Off-design simulation and performance of molten salt cavity receivers in solar tower plants under realistic operational modes and control strategies

Highlights

• Model developed for cavity receivers for design and off-design performance analysis.

• Receiver performance degraded with increased receiver inlet temperature.

• Receiver control strategies were found to alter the inlet temperature and DNI limits.

• A combined control approach was proposed to maximize receiver operation range.

• Off-design receiver efficiency correlations are provided for these strategies.

Abstract

Solar irradiation is intermittent, but concentrated solar thermal (CST) plants are typically designed and analyzed solely based on their steady design point. Unlike coal power plants, however, CST plants frequently experience thermal loads well above and below their rated design point, leading to off-design operation for much of the operational year. Importantly, if a latent heat thermal energy storage (LHTES) system is employed, the receiver inlet temperature can vary under these conditions. To date, there is a clear lack of knowledge for how to handle off-design conditions in terms of developing appropriate control strategies to maximize the receiver thermal output and its operational region. In this study, a thermal model was developed and validated that is suitable for design/off-design performance analyses of molten salt cavity receivers in both steady state and transient conditions. The study investigated two control strategies – a fixed receiver flow rate (FF) and fixed receiver outlet temperature (FT) – for their off-design performance in each of two off-design operational modes (storage and non-storage). Solar field utilization (SFU) is variable in non-storage mode, but in the storage mode, it is whether variable or fixed at design point (SFU = 1). The feasible operating region in this study refers to the zone restricted by maximum allowable operational parameters defined based on design point analysis, mainly maximum receiver outlet temperature, maximum flow rate, and maximum receiver surface temperature.

Through this analysis, it was found that receiver inlet temperatures above the design point (560 K) degrade the receiver performance in both control strategies and under all operational modes. The results also revealed that the maximum allowable receiver inlet temperature that maintains the receiver operation inside the feasible region could not go beyond ∼700 K or 600 K with the FF and FT strategies (in the storage mode with variable or fixed SFU), respectively. These values also indicate the charging cut-off temperature for the fluid flowing out in LHTES systems. In the non-storage mode, the receiver inlet temperature is remained constant at design point by varying the SFU over the time. While the design point direct normal irradiation (DNI) was 900 W m⁻², the maximum allowable DNI is 700 W m⁻² and 500 W m⁻² with the FF and FT strategies, respectively. These results motivate a hybrid control strategy that switches between the FF and FT strategies to maximize the performance and the number of operational hours of a CST plant during the day. As a final aspect of this study, off-design receiver efficiency correlations are developed that can be used in any simulation environment to accurately predict receiver performance.

Introduction

In response to worldwide energy and environmental concerns, replacing conventional fossil fuel-based energy conversion technologies with renewables has become a global priority [1], [2]. Concentrated solar thermal (CST) plants are a promising technological solution as they can be integrated with thermal energy storage (TES) to meet peak demand, even in times of low solar irradiance. Parabolic troughs technology dominates today’s CST market, but the future ascendancy of tower systems seems evident [3], [4], [5], [6]. The fundamental reason for this shift is related to the higher receiver and cycle efficiency in tower systems due to their higher concentration ratio (∼1000× as compared to ∼100× in parabolic trough plants) [7]. Accordingly, as reported in [8], [9], [10], tower systems represent the next generation of CST plants as they can achieve higher efficiency and lower cost.

The four main subcomponents of molten salt tower-based CST (CST-tower) plants are the heliostat field, receiver, a thermal energy storage system (TES), and a power block. Of the four main subcomponents, the thermal efficiency of the whole plant is most sensitive to the performance of the receiver as a supplier of heat for the Rankine cycle. Therefore, the receiver efficiency and reliability across the whole operational range of heat transfer fluid (HTF) temperatures and flow rates must be determined a priori – e.g. before building a CST plant costing upwards of ∼1 Billion USD [4], [11]. To date, many CST-tower designs have been evaluated with simulations and/or experiments. These include tubular, cavity, multi-cavity, volumetric receivers and direct absorbing receivers which can employ steam, molten salt, molten metal, gas, and particles [12], [13], [14]. Among them, the molten salt cavity receiver has been proposed as the most cost effective and efficient for the near term [7], [15], [16]. One advantage of molten salt cavity receivers – over gas receivers – is their relatively energy dense flow which goes directly to and from storage, enabling higher dispatchability and round trip storage efficiency.

