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Energy efficiency of building walls: thermal modeling, experimental testing, long term evaluation and correlation of building wall systems.


The building sector accounts for 25-40% of final energy demand. Globally, carbon could be reduced by 715 million tons through simply improving the energy efficiency in buildings and appliances (27% of the projected increase in Green House Gas emissions). In the United States, 65.2 percent of electric power is consumed by buildings every year. With renewed interest in conserving energy, the construction industry has focused on increased use of insulation in commercial building wall assemblies.

There is a strong need in properly establishing the thermal properties of new wall systems and products. Accurate characteristics are needed to demonstrate compliance with energy codes, to guide product development and manufacturing, and to support improvements in thermal designs. ASHRAE and IECC have prescriptively increased the required use of continuous insulation (ci) in steel stud exterior wall designs to reduce thermal bridging, where heat flows around the insulation by means of high conductivity attachments. Thermal bridging represents 1% of all energy use and over $5.5 billion in expenditures that could go to other needs. Understanding of the contributions and modes of heat transfer is critical in reducing thermal bridging, and improving the efficiency of wall systems, especially for new systems discussed in this paper. A better understanding of industry requirements regarding U-factor calculation procedures, and modeling guidelines, establishes the foundation for building envelope performance evaluation. The current study focuses on development of finite element analysis (FEA) based thermal simulation method and correlation with experimental testing of wall samples.

Traditionally, R-values (R) of insulation systems were calculated by simply adding up R-values of individual insulators. This 1D "resistances in series" approach only accounts for one mode of heat transfer, namely, conduction in a single direction, and assumes alignment of the components, and intimate thermal contact. When framing is not considered, it is termed 'Center-of-cavity R-value', but is usually termed 'Clear-Wall R-value' when the necessary framing is included. The 'Framing Factor' is used to express a percent of the total area occupied by framing members. When performing hot box testing, the framing factor is assumed to be 11-14%, but in reality the framing factor can be up to 27%. For most wall systems, the part of the wall that is analyzed is that which is uninterrupted by details (clear wall). Such an overestimation of wall thermal resistance leads to significant errors.

In the building industry, 2D methods are quite popular for the analysis of walls. With 2D tools, one can adequately represent the supports, and include all modes of heat transfer. Standards have been established by the International Code Council to correctly represent thermal efficiencies of building walls and roofs, and to determine R. The 2D software THERM uses a finite element analysis (FEA) to compute R. Oak Ridge National Labs (ORNL) developed the modified zone method (MZM) for 2D evaluation. It is similar to the ASHRAE Zone Method, and the Parallel Path Method, but with different estimates of the conductivity width effect of the steel studs, and has been found to correlate well with the THERM 2D FE analysis, and with testing. MZM was used for this research as an initial check on simplified systems. For internal air cavity convection, MZM requires a conduction approximation. Although quite robust in computation power, these tools are unable to account for 3 dimensional edge effects, such as framing and fasteners.

A 3D FEA is necessary to determine system R-value more exactly. It is the most holistic way of studying effects on the wall, but can be time consuming, and requires specially acquired skills. However, it provides greater flexibility to control material properties, detailed geometry, and boundary conditions. It also enables the evaluation of geometry changes and their design sensitivity. The first part of the work addresses issues related to effectiveness of 3D FEA modeling methods, and how to appropriately model wall systems for accurate results. Testing was used to assess and improve FEA 3D wall model through test correlation, and will be used in for TWS optimization. Figure 1 shows a schematic of the different approaches to calculating R-values of wall systems.


The R Value and U Factor of Insulators and Systems

Thermal conductivity of a component, k, is a material property used in the application of Fourier's Law, and in the material definition of a FEA model. For the heat flux (heat transfer rate per unit area), q", over section length, L, and with a temperature difference between the cold side, [T.sub.2], and hot side, [T.sub.1], and multiplying this by the cross- sectional area, A, a value for heat flow, q (= q'A), is defined, and is the result obtained in building wall tests. For building systems, the thermal resistance is termed R (the R-value). This value can be determined with a building wall test by measuring area, temperature difference, and heat flow rate:

R = L/k = A([T.sub.1] - [T.sub.2])/q = ([T.sub.1] - [T.sub.2])/q (1)

A larger R indicates a lower heat flow rate, and thus a better insulator and it can be increased by reducing thermal conductivity or by increasing insulator thickness. It is thought of as an intrinsic property of the wall, but the test and/or analysis setup can change its value. Its inverse is termed the thermal transmittance, U. Note that SI units were used in our testing and analysis, but the more familiar US units for R of "[ft.sup.2] x [degrees]F x h/Btu" are also quoted in this paper, with inch & foot units used for the building wall dimensions.

