Effect of Borehole Material on Analytical Solutions of the Heat Transfer Model of Ground Heat Exchangers Considering Groundwater Flow

Park, Sangwoo; Lee, Seokjae; Lee, Hyobum; Pham, Khanh; Choi, Hangseok

doi:10.3390/en9050318

Cited by 14 publications

(9 citation statements)

References 23 publications

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“…Analytical heat source models considering groundwater seepage may induce significant errors as the borehole diameter becomes larger [26]. The effects of impermeable materials like grout on analytical solutions of the heat transfer model may also need to be considered [27]. Hu [28] also provided a line heat source model for borehole GHE in multilayer substrates with groundwater flow.…”

Section: Existing Analytical Multilayer Heat Source Modelsmentioning

confidence: 99%

A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground

Pan

McCartney

et al. 2020

Energy

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This paper presents a new analytical multilayer cylindrical heat source model for vertical ground heat exchangers (GHEs) installed in layered ground using the new integral-transform method. The analytical model was validated by model degradation, numerical simulation, and a laboratory-scale experiment. Results indicate that temperature profiles of vertical GHEs in layered ground are quite different from those in homogeneous ground, and that temperature differences increase with time. Thermal property differences between ground layers were found to result in additional vertical heat transfer across layer interfaces, which is not observed in homogeneous ground. Cross-layer thermal interaction was found to be stronger when thermal property differences are larger. The new cylindrical heat source model was also compared with the multilayer line heat source model, and it was found that differences between the two models decrease with time. Further, larger GHE thermal loads and smaller ground thermal conductivity values led to larger error of multilayer line heat source model. The new multilayer cylindrical heat source model was found to be suitable for quickly considering the effects of ground stratification on the design of vertical GHEs. *Revised Manuscript with No Changes Marked Click here to view linked References

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Section: Existing Analytical Multilayer Heat Source Modelsmentioning

confidence: 99%

A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground

Pan

McCartney

et al. 2020

Energy

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“…More precisely, the inlet temperature of the heating tube-side fluid ϑ ti (t) can be taken as the control signal, whereas the variations in the inlet temperature of the heated shell-side fluid ϑ si (t) can be seen as disturbances. The typical control task is here to stabilize the outlet temperature of the heated shell-side fluid ϑ so (t) given by (7) on the desired setpoint, in the presence of disturbances caused by variations in ϑ si (t) given by (6).…”

Section: Governing Pdesmentioning

confidence: 99%

“…Therefore, a lot of attention has been devoted so far in the literature to the PDE-based modeling of these thermal devices, which are often described by hyperbolic equations resulting from the balance laws of continuum physics. The development of the PDE-based phenomenological modeling methods progressed in two parallel directions, with the use of either analytical [1][2][3][4][5][6][7][8] or numerical [9][10][11][12][13][14][15] approaches. The other approach consists of using data-based techniques, also known as black-box modeling or process identification [16][17][18], or even in using artificial neural networks [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger

Bartecki

2020

Symmetry

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Transfer functions of typical heat exchangers, resulting from their partial differential equations, usually contain irrational functions which quite accurately describe the spatio-temporal nature of the processes occurring therein. However, such an accurate but complex mathematical representation is often not convenient from the practical point of view, and some approximation of the original model would be more useful. This paper discusses approximate rational transfer functions for a typical thick-walled double-pipe heat exchanger working in the parallel-flow configuration. Using the method of lines with the backward difference scheme, the original symmetric hyperbolic partial differential equations describing the heat transfer phenomena are transformed into a set of ordinary differential equations and expressed in the form of N subsystems representing spatial sections of the exchanger. Each section is described by a rational transfer function matrix and their cascade interconnection results in the overall approximation model expressed by a matrix of rational transfer functions of high order. Based on the rational transfer function representation, the frequency and steady-state responses of the approximate model are evaluated and compared with those resulting from its original irrational transfer function model. The presented results show better approximation quality for the “crossover” input–output channels where the in-domain heat conduction effects prevail as compared to the “straightforward” channels, where the transport delay associated with the heat convection dominates.

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“…However, there are few studies on the internal force in the inhomogeneous temperature field. In addition, if the groundwater flow is significant: a larger temperature increment at the back side of the heat source can be observed than at the front side [17], which will also lead to a temperature difference in the geo-structures. Consequently, the internal forces of the underground structure, such as the bending moment, will change because of the inhomogeneous temperature field.…”

Section: Introductionmentioning

confidence: 99%

Internal Force Response of a Pile in an Inhomogeneous Temperature Field

2017

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An inhomogeneous temperature field was built in an experimental model of sand with an embedded pile. The temperature of the soil, as well as the temperature and strain on opposite sides of the pile were investigated in the process of temperature balance. The effect of the inhomogeneous temperature field on the internal force of the pile was analyzed. The experimental results show that the inhomogeneous temperature field will cause a bending deformation in the pile body according to the FBG (fiber Bragg grating) strain sensors. The distribution of the bending moment along the length of the pile is related to the temperature difference. The maximum bending moments reached −25.7 N•m when the temperature difference was about 1.3 • C. Therefore, the influence of the inhomogeneous temperature field o• the internal force of the foundation pile should be taken into account in the applications of a ground source heat pump system.

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Effect of Borehole Material on Analytical Solutions of the Heat Transfer Model of Ground Heat Exchangers Considering Groundwater Flow

Cited by 14 publications

References 23 publications

A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground

A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground

Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger

Internal Force Response of a Pile in an Inhomogeneous Temperature Field

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