# An Experimental and Numerical Case Study of Passive Building Cooling with Foundation Pile Heat Exchangers in Denmark

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## Abstract

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_{2}footprint of traditional air conditioning methods. The ground source heat pump system (GSHP) installed at the Rosborg Gymnasium in Vejle (Denmark) uses foundation pile heat exchangers (energy piles). Although designed for passive cooling, the GSHP is used exclusively for heating. In a five-week test during the summer of 2018, excess building heat was rejected passively to the energy piles and the ground. Measured energy efficiency ratios are 24–36 and the thermal comfort in conditioned rooms is improved significantly relative to unconditioned reference rooms. A simple model relating the available cooling power to conditioned room and ground temperatures is developed and calibrated to measured test data. Building energy simulation based estimates of the total cooling demand of the building are then compared to corresponding model calculations of the available cooling capacity. The comparison shows that passive cooling is able to meet the cooling demand of Rosborg Gymnasium except for 7–17 h per year, given that room temperatures are constrained to < 26 °C. The case study clearly demonstrates the potential for increasing thermal comfort during summer with highly efficient passive cooling by rejecting excess building heat to the ground.

## 1. Introduction

_{2}-emissions [1]. To ensure the transition to a fossil-fuel free energy supply, Denmark has set a number of intermediate goals, one of which is to produce all heat with renewable energy (RE) sources by 2035 [2]. Consequently, the share of fuel-based energy sources in the total heat production in Denmark (including CO

_{2}-neutral sources such as biomass) is expected to decline towards 2030, being replaced primarily by heat pumps according to a forecast by The Danish Energy Agency [3].

_{2}footprint of traditional air conditioning methods.

^{2}terminal building [19]. The study is based exclusively on TRNSYS-simulations and no experimental data are reported.

## 2. Materials and Methods

#### 2.1. Study Site and Geological Setting

_{s}and volumetric heat capacity pc

_{s}at Rosborg Gymnasium were estimated in [21] by means of thermal response testing (TRT) and transient plane heat source measurements on soil samples (Figure 2b). The upper 1 m of silty sand has a thermal conductivity and volumetric heat capacity of ca. 2 W/m/K and 2.8 MJ/m

^{3}/K, respectively. The organic clay is a poor conductor of heat, having a thermal conductivity of ca. 0.7–0.8 W/m/K. Samples of the fully water-saturated sand have significantly higher thermal conductivities (ca. 2.0–2.7 W/m/K) compared to the organic clay due to the high quartz content and lower porosity. The higher water content of the organic clay yields a relatively high volumetric heat capacity of 3–3.5 MJ/m

^{3}/K, while the sand is measured to ca. 2.0–2.5 MJ/m

^{3}/K. The laboratory measurements of the thermal conductivity (2.14 W/m/K) are corroborated by the corresponding TRT estimate of the average soil thermal conductivity along the energy pile (2.20 W/m/K).

#### 2.2. The Energy Pile Foundation and the Heating, Ventilation and Air Conditioning (HVAC) System

^{3}storage tank with water at 55 °C, supplying both domestic hot water and radiators for heating (Figure 4). The district heating network serves as an auxiliary heating system.

#### 2.3. Building Characteristics and Passive Cooling Test from 2018-06-30 to 2018-08-10

^{2}and 23,237 m

^{3}, respectively. The building includes a large open canteen area with external window walls and roof skylights with a single internal upper level bridge and additional corridors. There are smaller classrooms in the eastern part of the building while the western part includes a long corridor connected to the canteen and laboratories. The southern part of the building features eight teaching rooms and a large auditorium, all with the possibility of passive cooling (Figure 3b,c).

#### 2.4. Passive Heat Exchanger Model

_{c}[W] depends on the temperature difference between the ventilated air T

_{v}[K] flowing across the surface of the heat exchanger and the fluid inside T

_{f}[K] (the latter being the average temperature of the fluid circulating to and from the energy piles); the combined conductive and convective area-integrated heat transfer coefficient K [W/K]; and a displacement constant D [W]:

_{a}is the outside temperature [K] and; T

_{r}is the temperature in the conditioned rooms [K].

