Computer Software for Building Envelope Design:

Heat in 3 Dimensions

 

 

By: James Posey   

Introduction

Whole building energy models and 2D thermal models of windows are extensively used to refine building and envelope component designs. This article focuses on another class of thermal model that has yet to be widely applied, but that deserves to be—3D models of heat flow in envelope details (or 4D, if you count time).

We don't know enough about material properties, environmental loads, and limit states to answer questions like "how much air leakage will a double wythe masonry wall with 150 mm of expanded polystyrene foam insulation tolerate without damage, if the building is in Yellowknife and houses a swimming pool?" We know it will have to be uncommonly airtight, but what does that mean in L/s•m at 75 Pa, and how hard will it be to achieve? We know enough about properties of materials, expected loads, and limit states to design that same wall structurally with confidence that we are neither wasting material, nor risking premature failure. But, we are only just beginning to collect the information needed to apply the physics of heat and moisture, or the biology and chemistry of deterioration, in the way we already apply structural mechanics. Only when we have that information, and tools with which to use it, can we design novel building envelopes—as opposed to designing from past experience of what we know works. And, only then will we be able to put successful building envelopes into novel service conditions without unexpected failure, waste of resources, or both. Premature failure due to structural inadequacy is rare. Premature failure due to moisture-induced deterioration is not.

This does not mean that partial models can't be very useful. 2D steady state thermal models (using LBNL Optics, Window, and Therm) are extensively used for National Fenestration Rating Council (NFRC) qualification of windows. They make assumptions that are typically incorrect in service—but they are a valid substitute for actual testing when the assumptions match test conditions, and when model results compare well with test results for the same windows. Computer models of heat and moisture flow are useful for comparing one detail with another, and capable of predicting which will provide better performance. They are not capable of predicting absolute performance when there is potential for moisture-induced corrosion or biological attack. But they are a huge step forward from the 1D steady-state calculations many designers still use today.

3D Heat-flow—Examples

Heat-flow calculations ignore moisture. This does not mean they are useless. One can use them to compare one geometric configuration (where experience tells us condensation and drying are not problematic) with a proposed new configuration. If heat flows are lower, and temperatures of places in the detail where we suspect condensation might be a problem are not lower, then it's not hard to conclude that the new detail is an improvement. We can also compare details with which we have experience, and which are known to have condensation problems, with revised details. If a model of a revised detail predicts higher temperatures at the places where we expect condensation, then we can’t say for sure that the problem will go away, but we know the performance of the new detail will be better. Of course, we have to stick to materials that are not so different in their moisture related properties that they invalidate the comparison. Several examples applying 3D heat flow models to building envelope details follow.

Side-mounted brick ties for masonry veneer on steel stud framing

Steel studs are thermal bridges that lead to dust marking and sometimes condensation even on interior surfaces, in addition to substantial heat loss. It is often recommended, at the least, to add insulating sheathing to the outside of steel stud exterior walls in cold climates. When walls are clad with masonry, do side mounted brick ties make a big difference? Do holes in the tie in line with the exterior insulation help?

To answer these questions, look at the following 3D steady-state heat-flow model results. The model represents a section of wall that is 1 stud space x 1 tie space, so that heat flow through the model reflects total heat flow through the wall. Because the stud is not symmetrical in section, a full stud space is represented, but only half a tie, and half a tie space are included. That is because the wall is symmetrical in that direction. The temperature difference is 1 degree, because this makes comparing results easier. If you want to know what the temperature "really" is, multiply your chosen outdoor-to-indoor temperature difference by the reported temperature and add that to the outdoor temperature. To know the heat loss, multiply the reported heat loss by the actual outdoor-to-indoor temperature difference.

The components of this wall are

·    152 x 0.93 mm steel studs at 600 mm centres,

·    gypsum board inside,

·    mineral wool in the stud space,

·    50 mm of XPS outside,

·    1.6 x 50 x 170 mm side-mounted ties spaced at 400 mm centres, projecting 18 mm from exterior face of XPS.

