1、AN-04-6-1 Heat Transfer Analysis of a Between-Panes Venetian Blind Using Effective Darryl S. Yahoda Long wave Rad at ive ABSTRACT Center-glass thermal analysis programs based on one- dimensional models have proved to be exceptionally useful. Recently eforts have been made to extend the analysis to i
2、nclude venetian blinds. It is convenient to model the venetian blind as aplanar, homogeneous layer that is characterized by spatially averaged, or “eflective, ” optical properties. The blind is then included in a series ofplanarglazing layers. Ther- mal resistance values were calculatedfor a window
3、with two layers of uncoated glass and a venetian blind in an air-filled glazing cavity. Three pane spacings and a wide range of slat angles were examined. The longwave effective propertiesfor the blind were obtained using the analysispresented by Yahoda and Wright in a companion paper. The simulatio
4、n model was completed with one oftwo simple models dealing with convec- tive heat transfer in the glazing cavity. Calculated results were compared with earlier guarded heater plate measurements, and the agreement was encouraging in spite of the crude convection models used. INTRODUCTION Center-glass
5、 thermal analysis programs based on one- dimensional models have proved to be exceptionally useful (e.g., Wright and Sullivan 1995a; Finlayson et al. 1993). The models underlying these programs rely on the ideas that each glazing layer is flat and that each surface is a difise emitter/ reflector in
6、the longwave band (Le., far infrared wavelengths), although each layer can be treated as specular with respect to shorter wavelength radiation (i.e., solarhisible wavelengths). Recently, efforts have been made to extend the conven- tional one-dimensional analysis to include venetian blinds. The ener
7、gy flow analysis of a glazing system with shading, John L. Wright, Member ASHRAE Properties Ph.D, P.Eng. such as venetian blinds, can be simplified by modeling the shading device as a planar, homogeneous “black-box” layer included in a series of planar glazing layers. The front and back surfaces of
8、the shading layer are assigned spatially aver- aged optical properties, referred to as “effective” optical prop- erties, which describe the performance of the shading device with respect to the way in which it interacts with radiation. In particular, the glazing system, including the environment, ca
9、n be treated as an n-node array consisting of n-3 glazing layers, one shading layer, together with the indoor (i = 1) and outdoor (i = n) nodes, as shown in Figure 1. The goal of the current study was to develop a model able to calculate thermal resistance values for a glazing system that includes a
10、 between-the-panes venetian blind and then compare these values with data produced by Garnet et al. (1 995) and Garnet (1 999), who made measurements using a Planar, pecalar ladng Laper i i , - Pianar, Non-Specular hading Layer n-1 i+ 1 i 1-1 2 Figure 1 Layer representation of glazing system with ve
11、netian blind. Darryl S. Yahoda is a consultant at DBM Systems, Inc., Cambridge, Ontario, Canada. John L. Wright is Associate Professor in the Depar- ment of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada. 02004 ASHRAE. 455 i “Cold-Side” Copper Plate Guarded Heater - -Sytro
12、foarn Insulation ”Hot-Side” Copper Plate- Thermopile Junction rCold Glycol Loop /- -. Warm Glycol Loop / / Figure 2 Guarded heater plate apparatus. guarded heater plate apparatus. Both calculations and measurements were made for windows with two layers of uncoated glass separated by a venetian blind
13、 in an air-filled glazing cavity. The venetian blind examined by Gamet was a commercially available unit composed of painted aluminum slats. Three pane spacings and a wide range of slat angles were examined. The longwave effective properties for the blind were obtained using the analysis presented b
14、y Yahoda and Wright in a companion paper (Yahoda and Wright 2004). The simulation model was completed with one of two simple models dealing with convective heat transfer in the glazing cavity. Details regarding these convection models are presented in a subsequent section of this paper. THE GUARDED
15、HEATER PLATE APPARATUS The center-glass thermal resistance measurements of Garnet et al. (1995) and Garnet (1999) were obtained using a guarded heater plate apparatus (GHP). The GHP consists of “hot-side” and “cold-side” copper plates, each being isother- mal, and each maintained at a desired temper
16、ature by a water/ glycol solution circulated by a constant-temperature bath. The GHP is depicted in Figure 2. The hot-side copper plate has three recessed electric resistance heater plates, each made of copper. The center heater plate is used to make center-glass measurements. A heat flux meter is l
17、ocated between each heater plate and the hot-side plate, as shown in Figure 3. The electrical power supplied to the nichrome wire in the heater plate is adjusted until a null reading is obtained from the heat flux meter. Under this condition, there is zero temperature difference and, thus, zero heat
18、 transfer between the hot-side plate and the embedded heater plate, and it must be concluded that all the energy supplied to the resistance heater is trans- ferred across the test sample to the cold-side plate. Additional information about this particular apparatus can be found in the literature (e.