#### 2.5. Energy Pile Fluid Temperature Model

_{f}, is calculated by spatial and temporal superposition of responses of individual energy piles (see Equations (2) and (6), p. 204 in [22]):

_{u}is the undisturbed ground temperature [K]; L is the total combined length of the piles [m]; λ

_{s}is the thermal conductivity of the soil [W/m/K]; G

_{g}and G

_{c}are the dimensionless, transient temperature responses at the pile wall and the outer geothermal pipe wall, respectively; R

_{c}and R

_{p}are the thermal resistances of the concrete and the geothermal piping, respectively [m·K/W]. The model assumes instant steady-state heat conduction in the geothermal piping material as indicated by the R

_{p}term in Equation (3).

#### 2.6. Combined Passive Heat Exchanger and Energy Pile Temperature Model

_{c}, and the temperature difference between the heat exchanger fluid and the ventilation air T

_{v}-T

_{f}in Equation (1). The energy pile fluid temperature response (T

_{f}, Equation (3)) is precomputed for a twelve-year period (3 reiterations of the period 2015–2018) utilizing building energy simulation based estimates of the heating and cooling demand (described later in Section 2.8). The energy pile fluid temperatures from the twelfth year of operation form the basis for calculating the available cooling power in Equation (4). Associated predictions are then calculated with Equation (1) and the estimated values of the coefficients K and D, taking into account the statistical uncertainty on the linear regression model. To estimate this uncertainty, simultaneous prediction intervals for any additional predictions of cooling power are computed with the following equation:

_{v}and T

_{f}. P

_{cm}is the regression model estimate of the available cooling power; f is inverse of the F cumulative distribution function; s

^{2}is the mean squared error; x is a row vector of the design matrix X and; S is the covariance matrix. Equation (5) is evaluated at the 95% confidence level.

_{el}is the rate of electricity consumption of the circulation pump [W]. P

_{c}is estimated from the measured flow rate and temperature to and from the piles and the volumetric heat capacity of the brine. The EER is estimated for all data points recorded during the test. P

_{c}is calculated as follows:

^{3}/s], ΔT

_{f}is the temperature difference between the fluid to and from the piles [K]; and ρc

_{f}is the volumetric heat capacity of the brine [J/m

^{3}/K] which is set equal to 4.01 MJ/m

^{3}/K.

_{c}is the total cooling energy consumed during a typical cooling season [J]. E

_{el}is the corresponding energy consumed by the circulation pump [J].

#### 2.7. Predicted Mean Vote and Predicted Percentage Dissatisfied (PMV/PPD) Model of Thermal Comfort

#### 2.8. Building Energy Model

^{2}] and; accumulated precipitation [mm]. The meteorological station (DMI station no. 610200), from which the data was obtained, is situated 27 km from the gymnasium. EnergyPlus further requires the outside dew point temperature as input to the simulation, which is calculated directly from the measured mean temperature and humidity.

## 3. Results and Discussion

#### 3.1. Passive Cooling Test

#### 3.1.1. Temperature

#### 3.1.2. Humidity and Ventilation Rates

^{3}/s. The measured relative humidity in the auditorium is up to 35% higher than in the unconditioned reference rooms (absolute, not relative) due to significantly lower temperatures in the auditorium. The average daily variation in humidity reflect changes in room temperatures (Figure 6b). In conditioned rooms, the temperatures decrease initially as cooling is initiated in the morning hours after 7:00 causing relative humidity to increase. At roughly 9:30, the elevated thermal stresses on the building cause room temperatures to increase and humidity to decrease. After 16:00, temperatures decrease slightly in both the conditioned and unconditioned rooms due to the decreasing angle of the sun relative to the room windows facing south, resulting in a minor increase in humidity.

#### 3.1.3. Cooling Power and Energy Efficiency Ratio

^{2}during the test campaign and generally correlate positively with outside temperatures (Figure 5 and Figure 7a).