The masonry veneer and the cavity behind it are left out, and the exterior insulation and tie projection are assumed to be insulated from the exterior temperature only by a film of air.

 

 

	1D, ignoring studs and ties	2D, with studs, but no ties	3D, with plain ties	3D, with perforated ties
Heat flow, W/m2.C	0.147	0.194	0.258	0.242
Min. temperature on inside surface of XPS	0.289	0.296	0.293	0.293
Min. temperature on interior wall surface	0.981	0.915	0.844	0.855

Table 1: Numeric results for thermal models of side-mounted masonry ties.

By changing the conductivity of the mineral wool insulation to match the overall thermal resistance of a 153 mm airspace, and incrementing the thickness of XPS sheathing, one could discover how much XPS to add to compensate for leaving out the mineral wool. Why do this? Because with an indoor temperature of 24C, and an outdoor temperature of -20C, the interior surface of the XPS would be -7C. Without the stud and tie, it would be even colder. Since XPS is non-absorbent, condensation is likely to occur, with or without a vapour barrier, if the indoor RH is much more than 12%. In this situation, although the thermal bridge increases heat loss, it actually improves the situation where condensation is the concern.

Ledger angle for a masonry veneer steel stud wall

This model is for a wall similar to the previous one, with 92 mm studs. It includes the slab-edge detail and omits the ties.

Is it better for the temperature of the metal stud wall track to attach a masonry ledger angle continuously to the concrete slab edge, or to separate it from the slab with intermittent supports, and put insulation between the ledger and the slab?

Compare these two 3D steady state models. The wall is supported on a 200 mm concrete slab. The stud space is insulated. The vertical face of the 102 x 102 x 8 mm ledger is in line with the exterior face of the exterior insulation. In one case the ledger is supported with shims and grout, so that the slab is in thermal contact with the back of the ledger. In the second case, the slab stops in line with the exterior sheathing, and the ledger is supported on 10 x 102 mm knife plates at 1200 mm centres, so that there is insulation behind most of the ledger.

 

 

	% of total wall heat loss through ledger	Lowest temperature of stud track
Ledger in contact with slab	40	0.53
Ledger supported away from slab	19	0.72

Table 2: Numeric results for thermal models of slab edges.

HSS penetration of an insulated wall

If a heavy structural member passes through an exterior wall, exposed to both interior and exterior, where is it best to insulate it, inside or out? This model shows how to prevent condensation in this situation, with high indoor humidity. One way is to add insulation to the exterior, extending out around the member for a significant distance. The other way is to add a “radiator fin” to the interior side, to collect heat and keep the member warm—not an energy wise solution—but perhaps desirable for the designer who prefers a robust look, with the steel structure fully exposed inside and out. In the models, the structural member is a 120 x 120 x 10 HSS. One version (insulation outside) has the outside of the HSS covered for 500 mm away from the wall with 25 mm insulation, in addition to filling the inside of the tube. The other (not illustrated, with radiator fin inside) has a 200 x 200 x 10 mm steel fin welded to the tube at the interior. Illustration __ shows what happens when neither measure is taken.

	heat flow through HSS, W/DegC	Minimum temperature of HSS surface at interior
Insulation outside	0.107	.74
Fin inside	out of bounds, > 0.4	.74

Table 3: Numeric results for thermal models of HSS wall penetration.

Cast-in-place concrete building — where to insulate?

In some markets, cast-in-place concrete buildings are common. Developers from temperate coastal regions of Canada have moved inland, taking their favourite designs with them. Have mid-continental designers been wrong all these years about putting the insulation on the outside, and the structure on the inside? Are West Coast builders living in la-la land?

 

So far, these models indicate that in mild climates, insulation on the interior may make sense, but that in a cold climate, insulation on the exterior is required to avoid condensation. What if there’s a balcony cantilevered from the concrete slab?

