A fast and accurate semi-analytical method to determine the thermal response of bore fields

Enzo Zanchini; Francesco Zanchini

Home/Archive/arXiv

arXiv · 2412.07557

A fast and accurate semi-analytical method to determine the thermal response of bore fields

Enzo Zanchini·Francesco Zanchini

View original source ↗Read source document ↗Export metadata ↓

Abstract

The design and the simulation of a borehole-heat-exchanger (BHE) field is usually performed by simplified methods that yield either an overestimation or an underestimation of the thermal response. The methods employing the assumption of a uniform heat rate per unit BHE length overestimate the thermal response, while those employing the assumption of a uniform temperature of the external surface of the BHEs underestimate it. An accurate semi-analytical method to determine the g-function of a bore field with the real condition of BHEs fed in parallel with equal inlet temperature was developed by Cimmino (Int J Heat Mass Tran 91, 2015). An alternative semi-analytical method that yields the same results is presented in this paper. The method is implemented in a C++ program, available at the open-source online data repository of the University of Bologna. Thanks to several optimizations, the program yields a very accurate thermal response of bore fields of any shape with an extremely short computation time. The program is employed to analyze the inaccuracies caused by the assumptions of uniform heat rate and uniform surface temperature of the BHEs. It is also used to illustrate the low performance of the central BHEs in large and compact bore fields, and to show how the bore field can be optimized for a given plot of land and a fixed total length of the field.

Explore related subjects

physics.app-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Enzo Zanchini, Francesco Zanchini. 2024-12-10. A fast and accurate semi-analytical method to determine the thermal response of bore fields. https://arxiv.org/abs/2412.07557

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Pendellösung length-scale neutron and X-ray interferometry

Neutron and X-ray perfect-crystal interferometers (PCIs) are powerful platforms for studies of fundamental physics and phase-contrast imaging. Further enhancing several PCI capabilities requires reducing crystal blade thickness to the micron scale, which minimizes dynamical-diffraction image blur, permits operation in the pendellösung regime where blade thickness controls beam splitting, and reduces absorption for simultaneous neutron and X-ray operation. However, fabricating multiple crystal blades with identical micrometer-scale thicknesses over centimeter-scale areas remains a major challenge. Here, using a non-etching sub-micron fabrication technique, we demonstrate silicon triple-Laue interferometers with equal-blade-thicknesses of 110 $μ$m and 350 $μ$m, operated with both neutrons and X-rays. These devices are the thinnest PCIs realized to date, enabling a factor-of-six reduction in dynamical-diffraction beam spreading for improved phase-contrast imaging, while reaching the single pendellösung length regime in which crystal thickness provides an experimentally accessible control parameter for engineered quantum-optical beam splitting of plane-wave inputs. These results motivate multi-blade PCI designs utilizing identical half-pendellösung crystal lamellae that are proposed for neutron spin--orbit and electric dipole moment measurements.

physics.app-ph↗

arXiv2026

A State-Space Framework for trivial and Topological Metamaterial Stochastic Analysis

Topological phononic crystals and elastic metamaterials support edge states defined by global topological invariants, offering a route toward vibration-control and wave-guiding devices that remain functional in the presence of defects. However, manufacturing-induced spatial variability can perturb these invariants and compromise their robustness, making its quantification essential during design. In this work, we first demonstrate that a previously proposed linear time-varying (LTV) formulation is mathematically equivalent to the spectral element method based on transfer matrices for elementary rod, Saint-Venant shaft, and Euler-Bernoulli beam theories. The deterministic formulation is then extended to stochastic analyses through a stochastic linear time-varying (SLTV) framework. The proposed methodology combines Monte Carlo simulations with stochastic Fourier series and an analytical Karhunen--Loève expansion, providing closed-form stochastic fields and their derivatives required by the LTV formulation. The SLTV approach enables the computation of stochastic dispersion diagrams and forced responses of one-dimensional waveguides with arbitrarily varying geometry and mechanical properties. Because the LTV-based transition matrix isolates individual wavemodes without requiring the mode tracking needed by conventional eigenproblem-based formulations, the framework is particularly suited for evaluating topological invariants, specifically the Zak phase, and assessing the robustness of topological bands under spatial variability. Numerical results for rods, shafts, and Euler-Bernoulli beams demonstrate the applicability of the proposed framework as a unified methodology for deterministic and stochastic analyses of trivial and topological periodic waveguides under continuous spatial uncertainty.

physics.app-ph↗

arXiv2026

Low-loss phononic integrated circuits based on a silicon nitride-lithium niobate platform

Microwave-frequency acoustic waves in solids have emerged as a versatile platform for both classical and quantum applications. While phononic integrated devices and circuits are being developed on various material platforms, an ideal phononic integrated circuit (PnIC) platform should simultaneously support low-loss waveguide structures, high-quality-factor resonators, high-performance modulators, and efficient electromechanical transducers. Here, we establish a low-loss gigahertz-frequency PnIC platform based on patterned thin-film silicon nitride (SiN) on lithium niobate (LN) substrate. We develop low-loss PnIC building blocks including waveguides, directional couplers, and high-quality-factor (high-Q) ring resonators. As an application, we demonstrate a 1-GHz phononic oscillator based on a ring resonator, reaching a low phase noise of -159.0 dBc/Hz at a 100-kHz offset frequency. Our low-loss PnICs could meet the requirements in microwave acoustics, quantum phononics, and integrated hybrid systems combining phonons, photons, superconducting qubits, and solid-state defects.

physics.app-ph↗