**Dynamic Thermal Performance and Energy Benefits of Using Massive Walls in Residential Buildings**

Dynamic Hot Box Test and Development of Finite Difference Computer Model of the Wall

Dynamic Whole Building Energy Simulations of House Containing Wood-Framed and Massive Walls

Effective R-values and Dynamic Benefits for Massive Systems (DBMS)

Masonry or concrete walls having a mass greater than or equal to 30 lb./ft ^{2} (146 kg/m^{2}) and solid wood walls having a mass greater than or equal to 20 lb./ft ^{2}(98 kg/m^{2}) are defined by the Model Energy Code [1] as massive walls. They have heat capacities equal to or exceeding 6 Btu/ft^{2} ^{0}F [266 J/(m^{2}k)]. The same classification is used in this work.

The evaluation of the dynamic thermal performance of massive wall systems is a combination of experimental and theoretical analysis. It is based on dynamic three-dimensional finite difference simulations, whole building energy computer modeling, and dynamic guarded hot box tests. Dynamic hot box tests serve to calibrate computer models. However, they are not needed for all wall assemblies. For simple one-dimensional walls, theoretical analysis can be performed without compromising the accuracy when the computer model was calibrated earlier using similar material configuration.

The massive wall is typically tested in a guarded hot box under steady-state and dynamic conditions. These tests enable calibration of the computer models and estimation of the steady-state R-value as well as wall dynamic characteristics. Dynamic hot box tests performed on massive walls consist of two steady-state test periods connected by a rapid temperature change on the climate side. The finite difference computer code Heating 7.2. [2] is applied to model the wall under dynamically changing boundary conditions (recorded during the hot box test). The Heating 7.2 computer model was validated in the past using steady-state hot box test results [3].

For each individual wall, a finite difference computer model is developed. The accuracy of the computer simulation is determined in several ways. The first check is to compare test and simulated R-values. The simulated steady-state R-value has to match the experimental R-value within 5% to be consistent with the accuracy of hot box measurements [3]. Also, computer heat flow predictions are compared with the hot box measured heat flow through the 2.4 m x 2.4 m (8 ft by 8 ft) specimen exposed to dynamic boundary conditions. The computer program uses boundary conditions recorded during the test (temperatures and heat transfer coefficients). Values of heat flux on the surface of the wall generated by the computer program are compared against the values measured during the dynamic hot box test.

Response factors, heat capacity, and R-value are computed using the finite-difference computer code. They enable calculation of the wall thermal structure factors and development of the simplified one-dimensional “thermally equivalent wall” configuration [4,5,6]. 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 the complex wall tested in the hot box.

Development of a thermally equivalent wall enables usage of whole-building energy simulation programs with hourly time steps (DOE-2 or BLAST). These whole building simulation programs require simple one-dimensional descriptions of the building envelope components. The use of the equivalent wall concept provides a direct link from the dynamic hot box test to accurate modeling of buildings containing walls which have three-dimensional heat flow within them, such as the Insulating Concrete Form (ICF) Wall Systems [7,1].

The DOE-2.1E computer code is utilized to simulate a single-family residence in representative U.S. climates. The space heating and cooling loads from the residence with massive walls are compared to loads for an identical building simulated with lightweight wood-frame exterior walls. Twelve lightweight wood-frame walls with R-values from 0.4 to 6.9 Km^{2} / W (2.3 to 39.0 hft^{2} F/Btu) are simulated in six U.S. climates. The heating and cooling loads generated from these building simulations are used to estimate the R-value equivalents which would be needed in conventional wood-frame construction to produce the same loads as for the house with massive walls in each of the six climates. The resulting values account for not only the steady state R-value but also the inherent thermal mass benefit. This procedure is almost identical to that used to create the thermal mass benefits tables in the Model Energy Code [1]. The thermal mass benefit is a function of the climate. R-value Equivalent for Massive Systems is obtained by comparison of the thermal performance of the massive wall and light-weight wood-frame walls, and they should be understood only as the R-value needed by a house with wood-frame walls to obtain the same space heating and cooling loads as an identical house containing massive walls. There is not a physical meaning of the term “R-value Equivalent for Massive Systems.”

