The Green’s function based thermoelastic analysis of spherical geothermal tanks in a semi-infinite domain

Abstract

When an underground heat exchanger is subjected to a surface load on the ground and temperature change inside, the stress transfer between the thermal tank and the earth may cause the deformation and destruction of the tank. The bi-material thermoelastic fundamental solution of two-jointed dissimilar half-spaces is applied to elastic and thermal analysis of spherical heat storage tanks, where the continuity equations at the bi-material interface are satisfied. Using Hadamard’s regularization in the x3 direction, the two-dimensional bi-material thermoelastic fundamental solution can be obtained. By changing the material constants, the fundamental solution for a semi-infinite domain or an infinite domain with a single material can be recovered. In general, the storage tanks and soil exhibits different thermal and mechanical properties. A dual equivalent inclusion method (DEIM) is proposed to simulate the material mismatch of thermal conductivity and elasticity with continuously distributed eigen-temperature-gradients and inelastic eigenstrains on the tanks, respectively. Using the analytical domain integrals, no mesh is required for inhomogeneities. Due to the boundary effects and inhomogeneity interactions, the eigen-fields are expanded at the center of each inhomogeneity using the Taylor series with tailorable accuracy. The DEIM is verified by the finite element method and demonstrated by the geothermal applications using uniform, linear, or quadratic orders of eigen-fields. For a spherical heat exchanger in an infinite homogeneous domain, DEIM provides the exact solutions of the thermoelastic fields for a uniform heat source and a uniform far-field heat flux field.