Experimental procedure and uncertainty analysis of a guarded otbox metod to determine te termal transmission coefficient of skyligts and sloped glazing Elmady, A.H.; Haddad, K. NRCC-43378 A version of tis document is publised in / Une version de ce document se trouve dans : ASHRAE Transactions, v. 106, pt. 2, 2000, pp. 601-613 www.nrc.ca/irc/ircpubs
Experimental Procedure and Uncertainty Analysis of a Guarded HotBox Metod to Determine te Termal Transmission Coefficient of Skyligts and Sloped Glazing ABSTRACT A. H. Elmady and K. Haddad A laboratory test procedure and a guarded ot box facility to determine te termal transmission coefficient of skyligts are described. Skyligts can be tested at an angle of inclination tat can be varied from 20 to 90 o off te orizontal. Te experimental procedure, to determine te skyligt R-value, is based on a correlation for te convective eat transfer on te warm side and te weater side of te test specimen. Tis correlation is obtained from calibration measurements using a calibrated transfer standard (CTS in te inclined position. Te results sow tat te convective eat transfer along an inclined CTS is substantially different from tat along a vertical CTS. Tree-dimensional simulations of te conduction eat transfer witin te CTS assembly are found to be in good agreement wit te experimental results. A complete error analysis for te calibration experiments and for skyligt testing is presented. It is found tat te experimental relative uncertainty associated wit te termal transmission coefficient of te test specimen witout te frame is of te order of ±6%. INTRODUCTION For years, te overall termal transmission coefficient (U-factor of fenestration systems were determined in guarded ot box facilities, were te specimens are mounted in a vertical frame separating te two environmental cambers. Recently, te determination of te overall termal transmission coefficient of skyligts and sloped glazing at an inclined position was discussed in te researc and tecnical communities as a requirement to assess te energy rating and labelling of tis type of products. Correlation of film eat transfer coefficient on a vertical surface in a guarded ot box environment was documented earlier in te literature [Elmady, 1992]. However, scarce experimental data about te variation of te film eat transfer coefficient over te surface of fenestration products in inclined position is extremely scarce. Te focus of tis paper is on te development of a researc class guarded ot box facility to enable te accurate determination of te overall eat transfer coefficient (U-factor of skyligt and sloped glazing systems. Tis is in response to te needs of industry, researcers and standards writing autorities. Also, te results of tis researc work are critical for product certification and labelling, wic is demanded by industry and building code officials. ENVIRONMENTAL TEST FACILITY Te guarded ot box facility was designed originally to test windows in te vertical position. Detailed description of tis facility and te associated uncertainty analysis can be found in Elmady (1992. In order to accommodate te testing of skyligts mounted at an angle off te orizontal, te calorimeter and te surround panel
assembly were rotated about its central axis, as sown in Figure 1. Presently, te facility can be used to test special fenestration systems wit inclinations ranging from 20 to 90 o off te orizontal. A total of tree fans were installed on te weater side to mix te air and to obtain te desired eat transfer coefficient on tis side of te test sample, by means of canging te speed of te fan motors. On te room side, te eat was delivered troug a constant temperature baffle and a convection eater. Te baffle and te convection eaters are evaporating/condensing eat excangers using refrigerant R-134a. More details about te ot box facility can be found in Elmady (1992 and Brown et al. (1961. CALIBRATION OF THE HOT-BOX In order to use te ot box to determine te R-value of skyligts, it was necessary to caracterize te convection eat transfer on te room side and weater side of te specimen surface. Calibration experiments employing a Calibration Transfer Standard were carried using te ot box facility. Tese experiments were performed in te vertical and te inclined positions (at 20 of te orizontal. Terefore, it will be possible to test skyligts in tese two positions, wic will elp quantify te effect of te angle of inclination on te termal resistance of a fenestration system. A total of five data sets, corresponding to five different weater side temperatures, were collected during te calibration experiments for eac of te two orientations Description of te Calibration Transfer Standard A skyligt is usually installed on te outer side of te building envelope. As a result, a reentrant cavity is created between te inner side of te envelope and te warm pane of te skyligt. Te calibration transfer standard assembly was built wit tis in mind to try to duplicate as closely as possible te nature of a real skyligt, as sown in Figure 2. Te CTS is supported by a pine wood frame, wic is used to fasten te wole assembly to te surround panel. A side view of te CTS contained inside te frame is sown in Figure 3. Te total dimensions of te surface of te CTS are 1.26 m x 1.26 m, but only a 1.22 m x 1.22 m area can directly excange eat wit te warm or cold air streams due to te nature of te interface between te CTS and te frame. Tis smaller area is associated wit te surface of te CTS glass tat is in direct contact wit eiter te warm or cold air streams on te room and weater sides, respectively. Glue was applied along all te cracks to minimize te potential of any air leakage between te weater and te room sides of te ot box assembly. Te CTS was fabricated according to te guidelines presented by Goss et al. (1991. It consists of an 11 mm tick layer of expanded polystyrene (EPS sandwiced between two 4 mm tick clear glass panes, as sown in Figure 3. Guarded Hot plate experiments were performed on a sample of te EPS used to make te CTS to determine te variation of te termal conductivity of te material wit mean temperature. Two sets of twenty termocouples were installed on te room side and te weater side of te
