Numerical comparison between two advanced HGHEs

Transcription

1 Numerical comparison between two advanced HGHEs... Michele Bottarelli 1 * and Vittorio Di Federico 2 1 Dipartimento di Architettura, Università di Ferrara, Italy; 2 DICAM, Università di Bologna, Italy... Abstract Several solutions are currently being tested to improve the thermal efficiency of ground heat exchangers (GHEs) employed in geothermal closed loops. For shallow exchangers, the main effort is towards maximizing the surface available for heat exchange, while reducing the interference among exchangers; popular solutions towards this end are the slinky coil and the radiator shape. Recently, the flat panel has been proposed as a novel alternative to horizontal exchangers. In this study, the performance and thermal impact of the radiator and flat panel installations are compared by solving the transient flow and heat transport problem within the surrounding ground via a numerical model. Adopting the same computational conditions, the two installations yield different resulting domain thermal fields. The flat panel shows a higher capability to affect larger volumes of surrounding ground, so the soil temperatures reach values less extreme than in the radiator case. Since horizontal GHE temperatures remain 2 38 warmer in winter time, a higher coefficient of performance is expected for the flat panel. *Corresponding author: michele.bottarelli@unife.it Keywords: ground heat exchangers; radiator; flat panel; numerical comparison Received 27 October 2011; revised 15 December 2011; accepted 19 December INTRODUCTION Innovative solutions are being introduced to increase the efficiency of ground source heat pumps (GSHPs). Advanced generations of compressors and electronic controllers are raising the energy performance of heat pumps (HPs), and new shapes for ground heat exchangers (GHEs) are being tested to improve their power output per unit length. Since the performance control of GSHPs is tightly linked to the GHE, the best opportunity to improve global efficiency is to improve the heat transfer efficiency in the soil, adopting more advanced shapes and devices. Given the lower energy output of shallow horizontal GHEs (HGHEs), there is a great potential to improve their efficiency through the adoption of different geometries such as slinky coil, radiator or spiral, employing high-density polyethylene for the hull. The aim is always to increase the surface available for heat exchange, reducing at the same time the interference among exchangers. Numerical and experimental evidence concerning the energetic performance of shallow horizontal exchangers is available in the scientific literature. Most of it concerns tests of limited duration, so that performances lower than those reported are expected for longer operation times. Fujii et al. [1] reported on field tests conducted on a shallow slinky coil buried within a trench at the Ito Campus of Kyushu University, Japan; both the edgeways and planar arrangements were tested. Each trench was 72 m long and 1.5 m deep; 6.9 m of the tube was installed for each metre of the trench. Each spatial arrangement was tested twice: a short test was performed from 15 November to 2 December 2008 and a longer one from 19 January to 12 March The edgeways arrangement showed a lower performance (235%) than the planar one; the latter had an average heat exchange rate of 40 W per trench metre in the short test and 26 W/m in the long one, i.e. a 39% decrease. A somewhat similar field test was performed at Drayton St Leonard in Oxfordshire, UK [2]. There, slinky coils were buried in four parallel trenches 80 m long, and 1.2 m deep. The temperature was monitored from November to December 2009 at the HGHE inlet and outlet. The monitored temperatures decreased significantly with time, although without changes in the temperature difference. A group of thermocouples disposed in a vertical setting 2 m from a trench showed that after 55 days, the thermal plume reached a distance of 0.9 m from the HGHE. Applying a commercial CFD software, the energy performance was evaluated to decrease from 90 to 30 W per trench metre after 140 operation hours, i.e. a heat transfer reduction.60%. Recently, a novel shape of HGHE, consisting of a flat panel, has been analysed by means of a numerical model [3, 4]; its International Journal of Low-Carbon Technologies 2012, 7, # The Author Published by Oxford University Press. All rights reserved. For Permissions, please journals.permissions@oup.com doi: /ijlct/ctr050 Advance Access Publication 8 February

