1、2009 ASHRAE 45ABSTRACTA detailed borehole heat exchanger model is presented, cast as a TRNSYS component model, for use in ground source heat pump system simulations with optimization of system subcomponents. The proposed borehole heat exchanger model is based on non-dimensionalized short time step r
2、esponse factors, and includes a time-dependent borehole thermal resis-tance that is due to transient responses from the surrounding ground and short time-step thermal storage effects of the bore-hole grout and heat carrier fluid. These effects have been accounted for by developing a finite element m
3、odel of a bore-hole heat exchanger where the fully transient borehole thermal response is modeled and coupled to a short time step ground response factor model. Furthermore, each response factor function (g-function), describing the thermal response of a particular borehole field to a unit heat puls
4、e is developed to allow for varying borehole spacing-to-depth ratios so that borehole spacing is independent of the borehole depth. The model is developed with the specific objective use in optimi-zation problems for hybrid ground source heat pumps systems. A detailed model validation and sensitivit
5、y analyses are presented and discussed.INTRODUCTION AND BACKGROUNDIn the United States, ground source heat pump systems that utilize vertical U-tube ground heat exchangers in closed loop configurations have, over the last decade, experienced market growth in space air-conditioning for residential, c
6、ommercial, and institutional buildings. The upward trend in market growth is relatively steady and similar advances are expected in European and Asian markets (Lund et al. 2005 and Energy Information Agency 2008). The market gains are primarily due to the fact that ground source heat pump systems of
7、fer significant advantages over their conventional alterna-tives with respect to energy savings due to higher coefficients of performance and associated improvements in system life cycle and operating costs, reduced greenhouse gas emissions, and improvements in building thermal load profiles. In the
8、 past, many such systems were designed and installed with a “seat-of-the-pants” approach, and system sizes were mostly justified based on the experience of the design engineers, resulting mostly in oversized designs. With the development of more accurate and reliable system design and simulation too
9、ls that have been available to field engineers and the engi-neering design community, confidence of building owners in ground source heat pump applications has been increased significantly. Today, ground source heat pump systems pres-ent a very viable choice in air-conditioning especially consid-eri
10、ng the rapidly rising cost of energy and the urgent need for reductions in building energy consumption and demand management. The proper design and simulation of GHP systems requires accurate assessment of the thermal phenomena in and around vertical ground loop heat exchangers as the sizing of GHP
11、systems is highly sensitive to the accurate evaluation of heat transfer between the heat transfer fluid inside high density polyethylene (HDPE) U-tube pipes in the borehole and the ground formation that surrounds them. A detailed discussion of the heat transfer phenomena in ground coupled heat pump
12、systems along with a comprehensive literature survey on currently available design and simulation models are provided by Chiasson (2007). In general, mathematical models describing heat trans-fer phenomena in vertical borehole heat exchangers can be Simulation Model for Ground Loop Heat ExchangersC.
13、 Yavuzturk, PhD A.D. Chiasson, PhD, PE, PEng J.E. Nydahl, PhDMember ASHRAE Associate Member ASHRAEA.D. Chiasson is an assistant professort in the Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH. C. Yavuzturk is an assistant professor in the Department of Mechanic
14、al Engineering, University of Hartford, West Hartford, CT. J.E. Nydahl is professor emeritus in the Department of Mechanical Engineering, University of Wyoming, Laramie, WY.LO-09-004 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in
15、ASHRAE Transactions 2009, vol. 115, part 2. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.46 ASHRAE Transactionsclassified as either analytical, numerical, or thermal response fa
16、ctor. Several variations of two analytical models appear in the literature, and some have been incorporated into commercially- available design software (IGSHPA, 1988). These two models are known as Kelvins Line Source Model and the Cylinder Source Model. Some of the prominent models currently avail
17、able for design and simulation of ground source heat pump systems are briefly discussed below.Kelvins Line Source Model, described by Kelvin (1882), is a classic solution used to calculate the temperature distribu-tion around an imaginary line in a semi-infinite solid medium initially at a uniform t