CTS. Te layout of tese sensors is sown in Figure 4. Te temperature of eac of te four sides of te frame was measured using a total of eigt termocouples, four on te room side and four on te weater side. Te temperature of eac of te four surround panel sides, associated wit te flanking losses, was measured using a total of four termocouples. Initial Data Reduction Procedure Te total eat input to te calorimeter, Q t, is measured during a calibration experiment. Tis eat is transferred toward te cold side of te box troug several different pats. Figure 2 sows tat Q t can be expressed by Q = Q + Q + Q + Q + Q t m, i cts, i f, i cal fl (1 Were Q cts,i, Q m,i, and Q f,i are te eat transfers tat cross te room side eat transfer surfaces of te calibration transfer standard, te surround panel, and te support frame. Te surface area of te surround panel associated wit Q m,i does not include te side face of te surround panel associated wit te flanking losses Q fl. On te weater side, te eat transfer tat crosses te surfaces of te CTS, te surround panel, and te frame are designated by Q cts,o, Q m,o, and Q f,o, respectively, as sown in Figure 2. Te eat transfer troug te room side surface of a certain component is not necessarily equal to tat troug te weater side surface of te same component due to te existence of 3-D conduction effects. Te eat transfer troug te CTS is not purely 1-D in nature especially around te perimeter at te interface wit te support frame. However, a good first estimate of Q cts,i and Q cts,o is obtained from te 1-D eat conduction equation: Q cts,1 D = A cts( Tcts, Tcts, c R cts (2 were A cts is te glass area of te CTS tat directly excanges eat wit te warm air on te room side and te cold air on te weater side. Te measured termal resistance of te expanded polystyrene inside te CTS is R cts. Te measured area-weigted averages of te interface temperatures between te CTS core and te glass on te room side and on te weater side are designated by T cts, and T cts,c, respectively. Similarly, good estimates of te eat transfer troug te frame and te surround panel, excluding te franking losses, are obtained from te 1-D conduction equation: Q f,1 D = A f, i ( T f, Tf, c R f (3 Q m,1 D = A m, o( Tm, Tm, c R m (4
were A f,i and A m,o are te inside eat transfer area of te frame and te outside eat transfer area of te surround panel, respectively. It is to be noted tat te 1-D eat transfer estimates in Equations (2 and (3 are based on te smaller eat transfer area of eac component: A f,i in te case of te frame and A m,o in te case of te surround panel. Te termal resistance of te frame, R f, was determined troug Guarded Hot-plate measurements, and tat of te surround panel, R m, was determined troug ot box experiments. Te temperatures in Equations (3 and (4 are measured area-weigted averages of te frame and te surround panel surface temperatures on te weater side and te room side respectively. Once te eat transfer troug te CTS is determined from Equation (2, te temperatures on te outer surfaces of te room and of te weater sides of te CTS glass can be evaluated from T ' cts, = T cts, Q + cts,1 D A cts R glass (5 T ' cts, c = T cts, c Q cts,1 D A cts R glass (6 Ten te eat transfer coefficients on te room and te weater sides of CTS, te support frame, and te surround panel are obtained from: Qcts,1 D ( cts, i 1 D = ' A ( T T cts Q ( cts, o 1 D = ' A ( T cts cts,1 D cts, c cts, T c (7 (8 ( f, i 1 D = A f, i Q ( T f,1 D T f, (9 ( f, o 1 D = A f, i Q ( T f,1 D f, c T c (10 ( m, i 1 D = A m, o Q ( T m,1 D T m, (11 ( m, o 1 D = A m, o Q ( T m,1 D m, c T c (12 In reality, te eat transfers troug te CTS, te frame, and te surround panel is not purely 1-D. In fact tere are 3-D conduction effects especially at te interface
between te pine support frame and te CTS. Te 1-D eat flow rate estimates and te associated eat transfer coefficients can be improved troug 3-D conduction simulations of te eat transfer inside te calorimeter. Tese simulations can also be used to estimate te flanking losses troug te side face of te surround panel. Tree-Dimensional Heat Transfer Simulation Te results from te eat transfer simulation are based on te assumption tat tere are no local variations in te eat transfer coefficient on te warm side of te CTS. In addition, a total eat transfer coefficient was used on te warm side, and te effect of separating te radiative and convective components was not carried out. Te eat transfer troug te surround panel, te frame, and te CTS toward te cold side was simulated using te 3-D conduction computer program TRISCO (PHYSIBEL Inc. 1992.Te grid planes employed in te simulation of te eat transfer troug te surround panel, te frame, and te CTS are sown in Figure 5. Figure 5(b is te view from te top of Figure 5(a. Due to symmetry, only one quarter of te assembly was considered. A total of nine rows, seven columns, and seven layers were employed to mark te canges in material properties and geometry. However, tese planes were not enoug to obtain accurate solutions of te 3-D conduction witin te assembly. Additional rows, columns, and layers were defined between tose sown in Figure 5. A larger number of grid planes was employed in te regions were conduction eat