1、OR-05-4-2 Methods for Calculating the Effective Solar-Optical Properties of a Venetian Blind Layer Darryl S. Yahoda ABSTRACT mndow solar gain can strongly influence building energy consumption, peak loads, and comfort. Shading devices are routinely used to control solar gain. The use of venetian bli
2、nds is particularly common. There is a strong needfor models that can accurately simulate this type of device. As a Jirst step, previous research focused on the mechanisms of longwave radiant exchange. Methods were presented by which spatially averaged optical properties (referred to as “effective”
3、optical properties) can be calculated. An enclosure model was formu- lated to model the interaction of radiation with the slat surfaces. This optical model allows the venetian blind to be treated as aplanar, homogeneous “black-box”1uyer in aseries ofglazing layers and, coupled with the appropriate c
4、onvection model, can be incorporated within a standard one-dimen- sional center-glass heut transfer analysis. In conjunction with the longwave analysis, the current study deals with the mech- anisms of solar radiant exchange. Methods, based on geomet- ric considerations and fundamental radiation ana
5、lysis, are presentedfor determining the shading layers effective optical properties with respect to the beam component of incident solar radiation-at any angIe of incidence. Both specular and difuse rejection at the slat surfaces is included. Theperfor- mance of these efective properties is demonstr
6、ated and discussed in terms of expected results and compared with other models and experimental results found in the literature. INTRODUCTION One strategy for controlling solar heat gain through windows is the use of a slat-type shading device, in particular, a venetian blind, which can act as an ad
7、justable barrier to solar transmission. The selection of the correct shading system John L. Wright, PhD, PEng Member ASHRAE 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 of
8、available shading products, often with variable geometries, and the inability of current evaluation and rating techniques, based on center- glass one-dimensional computer analysis, to accurately simu- late shading systems. The result is that expensive and time- consuming calorimetric testing is the
9、only alternative for 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
10、 50 pm) by which radiant 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 spac
11、e. Second, a heat 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). The simultaneous solution of the resulting set of energy balance equations yields the temperatur
12、e of each glazing layer as weil as the various values of heat 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 “effect
13、ive” optical properties. The use of effective optical properties allows the shading layer to be treated as a homogeneous, planar layer that can be placed at any location within a glazing system (e.g., indoor side, between glazing layers). The entire glazing Darryl S. Yahoda is senior technology spec
14、ialist in the Market Knowledge Department, Union Gas Ltd., Toronto, Ontario, Canada. John L. Wright is head of the Advanced Glazing Systems Laboratory, associate professor and deputy chair in the Department of Mechanical Engi- neering, University of Waterloo, Waterloo, Ontario, Canada. 572 02005 ASH
15、RAE. system can be treated as an n-node array consisting ofn-3 glaz- ing layers, one shading layer, plus the indoor space (node 1) and outdoor environment (node n) as shown in Figure 1 where the shading layer is included as the ith node. A complete energy flow analysis requires the effective optical
16、 properties, both solar and longwave, of the shading layer. Methods for determining the longwave effective optical properties were dealt with in the first step ofthis study (Yahoda and Wright 2004). A number of models for solar radiation transport through venetian blinds exist in the literature. The
17、se models are briefly discussed in the following paragraphs. Rheault and Bilgen (1989) describe a heat transfer anal- ysis for an automated venetian blind window system where the blind is located between two glass panes. The model was used to simulate the thermal performance of the system to deter-
18、mine energy savings for summer and winter conditions. The solar radiation model considers a closed cavity that is bounded by the glass panes and two adjacent blind slats. The slat surfaces are divided in two, in proportions dependent on the incidence angle of the solar radiation. The assumption is m
19、ade that all slat surfaces can be characterized using a total (i.e., spectrally averaged) diffuse solar reflectivity. Longwave radi- ation exchange between surfaces is determined using a conventional irradiancehadiosity model (e.g., Incropera and deWitt 1996), each surface having a known emissivity.
