Thermal Bridge Assessments - Energy Systems Research Unit ...

input meshes, boundary conditions and two types ofoutput:1. The Linear Thermal Transmittance or Ψfactor; this is the heat loss per meter lengththrough a structural element containing athermal bridge minus the heat loss that wouldoccur if the thermal bridge was not present.2. The temperature factor of the surface,f = T s − T o(1)T i − T owhere T s is the internal surface temperature,T i is the internal air temperature and T o is theexternal air temperature. This gives anestimate of the ‘quality’ of the thermal bridgeindependently of the imposed boundaryconditions and can be used as an index of thelikelihood of mould growth.KOBRA is a program developed by the Belgiancompany Physibel to interrogate a database of 2-Dthermal bridge details. It provides quantitativeinformation on the linear thermal transmittances andtemperature factors, and allows the effect ofmodifications to be rapidly investigated.The EUROKOBRA database which can beinterrogated by KOBRA was developed under an ECSAVE project by eight participating countries, led bythe Belgian Building Research Institute. Thedatabase, or atlas, contains the 2-D geometry of thedetails (the left hand side of Figure 1 shows anexample) including the thermal conductivities ofeach of the materials; a rectangular grid for thecalculation is also specified. Within the giventopology of the detail, the user can vary theboundary conditions, the horizontal or vertical sizeof each element and the conductivities of eachmaterial. The outputs are calculated within a fewseconds on a standard PC. They include, as shownon the right hand side of Figure 1, the temperaturefactors at key points and warnings on the risks ofcondensation and the linear thermal bridges based onboth the internal and external dimensions of thebuilding. Colour pictures of the temperature andheat flow distributions through the section can alsobe displayed.The EUROKOBRA database, currently containingabout 1000 details of all parts of typical Europeanbuildings, is now available. Further specializedatlases covering details such as window frames andsteel-framed buildings are in preparation, andconsideration is being given to extending thecapabilities of the system to 3-D.MODELLING OF 3-D GEOMETRYWITH 1-D SIMULATION PROGRAMSAlthough the creation of the EUROKOBRAdatabase offers a significant advance in assessingsteady state 2-D losses (and potentially 3-D losses),for detailed studies it is clear that these heat lossesneed to be integrated more fully into dynamicsimulation programs which attempt to model theoverall building performance.Although in principle it is easy to formulate thediscretized equations for 3-D conduction (Clarke1985), in practice they have not been implementeduntil recently. The reasons for this are twofold - withregard to the computational effort, they result insignificantly larger program size, much longersimulation times, and time consuming modelspecification; on the other hand, it was consideredthat other uncertainties in thermal simulation gaverise to greater errors than those caused by the 1-Dconduction approximation. This perspective may bechanging, as computing power and user interfacesimprove, and thermal bridging and groundmodelling assume a more important role withinoverall building response.This need for improvement was clearlydemonstrated in a major European researchprogramme called PASSYS (Vandaele and Wouters1994). This programme, in which 10 Europeancountries participated, involved the establishment ofa series of test cells throughout Europe. One of theaims of the project was to use the test cells to gatherhigh quality data sets for use in the empiricalvalidation of dynamic simulation programs. Figure2 shows the test cell structure.A major difficulty encountered in the work was the(relatively) large 2-D and 3-D conduction losses inthe test cells resulting from the thick walls (0. 52m)of the cells. In the case of the test cell fitted with theinsulated calibration wall on the south facade, it wasestimated that the heat losses were 48% higher thanthose estimated from a simple 1-D heat losscalculation based on internal dimensions. The ideaof the test cell construction was to have highlyinsulating constructions on the floor, ceiling and allwalls except the south wall. Different wallcomponents could be mounted on the south wall - asthese would typically have much higher heat lossesthan the rest of the insulated cell, experimentaluncertainty of the south wall performance (the focusof the work) would be minimized.