18、emperature. A somewhat modified adap-tation of the Kelvins line source solution was given by Inger-soll and Plass (1948). A more appropriate analytical solution for modeling the heat transfer around a cylindrical borehole is the so-called Cylinder Source Model. This model was devel-oped by Carslaw a
19、nd Jaeger (1947), and then utilized by Inger-soll et al. (1954) to size buried heat exchangers. The ASHRAE (2003) procedure uses the cylinder source model as modified by Kavanaugh (1985) to determine the borehole heat exchanger length for commercial buildings. Bernier (2001) adopted the ASHRAE (2003
20、) method to perform hourly simu-lations of GHP systems. Berniers approach uses superposi-tion along with a loads aggregation scheme to account for hourly-varying heat transfer rates. Young (2004) employed an analytical model, referred to as the buried electrical cable model (Carslaw and Jaeger, 1947
21、), to evaluate the thermal capacitance effects of borehole elements on design borehole depths. Young (2004) replaces the electrical cable with the circulating fluid and the sheath with the grout, and draws anal-ogies from the elements of a buried electrical cable to a bore-hole, where the core is an
22、alogous to the circulating fluid and the sheath is analogous to the grout. Youngs resulting model was referred to as the Borehole Fluid Thermal Mass Model (BFTM model) and introduces a grout allocation factor (GAF) in order to improve accuracy of the BFTM model. Beier and Smith (2003) developed a so
23、lution to the one-dimensional (1-D) form of the heat diffusion equation using dimensionless groups. Their model accounts for thermal storage of the grout and circulating fluid. The U-tube is modeled using an equiv-alent diameter approach described by Gu and ONeal (1995). The 1-D heat conduction equa
24、tion is formulated for both the grout and soil. The boundary condition at the pipe wall is the heat flux due to the circulating fluid. At the grout/soil inter-face, the heat fluxes and temperatures are set equal. At infinite radius, the temperature is set at the undisturbed Earth temper-ature. The e
25、quations are solved using Laplace transforms, and the model was validated with experimental data.A number of numerical models for calculating the temperature distribution around a U-tube borehole have been developed. Each model has been created with slightly differ-ent purposes in mind. Some have be
26、en used for research purposes (i.e. examining the nature of heat transfer around borehole heat exchangers), while others have been developed for use in system simulations, or for evaluating field data from thermal response tests. Some existing numerical models include those of Eskilson (1987), Hells
27、trm (1989), Breger et al. (1996), Muraya et al. (1996), Rottmayer et al. (1997), Wetter and Huber (1997), Yavuzturk et al. (1999), Yavuzturk and Spitler (1999, 2001), Shonder and Beck (1999), Zeng et al. (2003), and that described by Young (2004) to develop GAFs. Existing thermal response factor mod
28、els include the long time-step response factor model developed by Eskilson (1987), and that of Yavuzturk and Spitler (1999), who extended Eskilsons work to short-time steps. The advantage of response factor models over fully numerical models is their greater computational efficiency. This may or may
29、 not be true for modeling single boreholes, but the response factor approach has proven to be quite convenient for modeling extensive multiple-borehole fields.The long time-step (LTS) response factors as developed by Eskilson (1987) have been referred to as g-functions. They represent the non-dimens
30、ionalized temperature response at the borehole wall (Tb) of a heat extraction (or rejection) bore-hole due to the thermal resistance of the surrounding soil/rock, and were calculated from a numerical model of the borehole. Eskilsons LTS response factors do not account for the bore-hole thermal resis
31、tance, and thus Eskilson estimates that the LTS g-functions are valid for time scales above , where rbis the borehole radius and is the soil/rock thermal diffusivity. Thus, below this time scale, borehole transients are significant. For typical borehole geometries and soil and rock thermal propertie
32、s, this implies a time scale (tb) on the order 4 to 8 hours. The g-function allows the calculation of the temperature change at the borehole wall in response to a step power pulse over an arbitrary time step.Yavuzturk and Spitler (1999) extended the work of Eskil-son (1987) to time scales of one hou
33、r or less. These are referred to as the short time-step (STS) response factors or g-functions. Yavuzturk and Spitler (1999) used the numerical model of Yavuzturk et al. (1999) to calculate the temperature response of the borehole wall due to a constant input power pulse at the U-tube pipe. Since the
34、 g-function only represents the temper-ature response at the borehole wall due to the surrounding ground, and Eskilsons original g-functions did not include borehole resistance effects, the removal of the borehole ther-mal resistance was accomplished through the assessment of its temperature impact
