Convective Transport from Geothermal Borehole Heat Exchangers Embedded in a Fluid-Saturated Porous Medium
Multi-dimensional natural convection and mixed convection have been studied numerically for the vertical borehole, a heated cylinder characterized by length Lb and diameter D, of a ground source heat pump in a fluid-saturated porous medium. The effect of natural convection over a range of ground properties characterized by Rayleigh number (RaL) is found to be significant and deviates strongly from boundary layer solutions for Rayleigh number less than 106, due to the flow turning required by the ground surface. For instance, the natural convection heat flux deviates from boundary layer prediction by over 20% for RaL = 104. Only at Rayleigh numbers of less than 2 x 103 can the heat transfer be treated as simple conduction, with the deviation less than approximately 5%, for fluid-saturated soil properties. The presence of groundwater flow, due to a hydraulic gradient, produces mixed convection leading to a convective heat transfer depending also upon Peclet number (PeD). A sufficient range of properties are examined such that the multi-dimensional mixed convection is shown to be captured between asymptotes to natural and forced convection. The dimensionless group (Lb/D)PeD/RaL is identified and shown to parameterize the variation between these two limits, with values less than 1.4 asymptoting to natural convection and values greater than 2.9 asymptoting to forced convection. Finally, a correlation encompassing all three regimes, natural, forced and mixed, is proposed.
G. Ravi Shanker and K. Homan, "Convective Transport from Geothermal Borehole Heat Exchangers Embedded in a Fluid-Saturated Porous Medium," Renewable Energy, vol. 196, pp. 328 - 342, Elsevier, Aug 2022.
The definitive version is available at https://doi.org/10.1016/j.renene.2022.06.089
Mechanical and Aerospace Engineering
Keywords and Phrases
Borehole Heat Transfer; Geothermal Heat Exchanger; Mixed Convection; Natural Convection; Porous Medium; Vertical Cylinder
International Standard Serial Number (ISSN)
Article - Journal
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01 Aug 2022