1、2010 ASHRAE 157ABSTRACTHeat transfer in a roof insulation assembly used in metalbuildings was investigated experimentally and using compu-tational fluid dynamics (CFD) based modeling. The experi-mental study was performed using a 2.445 3.054 m (96.25 120.25 in.) test frame for a Standing Seam Roof (
2、SSR) assem-bly. The SSR configuration involved installing NAIMA (NorthAmerican Insulation Manufacturers Association) 202-96 R19faced fiberglass insulation over and perpendicular to 0.203 m(8 in.) high metal roof purlins with 0.0667 m (2.625 in.) flanges.Two purlins were spaced 1.524 m (5 ft) on cent
3、er in the testframe creating three cavities in the metering area. The purlinswere connected to metal roof panels using standing seam panelclips designed to create approximately 0.0349 m (1.375 in.) ofspace between the top of the purlin and the bottom of the roofpanel. This space contained both compr
4、essed fiberglass insu-lation and 0.0254 m (1 in.) high by 0.0762 m (3 in.) wideextruded polystyrene (XPS) foam block insulation. The foamblocks were installed between the top of the fiberglass insula-tion layer and the roof panel.Heat flow through the test frame was measured in a hot-box set-up with
5、 the insulation side of the test frame facing airkept at an average temperature of 311.2 K (100.5F) and theroof side facing air maintained at an average temperature of283.4 K (50.4F). Mathematical modeling involved the formu-lation of the steady-state, three-dimensional natural convec-tion and heat
6、transfer problem in the SSR assembly. The modelaccounted for the relevant geometrical complexities andallowed for variations in fiberglass insulation thermal con-ductivity with density (i.e., compressed thickness). The gov-erning transport equations and the boundary conditions weresolved numerically
7、 using CFD software Fluent. Excellentagreement was observed between model predictions of theoverall heat transfer coefficient (U-factor) and calculationsbased on experimentally measured values. The model pre-dicted U-factor was 0.369 W/m2K (0.065 Btu/ft2hF) whennatural convection in various air gaps
8、 was accounted for and0.358 W/m2K (0.063 Btu/ft2hF) when the air was assumedto be stagnant. The measured value was 0.349 W/m2K(0.061 Btu/ft2hF).INTRODUCTIONThe term “metal building” is used to describe buildingstypically used for commercial, manufacturing and many otherapplications. Metal buildings
9、generally are relatively fast toconstruct, require low maintenance, and offer flexibility indesign, construction and expansion (Newman 1997). For thesereasons, metal buildings are widely used in U.S. and arebecoming popular elsewhere.In general, energy savings considerations have not been asignifica
10、nt factor in the design and construction of metal build-ings. That situation is changing due to concerns about higherenergy prices and a better understanding of building science inthe industry. Proper use of insulation materials in metal build-ing roofs and walls will likely improve the energy effic
11、iencyof these structures. Some common metal building insulationmaterials are fiberglass, foam board, spray-on cellulose andpre-insulated panels. A more recent development is the use ofspray-in-place polyurethane foam. All of these insulationmaterials are installed on-site during the construction. Fi
12、ber-glass insulation with an appropriate facing is predominant inmetal building roofs and is also widely used for the walls.During the late 1990s, the American Society of Heating,Refrigeration and Air-Conditioning Engineers (ASHRAE)Standing Standard Project Committee (SSPC) 90.1 EnvelopeASHRAE Stand
13、ard 90.1 Metal Building U-FactorsPart 1: Mathematical Modeling and Validation by Calibrated Hot Box MeasurementsM.K. Choudhary, PhD, PE C. KasprzakAssociate Member ASHRAER.H. Larson R. VenuturumilliM.K. Choudhary is a member of senior technical staff at Owens Corning Science Carpenter et al.2003; Ch
14、ristian and Kosny 1995; Enermodal 2001; Johannes-son and Vinberg 1986; Kossecka and Kosny 1996, 1997).While these earlier studies were not done for metal buildingassemblies except for the paper by Johannesson and Vinberg(1986) the approaches developed may be extended to metalbuilding assemblies. Stu
15、dies by Kossecka and Kosny (1996,1997), Enermodal (2001), and Carpenter et al. (2003) describean “Equivalent Wall Method” that allows one to account fortwo- and three-dimensional heat flow (e.g., near corners) andthermal bridging (e.g., due to steel studs in cavity walls)effects on the transient res
16、ponse of wall assemblies. Thismethod uses thermal structure and response factors that arecalculated using three dimensional heat conduction analysisfor various elements of the wall assembly. The zone method orthe modified zone method have also been used to calculate theU-factor for the metal buildin