#### 3.1.4. Thermal Comfort (PMV and PPD)

^{2}·K/W) corresponds to trousers, long-sleeved shirt, long-sleeved sweater and T-shirt. This assumption takes into consideration work places that impose a formal dress code. In the absence of a dress code, it is more likely that people choose a less insulating set of clothing such as a e.g., a T-shirt and pants corresponding to 0.5 Clo. Reduced clothing has a dramatic impact on thermal comfort. For the auditorium and the conditioned and unconditioned rooms, the mean PMV decreases to −1.8 (σ = 0.47), −0.94 (σ = 0.36) and −0.073 (σ = 0.58), respectively, assuming a clothing level of 0.5 Clo instead of 1 Clo. Reduced clothing lowers the average PMV to comfortable levels in unconditioned rooms, however, the standard deviation is more than doubled relative to increased clothing with passive cooling (σ = 0.58 and σ = 0.26, respectively). Thus, room conditioning, instead of reduced clothing, tends to lower the standard deviation on the PMV, thus reducing the duration of periods where PMV departs from comfortable levels.

#### 3.2. Comparison of the Required and Available Passive Cooling at Rosborg Gymnasium

_{f}in Equation (1) for 12 years of operation by reiterating the four-year heating and cooling demand profile, shown in Figure 10, three times. The twelfth year of operation, corresponding to the 2018 demand profile, is considered in the comparison of required and available cooling power, as energy pile fluid temperatures are no longer affected by the initial soil temperature conditions. For reference, the calculated T

_{f}is shown for the hot season in 2018 in Figure 10. T

_{v}is calculated from the corresponding outside temperatures included in the local climate data. The room temperature T

_{r}in Equation (2) is set equal to 26 °C to ensure consistency with the building energy model that uses an identical cooling set point temperature (Table 3).

^{2}) and the conditioned area during the cooling test (668 m

^{2}). Required cooling powers less than 2 kW are ignored in the comparison (Figure 11).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{m}over the length of the ground heat exchanger placed between the surface and depth L can be obtained by integrating the thermal disturbance from depth z = 0 to z = L [28]:

_{0}is the average ground temperature [K]; A is the amplitude of the seasonal temperature disturbance [K]; ω is the angular velocity [rad/s]; α is the thermal diffusivity [m

^{2}/s]; and t is time [s]. T

_{0}in Figure 1 (=9.03 °C) is estimated from monthly, average surface temperatures in Denmark for the period 2006–2015 [29] which roughly correspond to average undisturbed ground temperatures when disregarding paleoclimatic thermal disturbances.

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**Figure 1.**The annual variation in average, undisturbed mean temperature along typical ground heat exchangers (Denmark). Solar radiation is not considered (see Appendix A).

**Figure 2.**(

**a**) Location of Rosborg Gymnasium in Vejle, Denmark. (

**b**) Lithological profile from the field site at Rosborg Gymnasium including transient plane heat source measurements of soil thermal conductivity λ

_{s}and volumetric heat capacity pc

_{s}. TRT = Thermal Response Test. The × −scale in (

**b**) is indicated in the legend.

**Figure 3.**(

**a**) The building footprint and the energy pile foundation. The ground (

**b**) and first floor (

**c**) of the building. Cooled rooms are indicated with blue while the unconditioned rooms are marked with red. Black dots in (

**a**) and (

**b**) show the approximate position of the temperature loggers.

**Figure 5.**(

**a**) Fluid temperatures to and from the piles/ground and (

**b**) outside and average room temperatures. Raw data are shown as points (except highly noisy outside temperatures) while fitted, polynomial trends are drawn with full lines.

**Figure 6.**(

**a**) Ventilation rate and relative humidity in unconditioned and conditioned rooms, respectively. Vertical grid lines mark days for clarity. (

**b**) Average, variation in relative humidity (RH) and room temperature (T

_{r}) during the hours of the day (i.e., the sum of all daily responses normalized by the number of days summed).

**Figure 7.**(

**a**) Measured cooling power and (

**b**) energy efficiency ratios (SEER) during the test (right). Raw data are shown as points while fitted, polynomial trends are drawn with full lines.

