate into ease of implementation. The models described are based on conventional gray enclosure analysis and, thus, entail the assumptions that each surface is isothermal, uniformly irradi- ated, and a diffuse reflectorlemitter. The resulting effective longwave radiative properties of the blind
22、 layer are functions of the emissivity of the slat material and the blind geometry, which is composed of the angle of tilt of the slats (slat angle), 4, slat width, w, and the spacing between adjacent slats, s. Details regarding blind slat geometry are shown in Figure 2. - - Blind Slat ,- Shading La
23、yer _- - .- - “Blind Enclosure“ Figure 2 “Blind enclosure” representative of blind layec EFFECTIVE LONGWAVE RADIATIVE PROPERTIES The radiant analysis of the shading layer is based on the assumptions that the blind slats are fiat, have uniorm, non- temperature-dependent properties, and are opaque wit
24、h respect to longwave radiation. The slat material is also assumed to be gray and emit and reflect difksely in the long- wave spectrum. The blind slats are assumed to be long, allow- ing the geometry to be treated as two-dimensional. Enclosure Geometry The effective longwave radiative properties of
25、the shading layer can be determined by examining an area of the layer that will be representative of the layer as a whole. For a venetian blind composed of a sufficiently large number of slats, the optical characteristics of the area between two adjacent slats will be representative of the entire la
26、yer. The two adjacent slat surfaces, with fictitious surfaces at the front and back open- ings, constitute an enclosure. The blind enclosure is split into six surfaces: two fictitious surfaces represent the openings and each slat is divided into two surfaces, as shown in Figure 2. The surfaces are n
27、umbered as follows: surface 1 = ab, surface 2 = bc, surface 3 = de, surface 4 = ef, surface 5 = ad, and surface 6 = cf. The lengths of the slat subsurfaces (i.e., the locations of points b and e) depend on the ratio of slat width to slat spacing, wls. When the slat angle, +, is increased to 90, the
28、blind slats will be vertical and the blind is said to be in a “closed” position. Two situa- tions, dependent on the wls ratio, can arise when the blind is closed. If wls I 1, there will be a gap between the adjacent slat ends (and radiation transmission can take place even though the blinds are clos
29、ed) or the slats will be tip-to-tip for the case of wls = 1. For wls I 1, a four-surface enclosure is sufficient so point b is located coincident with the slat tip at point c, and point e is located coincident with the slat tip at point f. In other words, areas 2 and 4, bc and ef, respectively, vani
30、sh. Alterna- tively, if wls 1, the slats will overlap when the blind is closed. In this situation, no radiation transmission should occur. However, the use of a four-surface enclosure for wls 1 will produce a false transmittance, which will be discussed in 464 ASHRAE Transactions: Symposia Table 1.
31、Enclosure Line Segments Dependent on wls Ratio de ef W w-s S n 9 w-9 greater detail later, making a six-surface enclosure necessary to account for the slat overlap. In cases with w/s 1, point b and point e are positioned to account for slat overlap. For posi- tive slat angles, point b is positioned
32、a distances from point c, and point e is positioned a distance s from point d in order to have areas 1 and 4, ab and ef, respectively, represent the areas of slat overlap. For negative slat angles, point b is positioned a distance s from point a, and point e is positioned a distance s from point fin
33、 order to have areas 2 and 3, bc and de, respec- tively, represent the areas of slat overlap. Line Segment ac ad Enclosure View Factors Since the blind enclosure is modeled as a two-dimen- sional system, the radiative view factor from surface i to surfacej, Fp can be determined using Hottels crossed
34、 string method (e.g., Siegel and Howell 1992). In general, to find the view factor from surface i to surfacej, Hottels crossed string method can be expressed as Length W S Exsi. - c usi. F = I 2Li where the string lengths are: CXS, = the sum of the “crossed” strings joining the ith andjth surfaces,
35、CUS, = the sum of the “uncrossed strings joining the ith and jth surfaces, Li = the length of ith surface. The string lengths are determined by joining the end points of the two surfaces being examined using two “crossed” strings and two “uncrossed” strings. Table 1 lists the string lengths that are