A dynamic hot box test takes about 200 hours. It serves mainly to calibrate the computer model of the tested wall. This time consuming test-based calibration of the computer model is required only for complex massive wall configurations. In the case of simple one-dimensional walls only the theoretical analysis can be performed without compromising the accuracy. A dynamic hot box test performed on the massive walls consists of two steady-state test periods connected by a rapid temperature change on the climate side. In addition to calibration of the computer model, the test enables estimation of the steady-state R-value and wall dynamic characteristics.

Dynamic three-dimensional computer modeling is used to analyze the response of the complex massive walls to a triangular surface temperature pulse. This analysis enables estimation of the steady-state R-value of the wall, thermal capacity, response factors, and wall thermal structure factors [4,5,6]. The wall thermal structure factors are used later to create the one-dimensional equivalent wall, necessary for whole-building energy simulations.

A calibrated heat conduction, finite-difference computer code Heating 7.2, is used for this analysis [2]. The accuracy of Heating 7.2 is validated by examining its ability to predict the dynamic process measured during the dynamic hot box test for the massive wall [7]. The computer program uses recorded test boundary conditions (temperatures and heat transfer coefficients) at one hour time intervals.

Values of heat flux on the surface of the wall generated by the program are compared with the values measured during the dynamic test. The computer program has to reproduce the same wall thermal response as was recorded during the hot box test. Later, this calibrated computer model is used to generate the equivalent wall which enables one-dimensional whole building energy analysis.

The dynamic thermal performance analysis for massive walls that is described herein is based on whole building energy modeling results. A “real” three-dimensional description of complex walls cannot be used directly by whole-building simulations. Such walls must be simplified to a one-dimensional form to enable the dynamic whole building thermal analysis using DOE-2, BLAST or similar computer programs. The usage of the equivalent wall enables more accurate modeling of buildings containing complicated three and two-dimensional internal structures. Very often, such complicated walls are composed of several different materials with drastically different thermal properties. In prior works by Kossecka and Kosny [4,5,6] the equivalent wall concept was introduced.

The thermal structure factors constitute, together with wall R-value, and overall thermal capacity C, the basic thermal wall characteristics which can be determined experimentally. They represent the fractions of heat stored in the volume of the separated wall element, which are transferred across each of its surfaces.

A calibrated three-dimensional computer model of the complex wall serves for calculation of response factors. For a triangular pulse which is simulated on one wall side, the dynamic finite different computer code calculates a series of response factors.

Equivalent wall has the same steady-state and dynamic thermal performance as a real complex wall. As is shown in works of Kossecka and Kosny [4,5] even for the complex thermal bridge configuration, response factors for both walls (nominal complex wall and equivalent wall) as well as steady-state R-values and thermal structure factors have the same values.

Comparative analysis of the space heating and cooling loads from two identical residences, one with massive walls and one containing lightweight, wood-frame exterior walls, was introduced for development of massive wall thermal requirements in the Model Energy Code [1]. This procedure was adopted by the authors. The DOE-2.1E computer code was utilized to simulate a single-family residence in six representative U.S. climates. Twelve lightweight wood-frame walls with R-values from 0.4 to 6.9 Km^{2} / W (2.3 to 39.0 hft^{2} F/Btu) were simulated. The heating and cooling loads generated from these building simulations were used to estimate the R-value equivalents for massive walls. A list of the cities and then climate data is presented in Table 1.

**Table 1. Six U.S. climates (TMY) used for DOE 2.1E computer modeling**

Cities: | HDD 18.3 C(65 deg F) | CDD 18.3 C(65 deg F) |

Atlanta | 1705 (3070) | 870 (1566) |

Denver | 3379 (6083) | 315 (567) |

Miami | 103 (185) | 2247 (4045) |

Minneapolis | 4478 (8060 ) | 429 (773) |

Phoenix | 768 (1382) | 2026 (3647) |

Washington D.C. | 2682 (4828) | 602 (1083) |

To normalize the calculations, a standard North American residential building is used. The standard building selected for this purpose is a single-story ranch style house that has been the subject of previous energy efficiency modeling studies [9]. All U.S. residential building thermal standards, including ASHRAE 90.2 and Model Energy Code, are based on the whole building energy modeling performed with the use of this house. A schematic of the house is shown in Figure 1. The house has approximately 143 m^{2} (1540 ft^{2}) floor area, 123 m^{2} (1328 ft^{2}) of exterior wall elevation area, 8 windows, and 2 doors (one door is a glass slider; its impact is included with the windows). The elevation wall area includes 106 m^{2} (1146 ft^{2}) of opaque wall area, 14.3 m^{2} (154 ft^{2}) of window area and 2.6 m^{2} (28 ft^{2}) of door area.

