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Previous studies optimized the dimensions of coaxial heat exchangers using constant mass fow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar fow types. In contrast, in this study, fow conditions in the circular ring are kept constant (a set of fxed Reynolds numbers) during optimization. This approach ensures fxed fow conditions and prevents inappropriately high or low mass fow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic efort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass fow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefcients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy diference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy fux and hydraulic efort. The Reynolds number in the circular ring is instead of the mass fow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar fow and 60% for turbulent fow scenarios. Net-exergetic optimization shows a predominant infuence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the fow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.
A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.