2 M. Bottarelli and V. Di Federico field testing is under way at the Department of Architecture, University of Ferrara. In this study, the global performance of the flat panel is compared with that of a radiator, representing another innovative option to enhance the thermal exchange. The goal of the analysis is to understand the differences between the two geometries in terms of energy performance and thermal plume in the surrounding soil, when operating the two exchangers under identical conditions for a whole year in a heating and cooling mode. The plan of the study is as follows. First, the geometry of the flow and transport domain is described, and hypotheses adopted for domain properties listed. Secondly, the initial and boundary conditions adopted are discussed, highlighting the need for time-variable boundary conditions mimicking seasonal and daily temperature oscillations at the surface. Then, results from a year-long simulation of the exchanger-ground system are reported and discussed. A set of conclusions closes the paper. 2 METHODOLOGY In the following, two HGHEs installations are examined, consisting, respectively, of a radiator (R) and a flat panel (FP) installed horizontally at a shallow depth below the water table, and coupled with an ideal HP for building heating and cooling. The analysis is focused on determining the energy performance and thermal plume of the two installations; to do so, the unsteady-state three-dimensional (3D) numerical finite element code FEFLOW w was implemented and run. FEFLOW w allows us to determine the groundwater flow and heat transfer in saturated/unsaturated porous media, taking into account both conductive and convective heat transport [5]. 2.1 Model domains and material properties The model domain is described in the following for the two HGHEs simulated: flat panel and radiator. Both exchangers are supposed to be embedded in a trench 5.50 m long, 0.30 m wide and 2.49 m deep. The cross-section of the flat panel is represented by a hollow cm and the radiator by 20 square pipes, each with a 2 2 cm cross-section and 5 m long. The square pipes are spaced out by 2 cm, so the whole surface available for heat transfer is the same in both cases. A 0.14 m bentonite backfill layer is positioned at the trench bottom, followed by the exchangers and by an identical bentonite layer at the top. Thus, the HGHEs are between 1.55 and 2.35 m from the soil surface, taken to be horizontal in the entire domain. The space between the exchangers and the trench wall is again filled with bentonite. The presence of the pipe wall is neglected, under the rationale that its thermal resistance is negligible compared with that of the soil. The groundwater level is assumed to be 1.50 m from the surface, so that the exchangers lie entirely within the saturated zone, a situation relatively common in settings in the Pianura Padana (Italy). To investigate the impact of overall domain size on the numerical results, two computational domains having respective overall dimensions of and m were initially selected; preliminary long-term numerical simulations demonstrated that the adoption of the larger domain did not lead to significant changes in the results, while drastically increasing the computational times. The smaller domain of m was thus chosen for all subsequent simulations. Such a choice is supported by evaluating the order of magnitude of the thermal damping depth, assuming a thermal stress exists only at the soil surface. In this case, the damping depth is given by the simplified expression: rffiffiffiffiffi 2a D ¼ v where a is the soil thermal diffusivity, and v ¼ 2p/T, in which T is set equal to the year time period. Adopting the soil thermal properties reported in Table 1, the damping depth can be estimated in 2.4 m. The flat panel subdomain (Figure 1) is divided into 23 horizontal layers (24 slices); all of them have a 30 cm thickness, except the layers representing the bentonite backfilled HGHE, the layers immediately over and below these and the HGHE, which have thicknesses of 21/14/20/20/20/20/14/21 cm, respectively, for the layers from 5th to 12th. The numerical mesh is finer within and around the installation trench, to represent more accurately the difference in the hydraulic and thermal properties of the exchanger, the backfill and the surrounding soil. The computational mesh has more than nodes and elements, whose dimensions vary from 0.05 cm 2 for those representing the exchanger, to cm 2 for the outer ones. The radiator subdomain (Figure 1) is divided into 59 horizontal layers (60 slices). Like in the previous case, the natural soil is sliced in layers having 30 cm thickness, at the top and bottom of the HGHE, there are backfilling layers 14 cm high, and over and below them layers 21 cm thick. Hence, 39 layers with a 2 cm thickness define the radiator, alternating pipes to backfill, respectively, from the 7th to 45th layer. Here, the mesh has more than nodes and elements, whose dimensions are similar to the former case. The hydraulic and thermal properties attributed to the different materials constituting the domains (fluid, backfill and soils) are summarized in Tables 1 and 2. All properties adopted are within the ranges usually cited in the literature, [6 8], and are typical for water and sedimentary rocks. Here, the soil was considered to be homogeneous, since the heterogeneity effect remains marginal in horizontal and shallow GHEs [8, 9]. ð1þ 76 International Journal of Low-Carbon Technologies 2012, 7, 75 81

