1、2010 ASHRAE 177ABSTRACTIncreased thermal performance of metal building roof andwall assemblies can be achieved by using double layers offiberglass batt insulation. Determination of the installeddouble layer assembly U-factor is more complex than that ofa single layer assembly when each layer has dif
2、ferent materialproperties. Experimental data on the compression of typicalfiberglass batt insulation samples are presented along with thederivation of the double layer U-factor equations. Finally, anexample is presented to illustrate the application of the U-factor equations. These equations compris
3、e the basis for therevised double layer U-factors for ASHRAE Standard 90.1-2010.INTRODUCTIONThe ASHRAE Standards 90.1-1999 (ASHRAE 1999),90.1-2001 (ASHRAE 2001), 90.1-2004 (ASHRAE 2004) and90.1-2007 (ASHRAE 2007) contain appendices which list theinstalled U-factors for fiberglass batt insulation in
4、metal build-ing roof and wall assemblies. These U-factors were originallydeveloped through finite element analysis (FEA) models thatwere validated against calibrated hot box (CHB) measure-ments (Graber 1998). Each U-factor was based on manyassumptions that were considered to be typical or representa
5、-tive values at that time. The FEA models replicated the drapethat was observed in the CHB tests. However, the fundamentalquestion was whether the CHB drape was representative oftypical field installations and this has generated considerabledebate.The installation and subsequent centerline drape of
6、thefiberglass batts in metal building roof and wall assemblies arecontrolled by the insulation installer. Installation instructionsexist but there are no specific criteria regarding the centerlinedrape necessary to achieve the desired thermal performance(NAIMA 2006). Thus, field measurements of actu
7、al installa-tions provide the best record as to the actual drape that exists.Once the actual drape is known then it can be used to deter-mine the corresponding U-factor. Historically, the U-factorswere determined by either CHB tests or FEA modeling, andboth are expensive and time consuming.The SSPC
8、90.1 Envelope Subcommittee identified a needto be able to calculate these U-factors using simpler mathe-matical models. To develop these models they formed a taskgroup to address these problems which were divided into fourseparate activities. The first activity was to develop newcomputational fluid
9、dynamic (CFD) models which were thenvalidated against CHB test results (Choudhary et al. 2010).Second, a simplified model for a single layer of fiberglassbatts was developed and correlated back to the CFD results(Choudhary and Kasprzak 2010). Third was the developmentof a simple model for double lay
10、ers of fiberglass batts, whichis the focus of this paper. Fourth, field and experimental lab-oratory measurements of typical or representative drape pro-files, including center line measurements, were completed andthose results were used in combination with the simplifiedmodels to calculate the prop
11、osed roof and wall assembly U-factors for Standard 90.1-2010 (Christianson 2010).Double layers of fiberglass batt insulation are a typical con-struction option used to achieve higher thermal performance inmetal building roofs and walls. When the double layers have dif-ferent material properties it i
12、s more difficult to determine thecombined U-factor. To address this fundamental problem aseries of experimental tests were completed and the results wereused to develop a simplified U-factor calculation procedure.ASHRAE Standard 90.1 Metal Building U-FactorsPart 3: Equations for Double Layers of Fib
13、erglass Batt Insulation in Roof and Wall AssembliesMerle F. McBride, PhD, PE Patrick M. Gavin, PhDMember ASHRAEM.F. McBride and P.M. Gavin are senior research associates at the Center of Science and Technology, Owens Corning, Granville, OH.OR-10-019 2010, American Society of Heating, Refrigerating a
14、nd 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 prior written permission. 178 ASHRAE Transacti
15、onsOBJECTIVEThe objective was to develop a simplified calculationprocedure to determine U-factors for double layer fiberglassbatt insulation assemblies in metal building roof and wallassemblies.DERIVATION OF DOUBLE LAYER FIBERGLASS BATT INSULATION THERMAL PERFORMANCEThe U-factors for metal building
16、roof and wall assembliesare complex to calculate because they include non-typicalconditions including draped fiberglass batt insulation that iscompressed over the structural member to thicknesses whichvary with the clip height and the possible presence of a thermalblock. The complexity is further in