When it comes to minimizing the thermal heat loss of cavity receivers, several studies have found that all three mechanisms of heat transfer (conduction, convection, and radiation) play a role [17], [18], [19], [20], [21], [22]. Li et al. [20] has shown that apart from three conventional ways of heat transfer, the highest loss in cavity receivers corresponds to reflection losses, which can amount to 50% of the total loss. It has been shown that conduction heat loss accounts for the smallest share of heat loss (usually < 1%) in cavity receivers. Hinojosa et al. [23] presented numerical results of natural convection and surface thermal radiation for open cavity receivers based on the Boussinesq approximation. Gonzalez and Palafox [24] found that radiation heat transfer is greater than convection heat transfer when there is a large temperature difference between the hot wall and the bulk fluid (e.g. ΔT > 200 K). Clausing [25] showed that the influence of wind for normal operating conditions (<8 m/s) has minimal influence on convective heat losses for a cavity receiver. Along with these studies on the heat transfer mechanisms involved, there are also several studies in the recent literature focusing on improving the performance of molten salt cavity receivers.

Yang et al. [26] showed that the average Nusselt numbers inside a spiral tube in the receiver was about 3 times that of smooth tube. They also indicated that the convection losses of the molten salt receiver with a spiral tube were lower than a smooth one [26]. Fang et al. [27] used the Monte-Carlo method to determine the heat flux and temperature distribution inside the cavity. They found that the distribution of heat flux inside the cavity is non-uniform and that the roof gains more radiation than the walls of the cavity [27]. Yang et al. [28] used computational fluid dynamics to reveal the distributions of temperature and heat flux and the heat transfer characteristics of the receiver tube. Their results showed that the temperature distribution of the molten salt and the tube wall are very uneven in both the axial and radial directions, and that the temperature of the inner tube wall is an important parameter for preventing decomposition of the molten salt [28]. Zheng et al. [29] numerically investigated the enhancement for convection heat transfer of turbulent flow in a central receiver tube with a porous medium and non-uniform circumferential heat flux. They found that the porous insert can be used to avoid the hotspot caused by non-uniform heat flux. Jianfeng et al. [30] investigated the heat absorption efficiency and associated heat transfer characteristics of an external receiver pipe under unilateral concentrated solar radiation. They found that as the incident energy flux increases, the pipe wall temperature increases almost linearly, while the heat absorption efficiency will first increase and then decrease. It was also shown that as the pipe length increases, the average absorption efficiency of the pipe drops off rapidly [30]. Other researchers focused on the design and optimization of the receiver structure. Lata et al. [31] studied the receiver’s design and optimization and discovered that a smaller tube diameter produces higher efficiency and a lower tube surface temperature. Garbrecht et al. [32] presented a molten salt central receiver design which reduced the reflected energy losses effectively, according to CFD simulations.

All of the above numerical models are very detailed and correspond to non-conventional designs, which make them challenging to integrate with the other plant components (e.g. transient interaction of various subcomponents of CST plants).

Along these lines, there are a few relevant assessments of cavity receivers for integration purposes. Benammar et al. [21] proposed a model to predict the design point thermodynamic performance of cavity receivers, but no validation was presented. Li et al. [20] developed a global steady-state thermal model of a 100 kW_th molten salt cavity receiver. They have shown that the major design parameters of molten salt cavity receivers are receiver area, number of tubes in the receiver panel, tube diameter, and receiver surface temperature [20]. Li et al. also found that the receiver energetic efficiency increases when the incident power increased, but that the receiver energetic efficiency was more stable with a constant flow rate control strategy as compared to constant receiver outlet temperature operational mode [20]. Zhang et al. [33] experimentally investigated the thermal performance of a molten salt cavity receiver in transient conditions (e.g. variable incident power on the receiver). They found that the instantaneous energetic efficiency of the receiver is strongly influenced by input power [33]. They also stated that the closer the input power is to the design value, the less the instantaneous efficiency changes [33]. In a later study, Zhang et al. [34] developed a very detailed dynamic mathematical model of a generalized receiver using a commercial modeling software (Dymola) that couples the conduction, convection and radiation heat transfer processes in the receiver. Xu et al. [35] and Yao et al. [36] presented the dynamic and static characteristics of the 1 MW DAHAN power plant (direct steam generation) in China. Their results indicated that the receiver energetic efficiency is almost constant at 85% when the total incident energy on the receiver is above 2000 kW. Samanes and Garcia-Barberena [37] presented a model for the transient simulation of solar cavity receivers. The model involves partial differential equations that are solved numerically by applying the finite volume method [37]. Although no validation presented for this model, it was reported as a reliable controller for on-site monitoring of molten salt cavity receivers [37].