3 Numerical comparison between two advanced HGHEs Figure 1. Model domain (A), vertical sketch for both cases (B) and sketch of the GSHP (C). Table 1. Thermal properties. Material Volumetric capacity (MJ/m 3 K) Heat conductivity (W/m K) Longitudinal dispersivity, solid (m) Transversal dispersivity, solid (m) Liquid Solid Liquid Solid Water Backfill Soil Table 2. Hydraulic properties. Material Hydraulic conductivity (m/s) Storativity Porosity Water Backfill Soil Neglecting the presence of the panel wall allows us to attribute the hydraulic and thermal properties of water to the mesh elements representing the pipe, with a porosity equal to unity. This approach is in variance with other modelling efforts [7, 9], where the body of the exchanger is considered as a boundary condition for the mesh, using the law valid for an ideal heat exchanger. The feasibility of this scheme was checked analysing the model equations as reported in [5], and solving a simplified test case for the conduction problem in steady state, consistently with the analytical solutions reported in [10]. 2.2 Boundary and initial conditions The boundary conditions are set to represent natural groundwater flow and heat exchange among soil, air and HGHE in a real-world situation for both the flat panel and radiator cases. To reproduce local groundwater flow in the north south direction (parallel to the HGHE, which amounts to the least Figure 2. Surface soil temperature for the preparatory model run. favourable condition), constant piezometric head boundary conditions of and m are imposed, respectively, at the northern and southern boundaries; the natural hydraulic gradient is thus set to 2. Thermal boundary conditions are specified at the soil surface in the form of given heat flux density, and at the HGHE inlet as assigned flow rate with specified temperature. The soil heat flux density G is usually defined within the context of the surface energy balance as: R n G ¼ LE þ H where R n is the net radiation and LE and H the latent and sensible heat flux density. Since not enough data were available to provide a meaningful estimate of the surface energy balance, we obtained G as an indirect solution from a preparatory run of the model without any HGHE activity; in this run, a time series obtained from air temperature is imposed at the soil surface (Figure 2). The latter time series is conceptualized as a yearly sinusoidal trend, representing the seasonal temperature ð2þ International Journal of Low-Carbon Technologies 2012, 7,

4 M. Bottarelli and V. Di Federico variation for daily maximum and minimum air temperature. Further, a smaller sinusoidal oscillation is superimposed to the previous one to represent the hourly temperature variation. Finally, a simplified link between air and soil surface temperature is considered by means of a constant coefficient, as presented in [3, 4]. We consider the resulting soil temperature to be related to the soil flux G in the former Equation (2). The resulting degree-days are almost 2600 in a heating mode and almost 400 in a cooling mode. The preparatory model was run for a whole year, and the heat flux density was calculated at a group of fixed observation points onto the soil surface. The resulting heat flux density time series shows values included in the interval +100 W/m 2 ; the corresponding cumulative energy balance oscillates between +20 kwh/m 2 per year (Figure 3). Similar data are reported in [11, 12], where it is specified that the surface soil heat flux typically represents 1 10% of the net solar radiation. To define an hourly energy requirement in heating and cooling, we apply the methodology reported in [4], where the energy requirements of a conceptualized building are linked to the outdoor air temperature time series, and the building is represented as a homogenous lumped system, whose internal energy variation occurs owing to the heat transfer through its shell. The GSHP operation hours are selected to represent typical working conditions at the residential scale: 5 a.m. 9 a.m. and 5 p.m. 10 p.m. from Monday to Friday, 7 a.m. 11 p.m. on weekends. The system is operated in a heating mode from 15 October to 30 April and in a cooling mode from 1 June to 30 September. In deriving the following relationship, the GSHP is taken to be able to reach the target temperature in 1 h, and afterwards the heat exchange is taken to happen in steady state. For simplicity, we assume that the heat is supplied only from