For the base-case calculation of infiltration we used the Sherman-Grimsrud Infiltration Method, an option in the DOE 2.1E whole-building simulation model [12]. An average total leakage area of 0.0005 expressed as a fraction of the floor area [10,11,12] is assumed. This is considered average for a single-zone wood-framed residential structure. This number cannot be converted directly to average air changes per hour because it is used in an equation driven by hourly wind speed and temperature difference between the inside and ambient air data which varies for the six climates analyzed for this study. However, for the six climates this represents an air change per hour range which will not fall below an annual average of 0.35 ACH.

DOE-2.1E energy simulations for six U.S. climates are performed for light-weight wood frame walls (50 mm x 200 mm [2x4in] construction) of R-values from 0.4 to 6.9 m2 K / W (2 to 39 hft2F/Btu ). Steady-state R-values were computed for wood-framed walls using the Heating 7.2 - finite difference computer code. The accuracy of Heating 7.2's ability to predict wall system R-values was verified by comparing simulation results with published test results for twenty-eight masonry, wood-frame, and metal-frame walls tested at other laboratories. The average differences between laboratory test and Heating 7.2 simulation results for these walls were +/- 4.7 percent [13]. Considering that the precision of the guarded hot box method is reported to be approximately 8 percent, the ability of Heating 7.2 to reproduce the experimental data is within the accuracy of the test method [14]. Because of the high accuracy of these simulations, all steady-state clear wall R-values used in this procedure are directly linked to existing thermal standards where wall thermal requirements are based on clear wall R-values.

The total space heating and cooling loads for twelve lightweight wood-frame walls were calculated using DOE-2.1E simulations. Regression analysis was performed to analyze the relation between steady-state clear wall R-values (of wood-stud walls) and the total building loads for six U.S. climates. For all six climates, there was a strong correlation (r^{2} was about 0.99). Regression equation parameters are presented in Table 2.

(1)

where: | E - total building load [Mbtu/year], |

R- wall R-value. |

**Table 2. Parameters in equation (1) expressing the relation between steady-state clear wall R-values (of wood-stud walls) and total building loads for six U.S. climates.***

Cities: | a (Y-intercept) | b (slope) |

Atlanta | 1.8e8 | -4.69 |

Denver | 1.65e9 | -4.76 |

Miami | 2.97e18 | -11.0 |

Minneapolis | 3.25e12 | -5.95 |

Phoenix | 3.56e9 | -5.27 |

Washington | 3.01e9 | -5.01 |

* R-value range 0.4-6.9 m2 K / W (2-39 hft2F/Btu ).

The heating and cooling loads generated for 12 lightweight wood-frame walls can be used to estimate the R-value equivalents for massive walls. Equation (1) yields the wall R-value which would be needed in conventional wood-frame construction to produce the same load as the house with massive walls in each of six climates. There is no physical meaning for the term R-value equivalent for massive walls. This value accounts not only for the steady-state R-value but also the inherent thermal mass benefit. This procedure is similar to that used to create the thermal mass benefits tables in the Model Energy Code [1]. Thermal mass benefits are a function of the material configuration and the climate. A dimensionless measure of the wall thermal dynamic performance is proposed in this paper - Dynamic Benefit for Massive Systems (DBMS) defined by equation (2);

(2)

where: | : DBMS - Dynamic Benefit for Massive Systems, |

mR_{eqv} - R-value equivalent for massive wall, and | |

R- steady-state R-value. |

Equation (2) documents thermal benefits of using massive wall assemblies in residential buildings regardless of the level of the wall steady-state R-value.

© Oak Ridge National Labs and Polish Academy of Sciences

Updated August 9, 2001 by Diane McKnight