Furring fastened through exterior insulation

In cold climates, to avoid risk of condensation and mold in wall cavities, all the insulation is sometimes put on the outside. This allows a continuous air-and-vapour barrier to be put on the outside as well, and simplifies detailing of penetrations, leaving the framing space as open for electrical and mechanical services as an interior wall. But how do you fasten the cladding? Since a ventilated, drained cavity behind the cladding is also often wanted, one answer is to lag-bolt furring through the insulation, air barrier, and sheathing, into the framing. The resulting assembly, simplified by omitting interior finish, and cladding, looks like Illustration 10.

Because of the geometry of the most conductive part in this detail (the bolts), finite difference heat-flow programs like the one used to generate some of the previous examples cannot be used. Instead, a finite element method is used, with an automatically generated trapezoidal mesh (like the automatic triangular mesh in THERM, but in 3D). Steady state temperatures for a unit temperature difference are shown in Illustration 11.

From the model, we can see that, for the portion inside the vapour air barrier, the coldest part of the bolt is at 0.5. This means that if the temperature outdoors stayed at -20 C, with indoor temperature at 20 C, long enough to reach steady state the bolt would be near freezing at a point where moisture from indoor air could still reach it by diffusing through the wood of the stud and sheathing. Few climates are so cold that both the temperature, and wood moisture content would reach equilibrium with these conditions before the weather changed, but it's cold enough to raise a red flag and suggest further investigation.

Other applications

Adding insulation under slab on grade is a great energy-saving idea, especially for hydronic heated slabs, or a drive-in industrial oven. But foundation depths are based past performance of foundations  adjacent to heated spaces without under-slab insulation. Using transient 3D models, it is possible to determine for any thickness of sub-slab insulation, a reasonable configuration of exterior sub grade insulation that can ensure that the minimum annual footing temperature is not lower than it would have been for the traditional uninsulated configuration. This assumes that required footing depth without insulation is known, that the building is heated, and that thermal conductivity of the soil is known. Such a model will reveal that temperatures are much lower at exterior corners and projections (places where we know some buildings have trouble with frost heave) and that insulation can be configured to protect these locations. A steady state model with a one degree temperature difference is no help in this case. The temperature inside the building is fairly steady, the temperature at depth in the ground is constant (at the annual average air temperature, more or less), and the outside air temperature varies through the year.

The range of design problems that can be illuminated with thermal models has only been touched upon here.

Conclusion

Are you convinced that 3D heat flow models could be useful in building envelope detail design? 2D models have certainly been useful for designing windows. You can download a more technically-oriented paper from the author’s web-site if you want to know more about the software used, how it is applied, and the limitations of different software types. This article has focused on potential applications, the download focuses on software and methodology.

The author's website is http://bricks.bricks-and-brome.net.

References

Posey, James B. & Dalgliesh, W. Alan, "Thermal bridges—heat flow models with Heat2, Heat3, and a general purpose 3-D solver" 10th Canadian Conference on Building Science & Technology, May 2005. http://bricks.bricks-and-brome.net/Paper_S03_Final.pdf

Blomberg, Thomas, "Heat conduction in two and three dimensions—Computer modelling of building physics applications" Report TVBH-1008, Lund University, Lund Institute of Technology, Department of Building Technology, Building Physics, May 1996.

Backstrom, Gunnar, "Fields of physics by finite element analysis", GB Publishing, Malmo, 1997. http://web.telia.com/~u40124320/index.htm

Mitchell, Robin et al, "Therm 5.2 / Window 5.2 NFRC Simulation Manual", Laurence Berkeley National Laboratory, June 2006.  http://windows.lbl.gov/software/software.html

About the Author

Jim Posey, a specification writer since 1971, has been active in the Alberta Building Envelope Council South since 1985. He consults on building materials and assemblies, and does technical writing related to building construction. His experience also includes architectural drafting, building science research, hygrothermal and thermal modeling, and contract administration.