1、2011 ASHRAE 899ABSTRACTThe installation cost of a ground-source heat pump systemcan be minimized by optimizing the length of the ground heatexchanger. For a given system, the length depends, amongother factors, on the pipe thermal conductivity, which can beincreased by mixing additives to the polyme
2、r resin used toextrude the pipe. Using this method, IPL has manufactured anew high-density polyethylene pipe whose thermal conductiv-ity is 0.7 Wm1K1(0.40 Btuh1ft1F1), which is 75%higher than that of regular high-density polyethylene. Two-and three-dimensional numerical simulations were used toevalu
3、ate the performance of the thermally enhanced pipe invertical ground heat exchangers used with ground-coupledheat pumps. The borehole thermal resistance and the watertemperature inside the pipes during heat exchange were eval-uated numerically. Simulations show that the thermallyenhanced pipe reduce
4、s the borehole thermal resistance by upto 24% for ground heat exchangers made with a single U-bend,which can, in turn, shorten the required borehole length. Thewater temperatures for equivalent heat injection or extractionare also decreased and increased, respectively, with the ther-mally enhanced p
5、ipe, which therefore enhances heat pumpperformances.INTRODUCTIONGround-source heat pumps are the most efficient heatingand cooling systems currently available for buildings. Thistechnology uses the earths geothermal resources and offerssignificant energy savings that can contribute to a zero energyd
6、esign. Ground heat exchangers (Florides and Kalogirou2007), which consist of buried pipes for closed-loop configu-rations, are required in the construction of a ground-sourceheat pump system. The pipes are installed in the boreholesdrilled during construction of a vertical ground-coupled heatpump sy
7、stem. The installation of the ground heat exchangersrepresents additional costs associated to the ground-sourceheat pump system when compared to other conventional heat-ing and cooling systems. The costs are proportional to thelength of the heat exchanger, which is related to the boreholethermal res
8、istance. Technical innovations, such as space clips used to posi-tion pipes in boreholes or thermally enhanced grout used to fillboreholes (Kavanaugh and Allan 1999; Carlson 2000; Allanand Kavanaugh 1999), can reduce the borehole thermal resis-tance and, thus, the required length of vertical ground
9、heatexchangers. Heat transfer with the subsurface, and the effi-ciency of the heat exchanger, also depends on the thermalproperties of the pipes used. Recent technological develop-ments were carried out by the manufacturer, IPL, who mixedadditives with high-density polyethylene (HDPE) to increasethe
10、 thermal conductivity of the resin from which the pipes areextruded. The exact composition of the additives cannot bedisclosed here as the manufacturer has claimed a patent pend-ing for the resin, but the resulting pipe has a thermal conduc-tivity of 0.7 Wm1K1(0.40 Btuh1ft1F1), compared to0.4 Wm1K1(
11、0.23 Btuh1ft1F1) for regular HDPE. Thisnew pipe reduces the borehole thermal resistance, and it isexpected that it will lead to a reduction in the length needed forground heat exchangers, therefore reducing system costs. Thermal response tests were conducted to evaluate theborehole thermal resistanc
12、e of vertical ground heat exchang-ers equipped with thermally enhanced and regular 32 mm(1.25 in.) SDR 11 HDPE pipes with a single U-bend and wherepipes are placed with spacers (Pasquier and Groleau 2009).Numerical Modeling of Thermally Enhanced Pipe Performances in Vertical Ground Heat ExchangersJa
13、smin Raymond, PhD, PGeo Marc Frenette, PE Alexandre Lger, PEStudent Member ASHRAEric Magni, PE Ren Therrien, PhD, PEJasmin Raymond is a PhD student and Ren Therrien is a professor at Universit Laval in Qubec, Canada. Marc Frenette is head of theMechanical Department at the Centre specialis de techno
14、logie physique du Qubec in La Pocatire, Canada. Alexandre Lger is a projectengineer at IPL plastics in Saint-Lazare, Canada. ric Magni is a technical manager at IPL plastics in Saint-Damien, Canada. LV-11-0242011. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.a
15、shrae.org). Published in ASHRAE Transactions, Volume 117, 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.900 ASHRAE TransactionsTwo tests were carried out in two boreholes
16、 located 9 m(29.5 ft) apart at the IPL factory in Saint-Lazare, Qubec.Each borehole has a diameter of 152 mm (6 in.) and is filledwith sand packs. Analysis of the tests showed that the boreholethermal resistance of the ground heat exchanger equipped withthe thermally enhanced pipe was 0.068 mKW1(0.0
17、36hftFBtu1), and that of the borehole with the regular HDPEpipe was 0.082 mKW1(0.043 hftFBtu1) (Pasquier andGroleau 2009). The thermally enhanced pipe thereforedecreases the borehole thermal resistance by 17%.The objective of this work is to assess the advantage ofusing thermally enhanced pipes for