17、creased when there are twolayers of fiberglass batts present, each with different physicalproperties.The determination of the thermal performance of doublelayer fiberglass batt insulation was divided into four distinctsteps. First, the compression of double layer fiberglass batt in-sulation was expe
18、rimentally evaluated. Second, a simplifiedequation was developed to calculate the U-factor that accountsfor the fiberglass batt compression. Third, a correlation be-tween the detailed CFD modeling and the simplified equationfor a single layer of fiberglass batt insulation was used. Thiscorrelation a
19、ccounted for the additional details associatedwith the metal clips that were included in the CFD model butexcluded in the simplified model. Fourth, centerline drapemeasurements were used in the simplified model to calculatethe overall U-factors. Details on the experimental measure-ments, the develop
20、ment of the U-factor equations and an ex-ample using the equations follow.Experimental Measurements on Compression of Fiberglass Batt InsulationFor the purpose of computing the thermal performance ofdouble layers of fiberglass batt insulation, the relevant prop-erties of the individual layers need t
21、o be determined when theyare together subjected to a given level of compression, asshown in Figure 1.Starting with the individual layer reference propertiesgiven as,01= reference density of first layer, lb/ft3 (kg/m3)02= reference density of second layer, lb/ft3(kg/m3)W1= reference weight of first l
22、ayer, lb/ft2(kg/m2)W2= reference weight of second layer, lb/ft2(kg/m2)and the total compressed thickness,Yc= compressed thickness of the double layers, ft (m)the thicknesses of the individual layers need to be determined,Y1= compressed thickness of first layer, ft (m)Y2= compressed thickness of seco
23、nd layer, ft (m)The individual layer compressed densities needed todetermine the individual layer thermal conductivities followdirectly from the layer thicknesses, since the reference areaweights do not change during compression:1= W1/Y1(1)2= W2/Y2(2)In the case illustrated in Figure 1, each of the
24、layers issubjected to the same compression force,F = compression force applied to double layer, lb (N)When the compression force is linearly related tocompressed thickness, the problem reduces to the familiarcase of two springs in series. For fiberglass batt insulation,however, the problem is compli
25、cated by the fact that the force/thickness relationship is strongly nonlinear, as shown inFigure 2.The data in Figure 2 are for typical, single-layer fiberglassbatt insulation samples with the same cross-sectional area, butFigure 1 Geometry of double layers of fiberglass batts.Figure 2 Compression m
26、easurements for fiberglass insu-lation samples obtained on a universal testingmachine. 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, dist
27、ribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 179with different reference weights, compressed separately on auniversal testing machine. The nonlinearity in the compres-sion curves arises primarily because the
28、density of the fiber-glass is continuously increasing as it is compressed, andincreasing density leads to a continuously increasing effectivespring constant. This effect can be quantified by referring tothe literature on mechanical properties of cellular foams,whose compression curves strongly resem
29、ble those of fiber-glass batts. For foams, mechanical properties generally scalewith the square of the foam density (Zhang and Rodrigue2003). Assuming that the fiberglass batt effective springconstant (or compression modulus) obeys the cellular foam“square law,” then:(3)where is a constant of propor
30、tionality, and omitting thesubscripts on density (), thickness (Y ) and area weight (W ),results in considering compression of a single layer. Integra-tion of Equation (3) is:(4)Evaluating the integration of Equation (4) at the limits yields:(5)Recognizing that the (constant) area weight can beexpre
31、ssed in terms of the initial density, the following expres-sion is obtained:F 0( 0)(6)The fiberglass batt data in Figure 2 are re-plotted in Figure3 in accordance with this approach, and a single, nearly linearrelationship is observed.For the two-layer case, as noted above, the layers aresubjected t
32、o the same compressive force. Employing Equation(6), this means that:F 01(1 01) = 02(2 02)(7)Beginning with Equation (7), a quadratic equation can bederived (Appendix A) relating the compressed thickness of anindividual fiberglass layer to the total compressed thickness:(8)Example of Double Layer Fi
33、berglass Batt CompressionAs an example, consider the case of double layers of fiber-glass batt insulation with the following reference properties:01= 0.793 lb/ft3 (12.7 kg/m3)02= 0.463 lb/ft3 (7.4 kg/m3)W1= 0.231 lb/ft2(1.13 kg/m2)W2= 0.241 lb/ft2 (1.18 kg/m2)Y01= 0.292 ft (0.089 m)Y02= 0.521 ft (0.
