Foundation heat exchangers for residential ground source heat pump systems--numerical modeling and experimental validation.
Ground source heat pump (GSHP) systems are widely used in residential and commercial buildings due to their high energy efficiency. Two common types of heat exchanger usually used in GSHP systems are vertical ground heat exchangers and horizontal ground heat exchangers (HGHX). However, the high costs of trench excavation required for horizontal heat exchanger installation and of drilling boreholes for vertical heat exchangers are often a barrier to implementation of the GSHP system. In the case of net-zero-energy homes or other very low energy homes, the greatly reduced heating and cooling loads as compared to conventional construction give the possibility of using a ground heat exchanger that is significantly reduced in size.
Recently, a new type of ground heat exchanger was proposed as an alternative to conventional ground heat exchangers. By placing the pipes in the excavation made for the basement, "foundation heat exchangers" (FHXs) can significantly reduce installation cost compared with conventional ground heat exchangers. Although FHXs have been installed in some homes and have worked successfully, no scientific design procedure has been developed in order to size the FHXs for specific buildings. Figure 1 shows two pictures of the FHX installation process at the experimental facility near Oak Ridge, Tennessee.
[FIGURE 1 OMITTED]
Den Braven and Nielson (1998) modeled a coiled ground heat exchanger that was placed below a house slab-on-grade foundation using an analytical model of a ring source. Gao et al. (2008) modeled ground heat exchangers embedded in foundation piles with a numerical solution. However, neither of these geometries is very close to the FHX proposed here. HGHXs are somewhat closer in geometry, but these do not include the presence of a basement in close proximity to the heat exchanger tubing.
There are two types of approaches for solving the HGHX problem: analytical and numerical solutions. Both analytical and numerical methods have been used for modeling HGHXs for several years. Despite this, previously developed models do not both capture the requisite pipe configuration relative to the basement wall, nor do they consider important factors that affect the performance of HGHXs, including soil freezing and moisture effects.
Analytical solutions based on line source assumptions are able to solve the heat conduction problem of multiple pipes buried in semi-infinite medium with a constant heat extraction rate (Ingersoll and Plass 1948; Hart and Couvillion 1986). Along with Kelvin's line source solution, several other analytical solutions have been derived to solve the temperature profile around single or multiple line sources (Claesson and Persson 2005; Saastamoinen 2007). With superposition, it is possible to solve problems with varying heat extraction rates in a computationally efficient manner. However, such solutions require approximations for finite domains that may limit accuracy in practice. There fore, as demonstrated by Xing et al. (2010), analytical models are not well suited for the modeling of FHXs.
Compared with analytical models, numerical models require more computational time but are capable of more realistically calculating the performance of the system by considering such phenomena as soil freezing during winter operation, soil drying during summer operation, moisture transport, and snow cover or freezing at the ground surface. Many models exist that take into account various combinations of these factors (Metz 1983; Mei 1986; Tarnawski and Leong 1993; Piechowski 1996; Esen et al. 2007; Demir et al. 2009). Regardless, none of them are able to handle all of these important factors while still maintaining an acceptable computation time. For example, some do not account for the freezing/thawing behavior of the soil (Metz 1983; Piechowski 1996; Esen et al. 2007; Demir et al. 2009), while some consider the freezing of the soil but are not flexible enough to be applied to configurations containing multiple pipes (Mei 1986). Other models do not consider snow cover (Metz 1983;Mei 1986;Piechowski 1996; Esen et al. 2007), while one of these models (Tarnawski and Leong 1993) requires excessive computational time. One important detail noted by Piechowski (1996), whose model considers moisture transport, is that for determining the thermal performance of HGHXs, proper estimation of the soil type and its initial moisture content is more important than the moisture transfer calculation capabilities of the model.
From previous studies of numerical models of HGHXs, no existing model captures the pipe configuration relative to the basement wall and is suitable for implementation in a building system simulation program. Soil freezing and snow cover on the earth surface may be important factors that impact the performance of FHXs in some climates; these factors need further investigation. A detailed moisture transport model has not been included since the expected gain in accuracy is minimal for the large increase in computational time that would be incurred. Therefore, a 2D explicit finite volume FHX model is developed in this article, which is used to investigate the factors that can greatly affect system performance, such as the effect of any basement heat transfer, the freezing/melting process of moisture in the soil, and heat loss through evapotranspiration (ET) at the earth surface. Moisture transport and snow cover is not currently included in this model but are subjects for potential future consideration.
[FIGURE 2 OMITTED]
The FHX numerical model is an explicit two-dimensional finite volume model with a rectangular, non-uniform grid, which is implemented in the HVACSIM+ environment (Clark 1985). The two-dimensional model represents the three-dimensional geometric soil domain with a plane perpendicular to the tube, with the assumption that there is no heat transfer through the soil along the length of the tube. Additionally, corner effects are not accounted for in the model. As shown in Figure 2, the simulated soil domain is bounded by a basement (which may be temperature conditioned or unconditioned), the earth surface, and the surrounding ground. The inside basement wall and basement floor boundaries are convective so that the FHX tubes may extract some heat from the basement.
