- 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.
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