34、159 m)These correspond to layer 1 being nominally R-13hft2F/Btu (R-2.29 Cm2/W) and layer 2 being nominallyR-19 hft2F/Btu (R-3.35 Cm2/W).The behavior of the individual layer thicknesses as thisdouble layer is compressed to about one-fourth of its initialthickness is shown in Figure 4. As expected, th
35、e lighter densitylayer absorbs more of the compression initially, but as itsdensity increases, significant compression of the originallydenser layer occurs as well. Properly accounting for theseeffects via the methodology outlined above improves our abil-ity to characterize the thermal performance o
36、f double layers offiberglass batt insulation.Calculation of Overall U-factors for Double Layer Fiberglass Batt Insulation SystemsThe U-factor of metal building roof and wall assembliesthat are insulated with double layers of fiberglass insulationare calculated using the following procedure. This pro
37、cedureassumes that both layers of insulation are compressed over theframing member and there may be a thermal spacer blockpresent, see Figure 5.dFdY- 2W2Y2-=Fd0FW2Y2YdY0Y=F W21Y-1Y0-WWY-WY0-W 0()=Y1Yc-201W102W2o22o12Yc- 1Y1Yc-01W1o22o12Yc-+ 0=Figure 3 Linearized compression measurements for fiber-gl
38、ass insulation samples. 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 transmission in either print or digital form is no
39、t permitted without ASHRAEs prior written permission. 180 ASHRAE TransactionswhereX = distance from edge of purlin or girt, ft (m)Y = distance from edge of roof panel or wall panel, ft (m)L = half the spacing between the purlins or girts, ft (m)Yo= insulation thickness over the purlin or girt, ft (m
40、)Ym= maximum insulation thickness at center line of purlins or girts, ft (m)wf= width of framing member, ft (m)There are six steps in the calculation process:Step 1Characterize the thermal conductivity of thefiberglass. The thermal conductivity of the fiberglass battinsulation is represented by a th
41、ermal curve of the form inEquation (9) which characterizes typical insulation manufac-turers data in Table 1. This is a statistical regression equationwith the B and C coefficients determined by the regressionanalysis. The first term is the coefficient “A” which is the ther-mal conductivity of air s
42、ince that represents over 99% of thevolume of the insulation pack. The second term “B” repre-sents conduction through the insulation pack. As the densityincreases the fiber to fiber contacts increase causing theconduction heat transfer to increase. The third term “C/”represents radiation through the
43、 insulation pack. As thedensity increases there are more fibers per unit volume toabsorb and scatter the radiation causing the radiation heattransfer to decrease.k = A + B + C/ (9)wherek = thermal conductivity, Btu/hftF (W/mC) = density, lb/ft3(kg/m3)A = 0.014917 Btu/hftF (0.0258168 W/mC)B = 0.00043
44、77 Btuft2/lbhF (0.000047295 Wm2/kgC)C = 0.0056897 Btulb/hft4F (0.157740033 Wkg/m4C)The properties of fiberglass batt insulation are presentedin Table 1.Step 2Determine the U-factor (Uco) for the insula-tion in the cavity. Assume the double layer fiberglass battforms a parabolic profile defined by Eq
45、uation (10) (Choud-hary and Kasprzak 2010b).Y = Yo+ (Ym Yo)(10)Figure 4 Calculated individual layer thickness curves forcompression of R-13/R-19 double layer of fiber-glass insulation.Figure 5 Geometry of double layers of fiberglass batts.Table 1A. Fiberglass Reference Properties (I-P units)R-Value,
46、hft2F/BtuWeight, lb/ft2Density, lb/ft3Thickness, ftConductivity, Btu/hftF10 0.149 0.605 0.2458 0.024611 0.168 0.630 0.2667 0.024213 0.199 0.628 0.3167 0.024416 0.243 0.634 0.3833 0.024019 0.297 0.653 0.4542 0.023925 0.427 0.742 0.5750 0.023030 0.520 0.766 0.6792 0.0226Table 1B. Fiberglass Reference
47、Properties (SI units)R-Value, m2C/WWeight, kg/m2Density, kg/m3Thickness, mConductivity, W/mC1.76 0.727 9.680 0.075 0.04251.94 0.820 10.080 0.081 0.04202.29 0.971 10.048 0.097 0.04222.82 1.186 10.144 0.117 0.04153.34 1.449 10.448 0.138 0.04144.40 2.084 11.872 0.175 0.03985.28 2.538 12.256 0.207 0.039
48、2X2-2X2- 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 transmission in either print or digital form is not permitted wit
49、hout ASHRAEs prior written permission. ASHRAE Transactions 181The presence of two layers of fiberglass adds complexitybecause each layer has distinct reference properties, see Table 1.As the double layers are compressed the thickness of each layerneeds to be determined by considering that each layer experi-ences the same compress