19、g., ElSherbiny 1980; ElSherbiny et al. 1982, 1983). In the case of glazing system measurements, thin sheets of neoprene were placed between the copper plates and the exposed glass surfaces of the glazing units to eliminate ther- Heater Plate with - Nichrome Wire at Th 1. . ._ -Test Piece t -Neoprene
20、 Mat / Heat Flux Meter Warm Glycol Tube Carrying /, Figure 3 Detail of guarded heater: mal contact resistance. A fully detailed description of glazing system center-glass U-factor measurements using the GHP is given by Wright and Sullivan (1 988), and various measure- ment results can be found in th
21、e literature (e.g., Wright and Sullivan 1987, 1995b). Knowing the measured rate of electrical energy input to the center heater plate, the heat flux coming from the plate and going through the test sample, qff, can be very accurately deter- mined. Then, knowing the temperature difference across the
22、test sample, AT the R-value of the sample is - AT 4 R, - - It should be noted that AT is not measured directly. Instead, the temperature difference between the two large copper plates, ATpp, is measured. It is then possible to deter- mine AT by making the following adjustment: AT = ATpp - 2R,. 4 (2)
23、 where 2R, is the combined thermal resistance of the two neoprene mats. Note also that the subscript gg is a reminder that Rgg includes only the thermal resistance “from-glass-to-glass.” The resistances associated with the indoor and outdoor film coefficients, hin and hout, respectively, must be add
24、ed in order 456 ASHRAE Transactions: Symposia to obtain the result in the more customary form of a U-factor. Equation 3 shows the procedure. -1 -I U = (h;: + Rgg + ho,) (3) U-factors reported by Gamet (1 995, 1999) were based on GHP measurements with the resistances of the neoprene sheets replaced w
25、ith resistances based on indoor and outdoor film coefficients of hi, = 8 W/m K and hout = 23 W/m2K. THE TEST SAMPLES Gamets experiments (1 995, 1999) were conducted on glazing system test samples consisting of two 635 rnm x 635 mm (25 in. x 25 in.) sheets of uncoated glass encasing a vene- tian blin
26、d. The fill-gas was air. Three different pane spacings were used: 17.78 mm, 20.32 mm, and 25.40 mm. The same venetian blind was used in each experiment. The width of the blind slats, w, was 14.79 mm, with a slat spacing, s, of 11.84 mm. The hemispheric longwave emissivity of the slat surfaces was me
27、asured as ,=0.792 by Garnet using a Gier-Dunkel DB-I O0 infiared reflectometer. Garnet made thermal resis- tance measurements on each sample using slat angles (angle of tilt from the horizontal position) ranging from -75“ to 75“ in 15“ increments. 2 THE HEAT TRANSFER MODEL For the purpose of the cur
28、rent study, a heat transfer model was developed specifically to simulate the glazing system samples tested earlier by Gamet (1995, 1999). Specifically, this model can be applied to a venetian blind between two sheets of glass. The analysis can easily be modified and applied in a more general way to
29、other shading/glazing config- urations. Since the experiments did not involve solar radiation, the heat transfer model does not account for absorbed solar radiation. System Temperatures The model of the between-panes venetian blind glazing system consists of five layers in total: two layers of neopr
30、ene, two sheets of glass, and a shading layer, as shown in Figure 4. Five temperatures are used to describe the system: 1. 2. 3. 4. 5. The temperature of the indoor-facing surface of the hot side neoprene sheet, Ti,. The temperature of the indoor-side glazing, Tgl,. The temperature of the venetian b
31、lind layer, Tshade. The temperature of the outdoor-side glazing, Tgl,Our The temperature of the outdoor-facing surface of the cold side neoprene sheet, Tour The two glazing layers are treated as isothermal at - . temperatures TgI, and Tgl,out. The shading layer is assigned an average layer temperatu
32、re, Tshade. The temperatures of the indoor-facing and outdoor-facing neoprene sheet surfaces, Ti, and Tout, are equal to the GHP hot and cold plate temperatures and were fixed at the nominal values used in the experiments of Gamet (1 995, 1999) of 20“ and O“, respectively. The three system temperatu
33、res, Tgl,in, Tgl,out, and Tshade remain as unknowns. Knowing Ti, and Tout, the two glazing layer temperatures, can be determined from the temperature drop through the neoprene sheets as a function of q“ and R,. Using expressions similar to Equation 2: T g1,in . = Ti,-R,q (4) The resistance of the ne
34、oprene sheet, R, was obtained by direct measurement using the GHP apparatus. However, it is convenient to conceptualize the neoprene mat resistance in terms of its thickness, t, and its thermal conductivity, k, The relation between the three quantities is given by Equation 6. Garnet (1999) reported