A non-uniform grid with approximately 13,000 cells, shown in Figure 3 from Xing et al. (2010), is used to model the domain. The tube locations are inputs for the FHX model, and the grid is formed automatically. For the FHX, there are six tubes, all of which are assumed to have the same inside and outside diameters. Each tube is represented as an equivalent rectangular tube that is the same size as the smallest cell but covers portions of four cells. The grid spacing is smaller near the earth and tube surfaces and expands toward the adiabatic surfaces (left and right sides of the soil domain) and the bottom of the soil domain.
The numerical model is based on the finite-volume method--for the most part, it follows standard formulations for interior cells with conduction heat transfer, cells with adiabatic boundaries, convective boundaries, and temperature-specified boundaries. There are two special cases covered here--cells at the earth's surface that include convection, radiation, and heat loss through ET, and cells that represent tubes. For the surface cells, ET is the loss of water from the surface through two processes: evaporation from soil to plant surfaces and plant internal transpiration.
Figure 4 shows a cell labeled (m,n) at the earth's surface, which means it is the mth cell in the x direction and the nth cell in the y direction. Because the grid starts at the top of the basement wall, the value of n varies depending on the height of the basement wall above grade. In order to find the soil temperature at earth's surface directly, a half cell is used, as shown in Figure 4. An energy balance can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[DELTA][x.sub.(m,n)] is the cell (m,n) length in the x direction, m (ft);
[DELTA][y.sub.(m,n)] is the cell (m,n) length in the y direction, m (ft);
[[rho].sub.s] is soil density, kg/[m.sup.3] (lb/[ft.sup.3]);
[c.sub.ps] is the soil heat capacity, J/kg x K (Btu/lb x [degrees]F);
V is the cell volume, [m.sup.3] or ([ft.sup.3]);
[DELTA][T.sub.(m,n)] is the temperature increase in cell (m,n), [degrees]C ([degrees]F);
[L.sub.p] is the length of the FHX tubing, m (ft);
[q.sub.2], [q.sub.3], and [q.sub.4] are the heat conduction rates from surrounding cell, W/[m.sup.2] (Btu/hr x [ft.sup.2]);
[q.sub.1] is the net heat gain at the earth's surface, W/[m.sup.2] (Btu/hr x [ft.sup.2]); and
[[rho].sub.s][C.sub.ps]V [DELTA][T.sub.(m,n)] is the heat stored in the cell, W (Btu/hr).
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
The left side of Equation 1 represents the net heat gain to the cell, and the right side represents the increase in energy for the cell for a specific time step.
The heat transfers [q.sub.2], [q.sub.3], and [q.sub.4] are computed based on conduction only. The heat transfer rate [q.sub.1] represents the net heat gain at the ground surface due to absorbed short-wave irradiation, long-wave radiation to and from the environment, convection to and from the outdoor air, and heat loss by ET:
[q.sub.1] = [Q.sub.rad_s] + [Q.sub.rad_L] + [Q.sub.conv] + [Q.sub.evap], (2)
[Q.sub.rad_s] is the absorbed short wave radiation, W/[m.sup.2] (Btu/hr x [ft.sup.2]);
[Q.sub.rad_L] is the net long-wave radiation absorbed by the surface, W/[m.sup.2] (Btu/hr x [ft.sup.2]);
[Q.sub.conv] is the convection heat transfer to the surface, W/[m.sup.2] (Btu/hr x [ft.sup.2]); and
[Q.sub.evap] is heat transfer to the surface through ET (this will usually be negative, unless condensation is occurring), W/[m.sup.2] (Btu/hr x [ft.sup.2]).
[FIGURE 5 OMITTED]
The net heat gain [q.sub.1] at the ground surface can be calculated from Equation 2, and it requires the incident short-wave radiation on a horizontal surface and other weather-related boundary conditions. For general use of the model, it is anticipated that the weather-related boundary conditions will be taken from a typical meteorological year "TMY3" weather file (Wilcox and Marion 2008). The TMY3 weather files contain hourly values of weather a one-year period and are compiled from a dataset derived from the 1961-2005 National Solar Radiation Data Base (NSRDB) archives. In the validation presented in this article, the weather data are collected at the experimental site in Oak Ridge, Tennessee. The net long-wave radiation is determined by utilizing an effective sky emissivity based on humidity and cloudiness. The absorbed short-wave radiation is calculated with an absorptivity of 0.77; the value is chosen for grass cover using the procedure for ET set forth by Walter et al. (2005). The convection heat transfer coefficient is estimated as being linearly proportional to the wind speed, as described by Antonopoulos (2006). The ET model then gives the evaporation rate in mm/hr as a function of the type of vegetation. For this model, the heat loss through ET at the earth surface is calculated assuming a grass at a height of 12 cm (4.7 in.) covers the earth surface. This value is used as the reference condition by Walter et al. (2005); since the height of the grass at the experimental site is not measured and varies with time, this condition was used for the ET model. Once the ET rate is calculated, the heat loss by evaporation is determined by multiplying the ET rate by the density and latent heat of evaporation of water. The inclusion of ET has a significant impact in the prediction of the ground temperature.