transfer was determined to deviate from 1-D beavior more tan in te rest of te assembly. Tis was te case especially at te interfaces between te surround panel and te frame and te frame and CTS. Te air temperatures on te weater side and te room side were specified based on te measurements from te calibration tests. Te local eat transfer coefficients were estimated using Equations (7 troug (12. Adiabatic boundary conditions were used at te planes of symmetry, and at te outer edge of te surround panel. Te eat transfer coefficient at te surround panel sides, associated wit te flanking losses, was taken equal to tat along te room side of te frame. Tis is deemed to be a good assumption due to te geometrical similarities between tese two regions. In addition, te conduction resistance inside te surround panel dominates te total termal resistance, from te room side to te weater side. Terefore, any minor errors in te eat transfer coefficient along te surround panel sides would ave a very small effect on te predicted flanking losses. Te results of te simulations indicated a different eat flux troug te inner and te outer surfaces of te CTS, te frame, and te surround panel tan wat was predicted using te 1-D conduction equation. Tese new estimates of te eat flux levels were ten used to obtain better estimates of te eat transfer coefficients. Te new values of te eat transfer coefficients were ten used as part of te input for anoter TRISCO simulation. A listing of te 1-D eat transfer estimates, based on experimental temperature measurements, and tose from 3-D TRISCO simulations for te inclined position are sown in Tables 1 and 2. It is to be noted tat te TRISCO output provides estimates for te eat transfer troug te surfaces of a specific component on te room side (Q cts,i, Q f,i, and Q m,i and on te weater side (Q cts,o, Q f,o, and Q m,o, wic are not
necessarily te same due to te existence of 3-D conduction effects. In addition, te surround panel eat transfer listed does not account for te flanking losses. Te results sow tat te one-dimensional estimates of te eat transfers troug te CTS and te frame under predict te amount of eat tat actually crosses te inner surfaces of tese components, Q cts,i and Q f,i. In te case of te CTS, te 1-D eat transfer is a good approximation of te eat tat crosses te weater side surface of te calibrated transfer standard. Te opposite is true in te case of te frame were te 1-D eat transfer surface is a good estimate of te eat tat crosses te room side surface of te frame. Te eat transfer troug te cold surface of te surround panel is iger tan te 1-D value due to te contribution of te flanking losses. Figure 6 sows te variation of Q fl wit te air temperature difference between te room side and te weater side. Results for bot te inclined and te vertical position are sown. As expected te flanking losses increase as te air temperature difference increases. It can also be sown tat orientation as a minor effect on te flanking losses. Any differences in Q fl between te two positions are due to differences in te inside and te outside eat transfer coefficients between te two positions. Tese estimates of te flanking losses are needed wen performing ot box experiments wit an actual skyligt. Te data in Table 2 sows te measured total eat input to te calorimeter and te total eat transfer between te room side and te weater side predicted by te 3-D TRISCO simulations. Tere is a good agreement between te two values for te total eat input. Any discrepancy could be due to errors in te measurements of te termal resistance of te materials of te surround panel, of te CTS, and of te frame. In addition, small leaks of cold air from te weater side could lead to a sligt increase in te eat required to maintain te calorimeter at a certain temperature. Table 3 lists eat transfer coefficients on te room side and te weater side of te CTS and te frame. Te 1-D values are obtained using te measured surface temperatures and te 1-D eat conduction equation. However, te 3-D values are te refined estimates obtained using te eat fluxes from te TRISCO simulations. It is noticed tat te room side eat transfer coefficients are iger along te CTS tan along te frame. Te airflow on te CTS resembles tat of a cold plate facing downward wit an unstable boundary layer. On te frame, te airflow is similar to a vertical cold flat plate wit a more stable boundary layer. As te temperature driving potential on te room side increases, te total eat transfer coefficient increases as expected. Te small variations in te weater side film coefficient could be attributed to canges in te cold air density wit temperature and to minor canges in te RPM settings of te fans. Tere is more variation in te outside eat transfer of te frame probably due to te more unstable nature of tis separating flow. Convective Heat Flux Correlation for te CTS Te CTS eat flux on te room side as convection and a radiation component and it can be expressed by: " " q = ( q + ( q " cts, i cts, i conv cts, i rad (13