Efficiency of wall assemblies is subject to conduction through the different wall materials, convection to the ambient air on external and internal wall faces, and radiation to the ambient atmosphere on either side of the wall. In addition, all three modes of heat transfer are present in any internal air cavity. Edge effects and surface irregularities will affect the air film convection flow on the outside and inside surfaces of the wall. This results in a distribution of temperatures on the wall. Radiation is expected to have a similar distribution effect in walls, but a minor role in hot box testing. Our simulations include the surface temperature distribution. Internal convection can significantly change cavity insulation properties and was also included. All walls with metal will be affected by metal thermal bridging through steel studs and fasteners. Testing and analysis of 8' x 8' (2.44m) walls was used to assess this affect.

Conventional Building Wall Components

Typical building walls are a sandwich of two gypsum boards on either side of a batt insulation (see Figure 2), supported by vertical C channel steel beams (studs), and horizontally with top and bottom plates. The studs are generally 16" (406mm) apart and equally spaced. Note that we used 0.5" (13mm) gypsum, while some ASHRAE reports use 0.625" (16mm).


This entire assembly is held together by steel nails on both sides, equally spaced, forming a pattern on the two sides of the wall. A typical fastener schedule was used for the attachment of two 4' x 8' (1.22m x 2.44m) vertically mounted drywall sheets (see Figure 2). The drywall was attached to the studs using #6 screw fasteners (nominal dia. of 0.137" (3.48 mm)). Note the double fasteners at the center joint. A metal lath is then added to the exterior gypsum which is finished off with a stucco coat, brick exterior, or some other facing. The lath and stucco/brick were not part of the present paper, and the vapor retarder, tape or flashing are not included.

The Thermax Wall System (TWS)

Thermax Wall System (TWS) is unique to DOW (see Figure 3). It uses DOW STYROFOAM[TM] Brand Spray Polyurethane Foam (SPF), instead of the traditional batt insulation, and DOW THERMAX[TM] ci Exterior Insulation, a Polyisocyanate foam, and a very popular choice of building insulation material. The TWS mimics traditional walls in using the same C Stud for supports, with the same spacing of 16" (406mm), and the same gypsum board on the interior. However, the external gypsum board has been replaced by a 1.55" (39mm) THERMAX ci board, and the C stud is partially filled with SPF; leaving a 4.5" (114mm) air gap (conventional is fully filled with batt). Similar coats of metal lath and stucco are applied to the TWS exterior as in traditional walls. Interior gypsum board attachment is the same as conventional. Due to the air sealing capabilities of the close cell spray foam, an interior valor barrier is not part of the TWS.


The attachment schedule for the horizontally mounted 4'x8' (1.22m x 2.44m) exterior THERMAX[TM] ci Exterior Insulation was determined from structural testing for wind and gravity loads. The screw fasteners are #8 (nominal dia. 0.164" (4.17 mm)) with plastic retainer. Also shown is a unit cell that could be repeated to represent the entire wall if there were no edge effects. A close up top view of the THERMAX[TM] ci Exterior Insulation and gypsum attachment scheme is also shown in Figure 3. Note that the nail is shown at the center of the unit cell of a two nail model (i. e., similar to MZM), but is actually 3D in nature. This is also true for the gypsum attachment in the conventional wall.