17、g roof and wall insulation assem-blies (ASHRAE 2009). These methods are based on a two-dimensional, steady-state conductive heat transfer analysisand involve two separate computations: one for a zonecontaining the highly thermal conductivity materials and theother for the remaining portion of the as
18、sembly. The twocomputations of area-conductances (area multiplied by trans-mittance) are then combined using the parallel-flow method(i.e., heat flows in parallel paths of different conductances).The modified zone method is an improvement over the zonemethod in that the former has a more accurate tr
19、eatment of thezone containing the high conductivity materials.These earlier studies have played an important role in high-lighting the thermal bridging effect, provide useful insights intoheat transfer in metal building assemblies, and some of themhave been used to calculate the U-factors for metal
20、buildinginsulation assemblies. The models described in them, however,can not easily be extended or generalized to calculate complexthree-dimensional air flow and heat transfer phenomena thatmay occur in metal building insulation assemblies. Indeed, tothe best of authors knowledge, the only published
21、 detailednumerical modeling study of heat transfer in various metalbuilding assemblies was done on behalf of NAIMA in 1998(Graber 1998). Comprehensive experimental measurements(steady-state hot box testing) of heat transfer through variousmetal building assemblies have been conducted by the Building
22、Technology Center at Oak Ridge National Laboratory in itsLarge Scale Climate Simulator (Petrie 2004, 2007).This paper describes a three-dimensional mathematicalmodel for heat transfer in a metal building standing seam roofassembly and its validation with hot box measurements. Thepresent work present
23、s considerable advance over the earlierFigure 1 SSR assembly schematic. 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or tr
24、ansmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 159work (Graber 1998), in terms of its allowance for salientgeometrical features and its validation with respect to care-fully measured hot box data. The validated model will be
25、usedto calculate the thermal performance of SSR configurations ofinterest to the metal building industry and to update, wherenecessary, the relevant assembly U-factors in ASHRAEs 90.1standard. To reiterate, the objective of this work was todevelop a comprehensive and validated mathematical modelthat
26、 may be used to calculate the thermal performance of metalbuilding insulation assemblies. The measured and calculatedU-factors for the roof assembly presented in this paper are notintended to confirm or refute any values in the currentASHRAE 90.1 standard.HOT BOX SET-UP FOR SSR ROOF ASSEMBLYFigure 2
27、 shows a schematic of the hot box set-up that wasassembled for the SSR assembly. The schematic is shown inthe vertical orientation, while the assembly in this study wastested in the horizontal orientation. The test frame was a 2.445 3.054 m (96.25 120.25 in.) panel with the purlins mountedin the 2.4
28、45 m (96.25 in.) direction and the insulation drapingalong the 3.054 m (120.25 in.) length. Two purlins 1.525 m(5 ft) apart were used to secure the insulation in the test frame.The insulation used was faced NAIMA 202-96 R-19. Theinsulation was cut to 103% of the total length of the test appa-ratus (
29、i.e., 3.146 m or 123.858 in). A photograph of the testpanel is shown in Figure 3.The assembly was put inside the climate simulator withthe climatic chamber on top and at 283.4 K (50.4F) and themetering chamber (insulation and purlin side) on the bottomand at 311.2 K (100.5F). With this configuration
30、 the heat flowwas in the upward direction (from insulation and purlin side tothe roof) and the mean air temperature was 297.3 K (75.5F).A picture of the test panel closed between the two meteringchambers and rotated into the horizontal position is shown inFigure 4.Heat balance for the hot box system
31、 described above maybe expressed as follows.Qsp= Qmcp+ Qmcw+ Qinf Qfl(1)whereQsp= specimen heat flowQmcp= metering chamber input powerQmcw= metering chamber wall heat gain (+) /loss ()Qinf= heat transfer due to air leakageQfl= flanking loss through specimen frameFigure 2 A schematic of the hot box s
32、et-up that was assem-bled for the SSR assembly.Figure 3 A photograph of the test panel.Figure 4 A photograph of the test panel closed between thetwo metering chambers and rotated into the hori-zontal position 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.
