Heat loss from thermal energy storage ventilated tank foundations
Introduction
Concentrating solar power (CSP) is unique among renewable energy generators because even though it is variable, like solar photovoltaic and wind, it can easily be highly dispatchable. Most of the currently installed thermal energy storage (TES) systems in utility-scale solar thermal electric plants store energy using sensible heat, employing molten salts in an indirect two-tank design (Kuravi et al., 2013). The denominated cold and hot tanks are at two different temperature levels depending on the solar power plant (SPP) type (usually 292/386 °C for parabolic trough plants and 292/565 °C for central receiver plants). Even though the tanks are insulated, thermal losses from the tank to the environment (which occur through the tank’s walls, the roof and the foundation), while relatively small, are important and must be analyzed and minimized during the TES design process in order to improve the TES efficiency.
Heat transfer through the ground has long been recognized as being a substantially more complex problem compared with that through components above ground (Anderson, 1991). Due to the coupled nature of the problem, apart from the foundation construction characteristics, the soil properties also play an important role in the foundation heat losses. The thermal conductivity of soil is a major determinant of ground heat transfer: in first approximation the heat flow through an insulated floor is directly proportional to this quantity (Anderson, 1991).
A very important number of research efforts on ground-coupled heat losses applied to buildings can be found in the literature. Research on ground-coupled losses applied to buildings started during the 1940s and different analytical and semi-analytical methods for determining the earth-contact heat losses can be found in the open literature (Macey, 1949, Delsante et al., 1983, Hagentoft, 1988b, Anderson, 1991, Davies, 1993b). Numerical methods have been also developed to simulate complex systems, where the direct application of analytical solutions was not possible because of the simplifications that are required in order to produce a solution (Richards and Mathews, 1994, Zoras et al., 2001). Methods for the heat loss calculation of building structures in contact with the ground are also included in different design guides, such as ASHRAE, 1997, CIBSE, 1986, AICVF, 1990 or CEN (1992).
Contrary to the case of ground-contact building structures applications, much less information can be found in the literature for high temperature tank foundation heat losses. In some works, different TES tanks sub-models are used as a part of a global model of a SPP to take into account the tank’s heat losses in the calculations (Powell and Edgar, 2012, Mawire, 2013, Gabbrielli and Zamparelli, 2009, Rovira et al., 2011). However, in those sub-models, in some cases the simplifications are excessive (for example in Powell and Edgar (2012) it is assumed that no heat transfer occurs from the top or the bottom of each tank). In other cases either only an overall heat transfer coefficient is used to take into account the storage tank total heat losses (Mawire, 2013) (without distinguishing the contributions of the different parts: wall, top, bottom) or no information is provided in the methodology of obtaining the overall heat transfer (Gabbrielli and Zamparelli, 2009, Rovira et al., 2011).
More detailed thermal models to obtain the heat losses in TES tank’s plants can be found in references Schulte-Fischedick et al., 2008, Zaversky et al., 2013 and Rodríguez et al. (2013). In these investigations, a tank based on the geometry and operating conditions of the Andasol-1 commercial trough power plant is analyzed and the heat losses are evaluated. Foundation consist of a thin steel layer followed by a thin layer of dry sand, a foam-glass insulation layer and an air-cooled concrete foundation designed to keep the concrete temperature below a maximum admissible value. Although the tank geometry and the operating conditions used were similar, the reported results in terms of the heat losses are different, due to the different methodologies and model assumptions used in each model. Particularly, the foundation heat losses obtained using these complete thermal models were in the range of 23–49 kW for the cold tank and 31–62 kW for the hot tank. These different results and the lack of specific studies applied to TES tank foundation heat losses, suggest the necessity of a more accurate calculation methodology of this ground-coupled heat transfer problem. In the present work, the classical problem of ground-coupled conduction is revised for estimating the foundation heat losses for the practical application of TES tanks.
Section snippets
Problem definition
A description of the studied problem is presented in the next paragraphs.
Solution procedure
A one-dimensional steady-state multilayer model is used to solve the heat transfer through the tank foundation. Consequently, temperature gradients are considered to exist along only a single coordinate direction (z coordinate), and heat transfer is supposed to occur exclusively in that direction, being temperatures and heat fluxes independent of time. The equivalent thermal circuit representation is shown in Fig. 3, in which only the most important tank foundation layers from the heat transfer
Results and discussion
Firstly, using the described CFD model, a correlation for the soil equivalent thermal resistance is obtained numerically. Then, the described methodology is directly applied to typical state-of-the-art TES tanks and the results are discussed in detail and summarized, providing a quick method for the estimation of the total bottom heat losses and its components (the ventilation heat losses and the heat loss to the soil).
Conclusions
The loss of heat through ventilated TES tanks foundations has been analyzed for typical operating conditions in state-of-the-art SPPs using a one-dimensional steady-state multilayer model. The foundation ventilation system, which is designed to establish a temperature in the concrete layer below a maximum temperature, extracts to the environment a fraction of the total bottom losses and the rest is conducted through the soil. A CFD model is developed to derive a correlation for the soil
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