Resumo

O fluxo de calor entre o piso e o solo de uma edificação térrea é um dos aspectos mais influentes em seu desempenho térmico e energético. No entanto, há ainda um grande número de incertezas e poucos estudos nessa área. Neste trabalho comparam-se diferentes alternativas de modelagem nos programas EnergyPlus (8.5.0) e Slab (.75) dos parâmetros relacionados à transferência de calor entre o piso e o solo, e sua influência no desempenho térmico de uma edificação térrea naturalmente ventilada, localizada em São Carlos, Brasil. A comparação das alternativas de modelagem indicou grande variação nos resultados. Quando comparado ao Slab, o método KusudaAchenbach do objeto Ground Domain apresentou a maior variação, com diferença de 55,2 % no número de horas de desconforto. Observou-se que mesmo a forma de uso do Slab pode causar diferenças significativas nos resultados; por exemplo, a adoção ou não do procedimento de convergência. A condutividade térmica do solo foi um parâmetro de grande impacto, que implicou diferenças de até 57,5 % no desconforto. Tais resultados fornecem indicações da variabilidade e do impacto de uso das diferentes opções de modelagem desse fluxo de calor no EnergyPlus.

Palavras-chave:
Conforto térmico; Simulação computacional; EnergyPlus; Fundação em laje; Pré-processador Slab; Objeto Ground Domain

Abstract

The heat flow through the floor and the ground of a single-story slab-on-grade building is one of the most influential aspects in its thermal and energy performance. However, there are still many uncertainties and only few studies on the subject. This study compares different modeling alternatives of the parameters related to the heat transfer between the floor and the ground, and their influence in the thermal performance of a naturally ventilated single-story house located in São Carlos, Brazil, using the programs EnergyPlus (8.5.0) and Slab (.75). The comparison between the modeling alternatives indicated wide variation in the results. When compared with Slab, the KusudaAchenbach method of the object Ground Domain presented the largest variation, with a difference of 55.2 % in the number of degree-hours of discomfort. It was observed that even the way of using Slab - for example, with or without the convergence procedure - could cause significant differences in the results. The thermal conductivity of the soil was a parameter of great impact, resulting in differences of up to 57.5 % in discomfort. Such results provide indications of the variability and impact of the different modeling options for this type of heat transfer in EnergyPlus.

Keywords:
Thermal comfort; Computer simulation; EnergyPlus; Slab-on-grade; Slab preprocessor; Object Ground Domain

Introduction

The heat flow between the floor and the ground of a slab-on-grade single-story building is one of the most influential aspects in its thermal and energy performance. The heat transfer can be calculated in EnergyPlus (DEPARTMENT..., 2016a), with the aid of the Slab preprocessor (DEPARTMENT..., 2016bDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Slab. Version .75. US, 2016b. Available at: <https://energyplus.net/downloads>. Accessed: Oct. 15 2016.
https://energyplus.net/downloads... ), to generate more accurate results (DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.). EnergyPlus is a program validated by ASHRAE 140 (ASMERICAN..., 2014AMERICAN SOCIETY OF HEATING REFRIGERATING AND AIR CONDITIONING ENGINEERS. ANSI/ASHRAE Standard 140-2001: standard method of test for the evaluation of building energy analysis computer programs. Atlanta, 2014.) and used worldwide to assess the thermal energy performance of buildings. The calculation method used by Slab is based on the works of Bahnfleth (1989)BAHNFLETH, W. P. Three-Dimensional Modelling of Heat Transfer From Slab Floors. University of Illinois, Urbana, 1989. and Clements (2004)CLEMENTS, E. Three Dimensional Foundation Heat Transfer Modules for Whole-Building Energy Analysis. Pennsylvania: The Pennsylvania State University, 2004.. The Brazilian "Whole-Building Energy Efficiency Labeling Program for Residential Buildings" (INSTITUTO..., 2012INSTITUTO NACIONAL DE METROLOGIA, NORMALIZAÇÃO E QUALIDADE INDUSTRIAL. RTQ-R: Regulamento Técnico da Qualidade para o Nível de Eficiência Energética de Edificações Residenciais, Rio de Janeiro, 2012.) also indicates the need to use Slab in simulations of the slab-on-grade type when using EnergyPlus. Recently, a new object with the same functions as Slab was incorporated (Site: Ground Domain: Slab) in EnergyPlus 8.2. It calculates by using two methods, defined by the user: FiniteDifference (XING, 2014XING, L. U. Estimations of Undisturbed Ground Temperatures Using Numerical and Analytical Modeling. Stillwater: Oklahoma State University, 2014.) and KusudaAchenbach (KUSUDA; ARCHENBACH, 1965KUSUDA, T.; ARCHENBACH, P. Earth Temperature and Thermal Diffusivity at Selected Stations in the United States. ASHRAE Transaction, v. 71, n. 1, p. 61-75, 1965.).

