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Calculation ConcernsUntil 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 BestSimple 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:
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 ImpactsFor 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 SimpleSome 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).
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