Te warm CTS glass surface directly or indirectly excanges eat by radiation wit te frame at T f,, wit te surround panel side at T ms, wit te surround panel at T m,, wit te calorimeter at T cal, and wit te baffle at T b. Te baffle and te calorimeter surfaces can be grouped togeter because teir temperatures are very close. Te equivalent surface of te calorimeter and te baffle is at a temperature T bc. It can be sown tat te radiation eat flux component can be expressed by ( q " cts, i rad F = σ + F cts, ms ( T cts, bc 4 ms ( T T 4 bc 4 cts, T 4 cts, + F cts, m + F cts, f ( T 4 m, ( T 4 f, T 4 cts, T 4 cts, (14 Te appropriate radiation form factors are obtained using te computer program of Stepenson and Mitalas (1966. All te temperatures in Equation (14 are measured during a calibration test. Once te radiation component of te eat flux is found, te convection eat flux can be determined using estimates of te total eat flux on te room side of te CTS eiter from te 1-D conduction equation or from te TRISCO simulations. Te procedure described previously was applied to te calibration data to derive correlations for te convection eat flux on te room side of te CTS for te vertical and te inclined positions. A correlation was obtained wit te total CTS eat flux based on te 1-D conduction equation, and anoter correlation was obtained based on te total CTS eat flux from TRISCO simulations. Figures 7 and 8 sow te variation of te convection CTS eat flux wit te difference between te warm air temperature and te warm CTS glass surface temperature for te inclined and te vertical positions, respectively. One of te curves in eac of Figures 7 and 8 is associated wit te 1-D total CTS eat flux. Te oter curve is for te case were te total CTS eat flux is obtained from 3-D simulations. In accordance wit te results listed in Table 1, te convection eat flux based on te TRISCO simulations is always iger tan tat based on te 1-D model for bot inclinations. Te curves in Figures 7 and 8 associated wit te 3-D simulations are plotted togeter in Figure 9 to allow for a better comparison between te vertical and te inclined positions. In te vertical position, te flow along te CTS surface is in te laminar regime based on a transition Grasof Number of 10 9. In tis case, te average eat flux correlation is of te form A T 1.25 for a vertical isotermal flat plate (Incropera and Dewitt, 1985. Te correlation in Figure 9 sows an exponent very similar to tat reported for laminar vertical isotermal plates, wic is in agreement wit previous otbox calibration experiments (Elmady, 1992. In te inclined position, te boundary layer becomes unstable and te convection eat transfer is iger tan tat in te vertical position, as sown in Figure 9. For flow over inclined isotermal surfaces, Curcija and Goss (1995 reported te following expressions for te Grasof Number indicating te end of te laminar region:
Gr 2 10 Pr = tr 2. θ e ( 94 9 (15 were Pr is te Prandtl Number and? is te angle of inclination from te orizontal measured in degrees. At 20 o inclination from te orizontal, tis equation predicts tat te transitional Grasof number is 5.5 x 10 6. For te calibration experiments in te inclined position, te Grasof Number was of te order of 2 x 10 9. Terefore, te flow over te warm CTS surface ad a laminar region and a turbulent region. Tis is also in agreement wit te reported work by Al-Arabi and Sakr (1987. According to Al-Arabi and Sakr (1987 te average eat flux for unstable boundary layers over inclinedisotermal-flat plates can also be correlated by an expression of te form A?T B. Te exponent B is 1.25 for laminar flow and 1.333 for turbulent flow. Te correlation listed in Figure 9 for te inclined position as a iger exponent tan tat in te case of te vertical position probably due to te occurrence of turbulent flow. METHOD TO DETERMINE THE R-VALUE OF A SKYLIGHT During a ot box experiment, a skyligt is mounted on te surround panel as sown in Figure 10. A wood frame is used to secure te skyligt to te surround panel according to te recommendations of te manufacturer. Te total termal resistance of te assembly, skyligt plus frame, is te sum of te area-weigted contribution of te frame and of te skyligt. In order to determine te termal resistance of any of te two components of te assembly, it is necessary to determine te eat flow and te temperatures on te room side and on te weater side of tis component. Similar to te data reduction procedure for te calibration experiments, te eat flows witin te calorimeter are related by: Q = Q + Q + Q + Q + Q t m, i s, i f, i cal fl (16 were te total eat input, Q t, is measured during te experiment. Te eat transfer troug te calorimeter wall, Q cal, is negligible equal to ±0.7 W. Te flanking losses, Q fl, and te surround panel eat transfer, Q m,i, are estimated based on te results from te calibration experiments listed in Table 1. Tese results sould apply as long as te conditions, temperatures and eat transfer coefficients, on te room side and te weater side of te box are te same ranges as tose during te calibration experiments. Te flanking losses migt sligtly depend on te surface temperature of te skyligt employed. A different room side skyligt temperature would lead to a different total eat transfer coefficient along te surround panel side associated wit te flanking losses. However, tis variation in te eat transfer coefficient sould be small considering te limited range of room side temperatures associated wit different skyligts. In addition, te termal resistances associated wit te convection eat transfer on te room and weater sides are a very small fraction of tat associated wit conduction troug te surround panel. Te eat transfer troug te room side surface of te frame, Q f,i, can be evaluated from Equation (3 based on te 1-D conduction model. Termocouples sould
