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A Comparison of Two Techniques for R-Value Calculation, Using Winter In-Situ Data

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A Comparison of Two Techniques for R-Value Calculation, Using Winter In-Situ Data A COMPARISON OF TWO TECHNIQUES FOR R-VALUE CALCULATION, USING WINTER IN-SITU DATA Stephen N. Flanders Andre O. Desjarlais Timothy J. Kunz ABSTRACT Tllis stlldy employed will tel' ill-sitll temperatllre alld lIeat fllIX least sqllares. Tllese leclllliqlles were applied to tile data ob­ data from a blli/dillg ill Nortll Dakota alld two bllildillgs ill tailled alld tile res liltS call/pared. Tile colllparisoll reported ill IIpstate New York. Tile alltllors obtailled tile temperatllre alld tllis stlldy was of tile estill/ate of tile R-vaille obtailled, tile lIeat fllIX data accordillg to ASTM Stalldard Practice C 1046- speed at wllicll a stable vallie was obtailled, alld all assessmellt 91. A proposed revisioll of ASTM Stalldard Practice C 1155 of tile COllditiolls tllat provided tile 1II0St reliable res lilts frolll illellldes two enlcllialiollal teclllliqlles, sllmllwtioll, alld Slllll of eaell calclilatioll. INTRODUCTION understand the geometry of heat flow in the building cOlllponent to be nleasured, sometimes lIsing infrared Determination of In-Situ Thermal Resistance thermography. The user then strives to place the instru­ with one-dimen­ Determination of thermal resistance or R-value of mentation in areas predonlinantly sional heat flow perpendicular to the surface of the building envelope components is useful to ensure that component. The teclmiques are further limited to light­ construction standards have been filet or as a tool to and medium-weight construction. Courville et aJ. (1990) assess needed improvements in insulating levels. Such a fmOld that agreement between the hl'o teclmiques determination is more difficult to accomplish in settings improved when the measured heat flux was greater of actual use than in the laboratory because of the delays than ±1.5 W 1m2 (0.5 in thermal signals caused by thermal storage and insula­ Bh!/h.f~). tion effects. 11lis paper compares two teclmiques for cal­ Summation Technique The sUllunation teclulique culating R-value from in-situ data. uses accumulated temperature and heat flux data to esti­ In-Situ Data Two American Society for Testing and mate thermal resistance as follows: Materials (ASTM) standards are available for measuring L [T;n (I) - T",,, (t) 1 in-sih! temperature and heat flux data-C 1046-91 t:;: 0 (ASTM 1991) and then for determining thermal resis­ II (t) = '----'--:=----- (1) L q(t) tance from them, C 1155-90 (ASTM 1990c). In Europe, a t:o; 0 standard is under development to accomplish the same purpose (draft ISO Standard 9869). A variety of calcula­ where f is titne and T and q are the temperature and heat tional teclmiques have been proposed and tried, includ­ flux at a surface. ing modified summation teclmiques (Anderson 1986), Sum-of· Least-Squares Technique The sum-of-Ieast­ multiple linear regression (Anderlind 1992), sum-of­ squares technique adapts to multiple sensors placed at least-squares techniques (Beck et aJ. 1991; Bomberg et aJ. several boundaries between hOlnogeneous layers within 1994), and Fourier analysis (draft ISO Standard 9869). an insulated component. It assumes that one-dinlen­ 11,is paper focuses on comparing the hl'o procedures sional, transient conduction is the heat transfer mecha­ proposed for C 1155-90-the stunmation technique and nism. TIle governing equation, allowing for variable­ the sum-of-Ieast-squares technique. temperature thermal properties, is as follows: Assumptions Both techniques place constraints on a ( aT) aT aT (2) how the data were obtained. They require that the user dx A'dX = (p' Cp ) at with q = -A,ax Stephen N. Flanders Is with the U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, N.H. Andre O. DeSjarlais Is with Ook Ridge National Laboratory, Oak Ridge, Tenn. Timothy J. Kunz Is with Holometrix, Inc .. Bedford, Mass. Thermal Envelopes VI/Heat Transfer in Walls I-PrinCiples 151 where A is thermal conductivity and p and Cp are the Significant ~T. Therefore, long-term data sets were used material density and specific heat, respectively. wherever possible. TIlis teclulique solves Equation 2 numerically, using Speed of Determination Because of the delays in the Crank-Nicholson method, to obtain a finite-differ­ obtaining an output thermal signal of temperature 01' ence approximation. The measured temperature and/or heat flux on one side of the construction when the oppo­ heat flux histories on each side of the building compo­ site side has changes in temperature, it can take days to nent are the boundary conditions. One typically esti­ obtain a valid determination of R-value. If one teclmique mates apparent thermal conductivity as a function of is faster than the other in determining the final value temperature and a constant value of the product p and reliably, it would be preferred. Consequently, the authors compared the time that elapsed before each CII for each layer described in the system. teclulique began to stay within 10% of its final estimate