[en] Highlights: • A mathematical model for a PEMFC based cogeneration system is developed. • Developed model is validated using the available experimental data. • Performance of the plant at full load conditions is investigated. • Performance indices while applying two different modifications are determined. • System’s performance with and without modifications at partial loads is investigated. - Abstract: Polymer Electrolyte Membrane Fuel Cell (PEMFC) based systems have recently received increasing attention as a viable alternative for meeting the residential electrical and thermal demands. However, as the intermittent demand profiles of a building can only be addressed by a tri-generative unit which can operate at partial loads, the variation of performance of the system at partial loads might affect its corresponding potential benefits significantly. Nonetheless, no previous study has been carried out on assessing the performance of this type of tri-generative systems in such conditions. The present paper is the first of a two part study dedicated to the investigation of the performance of a tri-generative system in which a PEMFC based system is coupled with a desiccant wheel unit. This study is focused on evaluating the performance of the PEMFC subsystem while operating at partial loads. Accordingly, a detailed mathematical model of the fuel cell subsystem is first developed and validated using the experimental data obtained from the plant’s and the fuel cell stack’s manufacturer. Next, in order to increase the performance of the plant, two modifications have been proposed and the resulting performance at partial load have been determined. The obtained results demonstrate that applying both modifications results in increasing the electrical efficiency of the plant by 5.5%. It is also shown that, while operating at partial loads, the electrical efficiency of the plant does not significantly change; the fact which corresponds to the trade-off between the increment in the gross electrical efficiency and the lower slope of decrement in the auxiliary losses. The obtained results are suitable to be employed to assess the performance of the overall tri-generative system, conducted in the second part of the study, while meeting intermittent load profiles.

[en] Highlights: • Multi-objective optimization is utilized to optimize an HT-PEM fuel cell based CHP plant. • Net electrical efficiency and total capital cost are considered as optimization objectives. • A set of optimal points each of which is a trade-off between the objectives is obtained. • The effect of degradation on the performance of the system is taken into account. - Abstract: Multi-objective optimization method using genetic algorithm is employed in order to optimize design and operating parameters of a high temperature proton exchange membrane (HT-PEM) fuel cell based combined heat and power system. Net electrical efficiency of the plant, indicating the system's performance (to be maximized) and the total capital cost (to be minimized) are considered as optimization objectives. Current density (indicating the stack size), steam to carbon ratio, burner outlet temperature and auxiliary to process fuel ratio have been chosen as design parameters. Two different multi-objective optimization approaches have been utilized: steady state (without degradation) and long-term optimization while considering the degradation in fuel cell stack and the fuel processor. The results of the optimization procedures are Pareto frontiers which are a set of optimal points each of which is a trade-off between the considered objective functions. The performance indexes and operating conditions of three points with the maximum cumulative net electrical efficiency, minimum capital cost, and the same fuel cell area as that of the initial design are compared. It can be observed that while attempting to maximize the electrical efficiency, the cumulative net electrical efficiency of 29.96% can be achieved although it results in a total capital cost of 115711 €. On the other hand, the capital cost can be reduced down to 39,929 € which significantly diminishes cumulative net electrical efficiency. Finally, by locating the point on the Pareto frontier in which the fuel cell area is the same as that of the initial design, a cumulative net electrical efficiency of 27.07% was achieved which is 1% higher than the value obtained using the operating conditions of the initial design.

[en] Highlights: • A detailed FEM based dynamic model for a fire-tube boiler is developed. • Five configurations, representing different boiler models, are taken into account. • A PID controller is tuned for each configuration. • The performance of boilers, while addressing four demand profiles, is investigated. • Cumulative efficiency and pressure deviation in each simulation are determined. - Abstract: In the present paper, a detailed dynamic model of an industrial fire-tube boiler is first developed and five different geometrical configurations, each of which corresponds to a boiler model, are considered. Next, a PID controller is implemented and tuned for each configuration aiming at controlling the steam pressure, while addressing a demand with a variable flow rate. The operation of the developed boiler models, while providing four different steam demand profiles, are next simulated. The resulting cumulative average efficiency along with the cumulative pressure deviations and minimum and maximum pressure levels, which are achieved in each simulation, are then determined. The obtained results provide practical information regarding the trade-off between the size of the boiler and its corresponding performance and controllability. As an instance, the obtained results demonstrated that utilizing a boiler with the heat transfer surface of 36.76 m² instead of one with the corresponding surface of 56.55 m², in the worst-case scenario, leads to less than 2% of reduction in the efficiency and a negligible increment in the amplitude of pressure deviations. However, the former boiler is considerably smaller than the latter one and the mentioned choice can result in a significant saving in the required initial investment. Detailed information regarding the resulting pressure deviations has also been provided in order to facilitate verifying the consistency of the variations in each boiler’s supplied steam pressure with the corresponding acceptable range specified by the customer. Therefore, the provided results offer useful insights about the possible saving opportunities for small-medium scale industries, specifically in Italy, which are commonly employing oversized boilers with an On/Off control systems.