be placed on te room side and te weater side of te frame to determine te temperatures on bot sides of tis component. Depending on te specific geometry of te frame, te 1-D model may or may not give a good estimate of Q f,i. Tis metod would be more accurate for wider frames tat promote 1-D eat transfer. For better accuracy, 3-D conduction simulation could be employed as it was done in te case of te calibration experiments. However, tis may not be practical considering te lengt of time it would take to carry a test. It is to be noted also tat te use of te 1-D conduction model requires an estimate of te termal conductivity of te frame material. Tis information can be obtained from te literature or from separate guarded ot plate experiments. Te eat transfer troug te room side of te skyligt can ten be determined from Equation (16. Te eat flux associated wit tis eat flow troug te skyligt as a radiation and a convection component and it can be expressed by " " q = ( q + ( q " s, i s, i conv s, i rad (17 Tis skyligt eat flux is based on te surface area of te skyligt tat excanges eat wit te room side air. Te convection component of tis eat flux can be expressed by an expression of te form A?T B from Figure 9. For instance, for an inclined skyligt we can write: ( q = 2.01( T T " s, i conv s, 1.339 (18 Te temperature T s, is an estimated temperature of te warm side of te skyligt, wic still needs to be determined. Similar to te radiation eat flux of te CTS in te calibration experiments, te radiation component of te skyligt eat flux on te room side can be expressed by 4 4 4 4 4 4 4 [ F ( T T + F ( T T + F ( T T + F ( T T ] (19 " 4 ( q = σ s, i rad s, ms ms s, s, m m, s, s, bc bc s, s, f f, s, All te temperatures in tis equation are measured during te experiment except T s,, wic still needs to be determined. Te form factors are again determined using te program of Stepenson and Mitalas (1966. Equations (17, (18, and (19 can ten be solved by iteration for an equivalent warm side temperature of te skyligt T s,. An equivalent cold side temperature of te skyligt, T s,c, is obtained from:
q T s, c= T c+ " s, i o A A s, i s, o (20 were T c is a measured cold side air temperature, and o is te weater side eat transfer coefficient determined from calibration experiments. Te room side skyligt eat flux as been corrected for any difference in te eat transfer area between te room side and te weater side of te skyligt. Terefore, te termal resistance of te skyligt is given by: R s = A s, i ( T s, Q s, i T s, c (21 UNCERTAINTY ANALYSIS Te uncertainty levels are determined based on te metod described by Moffat (1985. It is assumed tat eac recorded element of data is an independent observation from a Gaussian population of possible values. If R is a given function of independent variables x 1, x 2,, x n, we can write R = R( x1, x2,..., xn (22 Te uncertainty associated wit te result is w R and tose associated wit te independent variables are w 1, w 2,, w n. If tese uncertainties in te independent variables ave te same odds, ten te uncertainty in te result aving te same odds is expressed by Kline and McLintock (1953 as w R 2 2 2 R R R 1 2... 1 2 + + w + w w x x xn = n 1 / 2 (23 Temperature Measurements Te temperatures were measured using a data acquisition system (DAU and type-t termocouples. Tese sensors connected to te DAU were calibrated using a water-glycol bat and a ig precision Resistance-Platinum Termometer for te range of temperatures used. Te uncertainty associated wit te temperature measurements was estimated to be ±0.1 o C. Power Measurements Te total power input to te calorimeter was measured using a current sunt and a voltage divider. Te DAU processed te output signal from tese devices to provide te actual current and voltage for te calorimeter. Tese power measurements were calibrated against readings of a calibrated voltmeter and current sunts tat were
traceable to primary standards. Te estimated error in Q t over te range of power used was ±0.01%. Conductance of te CTS Te calibration transfer standard was made of a layer of expanded polystyrene (EPS sandwiced between two layers of clear glass. Te termal resistance of te EPS was measured using te NRC Guarded Hot Plate apparatus, wic is traceable to primary standards. Based on a very large number of tests, te R-value of te insulating material was estimated to witin ±2%. Uncertainty Intervals for te Calibration Experiments Te uncertainty analysis teory presented above and te uncertainties associated wit te independent variables were used to estimate te error intervals for all te derived quantities. Tis was done for te five sets of data collected during te calibration experiments. Table 4 lists te raw experimental data and te uncertainty intervals for all te relevant derived quantities for one of tese cases. It can be seen tat te igest relative uncertainties are associated wit te outside eat transfer coefficients of te frame and te CTS. Te ig eat transfer coefficients on tis side of te assembly lead to lower temperature differences between te eat transfer surface and te cold air stream. As a result, te relative error associated wit te temperature driving potential is iger on te weater side. Analysis of te uncertainty of te oter calibration data indicates tat te relative uncertainty associated wit te outside eat transfer coefficients decreases as te eat flow troug te system increases. For instance, at a cold side temperature of 4 o C, te relative error associated wit te outside eat transfer coefficients of te CTS is 15.2%. However, tis uncertainty falls to 7.5% at a weater side air temperature of 29 o C. Te relative uncertainty of te convective eat flux also decreases as te weater side air temperature decreases. It varies from 5.5% at 4 o C to 3.5% at 29 o C. Uncertainty Intervals for Skyligt Testing Using te calibration data and uncertainties associated wit te measured variables to estimate te uncertainties associated wit skyligt testing. It is to be noted tat te calibration data applies to skyligts similar to te one sown in Figure 10. In te skyligt testing procedure described earlier, te eat transfer troug te support frame is determined, as in te calibration experiments, from surface temperature measurements and from a prior knowledge of te termal resistance of te frame material. Terefore, te error associated wit eat transfer troug te frame would be of te order of 2.2% as in te case of te calibration data. Tis assumes a relative uncertainty in te termal resistance of te material of 2%, and an uncertainty of ±0.1 o C in te temperature measurements. Te oter important uncertainty during skyligt testing is tat associated wit te termal resistance of te specimen R s. Te best estimate of te error related to R s can