the HGHE, and that the compressor works only to raise the energy to the requested plant temperature. This hypothesis, while simplifying the approach, overestimates the heat required at the HGHE, in proportion to the coefficient of performance (COP) for a given working temperature. Figure 3. Heat flux density and cumulative energy balance. Neglecting passive contributions, when the air-conditioning plant is turned off, the variation in time of the indoor air temperature can be estimated by means of an energy balance, influenced on the one hand by the changing outdoor air temperature and, on the other, by the building total mass. In turn, the latter is basically represented only by the roof, walls and floors, since the air contribution is absolutely marginal. Given (see the scheme in Figure 1) the building global equivalent transmittance (U), exchanging heat surface (S), volume (V), average density (r) and specific heat (c) (evaluated as weighted averages of the densities and specific heats of the individual building components) and ratio (r) between plenum over building volume, the energy balance can be written as [4]: r rv c dt ¼ U S ðtðtþ T air ðtþþ dt where T(t) and T air (t) are, respectively, the indoor temperature and the outdoor air temperature at time t. Assuming the outdoor air temperature to be independent from the heat exchange, the former Equation (3) can be easily integrated as: TðtÞ ¼T air ðtþþðt 0 T air ðtþþ e USðt t 0Þ=rrVc where T 0 is the indoor air temperature at times t 0. When the plant is switched on and a steady state is supposed, a constant target value T h/c (usually 208C in heating and 268C in cooling) can be assumed for the indoor temperature. For simplicity, we assume that the heating and cooling energy is the same as that requested at the closed loop, and that the HP compressor works only to raise it to the requested temperature. This hypothesis overestimates the required energy at the HGHE by a rate linked to the HP COP at the working temperature, but simplifies the flow rate appraisal in the closed loop. With reference to the scheme in Figure 1, the mass flow rate _m 56 per building unit volume provided by the GSHP can be calculated with the former approach as [4]: _m 56 ðtþ ¼ U S=V jtðtþ Tair ðtþj c w jdt 57 j where c w is the water specific heat and DT 57 the difference in temperature between the inflow and outflow water at the HP evaporator/condenser. To relate the mass flow rate only to the air temperature, we make the following assumptions. The difference in temperature DT 57 may be set to a fixed value, as usually done in practice. To do so within the FEFLOW simulations, a specific numerical loop was supplied directly from the FEFLOW s producer [13]; the value adopted for the temperature difference is equal to 38C. In this fashion, Equation (4) depends only on the building and air temperatures, and by the features of the building. These features have been defined by preliminary runs, setting the quantity U S/V to exclude overcooling in the ground; taking into account the lower performance of the radiator, the ð3þ ð4þ ð5þ 78 International Journal of Low-Carbon Technologies 2012, 7, 75 81

5 Numerical comparison between two advanced HGHEs resulting value of the former parameter is equal to 0.05 W/m 21 /K 21, and the maximum instantaneous flow rate is equal to 1.4 m 3 /day. As a consequence, all boundary conditions become dependent only upon the air temperature. 3 RESULTS The model was run for 365 days to obtain the annual behaviour for each exchanger, in terms of the time-varying temperature within the HGHE and the soil. The global results are reported in Table 3; since the energy requirement is invariant between the two cases, there is no difference in power. However, the power value reported in Table 3 represents the upper limit of the radiator s performance, since it barely allows the daily minimum temperature at its outlet not to drop,08c during 5 months of winter time; for the flat panel providing the same power output, the daily minimum temperature at the outlet is.08c, thus showing that the power output is potentially higher. The behaviour over time of water temperatures at the HGHE outflow (depth 1.95 m) and of soil temperatures at observation point 27 (depth of 0.6 m and distance of 4 m from the HGHE inlet) is illustrated for both cases in Figure 4, together with the temperature time series obtained at the equivalent point of the HGHE outlet in the absence of any HGHE activity ( preparatory model run, natural case). The temperature curves for both cases include Table 3. Results at the HGHEs. Season Degree-days (DD) Runtime (h/year) Global energy (kwh/year) Average specific power (W/m) Maximum specific power (W/m) Winter Summer also weekly oscillations due to higher energy requirements during the weekend, when the heating/cooling plant is more