Both alternatives (Slab and Site: Ground Domain: Slab) calculate the temperature of the interface between the ground and the building's floor, which must be entered in EnergyPlus to proceed with the simulation of the building. Silva, Almeida and Ghisi (2017)SILVA, A. S.; ALMEIDA, L. S. S.; GHISI, E. Análise de Incertezas Físicas em Simulação Computacional de Edificações Residenciais. Ambiente Construído, Porto Alegre, v. 17, n. 1, p. 289-303, jan./mar. 2017. pointed out that ground temperature is one of the most influential variables in EnergyPlus simulations, when performing a sensitivity analysis for a residential building located in Florianópolis/Brazil. Those authors also indicated this input variable as the most uncertain in the thermal performance results. However, there is a series of questions regarding the modeling in Slab and its input data, and the same is true for the object Site: Ground Domain: Slab (GDomain). Below, some studies on the subject are presented, which focus especially on slab-on-grade buildings.

Batista, Lamberts and Güths (2011)BATISTA, J. O.; LAMBERTS, R.; GÜTHS, S. Influências dos Algoritmos de Condução e Convecção Sobre os Resultados de Simulações do Comportamento Térmico de Edificações. Ambiente Construído, Porto Alegre, v. 11, n. 4, p. 79-97, out./dez. 2011., when calibrating the simulation data with experimental data from a single-story residential building located in Florianópolis/Brazil, saw that the best correlation for indoor air temperatures was found using the measured values of the ground temperatures, followed by a case using Slab.

Andolsun et al. (2012)ANDOLSUN, S. et al. EnergyPlus vs DOE-2.1e: the effect of ground coupling on cooling/heating energy requirements of slab-on-grade code houses in four climates of the US. Energy and Buildings, v. 52, p. 189-206, sep. 2012. quantified the differences among the slab-on-grade heat transfer models in the DOE-2, EnergyPlus/Slab and TRNSYS simulation programs for low-rise residential buildings in four climates of the US. The simulation with the TRNSYS program was considered the most accurate and correct model, and was therefore used as reference for comparison with the other models. When comparing the EnergyPlus/Slab and TRNSYS models, the results differed according to the way the ground was modeled. The TRNSYS results were sufficiently close to the simulations in EnergyPlus when Slab was run externally and with convergence temperatures. However, EnergyPlus with Slab running internally, and without convergence, presented heat load results 18 %-32 % lower than TRNSYS.

Another example that compared different alternatives for modeling slab-on-grade heat transfer in thermal performance simulation programs is the study by Larsen (2011)LARSEN, S. F. Modelización de la Transferencia de Calor al Suelo en los Programas de Simulación Térmica de Edificios EnergyPlus y SIMEDIF. Avances en Energías Renovables y Medio Ambiente, v. 15, p. 27-34, 2011., who verified which model of the SIMEDIF and EnergyPlus programs best represented the data from a slab-on-grade prototype measurement. The SIMEDIF program models the slab-on-grade heat transfer considering the ground temperature at a depth of 2m equal to the average outside air temperature, and the floor consisting of slab material and a 1m layer of soil. In EnergyPlus, three modeling options were adopted: the measured ground temperature, the modeling of slab-on-grade equal to the SIMEDIF program, and the Slab preprocessor. The SIMEDIF program presented the best results, with an average difference of 0.6 ºC for the internal temperature and 0.2 ºC for the floor surface temperature. The EnergyPlus models yielded similar indoor temperatures, with an average difference of about 1ºC in relation to the measured data. However, the floor surface temperatures given by the EnergyPlus models did not accurately represent the measured data. The EnergyPlus modeling of slab-on-grade equal to SIMEDIF was the model that best represented the measured data.

The above-mentioned references show that there is a lack of studies on this theme, especially in Brazil, where there is usually no thermal insulation on floors, many of the buildings are naturally ventilated, and most do not have artificial conditioning. In this context, the aim of this paper is to assess the impact of different modeling alternatives for heat transfer between the floor and the ground in EnergyPlus, evaluating the thermal performance of naturally ventilated slab-on-grade single-story houses in Brazil. The study focuses especially on the Slab preprocessor and its various operation options, as well as on comparing it to other modeling options.