**Figure 8.**(

**a**) Predicted Mean Vote (PMV) including mean (µ) and standard deviations (σ) and (

**b**) Percentage of People Dissatisfied (PPD) for the auditorium and the unconditioned (reference) and conditioned rooms. PMV mean and standard deviations are given in the left figure.

**Figure 9.**Linear, least square fit and simultaneous prediction intervals for the available cooling power P

_{c}(Equations (1) and (5)).

**Figure 10.**The EnergyPlus estimated heating and cooling demand for Rosborg Gymnasium. Corresponding energy pile fluid temperatures T

_{f}are plotted for the cooling season in 2018.

**Figure 11.**The required and available cooling power P

_{c}when utilizing the energy pile foundation at Rosborg Gymnasium for passive cooling.

M, metabolic rate (W/m^{2}) | 69.8 (1.2 met) |

W, mechanical power (W/m^{2}) | 0 |

I_{cl}, clothing insulation m^{2}⋅K/W | 0.155, 1 clothing unit (Clo) |

f, clothing surface factor (1) | Computed |

t_{a}, air temperature (°C) | Computed |

t_{r}, mean radiant temperature (°C) | t_{a} |

v_{a}, relative air velocity (m/s) | 0.2 |

p_{a}, water vapour partial pressure (Pa) | Measured (relative humidity) |

h_{c}, convective heat transfer coefficient (W/m^{2}/K) | Computed |

t_{cl}, clothing surface temperature (°C) | Computed |

Occupancy/Time | 7:30–8:00 | 8:00–11:30 | 11:30–12:00 | 12:00–16:00 |
---|---|---|---|---|

Classrooms | 10% (minor) | 100% (full) | 50% (medium) | 100% (full) |

Halls/corridor | 100% (full) | 35% (some) | 100% (full) | 35% (some) |

**Table 3.**Activity templates for the four room classes used in the EnergyPlus simulations. * see Table 2 for further details.

Parameter/Room Class | Hall | Laboratory | Class Room | General |
---|---|---|---|---|

Total area fraction (%) | 28.3 | 18 | 27.6 | 26.1 |

Occupancy density (people/m^{2}) | 1 | 0.25 | 0.65 | 0 |

Latent fraction | 0.5 | 0.5 | 0.5 | 0.5 |

Metabolic rate | Eating | Standing | Sitting | Walking |

Schedule * | Hall/corridor | Classrooms | Classrooms | Hall/corridor |

Laptop (W/m^{2}) | 1 | 1 | 1 | No |

Office equipment | No | No | No | No |

Miscellaneous (W/m^{2}) | 1 | 50 | 0 | 0 |

Lighting | Yes | Yes | Yes | Yes |

Cooling set point (°C) | 26 | 26 | 26 | 26 |

Heating set point (°C) | 22 | 22 | 22 | 22 |

Natural ventilation | No | No | No | No |

Mechanical ventilation (l/s/m^{2}) | 0.3 | 0.3 | 0.3 | 0.3 |

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**MDPI and ACS Style**

Poulsen, S.E.; Alberdi-Pagola, M.; Cerra, D.; Magrini, A.
An Experimental and Numerical Case Study of Passive Building Cooling with Foundation Pile Heat Exchangers in Denmark. *Energies* **2019**, *12*, 2697.
https://doi.org/10.3390/en12142697

**AMA Style**

Poulsen SE, Alberdi-Pagola M, Cerra D, Magrini A.
An Experimental and Numerical Case Study of Passive Building Cooling with Foundation Pile Heat Exchangers in Denmark. *Energies*. 2019; 12(14):2697.
https://doi.org/10.3390/en12142697

**Chicago/Turabian Style**

Poulsen, Søren Erbs, Maria Alberdi-Pagola, Davide Cerra, and Anna Magrini.
2019. "An Experimental and Numerical Case Study of Passive Building Cooling with Foundation Pile Heat Exchangers in Denmark" *Energies* 12, no. 14: 2697.
https://doi.org/10.3390/en12142697