active. The difference between the minimum temperature at the flat panel and the radiator reaches 2 3 degrees in March (after 60 days), when the radiator achieves its minimum temperature of 08C. The maximum difference from the natural soil temperature amounts to 108C for the radiator, owing to its worse performance. At observation point 27, the temperature difference between results for the two installations is The flat panel installation produces consistently a less impacting thermal plume within the soil, under an identical energy performance. Figure 4 also shows that the temperature shifting induced in the soil during winter is substantially recovered within 60 days, when the closed loop is turned off. Thus, no permanent temperature alteration is expected to be induced in the ground for this kind of installation. In Figure 5, the previous results are presented in terms of maximum and minimum temperature for all cases, together with the daily circulated volume and maximum flow rate. The radiator shows a higher difference in temperature for outflow water, reaching almost 48 in winter, and a similar behaviour is shown in summer. The maximum instantaneous flow rate is reached at the end of January (1.4 m 3 /s), but the maximum daily volume is at the end of February, owing to a longer daily operating time. In Figure 6, the temperature profile is showed along the HGHEs for two time steps. At Day 60.88, the difference in temperature between the flat panel and radiator inlet is 1.38, while it is more than 1.48 at the outlet. At Day , the differences do not change significantly and remain To assess to a first approximation the reliability of the soil thermal field evaluated numerically, we compare it with the analytical solution for the transient 1D heat transfer problem in a homogeneous semi-infinite solid, initially at a constant temperature T i, which is then instantaneously changed to T s in the origin. The unsteady-state solution is rigorously derived in Figure 4. Temperature at the HGHEs outlet and at observation point 27 from 1 January to 31 December. Figure 5. Daily maximum and minimum temperatures at the HGHEs outlet, daily circulated volume and maximum flow rate from 1 January to 31 December. International Journal of Low-Carbon Technologies 2012, 7,

6 M. Bottarelli and V. Di Federico Figure 8. Flat panel s domain temperature at day of year. Figure 6. Temperature profile along the HGHEs for two time steps. Figure 9. Radiator s domain temperature at day of year. Figure 7. Comparison of 3D numerical and 1D analytical temperature profiles. [10] and also reported in [14]. In the latter reference, the temperature field T(x,t) is given by the expression: x Tðx; tþ ¼T i þðt s TÞerfc p 2 ffiffiffiffiffiffiffiffiffiffiffi ð6þ a t where x is the spatial coordinate, t the time, a the solid thermal diffusivity and erfc the complementary error function. In our analogy, x is taken to be the orthogonal distance from the surface, T i the initial average ground temperature far from the HGHE and T s the HGHE temperature at time t. Clearly, the analogy is not a perfect one, since (a) the heat transport is 3D; (b) the domain is finite, hence the semiinfinite approximation is not satisfied; (c) the heat exchangers have a given spatial extension and shape and are not located in the domain s origin; and (d) the analytical solution implies a homogeneous initial thermal field, with a time-invariant boundary condition in the origin, whereas the numerical model works with an initial soil thermal stratification, and boundary conditions changing over time. In Figure 7, transversal temperature profiles resulting from 3D numerical simulations and 1D analytical model are compared for both HGHE installations and two values of time (Days and 60.88) during the winter season (heating mode). The soil temperature resulting from 3D numerical simulations (continuous lines for Day 30.88, dashed lines for Day 60.88) is always larger than that pertaining to the 1D analogy (squares for Day 30.88, circles for Day 60.88), except very close to the surface; the largest deviation between the numerical results and the analytical model occurs 1 m far from the HGHE, where the temperature difference reaches 1 28; at larger distances from the HGHE, the margin between the two curves narrows down to a fraction of a degree. Taking into account the approximations introduced, the 1D analogy captures the overall temperature trend; the agreement between the two sets of results is deemed satisfactory, and the numerical solution is supported by the 1D analogy. Moreover, Figures 8 and 9 illustrate 3D reconstructions of isothermal lines for the longitudinal section A A at Day for the radiator and flat panel installations, showing the difference in temperature distribution in the two cases. For the radiator, the soil volume involved in heat exchange is smaller than that for the flat panel, making the exchanger cooler; for the flat panel, the heat exchange affects a larger domain, even altering the temperature at the soil surface. Finally, Figures 10 and 11 depict the isothermal lines for the transversal B B at two times already considered: Days and Here, the filling colour represents the ground temperature difference between the flat panel and radiator; darker colours indicate cooler ground, owing to the larger volume of the surrounding 80 International Journal of Low-Carbon Technologies 2012, 7, 75 81

