1、416 2008 ASHRAE ABSTRACTIn groundwater filled borehole heat exchangers (BHE),convective flow inside the borehole water will affect the heattransfer. Since the convective flow is dependent of the temper-ature gradient, different injection rates and ground tempera-tures will result in different boreho
2、le thermal resistance. Thispaper describes the influence of natural convection in water-filled boreholes in impermeable bedrock for ground-coupledheat pump (GCHP) systems. An overview of groundwater-filled boreholes and the influence of groundwater movementsare presented followed by numerical simula
3、tions and fieldmeasurements to further investigate the influence. The resultsfrom the simulations of the three-dimensional, steady-statemodel of a 9.8 ft (3 m) deep BHE are compared to evaluatedresults from performed thermal response test (TRT). Theresults show that convective flow in groundwater-fi
4、lled BHEresults in 5-9 times more efficient heat transfer compared tostagnant water when heat carrier temperatures are in therange of 50 86F (10 30C). The size of the convective flowdepends on the temperature gradients in the borehole. Thisshows the importance of on-site investigation of thermal pro
5、p-erties using appropriate power injection rates similar to thosein the system to be built. This research is part of an on-goingproject to find ways to estimate the heat transfer includingconvective flow and to incorporate the findings into the designof GCHP systems. TRT are today a common way to de
6、termineheat transfer properties for a BHE and its surroundings.Performing TRT measurements with several injection rates isa way to evaluate the dynamic thermal response including thechange in convective flow due to changes in temperature levels.If this dynamic response would be included in design to
7、ols amore thorough design of the BHE system is performed. Here,the early result of this research is presented.INTRODUCTIONGround-coupled heat pumps (GCHP) are systems usingthe ground for space heating or cooling. In Sweden the mostcommon system is a closed-loop borehole heat exchanger(BHE) with grou
8、ndwater filling the volume between pipecollector and borehole wall. During heat injection or extrac-tion, the temperature gradient in and around the boreholeinduces convective flow in the groundwater.In general, the convective flow affects heat transportinside the borehole, reducing the thermal resi
9、stance comparedto stagnant water. A normal single U-pipe BHE in Sweden,results in a borehole thermal resistance of 0.10 0.14Ffth/Btu (0.06 0.08 Km/W) at heat injection. If no convectiveflow occurred, the resistance would have been approximately0.26 0.35 Ffth/Btu (0.15 0.2 Km/W). In fractured bedrock
10、 or high porosity ground material,convective flow may also influence the ground conductivity.Natural groundwater flow also occurs in areas with the rightgeohydrological conditions. It is therefore recommended toperform in-situ investigations of thermal conditions ratherthan laboratory core-sample te
11、sting, before constructing alarger BHE system.Thermal response test (TRT) is a common in-situ measure-ment method to estimate effective ground conductivity andborehole thermal resistance. With this method, groundwaterinfluence is embedded in the evaluated result. However,convective flow will depend
12、on temperature gradients, and willtherefore change during different operating conditions, e.g.,heat extraction during winter and heat injection during summer.Influence of Natural Convection in Water-Filled Boreholes for GCHPAnna-Maria Gustafsson Signhild Gehlin, PhDAssociate Member ASHRAEAnna-Maria
13、Gustafsson is a doctoral student in the Department of Architecture and Infrastructure, Lule University of Technology, Sweden.Signhild Gehlin is Technical Secretary at Swedish Society of HVAC Engineers, Stockholm, Sweden.NY-08-0492008, American Society of Heating, Refrigerating and Air-Conditioning E
14、ngineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.ASHRAE Transactions 417The influence of conve
15、ctive flow in the BHE depends ontemperature levels in the system. This is not included intodays commercial BHE design programs; instead designershave to rely on experience and estimations when designingdifferent working modes. The influence of groundwater onBHE is now being investigated at Lule Univ
16、ersity of Tech-nology and recent research is presented in this paper.NATURAL CONVECTION IN BOREHOLESWhen calculating heat transfer in BHE systems, heattransport is generally divided into two parts: borehole andbedrock. Heat is transferred by conduction through rock andborehole filling, and by convec
17、tive flow in the groundwater.However, convectional flow is usually not included in BHEcalculations neither for the bedrock nor for the borehole,although several examples of considerable influence ofgroundwater flow on the systems under certain geohydro-logical conditions have been described (e.g., S
