1、4686 Sensitivity Study of Slab-on-Grade Transient Heat Transfer Model Parameters Brian A. Rock, Ph.D., P.E. Member ASHRAE ABSTRACT Heat transfer between a building and its surrounding soil is a complex and transientphenomenon. Due to the unknowns and long time scales involved, predictions of the hea
2、t transfer rates to and from buildings via their ground contact tend to be somewhat or sign$cantly inaccurate. Physical experiments with an actual building over a short time period give good insight into its long-term thermal characteristics, but due to variations in building operation and weather c
3、onditions, long- term predictions will vary from the actual heat transfer rates. For buildings yet to be constructed, modeling of the ground- coupled heat transfer can give reasonable time-averagedjrst- order predictions if the input data are suflciently accurate. However, due to the range of variab
4、les involved and the unknowns, such as actual subgrade site conditions and future weathel; these models can give very inaccurate results too. This paper presents the results of a sensitivity study on some of these variables. These conditions and a detailed slab-on- grade construction were examined u
5、sing a fully transient FORTRAN code that evaluated heat transfer over an entire typical weather year. INTRODUCTION Heat loss from uninsulated foundations is substantial in the cool climates of the United States and elsewhere and significantly affects the needed size and energy consumption of heating
6、 and possibly cooling equipment. In HVAC load calculations, designers usually include perimeter heat losses when sizing heating equipment, but they often neglect ground- contact heat transfer in cooling load calculations because such heat loss is assumed to help cool the space or building. The slab-
7、on-grade and basement heat transfer submodels included in load calculation programs, if any, have historically been quite simplified and given limited-accuracy results. However, as computing power has increased, both load and energy calculation programs can now include somewhat more detailed ground-
8、contact heat transfer models. Highly detailed, fully transient, three-dimensional slab and foundation models are, however, still too computationally intensive and require too much input information for inclusion in load and energy analysis programs for everyday design use, but including such is a go
9、al for the future. In a previous paper, the author and another researcher reported on their study of slab-on-grade heat transfer model- ing and simplified coefficients (Rock and Ochs 2001). This initial paper includes a detailed discussion of prior research and a lengthy bibliography of such, The re
10、sults of the 2001 study were obtained using a steady-state version of a code written in a slowly executing programming language. In that papers conclusions, and as noted by reviewers, using a faster- executing language such as Fortran was a desirable extension of the work. The second author of that
11、paper has recently completed a comparison of the code to others results and some experimental data (Ochs 2003). The codes results were found to be reasonable for engineering work when appropriate input data were employed. The authors and a reviewer of the first paper, which also compares the codes r
12、esults to others findings, noted the need for parametric analyses of many vari- ables. The initial version of the codes steady-state approach was also a significant limitation, as the design weather condi- tion had to be estimated and, thus, limited the realism of the model. In the current study, so
13、me improvements were made to the approach, and the preceding limitations were removed. A fully Brian A. Rock is an associate professor of architectural engineering at the University of Kansas, Lawrence, Kans. 02004 ASHRAE. 177 transient, hour-by-hour Fortran version of the code was writ- ten that al
14、lows study of a detailed slab-on-grade geometry. The refined code uses standard hourly TMY2 weather data files (NREL 1995), so the geometry may be studied in 239 loca- tions. Code execution time was still long due to the greatly increased iterations of the transient solution, however. MODEL In this
15、multipart study, a traditional explicit finite differ- ence code was used, but with the following exceptions: (1) a detailed geometry was utilized where others often have used simplified geometries, and (2) fully transient routines were employed. A detailed description of the base codes develop- men
16、t can be found in the first paper (Rock and Ochs 2001). Even though the revised code was written using a much faster- executing language, Fortran (CCC 2001), solution times for each of the many combinations of input data were substantial and overall required months of total computer time due to the
17、detailed and transient features of the model. Detailed Geometry Figure 1 shows the detailed slab-on-grade geometry used for this study. This geometry is common in the U.S. for resi- dential and light commercial/institutional/industrial build- ings. Material #1 is the floor type. Vinyl flooring is mo