only be determined using te experimental data obtained during te testing of te specific skyligt. However, a very good estimate of tis uncertainty can be obtained using te calibration data and an assumed value for te total eat input Q t. During an actual skyligt testing, te flanking losses and te surround panel eat transfer would be very close to tose obtained during te calibration experiment for te same room and weater side conditions. Te frame eat transfer is also assumed to be equal to tat obtained during calibration. From te calibration data for te inclined position for T c = -17.5 o C, te following eat flow rates and uncertainty intervals are obtained: Q cal = ± 0.7 (W Q f,i = (38.1 ± 0.84 (W Q fl = (12.1 ± 0.24 (W Q m,i = (37.8 ± 0.8 (W Using tese eat transfer estimates, we can deduce tat tey contribute (88 ± 2.6 W toward te total eat input to te calorimeter. If we assume a certain total eat input to te calorimeter, we can follow te procedure outlined previously to determine te termal resistance of te skyligt tat would be associated wit te assumed value of Q t. Te temperatures of te room side of te baffle, of te surround panel, and of te frame needed to carry tis analysis are obtained from te calibration experiment for T c = -17.5 o C. It is expected tat tese temperatures would vary wit te skyligt tested. However, te effect of tis limited cange in te temperatures on te predicted relative certainty associated wit R s sould be small. Te uncertainty analysis tecnique of Moffat (1985 can not be used to estimate te uncertainty of te warm side skyligt temperature, because of te lack of a closed form expression for T s,. In te data reduction procedure, tis temperature is solved for by iteration using Equations (17, (18, and (19. However, tese equations can be solved for te lowest or te igest possible T s, using te appropriate combination of te igest or te lowest values for te variables appearing in tese equations. Te uncertainty analysis tecnique of Moffat (1985 can ten be used to determine te uncertainty associated wit te termal resistance of te skyligt. Te resulting relevant quantities and teir relative uncertainties obtained troug te previous procedure are sown in Table 5. It is to be noted tat te relative uncertainty, designated by R.U. in Table 5, is te ratio of te uncertainty to te absolute value of te quantity in question. Te results indicate tat te relative uncertainty of te eat transfer troug te skyligt decreases as te specimen eat transfer increases. Te uncertainties in Q cal, Q f,i, Q fl, and Q m,i are constant regardless of te total eat input. Terefore, teir relative contribution toward te uncertainty of te specimen eat flow rate is smaller at iger eat flow rates. Te relative uncertainty associated wit te termal resistance of te skyligt depicts an interesting trend. First it decreases as te total eat input increases. After reacing a minimum, R.U.(R s starts to increase wit increasing values for Q t. In order to illustrate tis better, te relative uncertainties of Q s, T s,, T s,c, and R s are sown togeter in
Figure 11. Te initial decrease in te relative uncertainty of R s is due to te decrease in te relative uncertainty of te eat transfer troug te specimen. Tis drop in R.U.(Q s more tan offsets te effect of te increase in R.U.(T s, and R.U.(T s,c. At a certain value for te total eat input, te effect of te rise in te relative uncertainties of te surface temperatures of te skyligt, especially T s,, overcomes te effect of te decrease in R.U.(Q s. It is to be noted also tat te relative uncertainty associated wit R s listed in Table 5 is in agreement wit values reported by Elmady (1992 in te case of window testing. In addition, some of te termal resistance values in Table 5 sould be realistic estimates for te termal resistance of certain skyligts. In fact te center glass R-value for double and triple-glazed windows, wit an air gap spacing between panes of 12.7 mm, is 0.195 and 0.390 m 2 -K/W, respectively, as predicted by te VISION computer program from te University of Waterloo (1992. Tese values fall witin te range of R-values included in Table 5. CONCLUSIONS Te experimental procedure presented in tis study can be employed to determine te termal resistance of an inclined skyligt similar to tat considered in tis paper. Based on te work performed for te purpose of te present study, te following conclusions can be made: 1 Te conve ction eat transfer along te warm side of an inclined CTS is substantially iger tan tat along a vertical CTS. Terefore, it is very important to perform a calibration experiment at te inclination at wic te skyligt termal resistance is desired. 2 Tere is a good agreement between te total calorimeter eat input from experiment and from tree-dimensional simulation. Te difference between te two values may be due to errors in te measurements of te termal resistance of te materials. In addition any minor air leakage from te weater side to te calorimeter would increase te required eat input, and ence a iger uncertainty. 3 Te flanking losses increase linearly wit an increasing temperature difference between te room side and te weater side. Tere is very little difference between flanking losses for a vertical and for an inclined ot box. 4 Te relative uncertainty of te outside eat transfer coefficient is te igest among all te relative uncertainties associated wit te calibration experiments. Tis uncertainty decreases as te total calorimeter eat input increases. 5 Te experimental relative uncertainty of te termal resistance of a skyligt is expected to be around ±6%. Initially, tis uncertainty decreases as te termal resistance of te skyligt increases. After reacing a minimum, te relative uncertainty starts to increase wen te skyligt termal resistance increases.
