2023 Theses Doctoral

# Thermomechanical analysis of geothermal heat exchange systems

Heating and cooling needs have been highly demanded as the extreme weathers become increasingly frequent and global warming becomes well-founded. Because ground temperature keeps relatively constant at 20-30 feet below the surface, using the earth as a thermal mass for temperature conditioning and thermal management creates an energy-efficient and environmentally beneficial approach to surface heating and cooling, which has been used in self-heated pavement, greenhouse, and building integrated photovoltaic thermal systems. Inspired by the human body wherein a blood circulation system keeps skin nearly at a constant temperature under environmental changes, a thermal fluid circulation system is introduced to the geothermal well system.

Through bi-directional heat exchange between surface space with the ground, heat harvested at high temperatures can be stored underground for utilization at low temperatures, so that the surface temperature variations can be significantly reduced for daily and yearly cycles minimizing the heating/cooling needs. Understanding the heat transfer under the ground and thermal stress of the heat exchange systems induced by the temperature changes is critical for system design, performance prediction and optimization, and system control and operation. This dissertation studies heat transfer and thermomechanical problems for different geothermal systems. The temperature field of the earth can be calculated given the heat source and ambient temperature. Due to nonuniform thermal expansion caused by temperature differences or material mismatches, thermal stress will be induced. Its interaction with surface mechanical load and displacement constraint will be investigated for the design and failure analysis of the fluid circulation and heat exchange system.

In the theoretical study, the earth is approximated as a semi-infinite domain. Green's function technique has been used in the analysis of heat conduction, elastic, and thermoelastic problems respectively. The semi-infinite domain with a surface boundary condition can be considered a special case of two semi-infinite domains with a perfectly bonded interface, which forms an infinite bi-material domain. For a Dirichlet boundary value problem with a constant temperature or displacement, the top semi-infinite domain can be considered with infinitely large conductivity or stiffness, respectively; for a Neumann boundary value problem with zero flux or traction, the top semi-infinite domain can be considered with a zero conductivity or stiffness, respectively. The general Green's functions of an infinite bi-material domain can recover the classic solutions for Boussinesq's problem, Mindlin's problem, Kelvin's problem, etc. The three-dimensional (3D) problems can be used to recover the corresponding two-dimensional (2D) problems by an integral of Green's function in one dimension through the Hadamard regularization.

Firstly, the heat transfer problem in an infinite bi-material is introduced and the Green's function is formulated for the temperature change caused by a point heat source in the material. It is used to simulate heat transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The temperature field of the spherical inhomogeneity embedded in an infinite bi-material subjected to a uniform far-field steady-state or sinusoidal heat flux is determined by solving the boundary value problem. Eshelby’s equivalent inclusion method (EIM) is used to consider the mismatch of the thermal conductivities of the particle from the matrix, which is simulated by a prescribed temperature gradient. When the material of one semi-infinite domain exhibits zero or infinite thermal conductivity, the above solution can be used for a semi-infinite domain containing a heat source with heat insulation or constant temperature on the boundary, respectively. The analytical solution has been verified with the finite element method. The formulation is used to simulate a spherical heat source embedded in a semi-infinite domain. The method can be immediately applied to the design of geothermal energy systems for heat storage and harvesting. When the heat exchanger is a long horizontal pipe, a similar procedure can be conducted for the corresponding 2D problem. If the temperature exhibits a cyclic change, such as daily variation, the formulation is extended to the harmonic transient heat conduction problems.

Secondly, a similar formulation has been introduced for the elastic problem of an infinite bi-material. The Green's function is formulated for the displacement caused by a point force in the bi-material. It is used to simulate the stress transfer for a spherical heat exchanger embedded underground in geothermal energy applications. The formulation of the heat transfer problem is extended to the corresponding elastic problem. How a surface mechanical load is transferred to the underground heat exchanger is illustrated. The interactions between a heat exchanger and the surface load are investigated.

Finally, the thermoelastic problem of an infinite bi-material is introduced and the Green's function is formulated for the displacement field caused by a point heat source in the material. It can be straightforwardly used to derive the thermoelastic stress caused by a distributed heat source by volume integrals. However, when the thermal conductivity and elasticity of the heat exchanger are different from the earth in actual geothermal energy applications, the Green's function cannot be directly used. By analogy to Eshelby's equivalent inclusion method, a dual equivalent inclusion method (DEIM) is introduced to address the dual material mismatch in thermal and elastic properties.

The fundamental solutions of a bi-material for thermal, elastic, and thermoelastic problems are versatile and recover the ones of the single material domain for both 2D and 3D problems. The equivalent inclusion method is successfully extended to the thermoelastic problems to simulate the material mismatch. The formulation can be used in designing a geothermal heat exchanger for heat storage and supply for energy-efficient buildings as well as other geothermal applications.

Future work will extend the fundamental solutions to time-dependent thermomechanical load and investigate the daily and seasonal heat exchange with the ground using different configurations of the pipelines. The algorithms will be integrated into the inclusion-based boundary element method (iBEM) for geothermal system design and analysis.

## Subjects

## Files

- Wang_columbia_0054D_17636.pdf application/pdf 7.39 MB Download File

## More About This Work

- Academic Units
- Civil Engineering and Engineering Mechanics
- Thesis Advisors
- Yin, Huiming
- Degree
- Ph.D., Columbia University
- Published Here
- January 18, 2023