Figure 5 shows the cells around the FHX tubing. The FHX tubing is surrounded by four cells, as shown. For each of the four cells, a quarter is occupied by the FHX tubing, with the rest being soil. Equations 3-5 show the method of calculating the temperature for one of the four cells (m,n). For the cell (m,n), there is conduction heat transfer from the surrounding four cells, as well as convection heat transfer from the fluid inside the pipe. The summation of the conduction and convection equals the heat stored in the soil portion of the cell, as described by Equation 3:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[R.sub.1] = ([DELTA][y.sub.(m,n)] + [DELTA][y.sub.(m,n + 1)] / 2) / ([k.sub.s] x [DELTA][x.sub.(m,n)] / 2) (4)
[R.sub.5] = 1 / (U [DELTA][x.sub.(m,n)] + [DELTA][y.sub.(m,n)] / 2), (5)
[T.sup.p.sub.f] is the fluid temperature at the previous time step, represented as a time-dependent boundary, [degrees]C ([degrees]F);
[T.sup.p.sub.(m,n)] is the cell (m,n) temperature at the previous time step, [degrees]C ([degrees]F);
[T.sup.z.sub.(m,n)] is the cell (m,n) temperature at the current time step, [degrees]C ([degrees]F);
U is the overall conductance through the fluid to the tubing outside, W /[m.sup.2] x K (Btu/hr x [ft.sup.2] x [degrees]F);
[DELTA][x.sub.(m,n)] is the cell (m,n) length in the x direction, m (ft);
[DELTA][y.sub.(m,n)] is the cell (m,n) length in the y direction, m (ft);
[[rho].sub.s] is the soil density, kg/[m.sup.3] (lb/[ft.sup.3]);
[C.sub.ps] is the soil heat capacity, J/kg x K (Btu/lb x [degrees]F); and
[K.sub.s] is the soil conductivity, W/m x K (Btu/hr x ft x [degrees]F).
[R.sub.1], [R.sub.2], [R.sub.3], and [R.sub.4] are the heat conductance resistances between cell (m,n) and the surrounding cells; they are all calculated in a similar manner. However, the resistance R5 between the fluid and the (m,n) cell node is calculated so that it is equal to the resistance between the fluid and one-fourth of the outside area of the tube. The resistances are adjusted to account for convective resistance inside the tube and the conductive resistance of the tube. The overall conductance is calculated by inverting the sum of the convective resistance, calculated with the Dittus and Boelter correlation (1930) and the conductive resistance of the tube.
Initial conditions and lower boundary conditions are set with the Kusuda and Achenbach (1965) model, which specifies temperature as a function of time and depth. The initial temperature profile parameters (deep ground temperature and annual surface temperature swing) for this experimental validation were curve-fit from one year of meteorological data measured at a location about 190 km (120 miles) away from the experimental site; this initialization could introduce some error. The inside basement wall and basement floor boundaries are convective, exchanging heat with the basement, while the house air temperature is assumed be held at a constant value. The vertical boundaries in the soil portion of the domain are assumed adiabatic--on the left-hand side, this is due to symmetry; on the right-hand side, the size of the domain was set so as to have negligible influence by the right-hand boundary.
The fluid temperature inside the FHX tubes is treated as a time-dependent inside boundary condition for the conduction problem. The fluid temperature used in the 2D cross-section of the FHX tubing is the average fluid temperature along the length of the tubing. The model assumes that there is no heat transfer in the third dimension so that the soil temperature will not change in the third dimension. However, the fluid temperature is changing along the length of the tubing. Therefore, the FHX is treated as a soil-fluid heat exchanger in the soil domain, and an NTU method is implemented, as shown in Equations 6-12:
[C.sub.min] = [m.sub.f] [C.sub.pf], (6)
[C.sub.min] / [C.sub.max] = 0 [C.sub.max] [right arrow] [infinity], (7)
NTU = UA/[C.sub.min], (8)
[epsilon] = 1 - [e.sup.-NTU], (9)
[Q.sub.max] = [C.sub.min] ([T.sub.i] - [T.sub.pw]), (10)
[Q.sub.flu] = [epsilon] [Q.sub.max], (11)
[Q.sub.flu] = UA ([T.sub.f] - [T.sub.pw]), (12)
[m.sub.f] is the fluid mass flow rate, kg/s (lb/s);
[C.sub.pf] is the fluid heat capacity, J/kg x K (Btu/lb x [degrees]F);
[T.sub.f] is the fluid temperature, [degrees]C ([degrees]F);
[T.sub.pw] is the tubing wall temperature, [degrees]C ([degrees]F);
[T.sub.i] is the inlet fluid temperature, [degrees]C ([degrees]F); and
[Q.sub.flu] is the heat transfer through the fluid to the tubing wall, W (Btu/hr).