Modeling Slab-on-grade heat transfer in EnergyPlus

To calculate the heat exchanges between the slab-on-grade building and the ground, the monthly temperature variation data for the external surface of the floor is necessary (surface in contact with the ground). Currently, EnergyPlus provides two ways of performing calculations for this temperature: the Slab preprocessor and the object Site: Ground Domain: Slab (GDomain). In addition, there is a simplified way, which is to directly enter this temperature information in the object Site: Ground Temperature: Building Surface (GT:BSurface). The Manual Auxiliary Program (DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.) indicates considering this value around 2 ºC below the mean indoor air temperature for artificially conditioned commercial buildings in the USA. Papst (1999)PAPST, A. L. Uso de Inércia Térmica no Clima Subtropical Estudo de Caso em Florianópolis - SC. Florianópolis, 1999. Dissertação (Mestrado em Engenharia Civil) - Escola de Engenharia, Universidade Federal de Santa Catarina, Florianópolis, 1999. and Venâncio (2007)VENÂNCIO, R. A Influência de Decisões Arquitetônicas na Eficiência Energética do Campus / UFRN. Dissertação (Mestrado em Engenharia Civil) - Escola de Engenharia, Universidade Federal do Rio Grande do Sul, Natal, 2007. suggest the use of monthly mean air temperatures from weather files as reference.

The site: Ground Domain, Slab object (GDomain)

The object GDomain allows modeling multiple floors in contact with the ground, including different thermal zones. GDomain is in the object class Site: Ground Temperature, as part of EnergyPlus. When added, it is automatically used by the program. "It uses an implicit finite difference formulation to solve for the ground temperatures" (DEPARTMENT..., 2016cDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Engineering Reference. US. Documentation, EnergyPlusTM Version 8.5, 2016c.).

As a basis for calculation, this object uses a definition for Undisturbed Ground Temperature, which can be based on three different models. The first, FiniteDifference, is based on the work by Xing (2014)XING, L. U. Estimations of Undisturbed Ground Temperatures Using Numerical and Analytical Modeling. Stillwater: Oklahoma State University, 2014.. The second model, KusudaAchenbach, was developed by Kusuda and Achenbach (1965)KUSUDA, T.; ARCHENBACH, P. Earth Temperature and Thermal Diffusivity at Selected Stations in the United States. ASHRAE Transaction, v. 71, n. 1, p. 61-75, 1965.. And the third, Xing, developed by Xing (2014)XING, L. U. Estimations of Undisturbed Ground Temperatures Using Numerical and Analytical Modeling. Stillwater: Oklahoma State University, 2014., is the most complex one, requiring a greater number of input variables (MAZZAFERRO; MELO; LAMBERTS, 2015MAZZAFERRO, L.; MELO, A. P.; LAMBERTS, R. Manual de Simulação Computacional de Edifícios Com o Uso do Objeto Ground Domain no Programa EnergyPlus. Florianópolis, 2015.).

The Slab preprocessor program

Slab is an auxiliary program linked to EnergyPlus. Its calculation algorithm was originally developed by Bahnfleth (1989)BAHNFLETH, W. P. Three-Dimensional Modelling of Heat Transfer From Slab Floors. University of Illinois, Urbana, 1989., and then modified by Clements (2004)CLEMENTS, E. Three Dimensional Foundation Heat Transfer Modules for Whole-Building Energy Analysis. Pennsylvania: The Pennsylvania State University, 2004.. Its numerical method is based on an operation of finite tridimensional differences, providing a well-detailed solution with great flexibility. Slab's input data refer to the EPW weather files, to the characteristics of the building and the soil, and to the operating conditions of the program itself. The Auxiliary Programs Manual (DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.) and the EnergyPlus University Course Teaching Material (GARD..., 2003GARD ANALYTICS. Lecture 24: ground heat transfer EnergyPlus. University Course Teaching Material, 2003.) present a description of the data (inputs and outputs) and basic instructions.

With the ground temperature provided by Slab, it is possible to simulate the building in EnergyPlus by entering this information in the object "Site:BuildingSurfaceGroundTemperature". There are two ways to run Slab. In the first, Slab runs individually and its output (ground temperature) is an input in EnergyPlus, which is then run ("slab operating externally", Figure 1). The second option makes the simulation process easier, running Slab internally in EnergyPlus ("slab operating internally", Figure 1). In this case, all Slab input data are entered in the input file in EnergyPlus (*.idf) itself, and the above-mentioned process becomes automatic.