Based on the available literature, it can be concluded that the vast majority of prior work was focused on investigating the molten salt cavity receivers in terms of an optimum geometric configuration, heat flux distribution inside cavity, and the heat transfer mechanisms involved. Ultimately, these analyses are limited to steady-state operation analysis (e.g. at the design point). To date, most off-design performance analysis studies in the literature are limited to parabolic trough CST technologies, and usually systems with two-tank molten salt TES systems [38], [39], [40], [41], [42]. From these studies, it is expected that a cavity receiver in CST-tower plants will involve complex interactions between subcomponents (e.g. rapidly changing temperature and flow between them). In addition, the CST plant will have frequent off-design operation since each CST component is connected through transient mass flow and temperatures to the other components. Interactions during these off-design conditions also include CST-tower components that are not coupled via the HTF – such as the receiver and heliostat fields. When the plant goes off the rated design point, the receiver mass flow rate or outlet temperature can both become variables. In this case, the plant operational parameters should be monitored to keep the performance of the system close to design point, and to ensure that the system is safe (e.g. the HTF does not decompose). This situation creates a ‘feasible operating region’ where operational parameters are less than or equal to design point. Since the Rankine cycle requires a very specific inlet temperature, 838 K [15], [43], [44], this is patently difficult to satisfy with a transient resource. Outside this feasible region, the receiver cannot generate heat and the HTF must bypass the receiver. Knowing that the receiver inlet boundary conditions are imposed mainly by the receiver inlet temperature and the DNI input, feasible boundaries beyond which the receiver cannot work must be identified. The purpose of this off-design analyzes is to investigate how the receiver performance and its operational region can be expanded upon in these conditions. Hence, the analysis presented here has three main aims.

The first (and primary) aim of this paper is to propose a straightforward model that predicts not only the energetic but also the exergetic performance of molten salt cavity receivers at design and off-design conditions and is suitable for steady state and transient simulations. Second, to the author’s best knowledge, analyses of cavity receivers in transient or off-design conditions are all limited to evaluation of cavity receivers under the variable solar irradiation (incident power) [20], [21], [33], [34], [35], [36], [37]. However, aside from the intermittent solar irradiations, another important parameter that can lead to off-design operation of the cavity receivers is the receiver inlet temperature, which can be a variable parameter over the time in certain cases. This is especially true when it comes to ‘next-generation’ storage units that work on a non-constant temperature difference basis (e.g. LHTES systems [45], [46], [47]). Unlike conventional two-tank molten salts TES units in CST plants, the outlet HTF temperature from LHTES facilities varies over time both in charging and discharging [43], [47]. The variable outlet HTF temperature from the storage subcomponent will influence the performance of the molten salt cavity receiver and the Rankine cycle (since this directly affects the receiver inlet temperature as shown in Fig. 1). Hence, this study investigates the effect of variable receiver inlet temperature in detail. Lastly, the current literature is mostly limited to a single control strategy where the outlet temperature is fixed, but this study expands upon the literature by investigating a wide range of different plant operational modes and control strategies. As such, two control strategies are compared in this study: a fixed receiver flow rate (FF) and a fixed receiver outlet temperature (FT) strategy. These analyses are conducted for two operational modes: storage and non-storage (fully charged).

Overall, this study seeks to broaden the feasible boundary conditions for cavity receivers in order to find the best methods for off-design operation. This is expected to increase the useful range of allowable receiver inlet temperatures or DNI inputs, factors that are not always correspond to the exact design condition for the plant. Off-design performance curves of the cavity receiver (e.g. off-design efficiency correlations) are also expected to be of value to researchers who would like to analyze a CST plant without performing detailed simulations.