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This article was originally published in the September/October 1999 issue of Home Energy Magazine. Some formatting inconsistencies may be evident in older archive content.

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# New Value for High-Mass Walls

by Jan Kosny

Jan Kosny is a staff scientist at the Buildings Technology Center, Oak Ridge National Laboratory

Calculating the heating and cooling needs of houses built with high-mass walls has never been straightforward. R-values tend to misrepresent the thermal performance of these building envelope systems. Now, a revised R-value simplifies such calculations.

This wall is constructed out of a foam form that is filled with concrete. Workers are covering the foam with stucco before the wall is tested.
Figure 1. All 19 multilayer walls are variations of these six structures. To create the walls with lower R-values, the thicknesses of the concrete and foam layers were changed.
 Table 1. Thermal Properties of Material for Multilayer Walls Material Thermal Conductivity Btu in/h ft2 °F Density lb/ft3 Specific Heat Btu/lb °F Concrete 10.0 140 0.20 Insulating Foam 0.25 1.6 0.29 Gypsum Board 1.11 50 0.26 Stucco 5.0 116 0.20
The dynamic hot-box test that these men are preparing this wall for will be used to calibrate computer modeling.
 Table 2. DBMS Values for R-17 Walls Wall Atlanta Denver Miami Minneapolis Phoenix Washington
1 2.08 1.86 1.89 1.47 2.43 1.78
2 2.12 1.86 2.07 1.48 2.48 1.80
3 2.15 1.85 2.44 1.47 2.46 1.83
4 1.34 1.4 1.07 1.30 1.44 1.34
5 1.6 1.53 1.56 1.37 1.67 1.51
6 1.5 1.48 1.44 1.35 1.56 1.59
 Table 3. DBMS Values for R-13 Walls Wall Atlanta Denver Miami Minneapolis Phoenix Washington 1 1.99 1.86 1.73 1.47 2.46 1.74 2 2.08 1.88 2.01 1.49 2.56 1.79 3 2.11 1.88 2.20 1.49 2.57 1.80 4 1.33 1.42 1.08 1.31 1.47 1.35 5 1.64 1.59 1.59 1.38 1.80 1.52 6 1.58 1.55 1.49 1.37 1.73 1.49
 Table 4. DBMS Values for R-9 Walls Wall Atlanta Denver Miami Minneapolis Phoenix Washington 1 1.87 1.79 1.61 1.39 2.45 1.64 3 1.94 1.80 2.10 1.40 2.58 1.70 4 1.32 1.39 1.03 1.24 1.52 1.31 6 1.59 1.55 1.45 1.31 1.86 1.47
 Table 5. DBMS Values for R-5 Walls Wall Atlanta Denver Miami Minneapolis Phoenix Washington 1 1.43 1.41 1.14 1.03 2.03 1.25 3 1.49 1.41 1.48 1.05 2.11 1.29 4 1.08 1.14 0.74* 0.94* 1.33 1.05
 Table 6. DBMS Values for Low R-Value Walls Wall Steady-state R-value (hft2F/Btu) Atlanta Denver Miami Minneapolis Phoenix Washington Solid 1.6 0.73 0.76 0.43 0.44 1.21 0.65 Two-core 2.3 0.89 0.91 0.62 0.57 1.46 0.78
 Table 7. ICF Steady-State R-Values 3-D model Equivalent Wall 1-D Approximation hft2F/Btu 11.95 11.95 16.54
In certain climates, construction of massive building envelopes--such as concrete, earth, and insulating concrete forms (ICFs)--can be one of the most effective ways of reducing building heating and cooling loads. In Europe, the vast majority of residential buildings have been built using massive wall technologies, making life without air conditioners relatively comfortable even in countries with hot climates, such as Spain, Italy, or Greece. Several comparative studies have shown that heating and cooling energy demands in buildings containing massive walls of relatively high R-values can be lower than those in similar buildings constructed using lightweight wall technologies. This better performance results because the thermal mass encapsulated in the walls reduces temperature swings and absorbs energy surpluses both from solar gains and from heat produced by internal energy sources such as lighting, computers, and appliances. Also, massive walls delay and flatten thermal waves caused by exterior temperature swings. Calculation Concerns Until now, however, calculating the thermal performance of high-mass walls has been difficult. The steady-state R-value traditionally used to measure the thermal performance of a wall does not accurately reflect the dynamic thermal performance of massive building envelope systems. Whole-building energy simulations for buildings containing massive wall systems are similarly problematic. For example, DOE-2 uses a one-dimensional calculation engine, which is inaccurate in simulations of complex building envelope assemblies. To enable these computer models to perform whole-building energy simulations, simplified one-dimensional descriptions of complex walls have to be developed for complex building envelope assemblies. Currently, the standard modeling process is to replace complex material configurations by one-dimensional multilayer structures with similar R-values and similar material arrangements. Unfortunately, such simplifications cannot accurately represent the complicated two- and three-dimensional dynamic heat transfer that can be observed in most massive-wall assemblies.

