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Keywords
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.
Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, “Time series aggregation for energy system design: Modeling seasonal storage”, has developed a seasonal storage model to address this issue. Simultaneously, the paper “Optimal design of multi-energy systems with seasonal storage” has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.
The Solar-Institut Jülich (SIJ) and the companies Hilger GmbH and Heliokon GmbH from Germany have developed a small-scale cost-effective heliostat, called “micro heliostat”. Micro heliostats can be deployed in small-scale concentrated solar power (CSP) plants to concentrate the sun's radiation for electricity generation, space or domestic water heating or industrial process heat. In contrast to conventional heliostats, the special feature of a micro heliostat is that it consists of dozens of parallel-moving, interconnected, rotatable mirror facets. The mirror facets array is fixed inside a box-shaped module and is protected from weathering and wind forces by a transparent glass cover. The choice of the building materials for the box, tracking mechanism and mirrors is largely dependent on the selected production process and the intended application of the micro heliostat. Special attention was paid to the material of the tracking mechanism as this has a direct influence on the accuracy of the micro heliostat. The choice of materials for the mirror support structure and the tracking mechanism is made in favor of plastic molded parts. A qualification assessment method has been developed by the SIJ in which a 3D laser scanner is used in combination with a coordinate measuring machine (CMM). For the validation of this assessment method, a single mirror facet was scanned and the slope deviation was computed.