Figure 1: Typical output from KOBRAFigure 2: PASSYS Test CellThe simulation program ESP-r was used withinPASSYS. In common with other comparablesimulation programs, ESP-r had only 1-Dconduction capability and was therefore unable tomodel explicitly the edge heat losses through the testcell envelope. The edge loss problem was addressedwith the use of extra "edge constructions" within themodel which attempted to account for the heattransfer in the edges of the test cell. The materialconductivity of these constructions were obtainedwith the use of 2-D and 3-D steady state analysesusing the program Trisco (Standaert 1989). A

similar procedure using 2-D steady-state analyseswas used in the recent IEA Annex 21 empiricalvalidation exercise (Lomas et al, 1994).In more detail, the technique employed was to keepthe same internal geometry of the test cells, but tochange the properties of the construction lyingwithin 0.4m of each edge. Beyond this distance fromthe edge, the 3-D analyses showed that theconduction was essentially 1-D. The resulting modelof the test room is shown in Figure 3.Figure 3: Test Cell Model with Edge ConstructionsThe conductivities of the edge constructions werethen modified to take account of the extra edgelosses, i.e. those obtained from the differencebetween the 3-D and 1-D steady-state analysis forthe particular edge or corner. To allow for thechanging area through the thickness of the cell, usewas made of the "developed area" (see Figure 4 foran example). Each edge construction was subdividedinto a number of strips. The inside layercorresponded to the actual material in the test cell,the other layers had artificial conductivity values,increasing in value from inside to outside so that:(a) the conductivity was proportional to thedeveloped area of the layer, and(b) the overall conduction losses were inagreement with the steady state analyses.With regard to capacity of these edge constructions,the capacity of the edge region was sized toapproximately match the time taken for the effect ofa step heat pulse to propagate from the internalsurface to the external surface of the edge (as theprimary interest was in the dynamic responseresulting from internal changes in temperature).0.42m0.070m0.070m0.070m0.070m0.070m0.070mlayer123456Area = 9.44 m21-D edge constructiondeveloped area oflayer 3 shown dotted0.004m 7plywoodNot to scaleArea = 3.77 m2Figure 4: Geometry of the Developed AreaActual constructionThe method and the results are written up fully in(Jensen 1993). In summary, the results of comparingpredicted data from a model with these edgeconstructions with measured data for the calibrationwalledtest cell showed:• The steady state model predictions were inreasonable agreement with the measured datawhen measurement and predictionuncertainties (in particular with respect tointernal convection and temperaturedependentconductivities) were taken intoaccount.• The dynamic response was poor.Figure 5 shows the measured results for acalibration-walled test cell, together with 1-Dsimulation results based on internal cell dimensions,and the results after adding edge constructions("modified 1-D").Within PASSYS, the results from the calibrationexperiments were used to calibrate the ESP-r modelof the test cell. In particular, the capacity derivedfrom the results of the application of systemidentification techniques was used to adjust thecapacities of the edge constructions to obtainsatisfactory agreement for the calibration-walled testcell (Clarke et al 1993). This calibrated model wasthen used for further comparisons of different testwalls.

55.050.0measuredsimulation (1D)simulation (modified 1D)test room air temperature ( C)45.040.035.030.025.020.015.0100.0 120.0 140.0 160.0 180.0 200.0day of year (1991)Figure 5: Measured, 1-D and Modified 1-D Air TemperaturesDEVELOPMENT AND IMPLEMENTATIONOF 3-D MULTIGRIDDING ROUTINESAlthough successful in the case of the PASSYSprogramme, it is clear that the use of separate 3-Dsteady state programs and/or the use of detailedexperimental data and analysis is not a usefulgeneral tool for dynamic modelling. Although thePASSYS test cell is an extreme example of theimportance of 3-D conduction heat flow, there aremany other cases where full 3-D modellingcapability would be useful, e.g. ground modellingand where it is required to predict surfacetemperatures near the corners of rooms.The discretized finite difference approximations for3-D conduction to be used within ESP-r have beenformulated (Clarke 1985). The major problem to beovercome for implementation was the developmentof an efficient gridding scheme. Since there is noone best grid generation technique for all purposes, astudy was carried out to develop an adaptive 3-Dgrid generation technique for transient heatconduction simulation in buildings. It was acombined study of grid generation techniques andnumerical solution methods for partial differentialequation of heat conduction. Accordingly, a schemefor 3-D gridding and modelling was developed.Unstructured meshes are generated by the griddingprocess for each zone element in insolation. Thisallows flexibility in the resulting model, for exampleallowing one particular part of the building, such asthe ground, to be modelled in 3-D, with the rest ofthe building in 1-D and/or 2-D.The flexibility was obtained by adopting the controlvolume approach. That is:V ρ C p∂T∂t=−∫q. → ndS+Vg → (2)swhere n → is the unit vector in the direction of theoutward normal to the surface, g is the energygeneration rate per unit volume V, and q is the heatflux per unit area. If the control volume surface areaS is divided into (m) plane segments Equation (2)becomes∂TV ρ C p = m∂tΣ A i λ ( ∇T i . n → i ) + Vg (3)i=1where→q ≈−λ∇TAlthough this method ensures energy conservation,with no limitation at the gridding level, the accuracyof the simulation is strongly dependent on thegenerated mesh. For example, steep mesh spacingchanges will magnify the local truncation (and hencethe simulation) error.There are several possible schemes for thepositioning of control volumes and their associatedgrid points (see Figure 6). For the 3-D gridgeneration, Approach 4 in the Figure was adopted.This gives continuity of heat capacity and density