To show the benefit of these assemblies, thermal-performance analysis must properly reflect the effects of thermal insulation and mass distribution inside the wall. Application of the recently developed equivalent-wall theory led to the development of a new analytical matrix of a high-mass wall's energy performance. We are calling it dynamic benefit for massive systems (DBMS). The thermal mass benefit is a function of the material configuration, building type, and climate conditions, since high-mass walls are of greatest benefit in climates with large diurnal swings in temperature.

DBMS values are obtained by comparing the energy performance of a one-story ranch house built with lightweight wood frame walls to the energy performance of the same house built with exterior massive walls. The product of DBMS and steady-state R-value is called an R-value equivalent for massive systems. This R-value equivalent does not have a physical meaning. It should be understood only as an answer to the question What wall R-value should a house with wood frame walls have to obtain the same space-heating and -cooling loads as a similar house containing massive walls?

We analyzed the dynamic thermal performances of more than 20 multilayer and homogenous wall material configurations using thermal-performance comparisons of massive walls and lightweight wood frame walls. A one-story ranch house was used for these comparisons, which we performed using DOE-2.1E, a whole-building energy computer code.

The evaluation of the dynamic thermal performance of these massive wall systems combined experimental and theoretical analysis. The theoretical analysis was based on dynamic three-dimensional finite difference simulations and whole-building energy computer modeling. Dynamic hot-box tests served to calibrate the computer models, and to estimate the steady-state R-value and the dynamic characteristics of the wall (see General Procedures).

Interior Concrete Insulates Best Simple multilayer walls without thermal bridges are accurately described by one-dimensional models. Because DOE-2 can simulate these walls without compromising their accuracy, dynamic hot-box tests were not performed on them except for one example. A wall constructed with a foam core and two equally thick concrete layers, one on each side, was tested in the hot box. Experimental results collected from this test were used to calibrate the computer model for the other simple multilayer walls analyzed in this section. The same material data were used for all of these wall configurations. Dynamic modeling was performed for six U.S. locations: Atlanta, Denver, Miami, Minneapolis, Phoenix, and Washington, D.C.

Six combinations of wall materials that yielded high-mass walls with an R-value of 17 are depicted in Figure 1. Changing the thicknesses of insulation and concrete layers generated another thirteen walls. These were grouped according to their respective R-values, which ranged from 5 to 13.

These walls represent the main wall material configurations that can be used to approximate most nonuniform massive walls. Each of the 19 walls we analyzed fall into one of four groups of wall material configurations:

• concrete on both sides of the wall, core of the wall made of insulation material;
• insulation on both sides of the wall, with the core of the wall made of concrete;
• concrete on the interior wall side, with the insulation on the exterior wall side; and
• concrete on the exterior wall side, with the insulation on the interior wall side.
DBMS values were calculated for all 19 wall material configurations in each of the six cities; see Tables 2-5. Data presented in these tables show that the most effective wall assemblies are those in which thermal mass (concrete) remains in good contact with the interior of the building (walls 1, 2, and 3 in Tables 2 and 3, and wall 1 in Tables 4 and 5). Walls in which the insulation material is placed on the interior side have the lowest DBMS values (wall 4 in Tables 2 and 3, and wall 4 in Tables 4 and 5). Wall configurations with a concrete wall core and insulation placed on both sides of the concrete have DBMS values that fall in the midrange (walls 5, 6 in Tables 2 and 3, also wall 6 in Table 4).