35、due to the heat pulse. Yavuzturk and Spitler (1999) implemented the STS g-function model into TRNSYS (SEL, 2000) as a component model for use in short time step system simulations. The instantaneous thermal performance of ground source heat pump systems is highly transient since it depends on the cu
36、rrent and past loading history of the ground, grout and fluid, and on the temperature difference between the source/sink. Despite this, most current numerical design and simulation tools ignore the thermal storage effects of the fluid and grout and therefore use a steady state approach for these com
37、po-nents. More attention has recently been given to these storage tb5rb2g=gASHRAE Transactions 47effects in the literature. It has been known for some time and recently addressed by Beier and Smith (2003), that borehole completion (i.e. grout thermal conductivity, U-tube spacing, and fluid thermal p
38、roperties) strongly affects the time needed to obtain sufficient data from an in-situ thermal response test of the ground. Also, Young (2004) indicates that the method used to calculate the borehole resistance can significantly affect design depths of borehole heat exchangers.The steady-state boreho
39、le thermal resistance is generally defined as the ratio of a temperature potential to the heat trans-fer rate due to the temperature potential per unit length of bore-hole. Although appearing simple to calculate, the steady-state borehole thermal resistance is quite complex. The heat fluxes associat
40、ed with each leg of the U-tube are not equal (except at the borehole bottom) and vary with depth. Further, each leg thermally interacts with the surrounding ground, as well as with each other. Calculation of the steady-state borehole ther-mal resistance is further complicated with multiple U-tubes.
41、There are a number of methods that attempt to approximate the steady-state borehole thermal resistance. Young (2004) exam-ined the accuracy of some of the methods by comparing the calculated steady-state resistance value by analyzing a total of 24 cases with varying borehole diameter, U-tube shank s
42、pac-ing, and grout thermal conductivity. The multipole method of Bennet et al. (1987) was found to be superior with an average error of about 0.1% for all cases. The next best method was the Gu and ONeal (1998a) approach with an average error of 7.2% for all cases. However, the error in the Gu and O
43、Neal (1998a) method was on the order of 20% for cases where the U-tube legs were very close or touching, combined with low thermal conductivity grout. The Paul (1996) method was found to be associated with the largest errors of all the cases examined, resulting in errors several times larger than ot
44、her methods in most cases. The average error in the Paul (1996) method for all cases was found to be about 18%, exceeding 55% in some cases.The objective of this paper is to develop a detailed bore-hole heat exchanger model, cast as a TRNSYS component model, for use in GHP system simulation with opt
45、imization. TRNSYS (SEL, 2000), developed at the Solar Energy Labo-ratory at the University of Wisconsin-Madison originally in the early 1970s, is a modular, transient systems simulation program where each component is described mathematically by a FORTRAN subroutine. The approach taken in the devel-
46、opment of the detailed borehole heat exchanger model is to expand the capabilities of the response factor ground loop heat exchanger model of Yavuzturk and Spitler (1999). The Yavuz-turk and Spitler (1999) model has a number of shortcomings with respect to modeling hybrid GHP systems. The first is t
47、hat, the model superimposes a pre-computed steady-state borehole thermal resistance with transient responses from the surround-ing ground, but in highly transient systems, short time-step thermal storage effects of the borehole grout and heat carrier fluid could be significant. These effects have be
48、en accounted for by developing a finite element model of a borehole heat exchanger where the fully transient borehole thermal response can be modeled and coupled to Yavuzturk and Spitlers (1999) response factor model. These model additions meant that the current short time-step g-functions needed im
49、provement. The second problem in the Yavuzturk and Spitler (1999) model is that each g-function describing a particular borehole field was developed with a fixed borehole spacing-to-depth ratio, and any adjustment of the depth in an automated optimization scheme is cumbersome. Thus, the final improvement to the Yavuzturk and Spitler (1999) model allows for a borehole spacing that is independent of the borehole depth.METHODOLOGY AND MODEL DEVELOPMENTA fundamental challenge in accurately modeling heat transfer phenomena in borehole heat exchangers lies in balancing acceptable