In Equation 7, [C.sub.max] approaches infinity based on the assumption that the heat transfer between the soil and fluid will not change the soil temperature in the third dimension. For Equations 6 to 9, the fluid-soil heat exchanger efficiency can be calculated based on the fluid mass flow rate and heat capacity and U, the overall conductance through the fluid to the one-quarter tube outside wall. From Equations 10 and 11, the average fluid temperature along the length of the tube can be calculated from previous time step inlet fluid temperature [T.sub.i] and tube wall temperature [T.sub.pw].
[FIGURE 6 OMITTED]
This approach for treating tube heat transfer was validated against an analytical line source solution. The grid size and the extent of the soil domain were chosen to give both grid independence and domain size independence.
When validating the model, without tube heat transfer, against experimental measurements of undisturbed ground temperature, it became apparent that freezing and melting of moisture in the soil can be important for colder climates. Therefore, freezing and melting of water in the soil is also considered. The effective heat capacity method (Lamberg et al. 2004) is utilized; this method artificially adjusts the volumetric specific heat of the soil in such a way that as it transitions from water in liquid form to water in solid form, the total energy reduction is the same as in the actual freezing process. However, it necessarily accomplishes this over a range of 0.5[degrees]C (0.9[degrees]F) rather than it nearly all occurring at 0[degrees]C (32[degrees]F).
The volumetric heat capacity of the soil is calculated (Niu and Yang 2006) based on soil type and volumetric water fraction for both liquid and ice conditions. Then, the energy change due to freezing or melting is assumed to occur between 0[degrees]C (32[degrees]C) and -0.5[degrees]C (31.1 [degrees]F), as shown in Figure 6. The values shown in Figure 6 are computed for clay loam soil containing 30% water by volume, or 60% of the saturation level, as used to compute the results shown in the experimental validation.
Even with the above approach, several phenomena that may be important are not modeled: saturated and unsaturated moisture transport, which directly affects the conduction heat transfer, and, for northern climates, snow accumulation. snow accumulation reduces the surface solar absorptivity and also adds an insulating layer.
A low-energy research house with an FHX in Oak Ridge, Tennessee, was chosen for validation of the numerical model. The selected house is one of four houses built in 2009 for a research project undertaken by Oak Ridge National Laboratory (ORNL) and several partners, including the U.S. Department of Energy, the Tennessee Valley Authority (TVA), and several industry partners. The house demonstrates one of four strategies implemented in the four houses, which are about 55%-60% more efficient than traditional new construction. The house is heavily instrumented (with more than 250 sensors) and has been monitored to assess its performance since construction was completed in 2009. The details of the house's specifications can be found in Miller et al. (2010).
The house, called the structural insulated panels (SIP) House, has 343.7 [m.sup.2] (3,700 [ft.sup.2]) of conditioned floor area, a cathedral ceiling, and a walk-out basement. The house has high levels of insulation (e.g., R-35 attic and R-21 exterior walls), a weather-resistive barrier, and low air leakage. The foundation wall is a 25.4-cm (10-in.) concrete wall with exterior 6 cm (2.375 in.) fiberglass drainage insulation board. As this house is unoccupied during the research, human impact on energy use is simulated to match the national average, with showers, lights, ovens, washers, and other energy-consuming equipment turned on and off on a schedule. Simulating occupancy eliminates a major source of uncertainty in whole-house research projects of this type. The house heating and cooling are provided by a relatively small 7.0-kW (2-ton) GSHP unit, which is adequate because of the house's energy-efficient features.
In designing the FHX, the heat exchanger run was laid out over the house plan to see whether the construction excavation and utility trench would be sufficient to provide the required length of heat exchanger pipe or whether additional conventional horizontal loops would be needed. Figure 7 shows the conceptual layout of the house with the designed FHX loop. Three parallel loops of 3/4"-diameter high-density polyethylene (HDPE) pipe--headered together in the basement--were placed in the foundation excavation overcut and in the runouts for the supply water and the septic field. The depth from the ground surface to the bottom of the foundation excavation is about 2.1-2.4 m (7-8 ft), and the distance from the excavation wall to the foundation wall is about 0.9-1.2 m (3-4 ft). The trenching itself does not make a continuous loop around the house, so each excavation contains six pipes: the runout and return for each of the three parallel loops. The layout of the FHX loops for the house includes additional trenches for the added length needed to support the home's heating and cooling loads based on preliminary calculations. Therefore, an additional trench was excavated and tubing was installed. This includes a feature labeled as "rain garden" in Figure 7. This is a low-lying portion of the property, and it could hold standing water under conditions of heavy rainfall. Nevertheless, all of the additional trenching was modeled as an HGHX. The total length of foun dation excavation and trenches for the SIP house is about 91.4 m (300 ft), which corresponds to three circuits (six pipes) in parallel for 548.6 m (1800 feet) total.