The most favorable location for massive wall systems is Phoenix. The worst location for these systems is Minneapolis. Different proportions in wall mass or insulation distribution result in notable differences in DBMS values in the same climate. Compare, for example, wall 1 to wall 2, or wall 5 to wall 6, in Table 2. These differences indicate both that the DBMS value is sensitive to the changes in wall exterior and interior layers, and that it is possible to improve building energy performance merely by changing the order in which the wall materials are configured. Data presented in Tables 2 through 5 cannot be used to predict the dynamic thermal performance of walls made of materials that are significantly different from those used in our modeling (for example, walls with brick or siding exterior finish). However, for walls made of materials similar to the ones we used in our modeling, the data in Tables 2-5 can be used to estimate R-value equivalents.

Potential Negative Impacts For buildings located in Minneapolis and Miami that have low R-value massive walls with the insulation material located on the interior side, total building loads can be higher with thermal mass than with the equivalent lightweight wall of the same steady-state R-value, as is indicated by a DBMS value less than 1. See, for example, wall 4 in Table 5. Extrapolating the data presented in Tables 2 through 5, we find that massive walls with R-values of less than 3 or 4 have a negative impact on the building load for all locations except Phoenix.

Two wall material configurations with a low R-value were simulated to analyze this interesting finding. The first was a solid wall 8 inches thick made of high-density concrete (140 lb/ft3). The second was a wall assembled out of two-core 11-5/8-inch-thick high-density concrete blocks, insulated with 1 7/8-inch foam inserts. These blocks are the most popular construction material used in the U.S. to erect 12-inch masonry walls. The thickness of the block concrete shells is approximately 1 3/4-inch. Each block has two internal cavities, and these are insulated with 1 7/8-inch thick foam inserts. The three-dimensional geometry of the wall assembled with two-core concrete blocks made it necessary to generate an equivalent wall. Steady-state R-values for these two walls are shown in Table 6.

Based on results of computer modeling, DBMS values were calculated for these two walls (see Table 6). These values show that only in the special climate of Phoenix do these massive systems, which are traditionally used for foundations, have benefit above grade. It is more efficient to use a lightweight wall of the same steady-state R-value.

ICF Walls--Not Always So Simple Some ICF walls have a complex three-dimensional internal structure that results in complicated two- or three-dimensional heat transfer processes. We analyzed a very good example of such a wall. The basic component of this wall is the 9 1/4-inch-thick expanded polystyrene (EPS) foam wall form. The thickness of the exterior and interior form walls varies from 1 1/2 to 3 1/2 inches. The interior and exterior foam components of the form are connected with a metal mesh going across the wall. Several horizontal steel components further complicate heat transfer in this wall. There is a three-dimensional network of vertical and horizontal channels (about 6 1/4 inches in diameter) inside the ICF wall form. These channels have to be filled with concrete during the construction of the wall. The exterior surface of the wall is finished with a 1/2-inch layer of stucco. The interior surface is finished with 1/2-inch gypsum boards. Reinforced high-density concrete is poured into the internal channels formed by the ICF units.

We developed a one-dimensional model of this complex ICF wall and tested its accuracy against the accuracy of an equivalent wall. The simple one-dimensional model of the ICF wall was based on the total thickness of the ICF wall--9 1/4 inches--and the approximate thickness of the exterior and interior foam shells, which varies from 1 1/2 to 3 1/2 inches, as explained above. The equal thickness for the exterior and interior foam forms was assumed to be 2 inches.

It was found that this one-dimensional approximate model of the complex structures based only on geometry simplifications was inaccurate, both in terms of R-values and in terms of the dynamic thermal response, as exemplified by response factors. However, the equivalent wall, which had a simple six-layer structure, had the same thermal response as the real wall. For the simple one-dimensional model, the R-value is 38% higher than the R-value calculated for the three-dimensional model of the ICF wall. At the same time, R-values for the ICF wall and the equivalent wall are equal.

