A spectral model for transient heat flow in a double U-tube geothermal heat pump system

Abstract

a b s t r a c tThis paper introduces a semi-analytical model based on the spectral analysis method for the simulation of transient conductive-convective heat flow in an axisymmetric shallow geothermal system consisting of a double U-tube borehole heat exchanger embedded in a soil mass. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the fast Fourier transform, for the time domain; and the complex Fourier and Fourier-Bessel series, for the spatial domain. Numerical examples illustrating the model capability to reconstruct thermal response test data together with parametric analysis are given. The CPU time for calculating temperature distributions in all involved components, pipe-in, pipe-out, grout, and soil, using 16,384 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 3 s in a normal PC. The model can be utilized for forward calculations of heat flow in a double U-tube geothermal heat pump system, and can be included in inverse calculations for parameter identification of shallow geothermal systems.

Numerical Investigation of the Coaxial Geothermal Heat Exchanger Performance

“…Table 5. Concrete grout physical properties of various materials studied [52][53][54]. should also be noted that the use of concrete results in reduced thermal heat storage due to its significantly lower thermal conductivity compared to the soil that could be directly employed underground [51].…”

A hybrid numerical-semi-analytical method for computer simulations of groundwater flow and heat transfer in geothermal borehole fields

“…Numerical simulations of unsteady heat transfer in borehole fields, without and with groundwater flow, and based on finite difference, spectral, unstructured finite volume, and finite element methods, are discussed, for example, in the works of Rottmayer et al (1997), Yavuzturk et al (1999, Li and Zheng (2009), Bauer et al (2011), Al-Khoury andFocaccia (2016), and Dai et al (2016). However, unsteady and fully multidimensional numerical simulations of the heat transfer processes in borehole fields, in both the ground and the boreholes, are quite expensive computationally [Yang et al (2010)].…”

Formulation of a 1D finite element of heat exchanger for accurate modelling of the grouting behaviour: Application to cyclic thermal loading

“…[19,20] propose a model dealing with vertical conduction as well as advection-diffusion in the soil and discontinuous loading. A classification procedure of these models is proposed in [21]. 45 Finally some other authors try to better estimate the variation of temperature within the pipe only in order to simplify the resistance parameter identification procedure.…”