18、deled, as is oak flooring, residential carpet and pad, and commercial padless carpet in this current study. In previously reported work (Rock and Ochs 2001), it was found that the conductive heat transfer through bare concrete floor surfaces was very similar to that of vinyl flooring, so the bare su
19、rface was not studied again. Material #2 is a 4 in. thick concrete slab that is 15 ft wide. It rests on 4 in. of gravel (#3) and may have a 0.5 in. thick expansion joint (#4) at its outer edge. Cases with and without this expansion joint were included in this current study. The surrounding soil was
20、divided into three parts: the inside soil (#5), which is 4 ft deep and 15 ft wide; the “deep” soil (#6), which is 8 ft deep; and the outside soil (#7), which is 4 ft deep and 15 ft wide like the inside soil. The overall soil depth was therefore 12 ft, and the total width was 30 ft plus the 8 in. wid
21、e foundation. This foundation (#8) was 4 ft, 8 in. tall to model its 4 ft wall and 8 in. footing. In milder climates, where the frost line is shallow or nonexistent, this foundation depth is likely excessive; however, the default soil thermal properties are not very different from those of concrete,
22、 so the results for warmer climates should be reasonably consistent with those that follow. Widths of actual footings vary from narrow “trench footings” to often two to three times the widths of the foundation walls depending on soil-bearing properties and design choices. The foundation may or may n
23、ot be insulated (#9) in the model. The insulation thicknesses studied were 0.0, 1 .O, and 2.0 in., which are typical for average-quality construction in the U.S. Passive solar and other super-insulated structures may have four or more inches of foundation insulation, but these greater thicknesses we
24、re not studied here. The rigid insulation included was that of commonly available closed-cell expanded polystyrene, so the thermal insulation values modeled were R-O, R-5, and R-1 O h.ft2.”F/Btu. Eight inches of the foundation were exposed abovegrade outside when no insulation was used. Six- to twel
25、ve-inch exposures are often constructed by builders, or required by building codes, to keep the abovegrade wall drier, minimize impact damage from yard maintenance, and to allow for termite inspections and resis- tance to infestation. The lower two feet of a lightweight 2 in. x 4 in. wood- frame wal
26、l was included in the model to characterize any wall/ foundation thermal-bridging effects. This frame wall was constructed of 0.5 in. thick gypsum wallboard (#lo); 3.5 in. of fiberglass batt insulation (#i 1); double sole plates made of 2 in. x 4 in. wood studs, whose actual dimensions are 1.5 in. b
27、y 3.5 in. each (#12); and 318 in. thick hardboard sheet siding (#13). This thin siding material, which does double-duty as the sheathing, is often used in low-cost construction4ther finishes, such as brick and stone, should be studied as well in the future. The density, thermal conductivity, and hea
28、t capacitance for the preceding materials and the soil are presented in Table I. These values may vary a bit from those used by other researchers; an attempt was made to select base values that are currently in everyday use in the U.S. However, significant variations in properties do occur by geogra
29、phic region, and through time as materials evolve. The computational cell dimensions shown in Table I will be discussed later. Transient Code This studys refined finite difference model is fully tran- sient, in that it solves hour-by-hour using the weather data for the entire typical year, but it al
30、so solves for the transients within each hour via nested loops. For numerical stability, the Figure 1 The detailed slab-on-grade geometry studied here is often found in modern residential and light commercial buildings in the US. The developed model allowed for variable thicknesses of external found
31、ation insulation (#9) and whether the expansion joint (#4) was present. i 78 ASHRAE Transactions: Research Table 1. Material Properties (ASHRAE 2001; Incropera and DeWiti 1985; Wang 1979; CRC 1984) and Cell Dimensions Used Heat Density Conductivity Capacitance Cell Dimensions P k CP x-dir. y-dir. Ma
32、terial lbm/ft Btu/h.ft.OF Btu/lbm.OF in. in. Concrete 140 1.125 0.2 15 Foundation 1 2 Slab 4 1 Gravel 120 1 O. 185 4 1 Soil 1 O0 0.9 0.4 Shallow 4 2 Deep 4 4 Foundation Insulation 2.65 0.0167 0.29 O to 0.5 2 Batt Wall Insulation 1.2 0.0225 0.23 0.5 0.5 Wood Studs 38.4 0.0883 0.39 0.5 0.5 Sheet Sidin
33、g 38.4 0.0528 0.29 0.375 0.5 Gypsum Wallboard 50 0.0925 0.26 0.5 0.5 Fiberboard Expansion Joint 18 0.03 17 0.3 1 0.5 1 Floor Vinyl 50 0.31 0.3 4 0.1875 Oak Flooring 50 0.3 1 0.3 4 O. 1875 Carpet 25 0.0675 0.33 Commercial (w/o pad) 4 0.25 Residential (w/ pad) 4 1 time steps are dramatically less than