The equivalent-wall technique is a relatively simple way to make whole-building energy simulations (using DOE-2 or BLAST) for buildings that contain complex assemblies. It is possible to generate a series of response factors or transfer functions for the complex wall and to modify DOE-2 source code in such a way as to make it possible to input these data. However, the number of response factors or Z-transfer function coefficients needed for massive walls can be from 60 to as many as 450. It is much simpler to use the equivalent-wall technique, which represents all the thermal information about the wall with only five numbers (R-value, C, and three thermal-structure factors).

### General Procedures

In a dynamic hot box, we tested each high-mass wall under one steady-state condition followed by a rapid temperature change on the exterior side, and then a second period of a steady-state condition. In each stage, heat transfer through the wall has to reach steady state conditions before moving on to the next stage. For example, a wall will be exposed to 20°F on the cold side and 80°F on the warm side, then be subjected to a rapid temperature change on the cold side to 40°F, and finally be allowed to reach steady state at this new set of temperatures. Altogether, each wall may be tested for as much as 600 hours.

For each individual wall, a finite difference computer model was developed. The accuracy of the computer simulation was determined in several ways. The first was to compare experimental and simulated R-values. The simulated steady-state R-value had to match the experimental R-value within 5% to be consistent with the accuracy of hot box measurements. Also, computer heat flow predictions were compared with measured heat flow through the 8 ft x 8 ft specimen exposed to dynamic boundary conditions during the hot box test. The computer program used boundary conditions (temperatures and heat transfer coefficients) recorded during the test. Values of heat flux on the surface of the wall generated by the computer program were compared with the values measured during the dynamic hot-box test.

Response factors (which are a measure of the heat flux response on a wall surface to temperature changes on the same or opposite surface), wall heat capacity, and R-value were computed using the finite-difference computer code. This made it possible to calculate the wall thermal structure factors and to develop the simplified one-dimensional thermally equivalent wall configuration. Thermal structure factors reflect the thermal-mass heat storage characteristics of wall systems. A thermally equivalent wall has a simple multiple-layer structure and the same thermal properties as the nominal wall. Its dynamic thermal behavior is identical to that of the complex wall tested in the hot box. Development of a thermally equivalent wall makes it possible to use whole-building energy simulation programs with hourly time steps (DOE-2 or BLAST). These programs require simple one-dimensional descriptions of the building envelope components.

We plugged the one-dimensional thermally equivalent wall configuration into the DOE-2.1E computer program and used it to simulate a single-family residence in representative U.S. climates, since the thermal mass benefit is a function of the climate. The space-heating and -cooling loads from the residences with massive walls were compared to loads for an identical building simulated with lightweight wood frame exterior walls. Twelve lightweight walls with R-values from 2.3 to 39.0 were simulated in six U.S. climates. The heating and cooling loads generated from these building simulations were used to estimate the R-value equivalents that would be needed in conventional wood frame construction to produce the same loads for the house with massive walls in each of the six climates. The resulting values account not only for the steady-state R-value but also for the inherent thermal-mass benefit. This procedure is an extension of the one used to create the thermal-mass benefits tables in the Model Energy Code, now known as the International Energy Conservation Code.

 Publication of this article was supported by the U.S. Department of Energy's Office of Building Technology, State and Community Programs, Energy Efficiency and Renewable Energy.
 This article was adapted from a technical paper whose authors were Jan Kosny, Elisabeth Kossecka, Andre Desjarlais, and Jeffrey Christian, respectively, which was presented at the Department of Energy's Thermal Envelope VII conference. For more details on the conference and information on how to get the papers, see Hot Topics Covered at Thermal VII Conference, HE May/June '99, p. 10 or go to www.ornl.gov Jan Kosny is a staff scientist at the Buildings Technology Center, Oak Ridge National Laboratory, where Andre Desjarlais is a group leader and Jeff Christian is director. Elisabeth Kossecka is a professor at the Institute of Fundamental Technological Research, at the Polish Academy of Sciences in Warsaw, Poland.

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