ADVANCES IN MODELLING THERMAL BRIDGES IN BUILDING ENVELOPES

Transcription

1 ADVANCES IN MODELLING THERMAL BRIDGES IN BUILDING ENVELOPES Stephen Carpenter Enerodal Engineering Liited Kitchener, ON, Canada ABSTRACT This paper describes recent techniques developed to siplify the analysis and iprove the accuracy of odeling theral bridges. Two techniques are presented for deterining the overall wall theral resistance. The first is a hand technique using weighting factors between the isotheral planes and parallel path results. The second is a MS-WINDOWS finite-volue coputer progra. A technique is presented that accounts for the ipact of theral bridges on the transient response of wall systes. The equivalent wall odel involves creating a fictitious ulti-layer wall with properties selected so that its dynaic response to the transient conditions is the sae as the real wall with two- and three-diensional effects. INTRODUCTION Most building envelopes have theral bridging: locations where the theral resistance of the assebly is coprised for structural or fraing reasons. Coon theral bridges include steel or wood studs in cavity walls, junctions between floors and walls, balconies and other structural protrusions, corners and extra fraing around doors and walls. These theral anoalies increase heat transfer to the outdoors and can be a site for condensation. Despite their coon nature, any building siulation progras and progra users ignore the ipact of theral bridging or attept to account for theral bridging with a siple correction factor to the R-value. This paper describes recent techniques developed to siplify the analysis and iprove the accuracy of odeling theral bridges. These techniques account for the ipact of theral bridges on theral resistance and transient response of the wall syste. BUILDING ENVELOPE THERMAL RESISTANCE Traditional Approach The negative ipact of theral bridges has been known for a long tie. Most building designers are aware of the reduction in wall R- value due to wood and steel fraing. The traditional analysis technique to deterine this reduction has been the Parallel Path ethod as described in the ASHRAE Handbook of Fundaentals. The resistances of each layer are added together to get a total path R-value. If there is ore than one path through the wall (e.g., through the wood stud and through the cavity insulation), the total resistance of each path is calculated. The U-value (reciprocal of R-value) of each path are area-weighted to deterine the total wall R-value. This approach iplies that the heat flows in parallel paths and does not adjust its direction to find an easier route through the wall. The reality of course is that heat takes the path of least resistance, and as such the parallel path ethod always over-predicts the actual R- value. Table lists the R-value over-prediction of the parallel path ethod for two coon wood and steel frae wall systes. The overprediction was calculated by coparing the results of the parallel path ethod to the results fro -D finite volue analysis (see Section ). The over prediction is ost severe with steel frae walls but also has an effect in wood frae walls.

2 Wall Type Table : Parallel-Path R-value Over-Prediction (%) 38 X 400 centers with 5 ins. Sheathing 38 X 400 centers with 5 ins. sheathing Wood Frae Steel Frae. % 54 %. % 86 % Hand Calculation Correction Factors The ASHRAE Handbook of Fundaentals recoends that both the parallel path ethod and the isotheral planes ethod be used to deterine wall R-value. The correct wall R-value will be soewhere between these two results. In the isotheral planes ethod, the effective R-value of each layer is added together. If a layer is ade up of ore than one aterial, the aterial theral conductivites are area-weighted. Unfortunately, the two ethods give very different results and soe inforation is needed to deterine where between these two extrees the correct answer lies. The results fro the two ethods can be weighted as follows: R wall =R isotheral planes *K +R parallel path *(-K) Where K is a weighting factor between 0 and Figure shows the weighting factor (K) for a variety of steel and wood stud asseblies [Enerodal, 996]. A value of.0 eans that the isotheral-planes result is correct and a value of 0.0 eans that the parallel-path result is correct. The lower the value K is, the higher the R-value will be. As the studs are placed closer together, theral bridging is ore significant and a higher weighting factor is required. Siilarly, deeper studs cause ore theral bridging. The above approach is useful for assessing theral bridging in siple stud walls, however, it does have three ajor liitations. First, the weighting factors are liited to the wall systes studied. Second, the ethod cannot be easily applied to non-parallel geoetries such as corners and wall/floor junctions. Third, the ethod does not account for lateral heat transfer caused by highly conductive layers. Two-diensional finitevolue heat transfer overcoes all of these liitations. Figure : Weighting Factor between Isotheral Planes and Parallel Path Results Two-Diensional Heat Transfer Several two-diensional coputer progras (such as FRAMEplus, Enerodal, 00a) are available to analyze ore coplicated wall asseblies. The speed of analysis and ease of use of these progras eans that practitioners can use the on a daily basis as part of their design practice. The latest version of FRAMEplus (5.0) allows users to draw and analyse wall and window sections in a MS-WINDOWS environent. The progra has a coprehensive aterials library and autoatically assigns environental boundary conditions, eshes the geoetry and perfors the calculations (usually within a few seconds). For coplex walls and windows, the progra area-weights individual results to obtain total wall (including corners etc) and window results.