However, regardless of the choice to run Slab internally or externally to EnergyPlus, a previous simulation in EnergyPlus, denominated preliminary simulation, is always necessary. Figure 1 ("preliminary simulation") illustrates this procedure. Its purpose is to obtain a first estimate for the building's indoor air temperature (monthly means), since it is an input for Slab. At the beginning of the simulation, there is no such data, especially for buildings in free-float conditions. The Auxiliary Programs Manual (DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.) recommends that in such simulation, a layer with high insulation on the floor be added.

After the preliminary simulation and the first run of the duo EnergyPlus/Slab, EnergyPlus may produce an indoor air temperature for the building (monthly means) that is very different from the temperature considered as input in Slab. To adjust this data, it is necessary to adopt the convergence procedure (Figure 2) described by Andolsun et al. (2012)ANDOLSUN, S. et al. EnergyPlus vs DOE-2.1e: the effect of ground coupling on cooling/heating energy requirements of slab-on-grade code houses in four climates of the US. Energy and Buildings, v. 52, p. 189-206, sep. 2012.. To perform it, it is necessary to carry out consecutive simulations with iteration between the results given by Slab and by EnergyPlus. Those authors consider that the convergence is obtained when the difference in the monthly mean indoor air temperatures in the thermal zone between the last two simulations is of ≤0.0001 ºC.

Another aspect to be highlighted about Slab is that it provides three monthly temperature series for the ground surface underneath the floor: the average temperature for the core, for the perimeter and the weighted average for the surface area. The temperatures can be applied in EnergyPlus in two ways. If the user selects the average temperature, a uniform distribution of heat transfer on the entire floor surface is assumed. If the core and perimeter temperatures are used, it is assumed that the heat transfer in the core is different from the one in the perimeter, leading to the adoption of independent ground temperature values for each surface.

Research method

The method consisted of tests with various modeling options for a naturally ventilated slab-on-grade single-story building in the EnergyPlus (version 8.5.0) and Slab (version .75) programs.

Building geometry and construction

The simulated building model was based on a social housing project usually employed by a major Brazilian housing funding agency (MARQUES, 2013MARQUES, T. H. T. Influência Propriedades Térmicas Envolvente Opaca no Desempenho Habitações Interesse Social em São Carlos, SP. Dissertação (Mestrado em Arquitetura e Urbanismo) - Instituto de Arquitetura e Urbanismo, Universidade de São Paulo, São Carlos, 2013.). The original project is a slab-on-grade single-story isolated house. The building has two bedrooms, a kitchen, a living room and a bathroom, with a total area of 37.1 m². The simulated model considered only the external walls, resulting in one thermal zone composed of all the rooms (Figure 3). The roof consists of a non-ventilated attic, which was also simulated as a thermal zone, exchanging heat with the interior of the building through the roof slab. The windows are positioned as in the original project, and their areas were also maintained the same. The dimensions of the windows are 1.2 x 1.0m (living room), 1.2 x 1.0m (bedrooms), 0.50 x 0.50m (bathroom) and 1.2 x 1.0m (kitchen).

Table 1 presents the constructive characteristics and the thermophysical properties of the building's elements. The choice was based on information given by the Brazilian funding agency previously mentioned (Caixa Econômica Federal, with data from Marques (2013)MARQUES, T. H. T. Influência Propriedades Térmicas Envolvente Opaca no Desempenho Habitações Interesse Social em São Carlos, SP. Dissertação (Mestrado em Arquitetura e Urbanismo) - Instituto de Arquitetura e Urbanismo, Universidade de São Paulo, São Carlos, 2013.), and it reflects what is usually employed in this type of building. There is no thermal insulation on the floor, which is common for all types of single-story houses in Brazil, not just social housing projects.

Internal gains

The internal loads due to internal heat sources (occupants, artificial lighting and equipment), and their use patterns, were defined as recommended by the "Whole-Building Energy Efficiency Labeling Program for Residential Buildings" (INSTITUTO..., 2012INSTITUTO NACIONAL DE METROLOGIA, NORMALIZAÇÃO E QUALIDADE INDUSTRIAL. RTQ-R: Regulamento Técnico da Qualidade para o Nível de Eficiência Energética de Edificações Residenciais, Rio de Janeiro, 2012.). The values are presented in Table 2.