36、 dependent on both the wls ratio and the slat angle. The remaining line segment lengths can be determined using Table 2. The self-viewing factors, Fii, will be zero because all surfaces are flat. Table 2. Enclosure Line Segments for Use with All wls Ratios I ae I Js2 + - 2s(e)sin+ I 22 I af I Js +w
37、-2wssine I I df I W Radiant Analysis It is convenient for the enclosure analysis to be under- taken using an irradiancehadiosity formulation. The irradi- ance at surface i, Gi, is simply the radiant flux incident at that surface. The radiosity of surface i, Ji, is defined as the radiant flux leaving
38、 that surface. Assuming that each surface is a diffuse emitterheflector and that each surface is uniformly irradiated, it can be shown that the irradiance at the ith surface can be expressed in terms of the radiosities of all of the enclosure surfaces. In an n- surface enclosure (in this study, n =
39、6), n (2) G, = E FilJi. j= 1 The radiosity at surface i includes the reflected portion of Gi as well as the radiant flux emitted by surface i itself. (3) ASHRAE Transactions: Symposia 465 where is the emissivity of surface i, o is the Stefan-Boltz- mann constant, and KirchofYs law lets the surface r
40、eflectivity to be expressed as (1 - q). Equations 2 and 3 were used to characterize the radiant exchange at surfaces 1 through that is, AkG5 -+AkG6. The rate of absorption will be equal to the rate at which energy is supplied to the enclosure less the rate at which energy is trans- mitted and reflec
41、ted. Thus, Rearranging and simpliing, while noting that Ak = A, = (9) Equation 9 represents a second method for determining the effective longwave absorptance of the shading layer. Again, it should be noted that ak,effJw is independent of the magnitude of Gk, which will be divided out of the express
42、ion when the solved irradiances are substituted. Effective Longwave Absorptance-Results Figure 4 shows the effective front absorptance, afront,eflJw as a function of slat angle, I$, for different w/s ratios (slat width/slat spacing) and = 0.8 and E = 0.7. Note that for w/s 2 1, when the blind is com
43、pletely closed (I$ = *90?), the value of afront,effJW is always equal to the absorp- tivity of slat surface facing the front of the enclosure. This should be expected. For w/s s), six surfaces are required to model the enclosure. Figure 11 compares the front effective properties deter- mined using a
44、 four-surface and six-surface model with w/s = 1.2 = 0.8, = 0.7) and shows that for high slat angles, the effective properties determined using the four-surface and six-surface models differ. In particular, the transmittance determined using the four-surface enclosure model does not approach zero wi
45、th the blind in the closed position. This occurs because the radiant analysis is based on the assumption that the irradiance of the ith surface, G, is uniform over the entire area, Ai. However, the slat surface facing the front open- ing will be partially blocked by the adjacent slat. In the four- s
46、urface model, with uniform slat irradiation, the overlapped portion of the slat will be treated as being uniformly irradiated as well. Since this overlapped portion sees the overlapped portion of the adjacent slat surface, and the adjacent slat surface sees the back opening, a false transmittance re
47、sults. By modeling the enclosure with six surfaces, the slat surface facing the fiont opening is split in two, with the exposed surface being irradiated and the overlapped surface treated as being completely shaded. Using the six-surface model, there is no false transmittance produced. a series of g
48、lazing layers. The effective longwave radiative property models for a venetian blind shading layer are based on a spatially represen- tative six-surface enclosure, which is bounded by two adjacent slats and the front and back openings to the blind. The long- wave radiation exchange between surfaces
49、in the enclosure is modeled, assuming each surface is a dimise emittedreflector, each surface is uniformly irradiated, and each surface is gray with respect to longwave radiation. The effective longwave absorptance, reflectance, and transmittance are determined by introducing an external irradiance on one opening of the enclosure and solving for the enclosure surface radiosities and irradiances. The resulting expressions for the effective long- wave radiative properties are functions of the hemispherical longwave emissivity of each slat surface, the slat an
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