[FIGURE 7 OMITTED]
During the first stage of experiments (December 2009 through November 2010), the house was served by a two-stage, 7.0-kW (2-ton) water-to-air heat pump (WAHP) unit for space conditioning and a specially built 5.3-kW (1.5-ton) water-to-water heat pump (WWHP) unit for domestic water heating. Both heat pumps were connected to a common FHX in the house. The WAHP unit's rated coefficient of performance (COP) (or energy efficiency ratio [EER]) under full-load and part-load conditions is 5.4 (18.5) and 7.6 (25.9), respectively, and electric heating elements are provided for emergency use if needed. Both the WAHP and WWHP contain multiple thermal wells for water and water/brine temperature measurements. In November 2010, the two heat pumps were replaced by an integrated heat pump (IHP) unit that provides space heating/cooling and water heating. It also has multiple thermal wells for temperature measurements.
ORNL has instrumented the FHX and heat pumps and collects data on water inlet and outlet temperatures, pipe surface temperatures at various points, soil temperatures both within the trenches and at undisturbed locations, heat flux across the foundation walls, and other variables of interest. There are approximately 70 thermistors installed for temperature measurements at various points (see Figure 7), and the data has been measured at 15-min intervals (with some data measured at 1-min intervals when the unit is running) since November 2010 for performance evaluation and model validation. Along with the data measurements on the FHX and WWHP/WAHP, an on-site weather station measures dry-bulb temperature, relative humidity, solar radiation, precipitation, and wind speed and direction at 1-s intervals. Before November 2010, the data were taken from the WWHP/WAHP unit; after this point, the data were collected from the integrated unit.
Before the construction excavation and utility trench were backfilled, the soil thermal conductivities were measured using a portable device at five spots in the excavation (shown as the large blue dots in Figure 7): at the north- and west-facing walls, in two utility trenches, and in the rain garden. In each spot, six measurements were performed: three times on the bottom of the trench/excavation and 0.31, 0.61, and 0.92 m (1, 2, and 3 ft) from the bottom of trench/excavation. Measurement results are shown in Table 1. As illustrated, the average values in the bottom of trench/excavation vary from 0.35 to 1.56 W/(m x K) (0.2 to 0.9 Btu/(hr x ft x [degrees]F)), and the average values in trench/excavation walls vary from 1.0 to 1.56 W/(m x K) (0.6 to 0.9 Btu/(hr x ft x [degrees]F)). For this article, an average of all the values of 1.17 W/(m x K) (0.68 Btu/(hr x ft x [degrees]F)) was selected for the thermal conductivity. This value is close to a value of 0.90 W/m (m x K) (0.52 Btu/(hr x ft x [degrees]F)) determined via the model of Lu et al. (2007) using a USDA soil survey data from Tennessee (Natural Resources Conservation Service 2011).
Validation results and discussion
The simulation of the SIP house FHX systems consists of the FHX model, as well as an HGHX model that is similar to the FHX model but without the basement interaction. The HGHX model represents the length of pipe placed in trenches not adjacent to the house foundation, such as the "conventional earth" and "rain garden" from Figure 7. The model simulates the entire ground heat exchanger loop by connecting an HGHX model in series with an FHX model. The fluid leaving the heat pump first enters the HGHX before entering the FHX; the exiting fluid temperature of the FHX model is then used as the heat pump entering fluid temperature (EFT) for the next time step. In addition to the measured ground thermal properties and weather data, inputs to the FHX model include the EFT, which is taken from the experimental measurement at the heat pump exit (equivalently, the FHX inlet), as well as experimentally measured flow rate. The FHX model then outputs the average fluid temperature in the FHX and the average pipe wall temperature, as well as the soil temperature at locations both near to and far a field from the FHX piping. The values of the model parameters used for the validation are summarized in Table 2. Most of these parameters are experimentally measured, except for the volumetric heat capacity of the soil, basement wall, and insulation. The soil volumetric heat capacity is calculated for a clay loam soil with 30% water by volume using the effective heat capacity method (Lamberg et al. 2004). The experimental house foundation walls and basement floor are made of concrete; since the thermal properties of the concrete were not measured, typical thermal conductivity, specific heat, and density values were chosen from within the range of values tabulated by ASHRAE (1997). Similarly, typical values for the fiberglass floor and wall insulation were taken from Incropera and Dewitt (1996).
The depths and distances from the basement wall of the FHX tubes are based on actual site measurements. A 3D model was generated for recording accurate dimensions for the FHX tubes and basement wall by using software that captures several photos taken from the experiment site. The depth and distance from the basement wall of the six pipes was measured every 10 ft (3 m) along the north and west walls from the 3D model, and average values were taken as inputs for the FHX model. The locations of each of the six FHX pipes are given in Table 3.
The validation of the FHX model was done in several steps. First, the undisturbed ground temperature was analyzed by comparing the ground temperature response of the model away from the foundation in response to only the outdoor weather conditions. For this test, the foundation was treated as adiabatic, and no heating or cooling loads were imposed on the FHX. In the second step, the actual behavior of the FHX model under load was checked by exploring the heat pump entering fluid and pipe wall temperatures, as well as the heat flux at the basement wall. Finally, some exploration was done on various parameters in the FHX model in an attempt to identify and partially quantify some of the reasons for differences between the model and the experimental data.