Climate

The chosen location is the city of São Carlos, with latitude 22º01'03''S, altitude of 863m, and situated in climate zone 4, according to the Brazilian Standard NBR 15220-3 (ABNT, 2005bASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 15220-3: desempenho térmico de edificações: parte 3: zoneamento bioclimático brasileiro e estratégias de condicionamento térmico passivo para habitações de interesse social. Rio de Janeiro, 2005b.). The EPW file used was developed by Roriz (2012)RORIZ, V. F. Arquivos EnergyPlus Weather Data. 2012. Available in: <http://www.roriz.eng.br/epw_9.html>. Accessed: 15 out. 2016. In Portuguese.
http://www.roriz.eng.br/epw_9.html... . Figure 4 represents Givoni's (1992)GIVONI, B. Comfort, Climate Analysis and Building Design Guidelines. Energy and Buildings, v. 18, n. 1, p. 11-23, 1992. climatic diagram generated by the EPview program (RORIZ; RORIZ, 2015RORIZ, V. F.; RORIZ, M. EPvieW. São Carlos: [s.n.], 2015.) using the above-mentioned weather file. The diagram shows that during most of the year (34.4 %) the city is within the comfort zone. It is also possible to see that there is a predominance of cold over heat, with 29.5 % of the year located in the solar heating zone, and 24.2 % in the thermal-inertia zone (heating).

Natural ventilation modeling

The building was considered naturally ventilated by the use of windows, as is common for residential buildings with these dimensions in the chosen location. Ventilation was modeled using the Airflow Network module in EnergyPlus. For the wind pressure coefficients for each façade, the values automatically calculated by EnergyPlus for rectangular geometries were adopted. The main input data adopted in the simulations for the Airflow Network module are presented in Table 3. Using temperature as the control for window opening, ventilation was allowed when the indoor air temperature was higher than the external air temperature (Tint >Text), and when the indoor air temperature was higher than the control temperature (Tint >Tsetpoint). The ventilation schedule was defined according to the users' occupation pattern (see Internal Gains section) as well as to previous studies about window operation conducted for the same climate, which indicate the need for nocturnal ventilation (MARIN; CASATEJADA; CHVATAL, 2016MARIN, H. F.; CASATEJADA, M. P.; CHVATAL, K. M. S. Impacto da Temperatura de Controle na Operação das Janelas e no Conforto Térmico Para Uma Habitação de Interesse Social Naturalmente Ventilada em São Carlos - SP. In: ENCONTRO NACIONAL DE TECNOLOGIA DO AMBIENTE CONSTRUÍDO, 16., São Paulo, 2016. Anais... São Paulo, 2016.). The percentage of window opening considered was 100 %, in accordance with what is proposed by the Brazilian Standard NBR 15220 (ABNT, 2005bASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 15220-3: desempenho térmico de edificações: parte 3: zoneamento bioclimático brasileiro e estratégias de condicionamento térmico passivo para habitações de interesse social. Rio de Janeiro, 2005b.) for climate zone 4. The standard recommends the use of medium openings for ventilation in this zone, with an effective opening area between 15 % and 25 % of the floor area.

Input data and simulation variations

The simulations are divided into three groups, as indicated in Table 4. In the first group, tests were run to evaluate the operation of Slab and other modeling alternatives for the heat exchanges between the building and the ground. In the second group, the objective was to evaluate the influence of certain input data from Slab on the output data. In the third group, tests were performed varying specifically one type of input data from Slab: the thermophysical properties of the soil.

Each of these groups was divided into a series of sub-groups. Tables 5 to 11 list all input data for Slab (Tables 6 to 11) as well as the data for the object GDomain (Table 5), identifying to which sub-group they belong. From sub-groups 4 to 9, the results of the considered variations were compared to a case designated as "reference". The reference case was considered as the most indicated, according to the literature and the Auxiliary Programs Manual and EnergyPlus University Course Teaching Material (GARD..., 2003GARD ANALYTICS. Lecture 24: ground heat transfer EnergyPlus. University Course Teaching Material, 2003.; DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.). The choice of what would be altered was also based on those references. All simulations followed the procedures outlined in the section "Modeling Slab-On-Grade Heat Transfer in EnergyPlus", unless otherwise stated. Table 6 also presents some additional details about the simulation procedure.

Form of analysis of the results

The output data used were indoor air temperature and operative temperatures (hourly), given by EnergyPlus, and ground temperature right beneath the floor (monthly means), given by Slab. The impact that the modeling possibilities explored in the simulations had on the hourly indoor air temperature was closely examined. As well as that, the study investigated how that impact reflected on the comfort evaluation of the house, by adopting the comfort limits given by the adaptive approach in Standard 55 (AMERICAN..., 2013AMERICAN SOCIETY OF HEATING REFRIGERATING AND AIR CONDITIONING ENGINEERS. ANSI/ASHRAE Standard 55: thermal environmental conditions for human occupancy. Atlanta, 2013.), which are specific to naturally ventilated rooms. The temperatures corresponding to those limits are a function of the outside air temperature, given by the weather file. As indicated in the Standard, the limits adopted corresponded to 80 % acceptability by users. Figure 5 presents the external air temperature, the comfort temperature and the upper and lower limits, as a function of the hours in a year, for the city of São Carlos, Brazil, given by the EPW weather file provided by Roriz (2012)RORIZ, V. F. Arquivos EnergyPlus Weather Data. 2012. Available in: <http://www.roriz.eng.br/epw_9.html>. Accessed: 15 out. 2016. In Portuguese.
http://www.roriz.eng.br/epw_9.html... .