[en] In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive ${\mathrm{\delta <!--\; ??\; -->}}^{\mathrm{\prime <!--\; ???\; -->}}$- interaction, of strength $\mathrm{\beta <!--\; ??\; -->}$, centred at 0 (the bottom of the confining parabolic potential), that was rigorously defined in a previous paper by means of a ‘coupling constant renormalisation’. Here we get the Hamiltonian as a norm resolvent limit of the harmonic oscillator Hamiltonian perturbed by a triple of attractive $\mathrm{\delta <!--\; ??\; -->}$-interactions, thus extending the Cheon–Shigehara approximation to the case in which a confining harmonic potential is present. (paper)

[en] We rigorously define the self-adjoint one-dimensional Salpeter Hamiltonian perturbed by an attractive $\mathrm{\delta <!--\; ??\; -->}-<!--\; ???\; -->interaction,$ of strength $\mathrm{\beta <!--\; ??\; -->},$ centred at the origin, by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, a technique used first heuristically in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the $\mathrm{\delta <!--\; ??\; -->}-<!--\; ???\; -->interaction$ in two and three dimensions. We show that the spectrum of the self-adjoint operator consists of the absolutely continuous spectrum of the free Salpeter Hamiltonian and an eigenvalue given by a smooth function of the parameter $\mathrm{\pi <!--\; ??\; -->}/\mathrm{\beta <!--\; ??\; -->}.$ The method is extended to the model with two twin attractive deltas symmetrically situated with respect to the origin in order to show that the discrete spectrum of the related self-adjoint Hamiltonian consists of two eigenvalues, namely the ground state energy and that of the excited antisymmetric state. We investigate in detail the dependence of these two eigenvalues on the two parameters of the model, that is to say both the aforementioned strength $\mathrm{\beta <!--\; ??\; -->}$ and the separation distance. With regard to the latter, a remarkable phenomenon is observed: differently from the well-behaved Schrödinger case, the 1D-Salpeter Hamiltonian with two identical Dirac distributions symmetrically situated with respect to the origin does not converge, as the separation distance shrinks to zero, to the one with a single $\mathrm{\delta <!--\; ??\; -->}-<!--\; ???\; -->interaction$ centred at the origin having twice the strength. However, the expected behaviour in the limit (in the norm resolvent sense) can be achieved by making the coupling of the twin deltas suitably dependent on the separation distance itself. (paper)

[en] Highlights: • A FEM based dynamic model for a fire-tube boiler with SPRF combustor is developed. • Dynamic behaviour of five boiler configurations, with a tuned PID, is simulated. • The simulations are conducted while addressing four demand profiles. • At each simulation, the mean efficiency and pressure variation are obtained. • The most economically profitable configuration is determined using NPV as the indicator. -- Abstract: In the first part of the present work, a detailed dynamic model of fire-tube boilers equipped with stagnation point reverse flow (SPRF) combustor is implemented. Experimental data, obtained through a testing procedure, are then employed to validate the developed model. Several boiler configurations with different sizes are next considered and a PID controller is subsequently tuned for each boiler model. In the next step, the dynamic behaviour of the considered boilers, while addressing different steam demand profiles, is simulated and the corresponding overall efficiency is determined. A comprehensive economic analysis is then conducted in order to choose the most suitable boiler model for each profile, taking into account both the corresponding fuel consumption and the required initial investment. The obtained results demonstrate that, beyond a certain size, increasing the dimensions of the boiler leads to a negligible increment in the efficiency. Accordingly, boiler No. 2, which is a notably smaller unit compared to the other configurations, is determined to be the most economically promising choice. Furthermore, the pressure variations of the steam supplied by different configurations have also been studied. The obtained results demonstrated that utilizing larger boilers leads to an insignificant reduction in the amplitude of pressure deviations and does not have any effect on duration of these variations. Therefore, the provided results can be utilized to choose the most economically suitable size of the boiler, considering the customer’s consumption profile, while guaranteeing that the specifications of the customer in terms of acceptable pressure deviation of the supplied steam are also addressed.

[en] Solar troughs are amongst the most commonly used technologies for collecting solar thermal energy and any attempt to increase the performance of these systems is welcomed. In the present study a parabolic solar trough is simulated using a one dimensional finite element model in which the energy balances for the fluid, the absorber and the envelope in each element are performed. The developed model is then validated using the available experimental data . A sensitivity analysis is performed in the next step in order to study the effect of changing the type of the working fluid and the corresponding Reynolds number on the overall performance of the system. The potential improvement due to the addition of a shield on the upper half of the annulus and enhancing the convection coefficient of the heat transfer fluid is also studied.

