Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

Abstract

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.