18、ground heat exchangers,compared to regular pipes, by simulating their impact on bore-hole thermal resistance and water temperature with a numer-ical model. Ground heat exchanger configurations with asingle and double U-bend are considered in the models.Steady-state conductive heat transfer in two di
19、mensions is firstsimulated to evaluate the borehole thermal resistance for thedifferent configurations. Three-dimensional transient conduc-tive and convective heat transfer is then simulated to evaluatethe water temperatures during heat injection or extraction.Modeling results combined with sizing c
20、alculations ofground-coupled heat pump systems demonstrate the potentialreduction of the ground heat exchanger length with the newthermally enhanced pipe.NUMERICAL MODEL DEVELOPMENT The finite element software COMSOL Multiphysics,Version 3.5a (COMSOL AB 2008) is used to simulate heattransfer associa
21、ted with ground heat exchangers. The softwarenumerically solves the following conductive-convective heattransfer equation: (1)where , , and c are the thermal conductivity, density, andspecific heat capacity of the materials considered, respec-tively, and u denotes the fluid flow velocity vector.Four
22、 different pipe configurations inside the borehole (a,b, c, and d) are investigated with the models (Figure 1). Theproperties and dimensions of the pipes are those of commer-cially available products (Table 1). A base case scenario hasbeen chosen where the thermal properties of the subsurface,the gr
23、out, and the water-propylene glycol mixture are thoselisted in Table 2. The properties of all materials are assumedindependent of temperature. Two-Dimensional ModelInitial simulations consider two-dimensional steady-stateconductive heat transfer to evaluate the temperature and heatflux distributions
24、 within the borehole and use those results tocompute the equivalent borehole thermal resistance. Thesimulation domain is a circle of radius equal to 25 m (82 ft),centered on the borehole. The space between the borehole andthe outer boundary of the domain is filled with the subsurfacematerial and the
25、 space inside the borehole is filled with thegrout material surrounding the pipes. Internal boundaries arespecified inside the domain and they correspond to the innerperimeter of the pipes inside the borehole (Figure 2a). Heattransfer inside the pipes is therefore not simulated. Thedomain is discret
26、ized with triangular elements, and the meshis refined near the borehole and the pipes (Figure 2a). Depend-ing on the borehole configuration represented, the meshcontains between 5000 and 10,000 elements since the meshesare adapted to the borehole geometry. First-type boundary conditions for temperat
27、ure areassigned at the boundaries of the domain. Constant tempera-tures of 34C (93.2F) and 31C (87.8F), which can beobserved in ground heat exchangers operated in cooling mode,are assigned to the inner perimeter of the descending andT()cu TcTt-=Table 1. Pipe Properties and Dimensions Used in the Num
28、erical Models Property Value, SI Units Value, I-P UnitsThermally Enhanced HDPEThermal cond. 0.7 Wm1K10.40 Btuh1ft1F1Spec. heat cap. 1958 JKg1K10.468 Btulb1F1Density 1040 Kgm364.9 lbft3Regular HDPEThermal cond. 0.4 Wm1K10.23 Btuh1ft1F1Spec. heat cap. 2300 JKg1K10.550 Btulb1F1Density 944 Kgm358.9 lbft
29、3Dimension Value, SI Units Value, I-P Units32 mm (1.25 in.) SDR 11Inner diameter 34 mm 1.34 in.Outer diameter 42 mm 1.65 in.19 mm (0.75 in.) SDR 11Inner diameter 21 mm 0.83 in.Outer diameter 27 mm 1.06 in.Figure 1 Location of pipes for borehole configurations a,b, c, and d.2011 ASHRAE 901ascending p
30、ipes, respectively. A constant temperature equal to10C (50F), representing the undisturbed subsurface temper-ature, is assigned at the outer boundary of the domain locatedat 25 m from the center of the borehole. It is assumed that theouter boundary is sufficiently far from the borehole such thatthe
31、temperature at that boundary remains constant and equal tothat existing at an infinite radial distance from the borehole. Using the specified boundary conditions, steady-stateheat transfer is solved and the borehole thermal resistance Rbhis determined from the computed temperatures with,(2)where Tin
32、and Toutare the constant temperatures assigned atthe inner perimeter of the pipes, is the average computedtemperature at the borehole wall (shown by the red circle inFigure 2a) and qbhis the total computed heat flux perpendic-ular to the borehole wall. These last two quantities are deter-mined by in
33、tegration, which involves summation of the nodalquantities that are weighted according to the distance betweennodes. Simulated temperature and heat flux direction for thebase case scenario are shown in Figure 2b for borehole config-uration a. The non-uniform temperature at the borehole wallaffects h
34、eat flux, whose distribution is anisotropic near theborehole (Figure 2b).Various combinations of temperature at the pipe innerboundaries and thermal conductivity of the subsurface mate-rial were simulated to verify if they influence the boreholethermal resistance for all configurations represented.
