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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.
Advanced window systems and building energy performance / S. Reilly ; J. Göttsche ; V. Wittwer
(1991)
The optical performance of a 2-axis solar concentrator was simulated with the COMSOL Multiphysics® software. The concentrator consists of a mirror array, which was created using the application builder. The mirror facets are preconfigured to form a focal point. During tracking all mirrors are moved simultaneously in a coupled mode by 2 motors in two axes, in order to keep the system in focus with the moving sun. Optical errors on each reflecting surface were implemented in combination with the solar angular cone of ± 4.65 mrad. As a result, the intercept factor of solar radiation that is available to the receiver was calculated as a function of the transversal and longitudinal angles of incidence. In addition, the intensity distribution on the receiver plane was calculated as a function of the incidence angles.
Large scale central receiver systems typically deploy between thousands to more than a hundred thousand heliostats. During solar operation, each heliostat is aligned individually in such a way that the overall surface normal bisects the angle between the sun’s position and the aim point coordinate on the receiver. Due to various tracking error sources, achieving accurate alignment ≤1 mrad for all the heliostats with respect to the aim points on the receiver without a calibration system can be regarded as unrealistic. Therefore, a calibration system is necessary not only to improve the aiming accuracy for achieving desired flux distributions but also to reduce or eliminate spillage. An overview of current larger-scale central receiver systems (CRS), tracking error sources and the basic requirements of an ideal calibration system is presented. Leading up to the main topic, a description of general and specific terms on the topics heliostat calibration and tracking control clarifies the terminology used in this work. Various figures illustrate the signal flows along various typical components as well as the corresponding monitoring or measuring devices that indicate or measure along the signal (or effect) chain. The numerous calibration systems are described in detail and classified in groups. Two tables allow the juxtaposition of the calibration methods for a better comparison. In an assessment, the advantages and disadvantages of individual calibration methods are presented.
Eldorado summer schools
(1994)