35、values of k, = 0.17 W/m.K, t, = 1.524 mm . These values correspond to R, = 0.009 m2K/W. To determine the shading layer temperature, Tshade, it is necessary to model the heat transfer in the cavities between the glazing layers and the shading layer. The Radiant Exchange Model The radiant exchange is
36、most readily modeled in terms of the flux of radiant energy incident at each surface, the irradi- ance, and the flux of radiant energy leaving each surface (including emitted, reflected, and transmitted components), the radiosity. The irradiance and radiosity are assigned the symbols G andJ, respect
37、ively, and each is assigned a subscript to specify one particular surface (see Figure 5). Figure 6 shows more detailed expressions for surface radiosities. Each radiosity consists of a combination of emit- ,. Outdoor Glazing Neoprene Sheet i - Neoprene Sheet i : Indoor Glazing I . r , .; i. :- Shadi
38、ng Layer /i ;i TI, Tgl,n Tshade Tg1,out Tout Figure 4 Heat transfer analysis model of between-panes venetian blind. ASHRAE Transactions: Symposia 457 Pane Spacing, 1 c 7 t 1 Figure 5 Longwave radiation exchange between surfaces. ted and reflected flux components and, because the shading layer is par
39、tially transparent to longwave radiation, J, and J3 also include transmitted flux components. Note that because the fill-gas (air) is nonparticipating, the irradiance at each surface has now been replaced by the radiosity of the opposite side of the cavity. The radiation balances shown in Figure 6 a
40、re given more formally in Equations 7 through 1 O. (7) 4 J, = E,oT+P,J (9) 4 J3 = z3csT3 + p3J4 + 5, (10) 4 J4 = + p4J3 Equations 7 through 1 O include various optical properties. At the glass surfaces, the hemispheric emissivity values are denoted and (E, = = 0.84 for uncoated glass). Noting that g
41、lass is opaque with respect to longwave radiation, and invoking Kirchoffs law, it is apparent that + pi = 1 and + p4 = 1. The effective longwave radiative properties for the venetian blind (E, p2, T, E, p3, z3) were calculated using the techniques described by Yahoda and Wright (2004). Each of the b
42、lind layer effective optical properties is a function of slat width, slat spacing, slat angle, and the emissivity of the slat surfaces. Note that, on the basis of second law arguments, the front and back transmittance values of the venetian blind, z2 and z3, must be equal. Energy Balances Two more g
43、overning equations are obtained by writing an energy balance at each of the two glazing surfaces. For surface 1, Figure 6 Expanded surface radiosities and irradiances. For surface 4, 4 = 3- 4 hcav2(Tshade- Tgl,out) . (12) Convective Heat Transfer Coefficients Equations 1 1 and 12 contain the convect
44、ive heat transfer coefficients hcavi and hcav2 used to describe natural convection in the tall, vertical, air-filled cavities between the shading layer surfaces and the glazing surfaces. Two simple models were devised to estimate hcavi and hcav2. Both of these models were based on the well-establish
45、ed procedure used to determine the heat transfer coefficient, say, h, associated with heat transfer by natural convection across a tall, vertical, rectangular gas- filled cavity. Summarizing, h, can be expressed in terms of the Nusselt number, Nu, the conductivity of the gas, k, and the distance bet
46、ween the vertical walls, L, as shown in Equation 13. (13) k h, = NU- L Various correlations are available to calculate Nu as a function of Rayleigh number, Ra. The correlation used in this study was developed by Wright (1996) and is shown in Equa- tions 14 through 16. Nu = 0.0673838 . Ra“3 Ra5. lo4
47、(14) 4 i0 Ra5.i4 (15) 0.4134 Nu = 0.028154. Ra 510 (16) 2.2984755 Nu = 1 + 1.75967. lo-“. Ra The Rayleigh number is given by p2L3gCpAT Ra = PkT, where p is the gas density, Cp is the gas specific heat, and p is the fill gas viscosity. These properties are evaluated at T,- the mean temperature of the
48、 fill gas. The temperature differ- ence between the vertical walls of the caviy is denoted AT. The remaining item, g, is the acceleration due to gravity. It is convenient to express h, as an R-value, R, as shown in Equation 18. 458 ASHRAE Transactions: Symposia Table 1. Effective Longwave Radiative
49、Property Values 0.387 0.047 0.372 0.329 0.571 0.581 0.610 0.061 0.655 0.086 0.259 0.120 0.167 0.775 0.161 0.064 0.792 0.208 Natural Convection-Model One The values of he, and Rcav were assessed by ignoring the presence of the venetian blind in the glazing cavity. That is, L was set equal to the distance between the two sheets of glass and AT = TgLin - Tgl,. Half of Rea, was assigned to cavity 1 and half to cavity 2. Then, in keeping with Equation 18, (19) - hcavi - hcav2 = 2hcav Natural Convection-Model Two A second convection m