3 Figure shows the FRAMEplus screen of an insulated concrete block drawing. Figure 3 shows the ain screen where the coponent area-weighting is perfored. This and siilar coputer progras provide a siple and accurate eans of deterining total wall properties to account for the theral resistance ipact of theral bridging. However, these theral anoalies can also have an ipact on the theral or transient response of wall asseblies. The tie-lag benefits of a theral assive wall syste can be partially negated by theral bridging. This speeds up the theral response of the wall. A different approach is needed to account for transient effects. Figure : FRAMEplus Model of an Insulated Concrete Block Figure 3: FRAMEplus Screen for Displaying Total Window/Wall Results BUILDING ENVELOPE TRANSIENT RESPONSE Equivalent Wall Model Most building energy analysis progras odel the transient response of walls as a series of one-diensional layers, ignoring the ipact that theral bridges have on the transient response of the assebly. A recent ASHRAE project developed the concept of equivalent wall layers to account for this ipact [Enerodal, 00b]. The equivalent wall technique is a relatively siple way to odel coplex building asseblies in wholebuilding energy progras that use a nodal network or require input of thero-physical properties of wall layers. The equivalent wall odel involves creating a fictitious ulti-layer wall with properties selected so that its dynaic response to the transient conditions is the sae as the real wall with two- and three-diensional effects. Thus, for exaple, a hoogenous wall layers could be defined with specific conductivities, densities, specific heats, etc., to give the sae dynaic (and steady-state) response as a steelfraed wall with gypsu wallboard sheathing. The equivalent wall ethod, developed by Kossecka and Kosny [996, 997], is incorporated into a specialized version of HEATING 7. [Childs, 993], called

4 EQV_WALL. This coputer tool aids in the odeling of dynaic theral perforance of coplex wall systes with significant theral ass, and is utilized for these siulations. The equivalent wall ethod uses, as its atheatical basis, conditions iposed on the response factors and z-transfer function coefficients by theral structure factors. Theral structure factors are diensionless quantities representing the fractions of heat stored in the wall volue, in transition between two different states of steady heat flow, which are transferred across each wall surface. Structure factors ϕ ii and ϕ ie for a wall coposed of n plane hoogeneous layers, nubered fro to n with layer at the interior surface, are given as follows: ϕ ϕ ii ie = = n R C = n R C = C C R 3 R 3 + R R e + R RR + + R e i R e where R is the total theral resistance per unit cross section area, R and C denote the theral resistance and capacity of the -th layer, whereas R i- and R -e denote the resistance for heat transfer fro surfaces of the -th layer to inner and outer surroundings, respectively. There are several ways the equivalent wall technique ay generate a siple onediensional ulti-layer structure with the sae theral properties and dynaic behaviour as the actual wall. The first step is to assue soe nuber of equivalent layers for the wall structure. Experience has shown that three-layer equivalent wall odels provide the best results. A siple way to solve for equivalent layer properties is to first generate, randoly or with soe logic, a set of capacitances C n (or resistances R n ) for each layer. Then seek the resistances R n (or capacitances C n ) to satisfy the above equations. The theral structure factors and overall R-value ust atch those for the 3-D wall assebly. Thero-physical properties of the layers ay then be established, if necessary, to atch R n and C n values and total thickness of the wall. The developent of the equivalent wall odel is an iterative procedure. By adjusting the nuber and capacitances of equivalent wall layers, the equivalent wall odel can generate results that ore closely reseble those of the 3-D odel. The equivalent wall odel results are not unique; however, different equivalent wall odels have, in general, very siilar dynaic theral properties. If desired, one ay exaine several generated odels to choose the best one. Equivalent Wall Model Exaple A coparison was ade between the theral response of the three-diensional coputer odel and the equivalent wall odel for an insulated concrete block wall (as shown in Figure ). The equivalent wall layers are shown in Table. The coparison was ade for a one-day period shown in Figure 4. The quantity Te is the exterior air teperature and Tes is the exterior sol-air teperature. The indoor air teperature was held constant at 68 F (0 C). The results of the coparison are shown in Figure 5. There is very good agreeent between the 3-D and the equivalent wall odel. For reference, the response assuing instantaneous heat flow (i.e., no theral lag) is also shown, labeled steady-state. The 3-D transient analysis results in a 4-hour shift in peak load and a considerably soother daily response. A tabulation of equivalent wall properties for 0 coon wall systes is contained in Enerodal, 00b.