Figures 8,9, and 10 show the undisturbed ground temperature at 0.31, 0.92, and 1.52 m (1, 3, and 5 ft) below the earth surface, respectively. The first of these three measurements is taken on the east side of the building, while the other two are taken on the west side. Overall, the plots show fairly good agreement in ground temperature, with root mean square errors (RMSEs) of 2.16[degrees]C (3.89[degrees]F) at 0.31 m (1 ft) depth, 0.91[degrees]C (1.64[degrees]F) at 0.91 m (3 ft) depth, and 1.61 [degrees]C (2.90[degrees]F) at 1.52 m (5 ft) depth. Additionally, the plots appear to show poorer agreement during the first 90 days or so. There are two possible explanations for the poorer agreement during the first 90 days--first, the initialization procedure, which relies on weather data from a station 190 km (120 miles) away, and second, the ET model which uses a constant reference condition, 12 cm (4.7 in.) tall green grass throughout the year. In the winter, though, the grass will likely be dormant.
[FIGURE 8 OMITTED]
To explore the effects of ET, the results of the base simulation were compared to a simulation with no ET for the entire year and one with no ET for the first three months. The resulting undisturbed ground temperatures 0.31 m (1 ft) below the surface are shown in Figure 11. With ET modeled for the entire year, the modeled undisturbed ground temperature is somewhat lower than experimentally measured. However, without the effect of ET, the temperatures match very closely during the first three months. Since the grass will be dormant during this period, there will be very little loss of water--and resulting heat loss from the surface--during the winter months. It is readily apparent, though, that the effect of ET is quite important during the remainder of the year, as model-predicted temperatures approach 55[degrees]C (130[degrees]F) in the summer without it. The behavior measured 0.9 m (3 ft) below the surface is quite similar to the model results without ET during the first three months, as depicted in Figure 11. This suggests that the model could be improved by incorporating dormancy in the ET model.
[FIGURE 9 OMITTED]
Some phase lag between the experimental results and the model can also be observed, particularly at the 1.52 m (5 ft) depth. This may be due to differences between the actual time-varying specific heat and density caused by changes in moisture content and the assumed fixed values. As the vegetation on the surface grows during the spring and summer months, moisture is brought up from the ground to the surface and transpired away into the atmosphere. The result is a ground that is significantly drier than in the winter months. To demonstrate this, Figure 12 shows the undisturbed ground temperature 1.52 m (5 ft) below the surface for three different moisture contents: completely dry, completely saturated, and 60% saturated or 30% moisture content by volume (the assumption used for initial determination of ground properties). As can be seen from Figure 12, the temperature during the summer months--which was previously where most of the difference occurred--is matched quite well by a completely dry soil. Similarly, the 60% of saturated moisture content estimate appears to be slightly high for the first three months, as the experimental value falls between this curve and completely dry, but it matches very well for the last three months. For these three cases, the thermal conductivity is constant at 1.17 W/m-K (0.68 Btu/hr x ft x [degrees]F), with the thermal diffusivity varying from 3.53 x [10.sup.-7] [m.sup.2]/s (3.79 x [10.sup.-6] [ft.sup.2]/s) (100% water content) to 4.72 x [10.sup.-7] [m.sup.2]/s (5.08 x [10.sup.-6] [ft.sup.2]/s) (60% water content) to 9.55 x [10.sup.-7] [m.sup.2]/s (1.03 x [10.sup.-5] [ft.sup.2]/s) (0% water content). This result suggests that varying the thermal properties of the soil over the course of the year by accounting, even in a simple piecewise fashion, for moisture transport would increase the accuracy of the model.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The EFT to the heat pump, which is assumed to be the same as the temperature exiting the FHX, was validated against a full year's experimental data. Figure 13 plots the heat pump EFT, averaged over each day, for both the model and the experiment. There are discontinuities in both datasets; for the experiment, this represents days on which the equipment was off, either due to inactivity/system maintenance, or on which the experimental data is missing (such as around days 10,275, and 290), or for the replacement of the heat pump (days 333-338 and 342-347). For the simulation, the temperature is reported at every time step; this temperature is defined as pipe wall temperature on times in which the heat pump is off. The daily average heat exchanger pipe wall temperature, plotted in Figure 14, does not show such discontinuities because the values can be reported at every time step or measurement interval without regard to the on/off state of the heat pump. The average pipe wall temperature is the average of the six individual pipe wall temperatures, with the individual temperatures being averaged over the total length of the pipe.