throughout the control volume, and continuity in theboundary conditions throughout each control volumesurface. The grid points are located at the geometriccentres for each control volume, which is expectedto give the best representation of the averagetemperature over the control volume. In addition,massless nodes are located at the constructionboundaries and layer interfaces in order to ensurecontinuity in the thermal conductivity between gridpoints and a better dynamic response to excitationsat the construction boundaries.approach 1 approach 2 approach 3 approach 4layer boundarycontrol volume boundarylayer and control volume boundariesmassless nodeconventional nodeFigure 6: Control Volume Nodal SchemesThere is a price to pay for the grid flexibility - morestorage is required for an unstructured mesh than foran equivalent structured mesh. In addition, thenumber of coefficients (connections) for each node isnot constant, and there is a potential for some nodesto have a relatively large number of coefficients.Thus, convergence of the iterative solution methodsis expected to be more difficult. Also, somerelatively fast direct solution methods for structuredgrids (such as the Alternating Direction Implicit(ADI) or Explicit (ADE) methods) are notapplicable. It should be noted that even forstructured meshes, the internal surface nodes areexpected to have a relatively large number ofcoefficients due to the internal longwave radiationprocess. For the present implementation, storageand speed problems were reduced by introducingsparse storage and matrix solution techniques.However, solution times are still restrictive(although this problem should in time be reducedwith increased computing power).VALIDATION OF 3-D CONDUCTIONIMPLEMENTED IN ESP-rThis section describes the first stages of thevalidation necessary to check on the implementation.As far as possible, the validation methodologydescribed in the EC PASSYS programme wasadopted (Jensen 1993), namely a thorough review ofthe theory and code implementation, followed byapplication of analytical, inter-model comparisonand empirical validation elements.For the analytical test, the ESP-r results from thedefault 1-D nodal scheme and the new 3-D nodalscheme (Approaches 1 and 4 respectively in Figure6) were compared with the analytical solution for a1-D transient heat conduction problem. The testdomain was a slab with an adiabatic boundary at oneside and a convective boundary at the other side. Theeffect of a step change from 50°C to0°Cintheambient temperature was monitored. Theconvective boundary surface temperature wasselected as the validation variable, as maximumerror is expected at that location. The measured andpredicted results when plotted on the usual lineartime basis are very close; for this reason they areplotted in the format of Figure 7 to accentuate thedifferences. The predictions from the 3-D schemeare considered acceptable; the 3-D scheme withmassless boundary nodes has a better response forthe surface temperature, but the default 1-D schemeprediction became slightly more accurate as the rateof temperature variations decreased. This isprobably due to the effect of a higher heat storageterm for the neighbouring control volume in the 3-Dscheme. These simulations were undertaken with 1hour timesteps; agreement with the analyticalsolution is improved if smaller time steps are used.simulation (degrees C)50.040.030.020.010.0timeexactconventional boundary nodesmassless boundary nodes0.00.0 10.0 20.0 30.0 40.0 50.0analytical (degrees C)Figure 7: Analytical Comparison:Decay from Step ChangeTwo inter-model comparisons were performed. Inthe first one, a comparison was made between thedefault 1-D scheme for ESP-r and the new 3-Dscheme on a 1-D zone model. Minor changes wererequired within the 3-D code so that the same nodal

