1、2007 ASHRAE 471ABSTRACTSolar gain has a strong influence on building energyconsumption and peak cooling load. Venetian blinds areroutinely used to control solar gain. Software based on 1-Dmodels is available to accurately predict the thermal perfor-mance of glazing systems but the development of mod
2、els forshading devices is at a very early stage. An accurate model hasbeen formulated to quantify the thermal resistance of a glazingsystem with an enclosed venetian blind. It is possible toaccount for pane spacing, slat angle, alternate fill gases andthe presence of a low-emissivity coating. Effect
3、ive longwaveoptical properties are assigned to the blind layer in order tocalculate radiant heat transfer. An exceptionally simple modelfor convective heat transfer, the reduced slat length (RSL)model, has been developed on the basis of guarded heater platemeasurements. CFD results reveal reasons fo
4、r the very closeagreement between measurement and the RSL model. The newsimulation capability can be applied to the quantification ofU-factor and Solar Heat Gain Coefficient. The simplicity of theRSL model is particularly valuable in the context of buildingenergy simulation where CPU time must be us
5、ed sparingly.INTRODUCTIONBackgroundWindow area, and its associated design, distribution,orientation, etc., effect solar gain and heat losses of a building.Proper fenestration design can greatly reduce unwantedenergy gains/losses and can help maintain a comfortableindoor space. Solar gain is of parti
6、cular importance because ofboth its magnitude and variability. Shading devices such asvenetian blinds, roller blinds and drapes are frequently used tocontrol solar gain. Therefore, the current effort to createmodels for shaded windows is expected to be of significantvalueespecially in the field of c
7、omputational building loadsand energy analysis.One-dimensional (1-D) centre-glass models have beendeveloped (e.g., Finlayson 1993; Hollands et al. 2001;Hollands and Wright 1983; Wright 1980, 1998; Rubin 1982;Van Dijk and Goulding 1996) to predict the thermal perfor-mance of glazing systems and these
8、 models are known to beaccurate (e.g., Carpenter 1992; Wright and Sullivan 1987,1988). Software based on these models is widely used fordesign, code compliance and rating. In contrast, the develop-ment of models for windows with shading devices is at a veryearly stage. One set of shading layer model
9、s is available (VanDijk and Goulding 1996) but the user is required to quantifythe air permeability of certain types of shading layers withlittle guidance except for the instruction that the appropriatevalue is to be determined by means of experiment or compu-tational fluid dynamics (CFD) modelling.
10、Overview of this StudyThe problem of interest and some of the nomenclature areshown in Figure 1. A venetian blind is positioned at the centreof a vertical glazing cavity. The temperature differencebetween the two glazing surfaces drives heat transfer acrossthe cavity. The radiant and convective heat
11、 transfer compo-nents are coupled because of the presence of the venetianblind. The goal of this research was to formulate a model toquantify this coupled heat transfer. The resulting model isbased on guarded heater plate (GHP) measurements. Parallelstudies, based on CFD modelling of the natural con
12、vection,provide insights regarding the flow field (Tasnim 2005, NaylorThermal Resistance of a Window with an Enclosed Venetian Blind: A Simplified ModelJohn L. Wright, PhD Michael R. Collins, PhD Ned Y.T. HuangMember ASHRAE Associate Member ASHRAEJohn L. Wright is a professor and Michael R. Collins
13、is an associate professor in the Department of Mechanical and Mechatronics Engi-neering, University of Waterloo, Waterloo, Ontario, Canada. Ned Y.T. Huang is a mechanical R once with the constanttemperature bath thermostats set to 30C (86F) and 20C(68F) Tbath= 10C (18F) and again with the cold baths
14、etting lowered to 10C (50F) Tbath= 20C (36F). Themeasured plate-to-plate temperature difference, Tpp= ThotTcold, is always less than Tbathand the difference between thetwo is influenced by the thermal resistance of the test sampleitself. Nonetheless, the difference between Tbathand Tppwas small (les
15、s than 5% of Tppin almost all cases) so the twovalues of Tbathused in the experiments can be viewed asnominal values of Tpp.It should be noted that the U-factors shown in Figure 2were obtained by replacing the thermal resistance of theneoprene mats with fixed indoor and outdoor heat transfercoeffici
16、ents, hiand ho. More specifically,(1)where measured values of Tppand heat flux, , were usedto obtain the total (i.e., plate-to-plate) thermal resistance of thesample-plus-mats assembly, Rtot.(2)The combined resistance of the two neoprene mats,measured by Huang (2005), was(3)Garnet (1999) and Huang (