NOMENCLATURE A cts Heat transfer area of te CTS (m 2 A f,i Heat transfer area of te room side of te frame (m 2 A f,o Heat transfer area of te weater side of te frame (m 2 A m,i Heat transfer area of te room side of te surround panel (m 2 A m,o Heat transfer area of te weater side of te surround panel (m 2 F i,j Gr t Radiation form factor between surfaces i and j Transition Grasof Number ( cts,i 1-D Room side eat transfer coefficient of te CTS from 1-D conduction model (W/(m 2 K ( cts,o 1-D Weater side eat transfer coefficient of te CTS from 1-D conduction model (W/(m 2 K ( f,i 1-D Room side eat transfer coefficient of te frame from 1-D conduction model (W/(m 2 K ( f,o 1-D Weater side eat transfer coefficient of te frame from 1-D conduction model (W/(m 2 K ( m,i 1-D Room side eat transfer coefficient of te surround panel based on 1-D conduction model (W/(m 2 K ( m,o 1-D Weater side eat transfer coefficient of te surround panel from 1-D conduction model (W/(m 2 K Pr Q cal Q cts,i Q cts,o Prandtl Number Heat transfer troug te calorimeter wall (W Heat transfer troug te room side surface of te CTS (W Heat transfer troug te weater side surface of te CTS (W
Q cts,1-d Heat transfer troug te CTS based on 1-D conduction model (W q cts,i Heat flux troug te room side surface of te CTS (W/m 2 (q cts,i conv Room side convection component of te CTS eat flux (W/m 2 (q cts,i rad Room side radiation component of te CTS eat flux (W/m 2 Q f,i Q f,o Q f,1-d Q fl Q m.i Q m.o Q m,1-d Q s,i Heat transfer troug te room side surface of te support frame (W Heat transfer troug te weater side surface of te support frame (W Heat transfer troug te frame based on te 1-D conduction model (W Flanking losses troug te surround panel side (W Heat transfer troug te room side surface of te surround panel (W Heat transfer troug te weater side surface of te surround panel (W Heat transfer troug te surround panel based on te 1-D eat transfer model (W Heat transfer troug te room side surface of te skyligt (W q s,i Total eat flux troug te room side surface of te skyligt (W/m 2 (q s,i conv Convection eat transfer component on te room side surface of te skyligt (W/m 2 (q s,i rad Radiation eat transfer component on te room side surface of te skyligt (W/m 2 Q t R cts Total eat input to te calorimeter (W Termal resistance of te CTS core (m 2 K/W R f Termal resistance of te frame (m 2 K/W R glass R m R s Termal resistance of te CTS glass (m 2 K/W Termal resistance of te surround panel (m 2 K/W Termal resistance of te skyligt (m 2 K/W T b Baffle temperature ( o C T bc Temperature of te baffle and calorimeter wall combined ( o C
T c Temperature of te air on te weater side ( o C T cal Calorimeter wall temperature ( o C T cts,c Temperature of te weater side surface of te CTS core ( o C T cts,c Temperature of te weater side surface of te CTS glass ( o C T cts, Temperature of te room side surface of te CTS core ( o C T cts, Temperature of te room side surface of te CTS glass ( o C T f,c Temperature of te weater side surface of te frame ( o C T f, Temperature of te room side surface of te frame ( o C T Temperature of te air on te room side ( o C T m,c Temperature of te weater side surface of te surround panel ( o C T m, Temperature of te room side surface of te surround panel ( o C T ms Temperature of te surround panel side ( o C T s,c Temperature of te weater side surface of te skyligt ( o C T s, Temperature of te room side surface of te skyligt ( o C w i x i Uncertainty associated wit x i Independent variable
REFERENCES Al-Arabi, M. and B. Sakr. 1987. Natural convection eat transfer from inclined isotermal plates. International Journal of Heat and Mass Transfer, pp. 559-565. Brown, R.P., K.R. Solvason, and A.G. Wilson. 1961. A unique ot box cold room facility. ASHRAE Transactions 67: 561-577. Elmady, A.H. 1992. Heat transmission and R-value of fenestration systems using IRC Hot Box: Procedure and uncertainty analysis. ASHRAE Transactions, Vol. 98, Part 2, 1992. Goss, W.P., A.H. Elmady, and R.P. Bowen. 1990. Calibration transfer standards for fenestration systems. Proceedings of a Worksop on In-Situ Heat Flux Measurements in Buildings, Applications and Interpretations of Results. U.S. Army Cold Regions Researc and Engineering Laboratory, Special Report No. 91-3. Incorpera, F.P. and D.P. Dewitt. 1985. Fundamentals of eat transfer. Jon Wiley and Sons, Inc., New York. Kline, S.J. and F.A. McClintock. 1953. Describing uncertainties in single sample experiments. Mecanical Engineering. Moffat, R.J. 1985. Using uncertainty analysis in te planning of an experiment. Journal of Fluids Engineering, ASME Transactions, No 107. Mitalas, G.P., and D.G. Stepenson. 1966. Fortran IV program to calculate radiant energy intercange factors. National Researc Council of Canada, Division of Building Researc, Computer Program No. 25. University of Waterloo. 1992. Vision3 glazing system termal analysis software. Advanced Glazing System Laboratory. PHYSIBEL, 1992. TRISCO: Computer program to calculate tree-dimensional steadystate eat transfer in objects described in a beam saped grid using te energy balance tecnique. Maldegem, Belgium.
