Background: A proven option to found buildings are geothermally activated steel pipes. Statics determine their dimensions. Energy improvement research focuses on the radius of inner pipe of such coaxial geothermal probes. Mass flow rate is often constant when optimizing inner pipe dimensions. In contrast, in this study flow conditions in outer pipe are constant (constant Reynolds number) to ensure that they not change during optimization. Aim is to maximize net exergy difference for the desired flow type by changing inner pipe radius (after deduction of hydraulic effort). System technology can be selected based on this optimal design and its associated boundary conditions for mass flow and temperatures.
Methods: Thermal calculations based on Hellström are carried out to quantify an influence of changing inner pipe radius on thermal yield. A hydraulic optimization of inner pipe radius is performed. Increasing inner pipe radius results in decreasing hydraulic losses in inner pipe but increases hydraulic losses in outer circular ring. Net exergy difference is a key performance indicator to combine thermal and hydraulic effects. Optimization of net exergy difference is carried out for selected scenarios. All calculations are based on various, but fixed Reynolds numbers in the circular ring (Re = [4e3; 1e4; 1e5]), instead of fixed mass flow rates. This ensures fixed flow conditions and no unnecessary high mass flow rate.
Results: Optimal inner radius is approximately as large as outer radius considering thermal results. Reynolds numbers are always bigger in inner pipe, due to the constant Reynolds number in circular ring. Both indicate that from a thermal point of view, a high mass flow rate and a high degree of turbulence are particularly important. Hydraulic optimal inner pipe radius is 54% of outer pipe radius for laminar flow scenarios and 60% for turbulent flow scenarios. Exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains.
Conclusions: Design of coaxial geothermal probes should focus on the hydraulic optimum and take energetic optimum as a secondary criterion to maximize net exergy difference.