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We consider a binary multivariate regression model where the conditional expectation of a binary variable given a higher-dimensional input variable belongs to a parametric family. Based on this, we introduce a model-based bootstrap (MBB) for higher-dimensional input variables. This test can be used to check whether a sequence of independent and identically distributed observations belongs to such a parametric family. The approach is based on the empirical residual process introduced by Stute (Ann Statist 25:613–641, 1997). In contrast to Stute and Zhu’s approach (2002) Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), a transformation is not required. Thus, any problems associated with non-parametric regression estimation are avoided. As a result, the MBB method is much easier for users to implement. To illustrate the power of the MBB based tests, a small simulation study is performed. Compared to the approach of Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.
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.
In this paper, we present the structure, the simulation the operation of a multi-stage, hybrid solar desalination system (MSDH), powered by thermal and photovoltaic (PV) (MSDH) energy. The MSDH system consists of a lower basin, eight horizontal stages, a field of four flat thermal collectors with a total area of 8.4 m2, 3 Kw PV panels and solar batteries. During the day the system is heated by thermal energy, and at night by heating resistors, powered by solar batteries. These batteries are charged by the photovoltaic panels during the day. More specifically, during the day and at night, we analyse the temperature of the stages and the production of distilled water according to the solar irradiation intensity and the electric heating power, supplied by the solar batteries. The simulations were carried out in the meteorological conditions of the winter month (February 2020), presenting intensities of irradiance and ambient temperature reaching 824 W/m2 and 23 °C respectively. The results obtained show that during the day the system is heated by the thermal collectors, the temperature of the stages and the quantity of water produced reach 80 °C and 30 Kg respectively. At night, from 6p.m. the system is heated by the electric energy stored in the batteries, the temperature of the stages and the quantity of water produced reach respectively 90 °C and 104 Kg for an electric heating power of 2 Kw. Moreover, when the electric power varies from 1 Kw to 3 Kw the quantity of water produced varies from 92 Kg to 134 Kg. The analysis of these results and their comparison with conventional solar thermal desalination systems shows a clear improvement both in the heating of the stages, by 10%, and in the quantity of water produced by a factor of 3.
Modeling and upscaling of a pilot bayonettube reactor for indirect solar mixed methane reforming
(2020)
A 16.77 kW thermal power bayonet-tube reactor for the mixed reforming of methane using solar energy has been designed and modeled. A test bench for the experimental tests has been installed at the Synlight facility in Juelich, Germany and has just been commissioned. This paper presents the solar-heated reactor design for a combined steam and dry reforming as well as a scaled-up process simulation of a solar reforming plant for methanol production. Solar power towers are capable of providing large amounts of heat to drive high-endothermic reactions, and their integration with thermochemical processes shows a promising future. In the designed bayonet-tube reactor, the conventional burner arrangement for the combustion of natural gas has been substituted by a continuous 930 °C hot air stream, provided by means of a solar heated air receiver, a ceramic thermal storage and an auxiliary firing system. Inside the solar-heated reactor, the heat is transferred by means of convective mechanism mainly; instead of radiation mechanism as typically prevailing in fossil-based industrial reforming processes. A scaled-up solar reforming plant of 50.5 MWth was designed and simulated in Dymola® and AspenPlus®. In comparison to a fossil-based industrial reforming process of the same thermal capacity, a solar reforming plant with thermal storage promises a reduction up to 57 % of annual natural gas consumption in regions with annual DNI-value of 2349 kWh/m2. The benchmark solar reforming plant contributes to a CO2 avoidance of approx. 79 kilotons per year. This facility can produce a nominal output of 734.4 t of synthesis gas and out of this 530 t of methanol a day.
As part of the transnational research project EDITOR, a parabolic trough collector system (PTC) with concrete thermal energy storage (C-TES) was installed and commissioned in Limassol, Cyprus. The system is located on the premises of the beverage manufacturer KEAN Soft Drinks Ltd. and its function is to supply process steam for the factory's pasteurisation process [1]. Depending on the factory's seasonally varying capacity for beverage production, the solar system delivers between 5 and 25 % of the total steam demand. In combination with the C-TES, the solar plant can supply process steam on demand before sunrise or after sunset. Furthermore, the C-TES compensates the PTC during the day in fluctuating weather conditions. The parabolic trough collector as well as the control and oil handling unit is designed and manufactured by Protarget AG, Germany. The C-TES is designed and produced by CADE Soluciones de Ingeniería, S.L., Spain. In the focus of this paper is the description of the operational experience with the PTC, C-TES and boiler during the commissioning and operation phase. Additionally, innovative optimisation measures are presented.
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.