20、 Parmelee and Aubele (1952) developed a solar transport model through slat-type shading as a research project for The American Society of Heating and Ventilating Engineers (ASHVE). The research describes equations for the determi- nation of the absorbing, reflecting, and transmitting charac- teristi
21、cs of slat-type shades for solar radiation (beam and diffuse). Each effective optical characteristic of the shade is dependent on the solar reflectance of the slat material, the profile angle, and the geometry of the slat assembly. The research is based on treating optical characteristics of the sla
22、t surfaces as either specular or diffuse. From the blind geometry, the fractions of the incident beam radiation that will undergo a given number of specular reflections are determined. The effective optical properties for the blind can be determined by considering the amount of beam radiation absorb
23、ed and reflected at each specular reflection. For slat surfaces whose optical characteristics are modeled as being perfectly difise, the slat that is directly illuminated by beam radiation can be split into illuminated and a shaded elements. The view factors between the openings, the two elements, a
24、nd the adjacent surface that is completely shaded from beam radiation can be computed. The effective optical properties for the blind can be determined by considering the beam radiation that is transmit- ted directly in addition to the transmission and reflection that occurs through the difise refle
25、ctions of the slat surfaces. The model also gives a treatment for diffuse solar radiation. The sky is treated as a quarter sphere and divided into 8 1 “patches.” The diffuse transmittance is determined by dividing the sum of the radiant energy transmitted through the shade by the sum of the radiant
26、energy fkom the patches incident on the shade. The WIS (Advanced Window Information System) program (Rosenfeld et al. 2000) contains a model for calcula- tions involving horizontal and vertical blind systems. The shaded fenestration system is modeled using multiple layers. The blind is represented a
27、s a layer with effective optical prop- erties, which are based on the optical properties of the slat surfaces, the blind geometry (slat width, slat spacing, slat angle), and the angle of incidence of the beam solar radiation. The beam radiation that is transmitted or reflected by the blind is split
28、in two parts-an undisturbed part and a disturbed part. The undisturbed part is transmitted as beam radiation by the blind directly without interacting with slat surfaces. The disturbed part interacts with the slat surfaces, which are assumed to be anisotropic difise reflectors only (no specular refl
29、ections). Each slat is divided into five equal elements with negligible improvement observed in considering more elements (IS0 2002). The effective properties are determined by considering two adjacent slats, with the front and back openings modeled as perfectly transparent surfaces. The model is de
30、scribed as follows (Rosenfeld et al. 2000): Firstly, the matrix of view factors is determined between each of the 1 O segments mutually and with the surfaces 1 and 2. Secondly, multiple reflections at the segments are taken into account by converting the view factor matrix into the configuration mat
31、rix using the reflec- tance of the lamellae. The process is carried out at each required wavelength (Rosenfeld et al. 2000). More detail is found in the IS0 DIS standard (IS0 2002). The Rosenfeld Simple Model (Rosenfeld et al. 2000) is based on a multi-layer representation of a complex glazing. This
32、 model was developed with the restriction that all solar radiation is normally incident. From the blind geometry, the fractions of the incident beam radiation that will undergo n specular reflections are determined. The beam radiation that is reflected diffusely is modeled as behaving in a quasi-spe
33、cular outdoor Bide (i=n) n-1 1+1 i 61 2 Figure I Layer representation of glazing system with venetian blind. ASHRAE Transactions: Symposia 573 fashion. For light undergoing two or more reflections on its way through the blind, at each subsequent reflection a fraction F ofthe diffusely reflected ligh
34、t is assumed to proceed through the blind in the same way as the specular component. The frac- tion (14) is reflected backward and retraces the path of spec- ular reflection, with portions being absorbed at each reflection, before emerging from the illuminated side (Rosen- feld et al. 2001). The mod
35、el uses the adjustable parameter Fto describe how closely the diffuse reflections are concentrated at angles near the specular direction. The fraction of light reflected and absorbed at each reflection can be determined to yield the effective transmittance, reflectance, and absorptance of the blind.