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
Overall, the experiment and simulation match well, with an overall RMSE in the heat pump EFT for the year of 0.90[degrees]C (1.62[degrees]F). The RMSE in the pipe wall temperature also matches fairly well, with an RMSE of 1.12[degrees]C (2.02[degrees]F). The largest differences occur on days 60-150 (February-May), as well as days 270-330 (October-November). These are the shoulder seasons, when the heat pump could be expected to run less because the outdoor condition is close to the thermostat set-point. In Figure 14, the large difference beginning at day 333 accompanies the switching of the heat pump equipment, during which time no flow rate or heat pump EFT/exiting fluid temperature (ExFT) data were recorded.
[FIGURE 14 OMITTED]
[FIGURE 15 OMITTED]
Measured temperature is averaged for each day, weighted by the flow rate at each measurement for a reason that is common to most, if not all, ground heat exchanger research. The temperature sensors measuring entering and exiting fluid temperature are not in the ground, but rather in the equipment closet in the house. When the heat pump and circulating pump are off, the fluid's temperature in the equipment closet tends to drift toward the air temperature in the equipment closet. Therefore, simple measurements that average the temperature over time without regard to equipment operation have increasing error as the equipment run time fraction decreases. Even when averages are weighted by the flow rate, there is a slightly increasing error in the model as the equipment run time fraction decreases. The temperature of the fluid inside the piping, which is inside the building, really does tend to drift toward the building air temperature. At the beginning of each equipment on-cycle, the temperature is influenced by the building air temperature. The model does not account for this, so the resulting small temperature differences at the beginning of each on-cycle cause some small errors. Figure 15 shows the fraction of time that the heat pump is operating each day. As can be seen, the largest errors in the model results, on days 60-150 and 270-330, correspond to the lowest equipment run times.
Figure 16 shows ground temperatures measured near the FHX tubing on the north side of the house. The FHX model assumes that ground above the FHX is exposed to solar radiation without any shading. Obviously, this is an approximation; as the days and seasons progress, the height of the building will cause parts of the ground above the FHX to become shaded at different times. Noting that the model results for this disturbed ground temperature seemed to show a systematic bias, the influence of solar radiation was checked by running the model with no solar radiation. As Figure 16 demonstrates, the experimental measurement falls between the full-radiation and zero-radiation cases during the summer months. Therefore, taking into account some fractional shading of the ground, likely varying throughout the year, could make the FHX model more accurate. It is noticeable, though, that between roughly days 0 and 90, as well as between days 300 and 365, the experimentally measured soil temperature rises above either model's prediction. This is due to an overprediction of the ET heat loss from the surface, as was shown in Figure 11.
[FIGURE 16 OMITTED]
[FIGURE 17 OMITTED]
[FIGURE 18 OMITTED]
The heat flux at the basement wall 0.31 m (1 ft) below the surface on the north side of the building (point 6 in Figure 7) is shown in Figure 17. In addition to the measured data and simulation results, the figure also shows the results of a simulation when there is no solar radiation. since the regular model results have no shading effects included, the true behavior of the system will lie somewhere between these two curves. As Figure 17 demonstrates, the model results with and without solar radiation bracket the experimental measurement, with the exception of the first two months or so and the last month of data. since the initial conditions of the model are based on weather data from a site some distance from the actual experiment, and because the soil was disturbed during the installation of the FHX, it is expected that the initial soil temperature profile is not exact. Thus, the heat flux through the basement wall during the first portion of the simulation is slightly different in the simulation than in the experiment. After the initialization effects disappear (around 60 days or so), the model curves follow the experimental data fairly well. At the end of the simulated year, the model results are approaching the heat flux values measured at the facility. It is expected that the analysis of a second year of experimental data and simulation results will show a closer match in winter than for the first year due to a lack of initialization effects.
Results shown so far are all based on daily averages. so, how well does the model do in predicting fluid temperatures entering the heat pump over a day? Experimental data were measured on 15-min or 1-min intervals; the 1-min interval data were averaged over 15-min periods. The simulation results in this article were run with 2.5-min time steps. Figure 18 shows a comparison of the model results and FHX exiting fluid temperature for a single day in August. The differences here might be thought of as two instances of the same type of error. The most obvious differences are due to the dynamic error at the beginning of the on-cycles preceded by the longest off-cycles; in particular, the on-cycle beginning near 8 a.m. shows temperature errors on the order of 2[degrees]C (4[degrees]F). As discussed earlier, the temperature of the fluid in tubing inside the house tends to drift toward the house temperature. In mid-August, the house is considerably cooler than the FHX fluid temperature, and hence, the actual measured temperature at the beginning of the on-cycle is somewhat lower than the model prediction. The three intervals in the afternoon (around 13, 18, and 22 h) are shorter-term instances of this same effect, as the heat pump shuts off for about 10 min preceding each of these drops. These are the only three occasions from the time that the heat pump turns on at 10 a.m. that it shuts off until the last time step of the day. While it is possible that this might be improved by dividing the fluid into volumes that behave differently during off-cycles, it seems unlikely to be worthwhile at present.