To evaluate the effectiveness of TWS versus traditional systems, a Guarded Hot Box (GHB) test was conducted at Exova following the ASTM C1363-05 test method. The wall cross-sectional area was 9216 [in.sup.2] for the 8'x8' wall, and they were sealed and insulated on the edges. Three different wall samples were tested to compare the traditional wall system and TWS, and to have three points for correlation with the simulations (see Table 1). All had metal studs 6" deep, and 1.625" wide. The traditional wall system, #1, was tested twice, to provide a measure of test repeatability. The only difference between the second and third walls was that the SPF foam was left out in the second wall. The 1.5" (38mm) nominal SPF is sprayed on, so 18 depth measurements were taken, and an average thickness of 1.98" (50.3mm) obtained.

Entry air nominal temperatures were -18[degrees]C on the cold side, and 21[degrees]C on the hot side. Nominal temperature difference was 39[degrees]C, but the area weighted average from the thermocouples covering the wall was used to obtain more exact inside and outside temperatures. These ranged from 34.5[degrees]C to 37.3[degrees]C. A 2.75m/s air flow was prescribed on the cold side of the wall. The heat flow rate, q, was obtained by measuring the power of both heater and fan, and correcting for wall and flanking heat losses. Wall and flanking heat losses were approximated as 10% of the power input. R was calculated using equation 1.


The FEA meshes were generated, and post processing work done, using Altair Hyperworks 10.0. Each of the geometries 1, 2 and 3 were modeled using 8 node solid elements (see Figure 4).


Analysis was done using the MSC NASTRAN2008r1 FEA solver, solution 153 (steady state heat transfer). The boundary conditions specified by ASHRAE correspond to a steady state case. The NASTRAN PCONV card was used to assign interface or film elements on either side of the wall (NASTRAN SPC ambient temperature nodes) to account for convection. A temperature difference was applied across the walls via a convection boundary condition, with convection coefficient, h = 8.3W/[m.sup.2]C (specified by ASHRAE). A temperature distant from the outside wall of -18[degrees]C, and from the inside wall of 21[degrees]C, was specified. Temperatures were averaged over the wall interior and exterior, and flux calculated from the convection boundary condition. Thus, R was calculated using the average wall temperature difference, the flux, and equation 1.

The most important aspects of the model were the NASTRAN MAT4 material properties, and the convection approximation. For all of the simulations, the insulating material properties were obtained from testing or ASHRAE standards, while the steel properties used values for mild steel studs and tracks. Table 2 shows the properties given to the models, with air properties given for both conduction and convection, discussed in the next paragraph. Without nails and studs, and ignoring convection (internal and external) and radiation, R is a simple addition of the individual R values, also shown in Table 2.

It was a critical challenge to correctly represent the air gap convection effects to get a realistic picture of wall efficiencies. To account for this, the air gap was filled with elements and modeled as a conduction region whose effective conductivity was separately calculated. The ASHRAE (ISO15099) effective conductivity cavity model is an iterative model to calculate an effective conductivity of air for given cavity dimensions. It takes into account air's contributions of conduction, convection and radiation, which will increase the air gap effective conductivity above that of still air. It is expressed using the Nusselt number (Nu), which will vary from one (conductivity) to a larger value (greater conductivity, and less insulation). In turn, it will depend on the Rayleigh number (Ra) and the Prandtl number (Pr), but, for air, the latter has a uniform value of approximately 0.71. The solution requires an iterative procedure estimating Ra, calculating Nu, calculating a temperature difference, and then iterating on this procedure. With the iterative technique, the Nu values for walls two and three were found to be 6.9 and 9.3, respectively, and this is shown in Table 2.

FEA Modification for Comparison to Clear Wall and Modified Zone Method

The use of FEA has an inherit benefit not available to testing--material properties and geometries can be modified easily to simulate other conditions. We utilized this benefit to make comparisons to clear wall cases, and to approximate MZM conditions, with the explanations given in Table 3. Thus, for the clear wall, thermal properties for metal parts were changed to the adjoining insulator (dry wall fasteners to dry wall, studs, top and bottom plate to batt or air, etc.). For MZM, the metal studs were unchanged, but top and bottom plates, and fasteners, were modified to the adjoining material, effectively making this a 2D simulation. Finally, fasteners only were changed to the adjoining insulator to assess their effect. Note that a typical wall tested will have 7 studs and 6 cavities, while the MZM model assumes an equivalent number. The various FEA models are shown in Figure 5.