33、ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 160 ASHRAE TransactionsLet us now consider each term on the r
34、ight hand side ofEquation (1).The metering chamber power, Qmcpconsists of DC fanpower, Qfan; DC heater power, Qhtr; and any other meteringchamber power inputs (in the present case the velocity sensorpower, Qvs). Each of this is calculated by multiplying thecorresponding voltages and amperages.Qmcp=
35、Qfan+ Qhtr+ Qvs(2)Metering chamber wall heat loss/gain, Qmcwis minimizedby keeping the surround room air temperature as close aspossible to the metering chamber air temperature. Its valuemay be estimated as follows.Qmcw= Aw(Tw)/Rw(3)whereAw= Exterior metering chamber area = 21.18 m2(228.0 ft2)Tw= Me
36、tering chamber wall temperature differenceRw= Metering chamber wall R-value (wall thickness/ thermal conductivity of wall) = 10.57 m2K/W (60 ft2Fh/Btu).The maximum allowed temperature difference betweenthe metering chamber air and the surround room air is 1K(2F). To meet ASTM C 1363 requirements, th
37、e meteringchamber wall heat loss/gain cannot exceed 10% of the speci-men heat transfer.Since heat transfer associated with air leakage (Qinf) isdifficult to accurately characterize and assess, air leakagethrough the test specimen was minimized by sealing theperimeter of the test specimen along with
38、all seams andfastener penetrations with tape and caulk. Air leakage throughthe frame/chamber interface was minimized by using foam“Camper Seal” tape around the perimeter of the test frame,ensuring that the rubber gaskets around the perimeter of eachchamber were in good shape and coupling the chamber
39、s to thetest frame with several tightened bolts. As additional air leak-age prevention, the refrigeration system air flow was restrictedwith an adjustable damper to maintain the climatic chamberair pressure as close as possible to zero. The tracer gas systemwas used to check for potential metering c
40、hamber air leakage.Flanking loss, Qflis the extraneous heat flow primarilythrough the perimeter 6.35 mm (0.25 in.) plywood face plateof the sample frame. It can also occur near the perimeter ofthe test specimen and in other sample frame components.Flanking loss may represent 1 to 20% of the total sa
41、mple heatflow, the magnitude of which depends on specimen thick-ness, geometry and surface heat transfer coefficients. ASTMC 1363 recommends that flanking loss be estimated usingtwo- or three-dimensional heat flow models that have beenverified by testing. Following this recommendation, we usedthe fo
42、llowing formula, derived from several finite elementanalyses conducted in the past for the hot box testing, to esti-mate the flanking loss.(4)whereQfl= flanking heat loss in Btu/hL = thickness of the specimen in inchTair, mc = average air temperature in the metering (i.e., warm) chamber in FTair,cc=
43、 average air temperature in the climate (i.e., cold) temperature in FThe term heffis an effective heat transfer coefficientdefined as follows.(5)where, hmcand hccare surface heat transfer coefficients in themetering and climate chambers respectively. These are calcu-lated as follows:(6a)(6b)whereA =
44、 test specimen area (7.48 m2or 80. 49 ft2)Tsur,mc= area-weighted specimen surface temperature on the metering chamber sideTsur,cc= area-weighted specimen surface temperature on the climate chamber sideMATHEMATICAL MODELTable 1 and Figure 5 provide the detailed profile informa-tion that was measured
45、for the insulation and air gap in the hotbox set up. This measurement information was used to gener-ate the CAD shown in Figures 6 and 7. Shown here are theprincipal components and dimensions. The roof panels are0.61 m (2 ft) wide. Because of assumed symmetry, we showhalf the width in Figure 6. The
46、details on the fiberglass andfoam insulation above the purlin and the connection of the roofpanel to the purlin are presented in Figure 7.As seen in Figures 6 and 7, the modeling domain consistsof the following components.1. A metallic purlin, 0.203 m (8 in.) high with a flangelength of 0.0667 m (2.
47、625 in.). 2. Fiberglass insulation (divided into left-, mid-, and right-sections).3. Compressed fiber glass insulation (9.53 mm or 0.375 in.thick) above the purlin.Qfl1.57181 heff0.812L+- Tair mc,Tair cc,()=heffhmchcchmchcc+-=hmcQmcpQmcw+ATair mc,Tsur mc,()-=hccQmcpQmcw+ATsur cc,Tair cc,()-= 2010, A
48、merican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs pri
49、or written permission. ASHRAE Transactions 161Table 1. Insulation and Air Gap Profile Measurements from Hot-Box (2.54 cm = 1.0 in.)Distance Left to Right (cm)Insulation Thickness (cm)Air Gap Thickness (cm)Distance Left to Right (cm)Insulation Thickness (cm)Air Gap Thickness (cm)Distance Left to Right (cm)Insulation Thickness (cm)Air Gap Thickness (cm)0.00 14.22 0.00 101
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