scheme (Approach 1) was used in both cases. Thepredicted temperatures were in agreement to betterthan 0.001°C. In the second inter-modelcomparison, ESP-r 3-D results were compared withresults obtained using the conduction modellingfacilities within the computational fluid dynamicspackage PHOENICS (Spalding 1991). A cubicroom with a homogeneous one layer constructionwas used. The thermophysical and geometricalsymmetry was required to cancel the effect ofinternal longwave radiation effects which are treatedin ESP-r but not in PHOENICS. Due to thesymmetry only one eighth of the room was modelledby PHOENICS. The effect of step excitation in theindoor air temperature was examined. The predictednodal temperatures with ESP-r and PHOENICSwere in agreement to better than 0.001°C.Finally, results from PASSYS test cell experimentswere used for empirical validation. Figure 8 showsthe measured results, with the modified 1-D and thenfull 3-D simulations. A portion of the graph isdisplayed at higher resolution to show shorter perioddynamics. At lower temperatures the 3-D simulationresults are in much better agreement with themeasured data, and in general the dynamic responseis better. At high temperatures, the measured andpredicted temperatures still differ. This is thought tobe mainly due to the effect of temperature on thethermophysical properties, particularly conductivity,for which the model inputs were based on measuredconductivity at the standard 10°C. Currently, theESP-r 3-D scheme is not capable of considering thetemperature dependence of thermophysicalproperties. However, for the default 1-D simulation,the impact of adopting a linear temperaturedependence for thermal conductivity for theinsulating materials in the test cell is shown inFigure 9. Application of such dependence wouldimprove agreement with measured data at hightemperatures.CONCLUSIONSTwo important recent developments have beendescribed. Firstly, there now exists a comprehensiveelectronic database of 2-D thermal bridges whichcan be selected, modified as necessary and theresulting linear thermal transmittance andcondensation risk evaluated. This should permit arapid assessment of thermal bridges withinbuildings, and possible remedies for unsatisfactoryperformance.projects has been outlined. An attempt has now beenmade to provide a more fundamental treatment of3-D conduction within the dynamic thermalsimulation program ESP-r. Results from somevalidation exercises applied to the new code showthat 3-D conduction can now be successfullyapplied, although further improvements in solutionspeed (or computing power) and ease of problemspecification is required before it can be routinelyapplied.REFERENCESClarke J A, 1985. Energy Simulation in BuildingDesign. Adam Hilger Ltd, Bristol and Boston.Clarke J A, Strachan P A and Pernot C, 1993. AnApproach to the Calibration of Building EnergySimulation Models. ASHRAE Transactions, 99(2),pp917-27.Lomas K, Eppel H, Martin C and Bloomfield D,1994. Empirical Validation of Thermal BuildingSimulation Programs using Test Room Data. IEAAnnex 21 (Calculation of Energy and EnvironmentalPerformance of Buildings).Jensen, S.O. (Ed.) 1993. The PASSYS Project.Subgroup Model Validation and Development - FinalReport, Parts I and II, 1986-1992. Commission ofthe European Communities, DGXII, EUR 15115EN.Spalding D B, 1991. The PHOENICS Beginner’sGuide, Heat and Momentum Ltd.Standaert P, 1989. TRISCO, Version 3.2, ComputerProgram to Calculate Three-Dimensional Steady-State Heat Transfer in Objects described in aRectangular Grid using the Energy BalanceTechnique, Physibel C.V, Maldagem, Belgium.Vandaele L and Wouters P, 1994. The PASSYSServices: Summary Report, European CommissionPublication No EUR 15113 EN.When detailed simulations of whole buildingperformance is required, it is sometimes necessary totake 2-D and 3-D effects into account. The method,and limitations, adopted in two recent international

45.035.040.034.0test room air temperature ( C)35.030.025.020.0measuredsimulation (modified 1D)simulation (3D)33.032.031.030.015.0100.0 120.0 140.0 160.0 180.0day of year (1991)174.0 176.0 178.0detail of main graphFigure 8: Measured, Modified 1-D and 3-D Air Temperatures29.045.0test room air temperature ( C)40.035.030.025.020.0measuredsimulation (constant conductivity)simulation (variable conductivity)15.0100.0 120.0 140.0 160.0 180.0 200.0day of year (1991)Figure 9: Effect of Conductivity Temperature Dependence