With the comfort range established, the total annual degree-hours of discomfort by heat and by cold were obtained. Each degree-hour corresponds to the discomfort caused when the operative temperature² 2 The uniform temperature of an imaginary black enclosure in which an occupant would exchange the same amount of heat by radiation plus convection as in the actual nonuniform environment" (AMERICAN..., 2013). is below the lower limit (cold) or above the upper limit (heat) by 1ºC during one hour. The annual levels are the sum of the degree-hours that occurred over the hours for a year (RORIZ; CHVATAL; CAVALCANTI, 2009RORIZ, M.; CHVATAL, K. M. S.; CAVALCANTI, F. S. Sistemas Construtivos de Baixa Resistência Térmica Podem Proporcionar Mais Conforto. In: ENCONTRO NACIONAL, 10.; ENCONTRO LATINO AMERICANO DE CONFORTO NO AMBIENTE CONSTRUÍDO, 6., Natal, 2009. Anais... Natal, 2009.).

Results and discussion

This section shows the results of the simulations. The sub-groups are described in Table 4 in Research Method and the results are divided into the following items:

Internal or External Slab activation on EnergyPlus

Simulations were performed with both types of activation using the same input data, according to the procedure indicated in the "Modeling Slab-On-Grade Heat Transfer in EnergyPlus" section and the input data described in Research Method. Both simulations presented all the output variables with identical values. This indicates that when Slab is internally activated, it works correctly. Besides, since it was only run once when externally activated, this confirms that the same occurred when it was internally activated, that is, no iterations were performed searching convergence. After this result, Slab was internally activated in EnergyPlus in all the simulations.

With or without using Slab, with or without Convergence Procedure

As presented in Research Method (simulations sub-group 2), the following situations were analyzed, regarding the scenarios with and without Slab:

The results are presented in Figure 6. It indicates the number of hours in a year in which the difference between the hourly indoor air temperatures in cases 2B, 2C and 2D and in Slab case 2A are found within the limits defined on the x-axis. The positive values correspond to indoor air temperatures in cases 2B, 2C and 2D higher than those in the Slab case, and the negative values indicate the opposite. The results show that without Slab there is a considerable impact on the hourly indoor air temperature, which increases for the most part of a year in all three alternatives. Case GT:BSurface presents differences smaller than or equal to +0.5 ºC in 63.8 % of the time. As for case GDomainFD, as well as GDomainKA, the differences are slightly higher, and their distributions are very similar to each other. There are values above +1.25 ºC in 14 % and 24.0 % of the annual hours, respectively, with the maximum value reaching + 3.06 ºC, in the GDomainKA case.

When opting to use Slab, Andolsun et al. (2012)ANDOLSUN, S. et al. EnergyPlus vs DOE-2.1e: the effect of ground coupling on cooling/heating energy requirements of slab-on-grade code houses in four climates of the US. Energy and Buildings, v. 52, p. 189-206, sep. 2012. state that, in order to obtain more accurate results, convergence of the internal air temperature is necessary. The final converged result is more correct, since it refers to the same monthly mean ground- and indoor air temperature combinations in both calculation algorithms: EnergyPlus and Slab. Before the convergence procedure, a preliminary simulation is run to obtain the first indoor air temperature estimate, which is an input data in Slab. The convergence procedure and the preliminary simulation are described in the section "Modeling Slab-On-Grade Heat Transfer in EnergyPlus".

Hence, the second test refers to the verification of the impact of adopting the convergence procedure, also considering different modeling alternatives in EnergyPlus from the preliminary simulation. Six cases were compared (detailed in Research Method, simulations sub-group 3):

As expected, cases 3A, 3B and 3C, at the end of the convergence procedure resulted in the same final indoor and ground temperature combination. Several iterations were required to achieve very similar convergences between them. Andolsun et al. (2012)ANDOLSUN, S. et al. EnergyPlus vs DOE-2.1e: the effect of ground coupling on cooling/heating energy requirements of slab-on-grade code houses in four climates of the US. Energy and Buildings, v. 52, p. 189-206, sep. 2012., on the other hand, indicated a significant reduction in the amount of iterations when adopting a case similar to A (with an insulation layer in the preliminary simulation). This is possibly due to the initial interior temperature values adopted to enter in the first run in EnergyPlus/Slab, which were already close to their final result.