34、 one hour (Rock and Ochs 2001; Ochs 2003) and are automatically calculated to be the largest that will just ensure stability of the solution. The code allows the solution to proceed to the next weather hour when either a steady condition is achieved within each hour, as was rarely the case, or the s
35、um of the completed time steps reaches the one-hour limit. In addition, the start-up transient is accounted for in this high mass problem. Many building energy analysis codes model the “mass effect” or “start-up” for transient analyses by repeating the first day, typically three to seven times, befo
36、re marching through all of the days of the year. Because the current prob- lem included a large quantity of high mass soil and concrete, repeating just the first day didnt seem sufficient. The sun and earth impose a highly seasonal mass effect, so it was assumed that the entire year must be repeated
37、 to fully initialize the spatially varying soil temperatures. As such, the code was written to obtain a steady-state solution for the first hour to help initialize the temperature arrays and then to repeat the 8760 hours-per-year calculations until the year-to-year varia- tions in cell temperatures
38、fell to near zero. This approach was highly computationally intensive and would not have been possible on desktop computers even a few years ago. But on a 1600 MHz P4-class computer, individual data points were obtained via 1.5-hour to 2-day-long runs for one weather site with small cell sizes. The
39、code allows all 239 sites to be solved in one massive run, but this feature was not needed for the results reported here. It is being used, however, for an ongoing study to obtain coefficients for simplified design models. The code performed the transient simulations and output the hour-by-hour resu
40、lts to large disk files. A brief post- processing code was written and then used to find the annual average hourly heat loss rates per foot of exposed perimeter (Btu/h.fi) for each run. Code Improvements More information about the finite differencing logic, boundary conditions, convergence criteria,
41、 stability, compar- isons to other results and data, and other details can be found in Rock and Ochs (2001) and Ochs (2003). Such is not repeated here for brevity. But the expanded code used for this current study included some significant improvements, such as variable outside air convection coeffi
42、cients based on the hourly wind speed, net solar energy absorption, and a nonlin- ear outside vertical soil temperature boundary condition based ASHRAE Transactions: Research 1 79 on experimental results by others (OSU 1988). After testing was complete and the researcher was confident that the phys-
43、 ics were being sufficiently characterized for engineering purposes, the code was then run repeatedly to perfom the sensitivity studies that follow. RESULTS AND DISCUSSION In this project, the variables of interest were computa- tional cell sizes, presence of an expansion joint, thickness of foundat
44、ion insulation, type of floor covering, soil density, and soil conductivity. It was hoped that a sensitivity study of these variables would help identify which constants and level of model should be used for further studies and what properties needed closer inspection for their influence on overall
45、heat transfer rates through a slab-on-grade. The weather data for Topeka, Kansas, were used for all runs as variations between the results were of interest and not the overall magnitude of the heat transfer rate. But this site in the central U.S. has wide vari- ations in temperatures, so its cold wi
46、nters, hot summers, and sometimes mild spring and fall seasons give the desired wide range of weather conditions. At this location, the average annual outside air temperature is about 54”F, and the annual heating degree-days base 65F are 55 15 as calculated from the TMY2 file. Computational Cell Siz
47、es As reported also in the previous paper, small cells were used with a non-uniform grid that was selected through expe- rience with finite differencing. This “art” of gridding is slowly becoming lost as prewritten codes often include automatic mesh generation routines. In essence, manual gridding,
48、like the automatic routines, places smaller cells where higher gradients are expected and larger cells where the transients are expected to be more gradual. So, for example, smaller cells would be expected near the soil surface rather than deep under- ground for this projects geometry. However most
49、previous studies, as described in the first paper (Rock and Ochs 200 i), used simplified geometries and very large cell sizes, typically on the order of 6 to 12 in. The computational step size is linked to the cell size in that smaller steps are needed to maintain stability and/or accuracy when the cell size is reduced. Reduc- ing both the cell and step sizes imply greatly increased computing time when using explicit finite differencing routines. With a detailed geometry composed of often-small components, and with the current studys transient boundary conditions, it was proposed
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