36、 More detail is found in Rosenfeld et al. (2001). The performance of the Simple Model in predicting the total solar energy transmittance was compared with the WIS model and experimental measurements (Rosenfeld et al. 2000). The Simple Model is in good agreement with the experimental measurements up
37、to slat angles of 60” while the WIS model underestimates the measured solar transmittance, in part, because of the assumption of “Lambertian distribution for reflection at the blind (Rosenfeld et al. 2000). It should also be noted that in the WIS/Simple Model comparisons, different values of slat re
38、flectance were used for each model. The magnitude of the slat reflectance used is not reported for either model. Pfrommer et al. (1 996) devised a model that divides solar radiation transmission through slat-type blinds into four different paths: (1) the unshaded transmission of the direct beam (dir
39、ect transmittance); (2) the directly reflected beam from the slat surfaces (directly reflected transmittance), which may be pure diffuse, pure specular, or any combination; (3) the unshaded transmission of diffuse radiation (diffuse transmit- tance); and (4) the reflected diffuse radiation at the sl
40、at surfaces (diffuse-reflected transmittance). The direct trans- mittance is calculated from the blind geometry and the projected sun height-angle (profile angle). The directly reflected transmittance consists of two parts: a direct-to- diffuse reflected radiation portion and a specular-reflected ra
41、diation portion, which are related by the shining factors of the slat material. The shining factor becomes 1 for diffuse reflection or O for specular reflection. The direct-to-diffuse reflected radiation is calculated by considering multi-reflec- tions up to the second reflection. This simplificatio
42、n was found to cause errors of less than 5% for light slats (slat reflec- tance = 0.6) and less than 1% for dark slats (slat reflectance = 0.2). Similarly to the Parmelee and Aubele (1 952) model for diffuse slats, the view factors between the illuminated slat area and the indoor space, the illumina
43、ted slat area and the upper slat, and the upper slat and the indoor space are determined. The direct-to-diffuse reflected radiation is computed from the view factors and the slat material reflectance. The model, as described, restricts the top and bottom slat surfaces to have the same reflectance. T
44、he specular-reflected portion of the direct transmittance is modeled using a rigorous analytical solution with no approximations. As with the Parmelee and Aubele (1 952) model and the Simple Model of Rosenfeld et al. (2000), the effective optical properties can be determined by consid- ering the amo
45、unt of beam radiation absorbed and reflected at each specular reflection. The diffuse transmittance is based on the assumption of an isotropic sky. Cutoff angles, which give an angular representation of the open space between the slats, are determined from the blind geometry. The diffuse transmit- t
46、ance is found by integrating the transmitted radiation from each slice of the sky (or ground) across the vault between the cutoff angles and dividing it by the total radiation from the sky (or ground). The diffuse-reflected transmittance uses an analytical solution, which requires the assumption tha
47、t the slat surfaces are purely diffuse. Pfrommer et al. (1996) investigated the effects of model- ling the slats as being flat and found that the influence of slat curvature decreases as the radius of curvature increases. For normal blind geometries (slat width - slat spacing), the influ- ence was n
48、egligible. However, for highly curved slats (slat radius of curvature s, no rays will be directly transmitted. If hl,O,LL I s, any ray entering the blind enclosure from this height or higher will be directly transmitted. The entrance height upper limit, hl,O,UL, will be equal to the slat spacing, s.
49、 Any rays entering the enclosure from a height lower than will be back- reflected through the enclosure entrance after the first reflec- tion at the slat surface. Case 5 blind enclosure. When L2 2 90, beam radiation will not interact with the Fractions for Transmission Through n-Reflections Using the appropriate set of equations, stated previously, for given values of $, Q s, and w, the upper and lower limits on the ray entrance heights for transmission through n reflec- tions can be calculated. Before the fractions for transmission through n reflections can be determined, the validity of