Experimental hot box test results are shown in Table 4. With a 10% flanking loss approximation, the R of the Conventional Building Wall results were equivalent to that of ASHRAE 90.1-2007 value for this wall with R20 batting. The loss approximation is based on earlier reported results, and those losses range from 5-15%. Note that the ASTM standard states that a 10% variation is possible when testing to this standard. However, in our repeated test of the first wall, the difference was less than 2%. Because of these approximations and variations, the results are shown with the given range of losses (5-15%). The replacement of ~R20 batt insulation between the steel studs with ~R15 THERMAX[TM] ci Exterior Insulation on the outside of the steel studs increased thermal performance of the wall by 14%. The replacement of ~R20 batt insulation between the steel studs with ~R24 THERMAX[TM] wall system increased thermal performance of the wall by 85% (Table 4).

Simulation results are compared with experimental results in Table 4. The results compare very favorably for the traditional wall, but less favorably for the wall with continuous insulation. Testing was conducted at a much earlier date, and it was not possible to assess whether the TWS w/ empty cavity tests may have been compromised by flanking air leakage. Good correlation for the simulation of Wall#1 and Wall #3 suggests that Wall #2 was compromised by air leakage.

Results for the seven FEA cases are shown in Table 5. MZM air conductivity is a resistance-in-a-series approximation for the air and SPF in wall#3, because MZM does not allow the definition of more than one material in the cavity. This was the likely difference in the given results--a reduction in heat flow through the SPF is not captured in the MZM model. Column 7 in Table 5 gives the results of the full 3D unmodified FEA model. The TWS increases R by 124%. Even without SPF the increase is 69%. Left of that column are the FEA results with fasteners modified to have the same conductivity as the adjacent wall element (gypsum or THERMAX[TM] ci Exterior Insulation). This did not significantly affect the conventional wall, but had a significant effect on the walls with continuous exterior insulation. The introduction of metal bridging reduces its effectiveness. Column 3 (FEA~R) used SPF Materials in place of studs, headers & footers


This paper presents a systematic modeling development strategy for wall systems, a better understanding of 2D modeling tool simplifications and limitations, and interesting results from the full 3D FEA modeling method. The following conclusions were derived from this work. First, adding R-values for insulators (i.e., the resistors in series model) cannot be used for wall comparisons when significant thermal wall bridging is present. Second, air cavities cannot be modeled with simple conduction, but must include the effects of convection. Third, the introduction of Thermax ci on the exterior wall is very effective at increasing R-value, and reducing the effects of wall bridging. The addition of spray foam in the cavity improves this even more. Fourth, although tools such as MZM are very useful for comparing walls, a 3D FEA model is necessary when 3D geometry is present. This will also be true for other conditions, such as the inclusion of windows and doors. Fifth, when using higher efficiency enclosures (continuous insulation), the negative effect of metal fasteners is more prevalent. Finally, TWS wall #2 needs to be tested again, with the Guarded Hot Box correlated, and with some assurance that no leakage or wall bridging occurred. The next phase of this work will also include comparisons of the modeled thermal profile of the Thermax wall System and an actual physical test assembly installed in a long-term exterior exposure test facility. The filed exposure test facility has been built in Michigan and includes the wall assemblies presented among others with the objective of providing comparative long-term wall systems performance data.


R = thermal resistance, T = temperature, k = conductivity, L = length of space


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Elena Enache-Pommer, PhD

Associate Member ASHRAE

Robert Mayer, PhD

Gary Parsons


Elena Enache-Pommer is a Sr. Development Engineer, Robert Mayer is a Research Scientist, and Gary Parsons is a Technical Fellow, at The Dow Chemical Company, Midland, MI.
Table 1. Wall Configurations For Correlation Tests

#1   L/2" (13mm) Int. Drywall (Type X) + 6" (152mm) R20 unfaced
       fiberglass batt + 1/2" (13mm) Ext. grade gypsum
#2   L/2" (13mm) Int. Drywall (Type X) + Cavity + (no SPF) +
       1.55" (39mm) THERMAX ci Exterior Insulation
#3   1/2" (13mm) Int. Drywall (Type X) + Cavity + 1.5" (38mm)
     SPF + 1.55" (39mm) THERMAX ci Exterior Insul.

