Note on Critical Exponents for a System of Heat Equations Coupled in the Boundary Conditions

As the energy efficiency demands for future buildings become increasingly stringent, preliminary assessments of energy consumption are mandatory. These are possible only through numerical simulations, whose reliability crucially depends on boundary conditions. We therefore investigate their role in numerical estimates for the usage of geothermal energy, performing annual simulations of transient heat transfer for a building employing a geothermal heat pump plant and energy piles. Starting from actual measurements, we solve the heat equations in 2D and 3D using COMSOL Multiphysics and IDA-ICE, and discover a negligible impact of the multiregional ground surface boundary conditions. Moreover, we verify that the thermal mass of the soil medium induces a small vertical temperature gradient on the piles surface. We also find a roughly constant temperature on each horizontal cross-section, with nearly identical values if the average temperature is integrated over the full plane or evaluated at one single point. Calculating the yearly heating need for an entire building we then show that the chosen upper boundary condition affects the energy balance dramatically. Using directly the pipes’ outlet temperature induces a 54% overestimation of the heat flux, while the exact ground surface temperature above the piles reduces the error to 0.03%.

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Energy Pile Field Simulation in Large Buildings: Validation of Surface Boundary Assumptions

Energies ◽

10.3390/en12050770 ◽

2019 ◽

Vol 12 (5) ◽

pp. 770 ◽

Cited By ~ 3

Author(s):

Andrea Ferrantelli ◽

Jevgeni Fadejev ◽

Jarek Kurnitski

Keyword(s):

Boundary Conditions ◽

Single Point ◽

Ground Surface ◽

Thermal Mass ◽

Heat Equations ◽

Outlet Temperature ◽

Surface Boundary ◽

Geothermal Heat ◽

Soil Medium ◽

Surface Boundary Conditions

As the energy efficiency demands for future buildings become increasingly stringent, preliminary assessments of energy consumption are mandatory. These are possible only through numerical simulations, whose reliability crucially depends on boundary conditions. We therefore investigate their role in numerical estimates for the usage of geothermal energy, performing annual simulations of transient heat transfer for a building employing a geothermal heat pump plant and energy piles. Starting from actual measurements, we solve the heat equations in 2D and 3D using COMSOL Multiphysics and IDA-ICE, discovering a negligible impact of the multiregional ground surface boundary conditions. Moreover, we verify that the thermal mass of the soil medium induces a small vertical temperature gradient on the piles surface. We also find a roughly constant temperature on each horizontal cross-section, with nearly identical average values when either integrated over the full plane or evaluated at one single point. Calculating the yearly heating need for an entire building, we then show that the chosen upper boundary condition affects the energy balance dramatically. Using directly the pipes’ outlet temperature induces a 54% overestimation of the heat flux, while the exact ground surface temperature above the piles reduces the error to 0.03%.

Download Full-text