18、anner et al.2000).The influence from regional groundwater flow on the heattransfer in the bedrock has been most studied. In the saturatedzone, under the groundwater table, groundwater flow dependson ground material, fractures and hydraulic gradient at the site.In hydrological calculations, the bedro
19、ck is often considereda porous medium, which for laminar conditions may bedescribed by Darcys law. This equation states that the ground-water flow depends only on hydraulic conductivity andhydraulic gradient.Chiasson et al. (2000) conducted a study on groundwaterinfluence on closed-looped GCHP syste
20、ms. They performed aPeclet number analysis and used finite element method (FEM)simulations to investigate the effect on several types ofbedrock based on a continuous model, where the rock isconsidered a porous medium and groundwater flow isdescribed by Darcys law. They concluded that groundwateronly
21、 influenced in bedrock with high hydraulic conductivities,such as coarse-grained soils and rocks with secondary poros-ities such as fractures and solution channels. Crystallinebedrock, as in Sweden, would therefore under normal condi-tion not show any influence from groundwater on the heattransfer i
22、n the bedrock in BHE systems.However, several TRT measurements suggest ground-water influence resulting in higher thermal ground conductiv-ity than expected. Witte (2001) investigated the effect of aknown controlled groundwater flow by extracting water froma borehole close to where a TRT was perform
23、ed. A modelbased on this experiment showed that already small flow rates,Darcy flow 11.5 ft/year (3.5 m/year), resulted in 6% higherestimation of the thermal conductivity for a 100 h test.This shows that modelling the bedrock as a continuousporous medium together with Darcys equation cannot alwaysbe
24、 used when studying groundwater influence on BHEs.Gehlin and Hellstrm (2003) simulated groundwater flow inhard rock using three different modelling approachescontinuous model, fracture zone and single fracture close tothe BHE. They concluded that single, larger fractures couldresult in an increase i
25、n heat transfer which would not be visibleusing the continuous model approach.Since Scandinavian BHEs usually are groundwater-filled, convective flow also influences the borehole thermalresistance. This was investigated by Kjellsson and Hellstrm(1999) in a laboratory experiment with a 9.8 ft (3 m) l
26、ong BHEin solid ground, i.e. no influence in the bedrock. Severalcollector arrangements were used and the result clearlyshowed a decrease in borehole resistance for higher tempera-tures in the borehole water.This was further modelled by Gehlin et al. (2003) in frac-tured rock. The BHE had connecting
27、 fractures at the top andbottom of the borehole. As the borehole was heated, risingpressure gradients forced the water to flow into and out fromthese fractures. This thermosiphon effect was shown to have aconsiderable effect on the borehole heat transfer.Studies to date have concluded influence on B
28、HE systemsfrom groundwater movements both in the bedrock and in theborehole. To fully understand the effect of temperature levels,injection rate and bedrock conditions, further studies need tobe performed. The situation with a groundwater filled bore-hole situated in highly fractured rock is quite c
29、omplex. In thispaper natural convection is only studied for groundwater-filled BHE in impermeable rock. Investigations are made withnumerical simulations as well as thermal response test. Futurestudies will be performed with fractured rock and with aregional groundwater flow.MODEL DESCRIPTIONA three
30、-dimensional steady-state model was built andsimulated in a commercial computational fluid dynamic(CFD) software for numerical studies of natural convectionin a BHE. The groundwater-filled borehole with a U-pipecollector is approximated with a water-filled annulus in solidrock. Using an annulus conf
31、iguration in these simulationshas been shown to result in a difference within a few per centcompared to a U-pipe configuration for solid rock (Gustafs-son 2006).In Figure 1, the schematics of the model are shown,consisting of two annular regions. The inner corresponds tothe groundwater filled boreho
32、le with a pipe radius, rp, of1.57 in. (0.04 m) and a borehole radius, rbh, of 2.04 in(0.0518 m). The outer annulus represents the impermeable,solid rock with an outer radius, rbrb, of 3.3 ft (1 m). A constantheat flux is applied over the pipe wall and a constant temper-ature at the outer bedrock bou
33、ndary.The length of the borehole is set to only 9.84 ft (3 m) inthe model, due to computer constrains. With this approxima-tion there may be effects in the convective flow that are notcaptured. For example a longer borehole will have a largertemperature difference between and along the two U-pipesha