Table 2. Material Properties & Theoretical R-values
(Nominal SPF Depth)

Material              Depth (L)       Thermal           R = L/k
                       In (mm)    Conductivity (k)    [degrees]F
                                    Btu x in/h x        x h/Btu
                                     [ft.sup.2]       ([m.sup.2]
                                     [degrees]F         x K/W)
                                     (W/m x K)

SPF                   1.5 (38)     0.161 (0.0232)     9.32 (1.64)
THERMAX               1.55 (39)    0.148 (.0213)      10.5 (1.84)
Fiberglass Batt       6.0 (152)     0.3 (0.0433)      20.0 (3.52)
Air (Convection)      6.0 (152)     1.67 (0.241)     3.58 (0.633)
Air (Convection)      4.5 (114)     1.26 (0.182)     3.63 (0.629)
Ext. Gypsum           0.5 (13)      1.11 (0.160)     0.45 (0.079)
Int. Gypsum           0.5 (13)      1.11 (0.160)     0.45 (0.079)
C Stud, 6 x 1.625     6.0 (152)      333 (48.0)      0.018 (.0032)
  x .0478
Nails                 1.55 (39)      333 (48.0)      0.005 (.0008)
R = [summation] L/k

Material                Wall #1       Wall #2        Wall #3

SPF                                                9.32 (1.64)
THERMAX                             10.5 (1.84)    10.5 (1.84)
Fiberglass Batt       20.0 (3.52)
Air (Convection)                    3.58 (0.633)
Air (Convection)                                   3.63 (0.629)
Ext. Gypsum           0.45(0.079)
Int. Gypsum           0.45(0.079)   0.45(0.079)    0.45(0.079)
C Stud, 6 x 1.625
  x .0478
Nails                 20.9(3.68)     14.5(2.56)     23.9(4.19)
R = [summation] L/k


Table 3. Nomenclature (See also Table 5)

1--Wall                 Three types of walls
                        investigated (conventional,
                        Thermax w/o SPF, Thermax w/

2--R = [summation]L/k   Simple sum of the R-values of
                        the individual components

3--FEA ~ R              Simplification of 3D FEA Model
                        to match geometry and
                        materials of column 2

4--MZM                  Modified Zone Method result,
                        based on ORNL Calculator

5--FEA ~ MZM            FEA model materials modified
                        to make a 2D representation
                        like MZM: fasteners modified

6--FEA w/o fasteners    Same as 7 (below) except
                        fastener material properties
                        were made the same as the
                        interior,  and exterior,
                        material they were attaching
                        (Gypsum or Thermax).

7--FEA                  FEA model with all the 3D
                        details included.

Table 4. Experimental & Simulation Values, [ft.sup.2] x [degrees]F
x h/Btu ([m.sup.2] x K/W).

Test   Wall                      Test R-value       FEA R-value

1      Traditional             7.6 [+ or -] 0.4     7.4 (1.30)
                             (1.34 [+ or -] 0.07)
2      TWS w/ empty cavity     8.5 [+ or -] 0.4     12.5 (2.20)
                             (1.5 [+ or -] 0.07)
3      TWS w/ cavity SPF      14.0 [+ or -] 0.7     16.6 (2.92)
                             (2.47 [+ or -] 0.12)

Table 5. Theoretical & Simulation Values
[ft.sup.2] x [degrees]F x h/Btu ([m.sup.2] x K/W).

Wall      R = [summation]   FEA~R        MZM

Wall #1   20.9(3.68)        21.2(3.73)   9.5(1.67)
Wall #2   14.5(2.55)        14.5(2.55)   13.9(2.45)
Wall #3   23.9(4.21)        23.9(4.21)   18.0(3.1)

Wall      FEA~MZM      FEA w/o      FEA

Wall #1   9.5(1.67)    7.5(1.32)    7.4(1.30)
Wall #2   13.9(2.45)   13.5(2.38)   12.5(2.20)
Wall #3   19.6(3.45)   18.1(3.19)   16.6(2.92)
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Author:Enache-Pommer, Elena; Mayer, Robert; Parsons, Gary
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2013
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