The impact of not adopting the convergence procedure (comparison between cases 3A, 3D, 3E and 3F), is presented in Figure 7. This difference ranges from 0 ºC to +0.3 ºC in 83.11 % of the annual hours, for case 3D (preliminary simulation with insulation). In case 3E (1^stT_{18 ºC}), the difference ranges between -0.1 ºC and +0.1 ºC for 95.74 % of the annual hours. And in case 3F (1^stT_25ºC), it is greater than +0.5 ºC in 24.97 % of the period. That is, if the convergence procedure is not adopted when using Slab for a building with these characteristics, the preliminary simulation with 25 ºC is the one that presents the greatest difference, followed by case 3D (1^st Slab) and the case with 18 ºC.

This indoor temperature difference is a consequence of the difference for ground temperature adopted in EnergyPlus, as presented in Table 12. The results show that it is in the case of 25 ºC (1^st T_{25 ºC}) - in comparison with the cases of 18 ºC (1^stT_{18 ºC}) and 1^stSlab case - that the greatest differences occur between the ground temperature used in EnergyPlus for these simulations and the temperature that would be the most correct. These results confirm what had previously been observed: on the floor without insulation, differences in the ground temperature directly impact the indoor temperature. The differences in the cases without convergence are smaller when the first simulation is run (1^st iteration) and the ground temperature is closer to the final one. In this specific case, this corresponded to the preliminary simulation of 18 ºC. However, this varies according to the climate and building characteristics, and it is not possible to predict the best solution. Since there is no thermal insulation on the floor, which is common in Brazilian slab-on-grade buildings, differences in the average ground temperature directly influence the internal environment.

Finally, the impact of the above-mentioned hourly temperature differences on the comfort assessment of the building was verified. Table 13 shows the degree-hours of discomfort by cold, by heat and the total discomfort, as well as their increase (+) or decrease (-) percentages in relation to case 2A (Slab). The other options reflect the previously observed internal temperature behavior: cases GDomainKA and GDomainFD present the greatest impact (decreases of 55.2 % and 44.0 % on total discomfort in relation to Slab). Cases GT:BSurface and 1^stT25 ºC present an intermediate difference (decreasing total discomfort by 26.2 % and 26.9 %). Case 1^stT18 ºC presents the smallest alteration (-0.2 %).

These results demonstrate the considerable impact of the studied alternatives both on the indoor temperature and on the comfort evaluation, indicating not only the importance of using Slab but also the convergence procedure. The considerable differences observed between the object GDomain and Slab, indicate the need to better understand both methods. In addition, a comparison to real measured data would show which method would be more adequate for the building type in question.

Influence of Slab input data

Although the importance of using Slab in slab-on-grade simulations has been confirmed, there are still many uncertainties related to its input data, especially in Brazil, where there are no studies pertaining such issues. To evaluate the impact of some of these input data, selected as relevant, eight cases were simulated. Their detailed description can be found in Research Method. In all cases, the convergence procedure was adopted.

The alteration that presented the largest difference in relation to the reference case was the one with evapotranspiration deactivated (Figure 8). It varied between -1.13 ºC and +1.78 ºC with 50.7 % of the differences above 0.3 ºC. As for the comfort evaluation (Table 14), this was the parameter with the greatest impact, with 23.8 % less degree-hours of total discomfort in a year. This result corroborates the results obtained by Bahnfleth (1989)BAHNFLETH, W. P. Three-Dimensional Modelling of Heat Transfer From Slab Floors. University of Illinois, Urbana, 1989., who conducted a study comparing activated and deactivated evapotranspiration in different climate conditions. He found that the greater differences between using evapotranspiration or not occurred in dry and hot climates.

The other alterations (zero amplitude, slab temperature, horizontal domain and years to iterate) presented medium to low impact. The difference between these cases and the reference case ranged between -0.1 ºC and +0.2 ºC for 62.6 % to 99.7 % of the year, with a maximum value of -2.37 ºC in the Slab temperature case.

As for the amplitude, the EnergyPlus manual informs that this data has little influence. This was, in fact, observed in this building, whose annual average amplitude is equal to 5.86 ºC. In the comfort evaluation, this case presented an 11 % decrease in total discomfort.

With regard to Slab temperature, Clements (2004)CLEMENTS, E. Three Dimensional Foundation Heat Transfer Modules for Whole-Building Energy Analysis. Pennsylvania: The Pennsylvania State University, 2004. informs that the use of the core and perimeter temperatures yields better heat transfer results, than when average temperature is used. The most detailed simulation produced an evaluation with 6.7 % discomfort for this building.