To obtain the best estimates for as many parameters of R-value. as required, one computes temperatures and heat fluxes Sensitivity to ~T It was mentioned previously with trial initial values of the parameters. Next, one (Courville et al. 1990) that the sum-of-least-squares tech­ compares thenl to measurements at the interior nodes, nique succeeds at lo\\' !lTs, whereas the sumlnation tech­ where independent Ineasurements are available. Then nique becomes unstable when the denominator of one COInputes a weighted sllln~of-squares function, r, Equation 1 is near zero as a cUlnulative result of rever­ from the differences between calculated and measured sals of ~T. TIle sum-of-least-squares teclmique works heat fluxes and temperatures, as follows: well during changing ~T, even when ~Ts are small, because iJT liJt is the key variable in Equation 2. Does this or any other aspect of ~T cause a more reliable or rapid solution for one technique or the other? Indica­ tions were sought that may have made one teclUlique where each W is a weighting fact01~ Tllli and qlli are the calculated temperature and heat flux at a node 111 or 11, advantageous over the other. and a time i and F ; are the measured temperature and II Comparison of Measurement Sites heat flux at a node 111 or 11 and a titne i. Finally, one uses the Gauss linearization method Table 1 summarizes the building locations and types. (Beck and Arnold 1977) to minimize r as the analysis TIle climatic conditions, Ineasurement duration, and iterates with better and better estimates of the desired building types are significant to the outcome of the mea­ properties until the desired convergence is obtained. surements. With only t\vo surfaces instrumented, the assembly was TABLE 1 Summary of R-Value Measurement Locations approximated as a unifol'ln slab and values were assluned for thernlal conductivit}~ thickness, density, Component Duration of and specific heat as a starting point for the estimate. It Location Type Measured Measurement was further assumed that thermal conductivity varies with temperature. Riverdale, Metallnsuloted Walls 467 hours N.D. Panel Comparison of Techniques Fort Drum. Metal Insulated Wall 331 hours N.Y. Panel Previous experience with the sununation and the Masonry Wall. Attic 240 hours sum-of-least-squares teclUliques (Courville et al. 1990) suggests that the latter teclUlique is advantageous at Cold Climates TIle experience in previous ,vork in times of low temperature difference (~n between a temperate climate (Courville et al. 1990) suggested indoors and outdoors. The purpose of this study was to choosing a colder clinlate to expand the wlderstanding compare the two tecluliques at conditions with a higher of the effects of tlT on R-value measurements. Riverdale, ~T. Three points of comparison are of interest: (1) N.D., and Fort Drum, N.Y., have temperahlres that reach whether they obtain the same correct answer, (2) how -20"C (-4"F) and below. quickly they reach that answel~ and (3) the sensitivity of Building Types 111e building in Riverdale was a each teclmique to temperature conditions such as ~T heated maintenance building serving the Corps of Engi­ and variations in !IT. neers' Garrison Dam, with metal panels that sand­ R-Value Agreement TIle authors compared how wiched 51 mm (2 in.) of fiberglass insulation between closely the hvo techniques came to producing the same steel skins. TIle buildings at Fort Drum serve military R-value. It was impossible to test independently for purposes. The metal-paneled building was a motor \\'hether the value was correct; however, experience sug­ vehicle maintenance building, where the lllechanical gests that any biases due to calculation and not instru­ foom was instnnnented, \\'hich also had 51 nun (2 in.) of mentation becOIne small with titne in the presence of a fiberglass insulation sandwiched between steel skins on 152 Thermal Envelopes VI/Heat Transfer in Wolfs I-Principles the walls. The masonry building serves as a battalion Roof headquarters. Its walls-which consisted of 102-nun [J I!J (4-in.) brick, 25-mm (I-in.) air space, 51 rnrn (2 in.) of foil­ Metal Panel faced polyisocyanurate insulation, and 203-mm (8-in.) EI Group 3 I!JEJ Group 2 concrete masonry units-were instrumented. Likewise, EI I!J Metal the attic, with its 254 mm (10 in.) of fiberglass insulation, Panel was instrumented. Masonryl El Masonryl Metal EJ Group 1 Metal FIELD PROCEDURES Panel Panel Ii1I Heat flux and temperature data were obtained using oor the procedures in ASTM Standard Practice C 1046-91. In North Side South Side each case, a thermographic survey was performed using the techniques discussed in ASTM Standard Practice C Figure 1 Location of sensor sites at the Riverdale, NO, 1060-90 (ASTM 1990a), which revealed no unexpected building. (Nolto scale.) thennal anomalies. Instrumentation TI,e heat flux transducers (HFrs) Sensor Group 3 - Sensors 7, 8, and 9 were placed on used were 305 mm (12 in.) square, 0.81 nun (0.032 in.) the same north-facing wall as sensor group 1, above the thick, and had an active metering area of 152 mm (6 in.) masonry block level on insulated metal panels.
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