17、2005) chose to use fixed valuesof hi=8.0 W/m2K (1.41 Btu/hft2F) and ho= 23.0 W/m2K(4.05 Btu/hft2F) and this choice is reflected in Figure 2.HEAT TRANSFER MODELModel StructureSeveral models were devised in an attempt to reproducethe GHP measurements of Huang. In each instance the focusof the model wa
18、s the heat transfer within the glazing cavity.Each model was based on a structure of three temperaturenodes. These nodes correspond to the glass surface tempera-tures, T1and T3, plus the temperature of the venetian blind, T2.See Figure 1. A more sophisticated model might have beenchosen, perhaps wit
19、h two or more temperature nodes assignedto the venetian blind layer, but it was hoped that the simplerapproach would be sufficient. The simplicity of a three-nodemodel is especially useful in the context of building energyanalysis software where CPU time must be used sparingly.Boundary ConditionsThe
20、 glass surface temperatures, T1and T3, needed tocomplete each simulation were obtained using measured heatflux and plate temperatures from individual experiments.(4)(5)where the thermal resistance of each glass layer was taken as:(6)Calculation of U-FactorU-factors produced by simulation models, Usi
21、m, werecompared to the GHP measurements shown in Figure 2. Ineach case the heat flux predicted by the simulation, , wasconverted to a U-factor using Equation (7).(7)The mean temperatures in sub-cavities 12 and 23, Tm,12=(T1+ T2)/2 and Tm,23= (T2+ T3)/2, were used to determine theair properties in th
22、e two sub-cavities. The blind layer temper-ature, T2, was determined by iteration and the air propertieswere updated at each step of the process.The Radiant Exchange ModelThe longwave optical properties of each component influ-ence heat transfer across the cavity. At the glass surfaces thehemispheri
23、c emissivities are denoted 1and 3. Glass isopaque with respect to longwave radiation so the longwavereflectivities of these surfaces are 1=11and 3=13.The venetian blind was treated as a continuous, uniform layerby assigning it effective (i.e., spatially averaged) front-sideand back-side longwave pro
24、perties: f,2, f,2, b,2, b,2and 2.This set of blind layer properties was evaluated, as a functionof slat geometry and emissivity of the slat surfaces, using thefour-surface/flat-slat model presented by Yahoda and Wright(2004a). The front-side and back-side effective properties ofthe blind layer do no
25、t differ (f,2= b,2and f,2= b,2) becausethe two slat surfaces have the same properties. The effectiveblind-layer properties are presented as functions of slat anglein Figure 3.The radiant mode of heat transfer was quantified in termsof the radiosities shown in Figure 1 (J1, Jb,2, Jf,2, J3). Thismetho
26、d is well documented (e.g., Hollands et al. 2001,Hollands and Wright 1983, Rubin 1982, Yahoda and Wright2004b). Each radiosity is simply the radiant flux leaving asurfaceincluding emitted, reflected and transmitted compo-nents. The net radiant heat flux across either sub-cavity is justUmeasRtot2Rn1h
27、o-1hi-+1=qRtotTppq-=2Rn0.01m2KW- 0.0568hft2FBtu-=T1ThotRnRg+()q=T3TcoldRnRg+()q=Rg0.003m2KW- 0.017hft2FBtu-=qsimUsimT1T3qsim- 2 Rg1ho-1hi-+1=474 ASHRAE Transactionsthe difference between the radiosities of the boundingsurfaces.Note that each radiant flux is presumed to be diffuse andshape factors be
28、tween adjacent layers are all equal to unity.The air is non-participating. Also note that Jf,2and Jb,2eachinclude a transmitted flux component because the venetianblind will in general be partially transparent to longwaveradiation:Equations (8) through (11) describe the interactionbetween, and the c
29、omponents of, the various radiosities. Theseequations comprise a complete radiant exchange model for thesystem of interest. (8)(9)(10)(11)If T2is known this system of equations can be solved by vari-ous methods including matrix reduction. The system is smallenough to algebraically obtain explicit ex
30、pressions for thefour radiosities (Huang 2005).Convective Heat TransferThe various heat transfer models described in the follow-ing sections make use of a convective heat transfer coefficient,h, that is estimated using a correlation that applies to heattransfer across a tall, vertical, gas filled, r
31、ectangular cavitysuch as a conventional glazing cavity. In each case, havingchosen a characteristic length, x, the Nusselt number based onx, Nux, is calculated as a function of the Rayleigh number, Rax.The Rayleigh number is a function of the temperature differ-ence across the cavity, several gas pr
32、operties and the charac-teristic length, x. In the case of a glazing cavity x is generallychosen to be the pane spacing. Equations (12) and (13) showsome of the detail. (12)(13)Air properties (specific heat at constant pressure Cp, dynamicviscosity , thermal conductivity k) were determined as afunct
33、ion of air temperature using regressions fitted to data(Hilsenrath 1955) over the temperature range from 283 K to303 K. The air density, , was determined using the ideal gasrelationship. The compressibility factor was found to bewithin 1% of unity for all cases (z = 0.995 was used). Thelocal value o