35、Thetemperature assigned at the pipe inner boundaries and the ther-mal conductivity assigned to the subsurface material werevaried from 10C to 45C (14.0F to 113.0F) and 0.5 to4.5 Wm1K1(0.29 to 2.60 Btuh1ft1F1), respectively.The temperature difference between the descending and theascending pipe was a
36、lso varied by 0C to 5C (0.0F to 9.0F)to simulate the temperature distribution at various depths inthe ground heat exchanger. For these parameters, these rangesspan the most common values for vertical ground heatexchangers. The computed borehole thermal resistancesremained constant for configurations
37、 b and c for the variouspipe temperature and subsurface thermal conductivity tested.For configuration a, the borehole thermal resistance varied byabout 10% for the range of subsurface thermal conductivitytested and was not affected by temperature changes at the pipeinner boundaries. Simulations for
38、configuration d producedlarger variations of the borehole thermal resistance whenassigned temperature at the pipe inner boundaries and thesubsurface thermal conductivity were varied. These variationsare due to the non-uniform temperature distribution at theborehole wall, which introduces anisotropy
39、in the computedTable 2. Properties of Materials Used for the Base Case Scenario Property Value, SI Units Value, I-P UnitsSubsurfaceThermal cond. 2.5 Wm1K11.45 Btuh1ft1F1Spec. heat cap. 800 JKg1K10.191 Btulb1F1Density 2500 Kgm3156.1 lbft3Thermally Enhanced GroutThermal cond. 1.5 Wm1K10.87 Btuh1ft1F1S
40、pec. heat cap. 1700 JKg1K10.406 Btulb1F1Density 2000 Kgm3124.9 lbft3Water-Propylene Glycol MixtureThermal cond. 0.48 Wm1K10.28 Btuh1ft1F1Spec. heat cap. 3795 JKg1K10.907 Btulb1F1Density 1052 Kgm365.7 lbft3RbhTinTout+2- Tbhqbh-=TbhFigure 2 a) Mesh near the borehole, which is indicated bythe solid lar
41、ge circular line; b) simulatedtemperature and heat flux (arrows) for a groundheat exchanger with configuration a, 152 mm(6 in.) borehole diameter and 32 mm (1.25 in.)SDR 11 thermally enhanced pipes.902 ASHRAE Transactionsheat flux that affects the borehole thermal resistance, since thatresistance is
42、 a scalar value representative of average condi-tions at the borehole wall. This anisotropy is stronger for thea and d configurations than for the b and c configurations. To eliminate the effect of varying pipe temperature andsubsurface thermal conductivity, the thermal resistance forconfigurations
43、a and d can be evaluated at a distance equal totwice the radius of the borehole, where the temperature distri-bution tends to be more uniform. The choice of the distancehere is arbitrary and could, for example, be three or four timesthe borehole radius. The radial distance must, however, belarge eno
44、ugh for the temperature to be more uniform. Thedistance must also remain constant between simulations tocompare the thermal resistances that are now influenced by thesubsurface thermal conductivity assigned to the materiallocated between the borehole radius and the distance wherethe thermal resistan
45、ce is determined. The computed thermalresistances for the a and d configurations are then independentof the temperature assigned to the inner pipe boundaries andthe subsurface thermal conductivity assigned outside theregion where the borehole thermal resistance is determined.The thermal resistances
46、determined at twice the boreholeradius cannot, however, be compared to those determined atthe borehole radius. The distance at which the thermal resis-tance is determined must also be accounted for in furthersizing calculation. Three-Dimensional ModelTransient simulations of conductive and convectiv
47、e heattransfer for three-dimensional ground heat exchangers wereconducted to determine water temperature in pipes duringperiods of 100 h of heat injection or extraction. The modelsdeveloped here have geometries, meshes, and boundary condi-tions similar to those described by Marcotte and Pasquier(200
48、8). Using the symmetry of geometry of the system toreduce the number of elements and nodes, only half the bore-hole needs to be discretized (Figure 3a). The simulationdomain is therefore a half-cylinder centered on the boreholeand having a radius of 10 m (32.8 ft) and a length of 152.4 m(500 ft). Th
49、e pipes containing water, which are located insidethe borehole, are represented with two concentric half-cylin-ders. The distance from the borehole center to the modelsouter boundary is shorter than that for the steady-state two-dimensional models, which is appropriate here because theradius of influence of