The horizontal domain test was performed to verify the impact of this aspect, since the information found in the literature regarded only the vertical domain (BAHNFLETH, 1989BAHNFLETH, W. P. Three-Dimensional Modelling of Heat Transfer From Slab Floors. University of Illinois, Urbana, 1989.; BAHNFLETH; PEDERSEN, 1990BAHNFLETH, W. P.; PEDERSEN, C. O. A Three-Dimensional Numerical Study of Slab-on-Grade Heat Transfer. ASHRAE Transactions, St. Louis, v. 96, n. 2, p. 61-72, 1990.). This aspect presented an impact of less than 0.5 % on the discomfort evaluation.

In relation to iteration time, when it was equal to 20 years, the difference was always zero. For a 5-year period, the influence on the degree-hours of discomfort was also very low, at +0.5 %. This shows that a period of 10 or more years is satisfactory for the convergence calculations, according to what is suggested in the Auxiliary Programs Manual (DEPARTMENT..., 2016dDEPARTMENT OF ENERGY EFFICIENCY AND RENEWABLE ENERGY. Ground Heat Transfer in EnergyPlus. Documentation, EnergyPlusTM Version 8.5 - Auxiliary Programs, p. 103-142, 2016d.), and also that increasing the number of years adopted has no effect on the results.

Influence of the thermophysical properties of the soil

The values referring to the thermal properties of the soil are among the input data that generate most doubts during a simulation. The lack of information about this aspect in Brazil is compounded by the difficulty to determine the properties that vary with time, location, roof type and soil composition.

To verify the impact of the properties of the soil, three sets of values selected from Bahnfleth (1989)BAHNFLETH, W. P. Three-Dimensional Modelling of Heat Transfer From Slab Floors. University of Illinois, Urbana, 1989. were used. These sets of values represent the soil in conditions of high, medium and low conductivity, given that the soil with low conductivity is dry and the one with high conductivity is humid. Thus, the following cases were compared:

More detailed information about these cases can be found in Research Method. All cases were simulated using the convergence procedure. The average conductivity value was adopted as reference solely to serve a comparison parameter; it is not considered the most correct. The thermophysical properties of the soil are variable over time and space, and the most adequate procedure would be to measure its properties in loco. The purpose of this test was to verify whether, in the Slab model, variations measured from this value would cause an impact on the interior temperature.

The differences in indoor air temperatures are shown in Figure 9. In the Dry Soil (low k) case, for 35.11 % of the year the temperature was 1ºC higher than in the case with medium k, with a maximum difference of 1.7 ºC. The Humid Soil (High k) presented a maximum difference of +1.8 ºC, and 93.12 % of the time with differences between 0 ºC and -0.4ºC.

The observed impact reflected significantly on discomfort (Table 15). The Dry Soil (Low k) case presented 58.6 % less discomfort by cold in relation to the Medium k, 92.3 % more discomfort by heat and 57.5 % less total discomfort in a year. The Humid Soil (High k) also had high impact, with 25 % more total discomfort (always presenting inferior temperatures).

Conclusions

This study investigated different modeling alternatives for the parameters related to the heat transfer between the floor and the ground, with an emphasis on the Slab program linked to EnergyPlus. The method consisted of computer simulations of a naturally ventilated single-story slab-on-grade house located in São Carlos, Brazil.

The results indicated that not using Slab generates a very significant difference in the performance evaluation. Directly entering the ground temperature, with the adopted value equal to the air temperature in the weather file, resulted in a 26.2 % reduction in the total degree-hours of discomfort. As for adopting the object Site: Ground Domain, there was an even greater impact on total discomfort, with differences of -44 % for the FiniteDifference method and -55.2 % for the KusudaAchenbach method. The simulations also demonstrated the need for the convergence procedure should Slab be used. This procedure considers several iterations between Slab and EnergyPlus, which are currently not performed automatically. Using the iteration only once resulted in a reduction of the total annual degree-hours of discomfort, when considering the comfort evaluation for the studied building.

As for the input data for Slab, the thermophysical properties of the soil were the data that had the most influence. The building was evaluated as being 57.5 % less uncomfortable with the dry soil, and 25 % more uncomfortable with the humid soil, in relation to an intermediate humidity level. The literature indicates the difficulties pertaining these parameters, since they vary during the year and should preferably be taken from measurements.

Acknowledgments

The authors would like to thank CAPES Foundation for funding this research study.

References

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