34、f acceleration due to gravity is g = 9.8064 m/s2(g = 32.173 ft/s2) (Bolz and Tuve 2000). The thermal expan-sion coefficient is =1/Tmfor a perfect gas. In this study the correlation of Wright (1996)* was usedto evaluate the function Nux=Nu(Rax) but any one of severalsimilar correlations (e.g., Shewen
35、 et al. 1996, Elsherbiny et al.1982) could have been used to obtain the same results.Coupled Heat TransferExpressions for heat flux across each of the two sub-cavities can be written by considering the components ofconvective heat transfer and longwave radiant exchange:(14)(15)If the convective heat
36、 transfer coefficients, h12and h23, areknown Equations (8) to (11) plus (14) and (15) constitute acomplete model for heat transfer across the cavity. The goal isto find T2such that and since the convective heattransfer coefficients and radiosities are all influenced by T2thesolution must be generate
37、d by iteration. The details of the solu-tion algorithm are of little importance; any one of many tech-niques can be used.NATURAL CONVECTION MODELSSimple Natural Convection Model, M1To establish a point of reference a relatively simple modelfor convective heat transfer (M1) is presented. This model i
38、salmost identical to one of the models examined by Yahoda andWright (2004b) whose simulation results agreed only moder-ately well with measured data (Garnet et al. 1995)generallywithin 10%. Similarly, in the current study model M1 did notperform well when compared to the measurements of HuangFigure
39、3 Effective longwave properties of venetian blindlayer.J11T141Jb 2,+=Jf 2,f 2,T24f 2,J32J1+=Jb 2,b 2,T24b 2,J12J3+=J33T343Jf 2,+=*A correction: In (Wright 1996) the exponent in Equation 9b shouldbe 0.41399 instead of 0.4134.Rax2gCpT x3k-=h Nuxkx-=q12h12T1T2()J1Jb 2,+=q23h23T2T3()Jf 2,J3+=q12q23=ASHR
40、AE Transactions 475(Huang et al. 2006). Nonetheless, because this convectionmodel does not include the influence of slat angle, it highlightsthe need to account for slat angle in more than just the radiationexchange and additional models are presented that explorethat aspect of the problem.Model M1
41、was devised by assuming that the venetianblind segregates the flow of the fill-gas as if there were twoseparate cavities. The heat transfer coefficients, h12and h23,were approximated using Nuxdetermined separately forcavity 12 and cavity 23. In each case, x was set equal to halfof the pane spacing (
42、x12= x23= L/2). Yahoda and Wright(2004b) set the temperature difference across each sub-cavityequal to half of the temperature difference between hot andcold glazing (T12= T23=(T1 T3)/2). In the present study themost recent estimate of T2was used (T12= T1 T2andT23= T2 T3) at each iteration of the so
43、lution process. No ther-mal resistance was assigned to the venetian blind layer.Figure 4 includes a comparison of model M1 versus GHPmeasurements for one particular test sample (L =17.78 mm(0.7 in.), Tbath= 20C (68F), low-e coating present).U-factors are shown as a function of slat angle, . This sim
44、plemodel agrees closely with measurement when the blind isfully closed (extrapolating the measurements to = 90), asmight be expected, but it does not account for the variation of as the slats are opened.An important observation regarding Figure 4 is that theM1 model shows so little variation with .
45、The convectioncomponent of the M1 model is not influenced by . Therefore, influences the M1 results only through changes in the effec-tive optical properties of the blind layer and the resultingchange in radiant heat transfer. In this case some of insensi-tivity with respect to will be due to the pr
46、esence of the low-e coating. Assuming that the radiation model is accurate, anassertion supported by the close agreement at = 90, it canbe concluded that the influence of on the heat transfer acrossthe cavity arises largely through its influence on convectiveheat transfer.Tip-to-Glass Natural Convec
47、tion Model, TGA second model, TG, was devised by again assuming thatthe venetian blind segregates the glazing cavity in two cavi-ties. This model is identical to model M1 except that in thiscase the width of each cavity was taken to be the distance fromthe tip of the blind slats to the adjacent glas
48、s surface x12= x23= (L wcos)/2. Again, no thermal resistance was assignedto the venetian blind layer.A comparison between model TG and GHP data is alsoshown in Figure 4. Again simulation and measurementapproach each other as the blind is closed, and the slat angleclearly has an influence on calculated U-factors but this influ-ence is far too strong. At this stage a third model was devised.Reduced Slat Length Model, RSLThe TG convection model was modified in order toreduce its sensitivity to slat angle. This was accomplished byintroducing a factor, N, by which the slat width, w, would bereduce