This work has presented an alternative type of ground heat exchanger, the FHX. The FHX can reduce the costs of installing a ground heat exchanger when compared to installing conventional horizontal or vertical ground heat exchangers by utilizing existing excavation to place the heat exchanger pipes. A two-dimensional finite-volume numerical model of the FHX was developed and implemented, and this model has been validated against a full year of experimental data from a test house located near Oak Ridge, Tennessee. soil temperatures, heat pump EFTs, and heat exchanger pipe wall temperatures all matched well, with differences in daily average values on the order of 1[degrees]C (1.8[degrees]F). The following reasons for minor discrepancies between the model and the experimental results were found.
* The numerical model considers ET year-round, when, in reality, it will only be significant when the ground cover is not dormant. This might be improved by implementing an algorithm that would decide on growth rate or, at least, distinguish between weather conditions that cause the ground cover to grow and those that cause it to go dormant.
* The thermal properties of the soil are based on an initial assumption of the soil type and soil moisture content. The soil properties, particularly the moisture content and, consequently, the thermal mass of the soil will change throughout the seasons. While it is not clear that a full moisture transport model would give sufficient accuracy improvements to justify the significantly increased computational requirements, it might be possible to develop an intermediate-level model that roughly predicts the changes in moisture level, so as to allow the moisture-dependent thermal properties to be better estimated.
* The FHX was assumed to be completely unshaded from solar radiation in the numerical model. Incorporating a shading model that accounted for the projection of the building shadow on the surrounding ground should improve the accuracy of the model.
In addition, the moderate climate of the test house did not allow for a thorough testing of the soil freezing/thawing model, so additional validation of this portion is recommended. Likewise, it is possible that a snow cover model may be important for colder climates; this remains a topic for future investigation.
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Lu Xing, (1) * James R. Cullin, (1) Jeffrey D. Spitler, (1) Piljae Im, (2) and Daniel E. Fisher (1)
(1) Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74075, USA
(2) Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
* Corresponding author e-mail: firstname.lastname@example.org
Received March 7, 2011; accepted July 7, 2011
Lu Xing is Research Assistant. James R. Cullin Student Member ASHRAE, is Research Assistant. Jeffrey D. Spitler, PhD, PE, Fellow ASHRAE, is Regents Professor and C. M. Professor. Piljae Im, PhD, Associate Member ASHRAE, is R&D staff. Daniel E. Fisher, PhD, PE, Fellow ASHRAE, is E. Fisher Professor.
Table 1. Soil thermal conductivity, W/(m-K) (Btu/(hr-ft-[degrees]F)). Measured spot 1. North wall 2. Utility trench 3. West wall Bottom, average 0.76 (0.44) 0.40 (0.23) 1.11 (0.64) Wall, average 1.70 (0.98) 1.49 (0.86) 1.16 (0.67) Measured spot 4. Utility trench 5. Rain garden Bottom, average 1.56 (0.90) 1.00 (0.58) Wall, average 1.52 (0.88) 1.06 (0.61) Table 2. Model parameters. Model parameters Values units Incident solar radiation Hourly boundary W/[m.sup.2] (Btu/ condition hrx[ft.sup.2] Air temperature [degrees]C ([degrees]F) Relative humidity % Wind speed m/s (ft/s) Mass flow rate L/s (gallons/minute) Basement air temperature [degrees]C ([degrees]F) Pipe EFT [degrees]C ([degrees]F) Length of each FHX tube 36.80 (120.73) m (ft) Length of each HGHX tube 54.60 (179.13) m (ft) Tube inside diameter 21.84 (0.86) mm (in.) Tube outside diameter 26.67 (1.05) mm (in.) Basement wall depth 2.54 (8.33) m (ft) Basement wall height 0.41 (1.35) m (ft) Basement wall thickness 0.30 (12.00) m (in.) Basement floor thickness 0.25 (10.00) m (in.) Fiber glass thickness 0.06 (2.38) m (in.) Fluid (water mixed with 20% propylene Soil thermal conductivity 1.17(0.68) W/mxK (Btu/hrxft x[degrees]F) Soil volumetric heat capacity 2.48 (36.74) MJ/m3xK(Btu/ft3 x[degrees]F) Basement wall and floor conductivity 1.70 (0.99) W/m.x (Btu/hrxft x[degrees]F) Basement wall volumetric heat 2.06 (30.52) MJ/[m.sup.3]xK Btu/[ft.sup.3] x[degrees]F) Fiber glass thermal conductivity 0.04 (0.02) W/mxK (Btu/hrxft x[degrees]F) Table 3. FHX pipe location. Distance from Pipe no. Depth, m (ft) basement wall, m (ft) 1 2.2(7.2) 0.7(2.3) 2 2.2(7.2) 1.0(3.3) 3 2.2(7.2) 1.2(3.9) 4 1.9(6.2) 1.4(4.6) 5 1.7(5.6) 1.4(4.6) 6 1.4(4.6) 1.4(4.6)
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|Author:||Xing, Lu; Cullin, James R.; Spitler, Jeffrey D.; Im, Piljae; Fisher, Daniel E.|
|Publication:||HVAC & R Research|
|Date:||Nov 1, 2011|
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