5 Table : Equivalent Wall Layers for an Insulated Concrete Block Wall Figure 4: Daily Profile of the Exterior Air (Te) and Sol-Air (Tes) Teperatures WALL DESCRIPTION Coponents Total R-Value Te Tes.65 in. Core Concrete Block in. Mortar.875 in. Foa inserts ft - F-h/ Btu.3 teperature [F] tie [h] EQUIVALENT WALL THERMOPHYSICAL PROPERTIES N R n C n l n k n ρ n c pn ft - F h/btu Btu/f t - F in Btuin/h-ft - F lb/ft 3 Btu/l b- F Total.3 Figure 5: Coparison of Results for 3-D Transient Model and Equivalent Wall Model heat flux [Btu/h ft] 3-D response factors 3-D z-transfer functions 4 equivalent wall steady state tie [h]

6 CONCLUSIONS The conventional parallel-path ethod can significantly over-predict the R-values of walls with theral bridging. This overprediction can be corrected using one of two siple techniques. First, a weighting factor between the isotheral planes and parallelpath ethods is the easiest technique for siple wall asseblies. Second, user-friendly -D coputer siulation tools can be used for ore accurate assessent and for ore coplex asseblies. Theral bridging can also ipact the transient response of walls. An equivalent wall odel is a siple way of accounting for the transient response. This technique shows excellent agreeent with detailed 3-D heat transfer odels. Kossecka E. and J. Kośny Equivalent wall as a dynaic odel of the coplex theral structure. Journ. of Theral Insulation and Building Envelopes, Vol. 0, ACKNOWLEDGEMENTS The author wishes to acknowledge the work of the co-authors of the ASHRAE research project on equivalent wall odels: Jan Kosny of Oak Ridge National Laboratory, Elizabeth Kossecka of the Polish Institute of Sciences and Tracey Forrest of Enerodal Engineering Liited. REFERENCES Childs K.W HEATING 7. User s Manual. ORNL/TM-6. Oak Ridge National Laboratory, Oak Ridge, TN. Enerodal, 996. Building Insulation Syste Theral Anoalies 785-RP, report prepared for ASHRAE, Atlanta, GA Enerodal, 00a. FRAMEplus Coputer Progra Version 5.0 ( developed for Natural Resources Canada, Kitchener, ON Enerodal, 00b. Modeling Two- and Three- Diensional Heat Transfer Through Coposite Wall and Roof Asseblies in Hourly Energy Siulation Progras (45- RP), report prepared for ASHRAE, Atlanta, GA Kossecka E. and J. Kośny Relations between structural and dynaic theral characteristics of building walls. Proceedings of 996 International Syposiu of CIB W67 Energy and Mass Flows in the Life Cycle of Buildings, Vienna, 4-0 August, pp