7 Numerical comparison between two advanced HGHEs Figure 10. Isothermal lines at day of year for the radiator (dash) and flat panel (solid) (8C). linked only to the hourly air temperature. Our simulations resulted in a maximum specific power output around 40 W/m, which is very similar to that available from vertical installations. The resulting soil thermal field differed quite substantially between the two shapes; the flat panel showed a higher capability to affect larger volumes of the surrounding ground; as a consequence, the soil temperatures exhibited more limited oscillations than in the radiator case. Under identical boundary conditions, the radiator reached a minimum outlet water temperature 38C lower than that of the flat panel. Even if the exchanging surface is the same for the two HGHEs, the radiator has a disadvantage over the flat panel, linked to a lower exchange surface looking out directly on the ground, because half of the surface is closest to the nearby pipe; thus, the thermal resistance is higher than for the flat panel. Since the COP for the HP coupled to the HGHE depends on its outflow water temperature, the energy performance of the radiator is lower than that of the flat panel. Figure 11. Isothermal lines at day of year for radiator (dash) and flat panel (solid) (8C). soil involved. Even if the exchanging surface is the same for the two cases, only half of the radiator surface looks out directly on the ground, while the other half is facing the next surface pipe. As a consequence, the thermal resistance is higher for the radiator than for the flat panel. Inspection of Figures 8 11 shows that the fluctuation of the thermal field affects the bottom of the computational domain only to a limited extent, further checking the initial sizing for the domain. Actually, the highest heat exchange occurs at the surface, where the heat power can vary in the range kw, when compared with a kw variation of the maximum power of the heat exchangers. 4 CONCLUSIONS An analysis of heat transport in the ground induced by the operation of two different shallow HGHE belonging to the ground loop of a GSHP system has been presented. The study was conducted via the implementation of the unsteady-state 3D numerical finite element method FEFLOW w, modelling the HGHE and the surrounding soil as a unique system. Two possible shapes for an HGHE were analysed: a flat panel and a radiator, having the same exchanging surface. Their behaviour was analysed for a whole year in the heating and cooling mode, adopting building energy requirements REFERENCES [1] Fujii H, Okubo H, Cho N, et al. Field tests of horizontal ground heat exchangers. In: 4th World Geothermal Congress, Bali, [2] Wu Y, Gan G, Verhoef A, et al. Experimental measurement and numerical simulation of horizontal-coupled slinky ground source heat exchangers. Appl Thermal Eng 2010;30: [3] Bottarelli M, Di Federico V. Adoption of flat panels in soil heat exchange. In: XI World Renewable Energy Congress, Abu Dhabi, [4] Gabrielli L, Bottarelli M. Economic performance of ground source heat pump: does it pay off? In: XII World Renewable Energy Congress, Linköping, [5] Diersch H-JG. FEFLOW finite element subsurface flow and transport simulation system. Reference Manual, User s Manual and White Papers Vol. I, II, III, IV. Institute for Water Resources Planning and Systems Research, [6] Chiasson AD. Advances in modeling of ground-source heat pump systems. M. SC. Thesis. Oklahoma State University [7] Hidalgo JJ, Carrera J, Dentz M. Steady state heat transport in 3D heterogeneous porous media. Adv Water Resour 2009;32: [8] Lee CK, Lam HN. Computer simulation of borehole ground heat exchangers for geothermal heat pump systems. Renew Energy 2008;33: [9] Bottarelli M. Numerical analysis of heat transfer induced by an horizontal ground heat exchanger in an heterogeneous soil. Int J Energy Technol 2010;28: [10] Carslaw HS, Jaeger JC. Conduction of Heat in Solids. Oxford University Press, [11] Sauer TJ, Horton R. Micrometeorology in agricultural systems. Soil Sci Soc Am 2005;47: [12] Hillel D. Introduction to the Soil Physic. Academic Press, [13] DHI-WASY GmbH. OpenLoop IFM Module [14] Cengel Y. Termodinamica e trasmissione del calore. McGraw-Hill, International Journal of Low-Carbon Technologies 2012, 7,