[en] We rigorously define the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ′-interaction, of strength β, centred at 0 (the bottom of the confining parabolic potential), by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the δ-interaction in two and three dimensions. The way the δ′-interaction enters in our Hamiltonian corresponds to the one originally discussed for the free Hamiltonian (instead of the harmonic oscillator one) by P Sěba. It should not be confused with the δ′-potential perturbation of the harmonic oscillator discussed, e.g., in a recent paper by Gadella, Glasser and Nieto (also introduced by P Sěba as a perturbation of the one-dimensional free Laplacian and recently investigated in that context by Golovaty, Hryniv and Zolotaryuk). We investigate in detail the spectrum of our perturbed harmonic oscillator. The spectral structure differs from that of the one-dimensional harmonic oscillator perturbed by an attractive δ-interaction centred at the origin: the even eigenvalues are not modified at all by the δ′-interaction. Moreover, all the odd eigenvalues, regarded as functions of β, exhibit the rather remarkable phenomenon called ‘level crossing’ after first producing the double degeneracy of all the even eigenvalues for the value displayed. (paper)

[en] Highlights: • An exergetic-economic-environmental analysis of an SOFC-GT-ST plant was performed. • Exergetic efficiency and total cost rate of the plant were considered as objectives. • Multi-objective optimization was conducted to obtain a set of optimal solutions. • Exergy destruction rate and capital cost of components of the plant were determined. • The Rankine bottoming cycle enhanced the exergetic efficiency of the plant by 8.84%. - Abstract: In the present study, a detailed thermodynamic model for an internal-reforming solid oxide fuel cell-gas turbine (SOFC-GT) hybrid system integrated with a Rankine (steam) cycle is developed, and exergetic, economic and environmental analyses have been carried out on the plant. Considering the exergetic efficiency and the total cost rate of the system as conflicting objectives, a multi-objective optimization of the system is conducted to determine the optimal design point of the plant. A set of optimal solutions (Pareto front) is achieved, each of which is a trade-off between the chosen objectives. Finally, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) decision-making method is used to choose the final optimal design parameters. The results demonstrate that the final optimal design of the proposed plant leads to an exergetic efficiency of 65.11% and total cost rate of 0.13745 €/s. Furthermore, the optimization results reveal that the integration of the Rankine cycle with the SOFC-GT system has led to an 8.84% improvement in the total exergetic efficiency of the plant, producing additional 8439.2 MW h of electricity and avoiding ∼5900 metric tons of carbon dioxide emissions annually.

[en] The Thermogravimetric Heat Pump (TGHP) is a non-conventional system, implementing a reverse cycle, the main difference of which from the usual vapor compression (Rankine) cycle is a quasi-isothermal compression of the working fluid by a high heat capacity carrier fluid. Previous studies showed that employing HFC134a or PF5050 as working fluids may be promising in terms of thermodynamic performance, though the corresponding required plant heights confine its application to tall buildings (from minimum height of 10–12 storeys to skyscrapers). Accordingly, an investigation has been carried out in the present study in order to determine a group of fluids which allow lower heights under the same input conditions. In order to investigate the performance of the system and the required plant height, operation of a 100 kW TGHP has been simulated for 17 different fluids. Accordingly, the corresponding COPs and required heights are determined and based on the achieved COPs, the optimum fluid for each range of building height is selected. The resulting plant heights range from 20 m to nearly 200 m and R245ca is shown to be the most promising fluid for the lowest plant height range. A parametric study is next carried out in order to study the effect of variations in the condensation temperature and the dimensionless plant height on the performance of the system. The obtained results demonstrate that an increase in the former from 313 K to 348 K, for almost all of the analyzed fluids, causes a reduction of around 50% in the COP. It is also shown that, almost independent of the employed fluid, the maximum values of COP are reached for a dimensionless plant height of around 1.8. Moreover, all the analyzed fluids show basically the same COP trend and, at the same operating conditions, the COP values for all fluids are within a 10% range of variation. This leads to the conclusion that the thermophysical properties of the employed fluid mainly influences the required height of the system, while the COP values remain in a relatively small range. - Highlights: • The required plant height with different working fluids for a thermogravimetric heat pump was determined. • A fluid selection diagram including COP and the required height for different fluids was presented. • Sensitivity analysis to study the effect of height increasing factor on COP was performed. • Sensitivity analysis to investigate the effect of condensation temperature on the COP was also carried out