Room Side Weater Side Air Outlet Support Frame Cylindrical Guard R-11 Cooling Coil Fan Mask CTS or Skyligt Resistance Heater Pine Frame Cilled Water Coil (Deumidifier Buffle R-11 Cooling Coil Air Inlet Calorimeter Wall Convection Heater Figure 1: Scematic of te NRC/IRC ot box facility for inclined skyligt testing
Weater Side T f,c Q f,o T cts,c Q f,i Q Q cts,i cts,o T c CTS Support Frame of CTS T cal T m, T f, T ms T T b cts, Q fl Q m,o Q m,i Q cal Q t Figure 2: Details of te mounting of te CTS to te ot box and te relevant eat flows and temperatures
Polystyrene 4 mm 11 mm Clear Glass Clear Glass 40 mm 20 mm Pine Wood Frame Plywood 40 mm 6 mm Figure 3: Details of te interface between te CTS and te support frame
1.26 m 1 2 19 3 4 5 6 1.26 m 10 13 11 12 0 9 8 7 14 15 16 20 mm 17 18 Region of contact wit pine frame Figure 4: Layout of te termocouples on te room and weater sides of te CTS
C7 C1 C3 C5 C9 0.019 m C11 C13 R1 Flange R3 R5 R7 R9 R11 Frame 0.006 m CTS 0.138 m R13 0.197 m Mask R15 1.22 m R17 (a C13 C7 C1 C3 C5 C9 C11 L1 L3 0.610 m 0.570 m CTS Frame 0.040 m 0.020 m L5 L7 L9 Mask L11 (b L13 Figure 5: Rows, Columns, and Layers employed in te tree-dimensional conduction simulation using TRISCO
Table 1: Comparison of te 1-D and te 3-D eat transfers troug te CTS and te frame for te inclined position T c Q cts,1-d 3-D Q cts,i 3-D Q cts,o Q f,1-d 3-D Q f,i 3-D Q f,o ( o C (W (W (W (W (W (W -4.5 71.6 75.3 71.3 23.1 24 26.1-11.5 89.8 93.6 88.4 29.5 30.7 33.5-17.5 110.1 117.3 110.8 36.7 38.1 41.7-23.4 128.9 136 128.4 43.7 45.4 49.6-29.5 149.3 157.8 148.9 51.2 53.2 58.1 Table 2: Comparison of te 1-D and te 3-D eat transfers troug te surround panel and te total eat input from experiment and from simulation T c Q m,1-d 3-D Q m,i 3-D Q m,o (Q t exp (Q t sim ( o C (W (W (W (W (W -4.5 26.9 24.9 30.8 135.7 132.3-11.5 33.3 30.8 38.0 169.5 165-17.5 40.4 37.8 46.6 209.1 205.6-23.4 47.1 43.4 53.5 246 239.2-29.5 55.4 49.7 61.5 285.5 277.1 Table 3: Comparison of te 1-D and te 3-D eat transfer coefficients T c ( cts,i 1-D ( cts,i 3-D ( cts,o 1-D ( cts,o 3-D ( f,i 1-D ( f,i 3-D ( f,o 1-D ( f,o 3-D ( o C (W/m 2 -K (W/m 2 -K (W/m 2 -K (W/m 2 -K (W/m 2 -K (W/m 2 -K (W/m 2 -K (W/m 2 -K -4.5 6.8 7.2 27.5 27.4 5.4 5.6 29.6 26.9-11.5 7.1 7.4 26.5 25.8 5.7 5.8 30.7 28.1-17.5 7.3 7.7 26 25.7 5.9 6.1 31.7 29.0-23.4 7.4 7.7 26.5 26.2 6.1 6.2 32.8 30.3-29.5 7.6 7.9 27.6 27.3 6.2 6.4 34.6 31.6
20.0 18.0 16.0 Vertical Position Inclined Position 14.0 12.0 Q fl (W 10.0 8.0 6.0 4.0 2.0 0.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 T - Tc o ( C Figure 6: Variation of te flanking losses wit te air temperature difference between te room side and te weater side
75.0 70.0 65.0 3-D Inclined 1-D Inclined 60.0 55.0 2.01 T 1.339 2 (q" cts,i conv (W/m 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 1.996 T 1.309 10.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 T -T ' ( C Figure 7: Variation of te convection eat flux on te room side of te CTS wit te temperature driving potential in te inclined position cts, o
60.0 55.0 3-D Vertical 1-D Vertcal 50.0 45.0 1.773 T 1.268 2 (q" cts,i conv (W/m 40.0 35.0 30.0 25.0 1.764 T 1.224 20.0 15.0 10.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 T -T' ( C Figure 8: Variation of te convection eat flux on te room side of te CTS wit te temperature driving potential in te vertical position cts, o
75.0 (q" (W/m 2 conv cts,i 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 3-D Inclined 3-D Vertical 2.01 T 1.339 30.0 25.0 1.773 T 1.268 20.0 15.0 10.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 T -T ( C Figure 9: Comparison of te room side convection eat transfer along te CTS for te vertical and te inclined positions ' cts, o
T f,c T s,c Weater Side at T c Skyligt Glazing Q f,i T f, Q s,i T s, Support Frame of Skyligt T cal T m, T ms T b Q fl Q m,i Q cal Q t Figure 10: Details of te mounting of te skyligt to te ot box and te relevant eat flows and temperatures
Table 4: A sample of te calibration data and te uncertainty levels associated wit te measured and derived quantities Variable Equation Quantity Absolute Uncertainty Relative Uncertainty (% Q t Measured 169.5 0.017 W ±0.01 T Measured 18.9 o C ±0.1 o C ±0.5 T c Measured -11.5 o C ±0.1 o C ±0.8 T cts, Measured 10.3 o C ±0.1 o C ±1.0 T cts,c Measured -8.9 o C ±0.1 o C ±1.1 R cts Measured 0.32 m 2 -K/W ±0.0064 m 2 K/W ±2.0 Q cts,1-d Equation (2 89.8 W ±2.01 W ±2.2 T cts, Equation (5 10.5 o C ±0.1 o C ±1.0 T cts,c Equation (6-9.2 o C ±0.1 o C ±1.0 ( cts,i 1-D Equation (7 7.1 W/m 2 -K ±0.23 W/(m 2 K ±3.2 ( cts,o 1-D Equation (8 26.5 W/m 2 -K 2.4 W/(m 2 K ±9.0 T f, Measured 9.9 o C ±0.1 o C ±1.0 T f,c Measured -9.8 o C ±0.1 o C ±1.0 Q f,1-d Equation (3 29.5 W ±0.65 W ±2.2 ( f,i 1-D Equation (9 5.7 W/m 2 -K ±0.19 W/m 2 -K ±3.3 ( f,o 1-D Equation (10 30.7 W/m 2 -K ±3.6 W/m 2 -K ±11.7 T m, Measured 18.1 o C ±0.1 o C ±0.5 T m,c Measured -10.8 o C ±0.1 o C ±0.9 R m Measured 3.83 m 2 -K/W ±0.076 m 2 K/W ±2.0 Q m,1-d Equation (4 33.3 W ±0.7 W ±2.1 (q cts,i rad Equation (14 26.6 W/m 2 ±0.5 W/m 2 ±1.9 (q cts,i conv Equation (13 33.7 W/m 2 ±1.45 W/m 2 ±4.3
Table 5: Relative uncertainties associated wit te data reduction procedure for skyligt testing Q t Q s R.U.(Q s T s, R.U.(T s, T s,c R.U.(T s,c R s R.U.(R s (W (W (% ( o C (% ( o C (m 2 -K/W (% 150 61.94 ±6.5 13.4 ±3.8-15.9 ±1.2 0.705 ±6.8 175 86.94 ±4.9 11.7 ±4.8-15.3 ±1.6 0.461 ±5.4 200 111.9 ±4.0 10.0 ±6.2-14.6 ±2.0 0.327 ±4.9 225 136.9 ±3.5 8.3 ±7.5-14.0 ±2.5 0.242 ±4.9 250 161.9 ±3.1 6.7 ±10.8-13.3 ±3.1 0.184 ±5.2 275 186.9 ±2.8 5.1 ±15.4-12.7 ±3.7 0.142 ±5.8 300 211.9 ±2.6 3.6 ±23.3-12.0 ±4.3 0.109 ±6.8
24 22 20 18 16 R.U.(T s, R.U. (% 14 12 10 8 6 R.U.(R s R.U.(Q s R.U.(T s,c 4 2 0 150 175 200 225 250 275 300 Q (W t Figure 11: Variation of te relative uncertainties wit te total eat input to te calorimeter