Previous studies optimized the dimensions of coaxial heat exchangers using constant mass flow 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 flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow 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 coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow 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 flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow 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.

中文翻译：

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使用固定流量条件而不是固定流量的同轴换热器的净能、水力和热力优化

以前的研究使用恒定质量流量作为边界条件优化了同轴换热器的尺寸。它们显示出几乎为零的热最佳圆环宽度。水力优化是湍流类型的内管与外管半径比为 0.65，层流类型为 0.68。相比之下，在本研究中，圆环中的流动条件在优化过程中保持不变（一组固定的雷诺数）。这种方法可确保固定的流量条件并防止不适当的高或低质量流量。优化针对三个目标进行：最大能量增益、最小水力工作和最终最佳净火用平衡。优化改变了内管半径和质量流量，但不改变圆环的雷诺数。热力计算基于 Hellström 的钻孔阻力和单独计算的水头系数线性损失的水力优化。增加内管半径导致内管中的液压损失减少，但圆环中的损失增加。净火用差异是一个关键性能指标，它结合了热力和水力计算。它是热能通量和水力作用之间的差异。在所有优化过程中，圆环中的雷诺数代替质量流量常数。从热学角度来看，结果是圆环的最佳宽度几乎为零。水力最佳内管半径对于层流是外管半径的 54%，对于湍流场景是 60%。净能优化显示水力损失的主要影响，特别是对于小温度增益。确切的结果取决于地球的热特性和流动类型。总之，同轴地热探头的设计应以水力优化为重点，由于水力占主导地位，将热优化作为次要标准。