34、nks due to a larger accumulated heat loss in the circulatingfluid. The friction along the borehole wall and U-pipe wallmay cause multicellular convective flow patterns. Natural418 ASHRAE Transactionstemperature difference in the ground along the borehole mayalso alter the flow pattern. These effects
35、 are not considered inthis model and need to be further investigated.The radius of outer bedrock boundary is chosen small inorder to minimize the mesh size. The assigned boundarytemperatures are chosen to achieve appropriate temperatureinside the borehole. During long-term operation of the bore-hole
36、 the area influenced of the heat flow will reach further outthan 1 m. Since the heat transfer in the bedrock is only byconduction (in this model) the appropriate temperature chosenat the bedrock boundary can easily be calculated knowing theheat flow, undisturbed ground temperature and the steady-sta
37、te influence radius. In these calculations however, the steady-state modelsimulates a transient process. This approximation had to bemade due to computer constrains. In the beginning of the heattransfer process for a TRT some energy will be stored in theborehole water, heating it, until stead-state
38、conditions areachieved. Here, the steady-state model is compared to 72hours TRT measurements. The major difference here is thatthe heat flow may not have taken steady-state appearance andthat not all of the heat is transferred to the bedrock. If steady-state is achieved, all injected heat will be tr
39、ansferred to thebedrock and no further energy is stored in the borehole. Performing a transient calculation of the temperatureincrease in the borehole water after 72 h of 83.2 Btu/hft(80 W/m) heat injection in a TRT measurement, results in aminor temperature increase of 0.03 K from hour 72 to hour 7
40、3.For the 9.84 ft (3 m) long BHE this is approximately 0.68 Btu/h (0.2 W) that is heating the borehole water instead of beingtransferred to the bedrock. That is, 0.1% of the injected heat isstored in the borehole water and 99.9% is transferred to thebedrock. Such small difference in heat flow may be
41、 disre-garded and performing the calculations in steady-state isacceptable.In the CFD program, simulating steady-state naturalconvection requires the Boussinesq approximation for thedensity. In this approximation a constant density value is usedin all equations except in the momentum equation where
42、it hasa linear relationship to temperature. According to Cawley andMcBride (2004) Boussinesq approximation is not sufficient forsimulations of natural convection close to the density maximum(39.2F, 4C). The numerical studies in this paper are hencelimited to borehole water temperatures above 50F (10
43、C).In these studies of the effects of natural convection onU-pipe BHE, the main interest is in the relationship betweenheat carrier temperature, power injection and borehole ther-mal resistance. Temperatures are calculated at the outside ofthe collector wall. Conductive heat transport through thecol
44、lector pipe is therefore added to find the heat carriertemperature. A DN40PN6 polyethylene pipe has a wall thick-ness of 0.09 in (0.0024 m) and a thermal conductivity p= 0.24Btu/hft2F (0.42 W/mK). The estimated heat carriertemperature is then calculated as the mean value of the walltemperature insid
45、e the collector.In the numerical simulations all material properties areheld constant for each simulation except for the density, wherethe Boussinesq approximation is used. Water parameters aretaken from a standard water properties table (Incropera anddeWitt 1996) for approximately the temperature a
46、t the collec-tor pipe wall, T0, Table 2. The buoyancy term (Equation 1) inthe momentum equation is approximated, using the Bouss-inesqs, to.(1)Fluent uses a finite volume method to convert the govern-ing equations. In this model, turbulence model was usedtogether with a node based first-order upwind
47、 discretizationscheme, except for the pressure and energy correlations wherebody-force weight and second-order upwind, respectively,were used.FIELD MEASUREMENTSThermal response test is an in-situ measurement methodto determine the heat transfer properties of a BHE and itssurrounding ground in order
48、to predict the performance ofground-source energy systems. The equipment was developedin the mid-nineties independently in Sweden and USA (Eklfand Gehlin 1996, Austin 1998) and is today an establishedmethod. The test is performed by injecting or extracting aconstant power into the BHE by circulating
49、 a heated or chilledfluid inside the collector. The thermal response is studied bymeasuring the change in circulating fluid temperature overtime, which is dependent on the heat transport under ground,the injection rate and flow rate. From measurement data theeffective ground conductivity, e, and borehole thermal resis-tance, Rb, are evaluated.Field measurements were performed with the SwedishTRT rig, TEDhc, which was constructed in 2004 (Gustafsson2006) and may both inject and extract heat. TEDhc has sepa-rate heat and cold injection systems. In
