Simplified heat transfer model for parabolic trough solar collectors using supercritical CO2
Introduction
Energy production is undoubtedly one of the challenges facing present-day society. The increasing energy demand, the harmful effects caused by greenhouse gases, as well as the depletion of fossil fuel resources, makes the current energy mix environmentally unsustainable [1]. Such environmental energy issues have fostered the development of renewables energies in general and Concentrated Solar Power (CSP) technologies in particular. Among all solar thermal technologies, Parabolic Trough Collector (PTC) is the most commercially deployed technology [2], [3], however the electricity cost is still not competitive with fossil fuels. So, in order to increase PTC solar-to-electric efficiency and reduce its costs, several research initiatives are in progress [4].
Increasing the outlet Heat Transfer Fluid (HTF) temperatures are currently pursued to increase the PTC thermal-to-electric efficiency. On the one hand, increasing the temperature increases the PTC thermal losses, but on the other hand, it increases the power cycle efficiency [5]. It is demonstrated that each concentration factor presents a temperature at which the thermal-to-electric efficiency gets a maximum.
Nowadays, one of the main constraints of PTC facilities comes from the HTFs [6], because the most widely used commercial fluid in PTC plants is biphenyl/diphenyl oxide synthetic oil that is rapidly degraded if 400 °C is exceeded, conditioning its performance by delimitation of the operation range temperature [7].
The use of alternative HTFs that are not temperature limited is a must [8], and pressurized gases enable to reduce the difficulties related to actual HTFs. Besides that, the wider operational temperature range increases the overall plant performance. Recently, carbon dioxide (CO2) has been considered an alternative to conventional HTF in PTC [9], which have been used for cooling applications of nuclear reactors since 1970 [10]. A remarkable aspect of CO2 is that its critical state is easily reached with PTC systems [11]. Specifically, it behaves like a supercritical fluid above its critical temperature (304.13 K) and critical pressure (7.38 MPa) adopting properties half-way between a gas and a liquid. Supercritical state provides to CO2 (sCO2) advantages for reaching higher efficiencies in super-critical cycles [12] at relatively low temperatures, since it can be used in the receiver and the gas turbines at same time removing heat exchanger for energy production [13]. The potential of sCO2 as HTF explains the growing interest in the development and design of suitable components for commercial applications [14]. A detailed literature review of sCO2 Brayton cycles in a wide variety of power generation applications has been performed by Manjunath et al. [15].
The heat transfer characteristics of PTC are essential to evaluate the thermal losses and improve its thermal performance, and they have received much attention in the literature. Briefly, the main works dealing with the thermal analysis of PTCs are presented. Forristall [16] carried out a detailed numerical heat transfer analysis of PTC, implemented in Equation Engineering Solver (EES), validated with experimental data from Sandia National Laboratories (SNL), using thermal oil as HTF. Dudley et al. [17] developed an analytical one dimensional (1-D) steady state model of a LS-2 parabolic solar collector under three different receiver configurations and two different selective absorbing coatings validated with experimental data collected by SNL. Gong et al. [18] presented an optimized model, programmed in Matlab that was compared with tests performed in the first high temperature PTCs, in China. A detailed radiative heat transfer analysis and more accurate heat transfer correlations were proposed by Padilla et al. [19] showing good agreement with experimental data, and in comparison with other heat transfer models. Kalogirou et al. [20] considered conduction through the absorber pipe and glass cover simultaneously, modelled in EES, and validated with data of existing collectors. A new numerical thermal model for Direct Steam Generation (DSG) in PTC with non-uniform heat flux implemented in Matlab was developed by Serrano-Aguilera et al. [21] evaluating thermal gradients in the absorber wall, and glass envelope. Qiu et al. [22] develop a detailed three-dimensional model combining Monte Carlo ray tracing and finite volume method to investigate the thermal performance of a PTC using sCO2 as the HTF under two typical conditions for the sCO2 Brayton and Rankine cycles.
This work presents a simplified 1-D model for a PTC to be used for different operating conditions and HTFs, focusing in sCO2 in an attempt to provide knowledge about the thermal performance with PTC. Firstly, the implemented thermal model is used for state-of-the-art silicone thermal oil, and carbon dioxide at subcritical state and the numerical results are compared with experimental tests from Plataforma Solar de Almería (PSA), Spain. Secondly, the sCO2 is considered as HTF in the 1-D model and the numerical results are compared with numerical literature data, as there are not available experimental results. Finally, a sensitivity analysis for sCO2 has been carried out to analyse the influence of the main operational PTC parameters, solar irradiation, mass flow rate and HTF inlet temperature, on the outlet fluid temperature in order to asses operational conditions.
Section snippets
Solar receiver description
A PTC consists of a parabolic reflector with solar tracking that reflects the direct solar radiation concentrating it on a linear receiver placed in the focus of the parabola, heating up the fluid that flows through, transforming the solar radiation into thermal energy. These collectors use support structures to conform the reflecting surface. In order to compare the numerical results obtained in this work with experimental values published previously, two collector designs have been
Results and discussion
The most meaningful outputs among the responsible variables of the thermal behaviour of the PTC are the HTF outlet temperature and the thermal efficiency of the PTC. So, these variables are adopted for comparison between experiments and simulations. The deviation (D) between the results and the reference data considered is presented.where and represent the simulated and experimental values respectively.
Conclusions
This work presents a simplified one-dimensional thermal model to study the thermal behaviour of PTC using carbon dioxide at supercritical conditions as HTF. Its implementation has been performed from the basic governing equations, and has been written in Matlab®. A complete description of all the equations, parameters, and variables is given. The methodology to perform a mesh independence study to get accurate approximations in the simulation results has been devised and incorporated into the
Declaration of Competing Interest
None.
Acknowledgements
The research work leading to this article has been developed under the framework of the DETECSOL project (ENE2014-56079-R), supported by the Spanish Department of Research, Development and Innovation. First author wishes to thank to CIEMAT for granting his Ph.D. research at Plataforma Solar de Almería.
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