Concentrated solar power (CSP) is an important technology for realizing solar thermal power generation [1
] and solar thermal energy storage [4
]. The parabolic or hyperboloid reflecting dish is used to focus the solar radiation, and the thermal cavity receiver is used to absorb heat to provide a high-temperature working medium, which can be used as the thermal energy storage component [6
]. The parabolic dish collector (PDC) is one of the main types of CSP systems. However, the concentrated solar flux distribution in the CSP system is extremely non-uniform, which causes local high temperatures and large temperature gradients in the receiver and seriously affects the safety performance and service life of the CSP system [7
]. The typical problems include degeneration of the materials, thermal stress, deformation, and overburning [10
At present, parametric research on improving the thermal performance of the receiver mainly focuses on the influence of the receiver’s shape, geometric parameters of the receiver, and tube diameter on its thermal performance. In the early stages, most studies focused on the influence of the cavity shape of the receiver, such as cylindrical, cuboidal, hemispherical, conical, and other irregular shapes [11
]. For instance, Karwa et al. [14
] studied receiver shape optimization and proposed a new receiver design for a compound parabolic concentrator. For a given cavity shape, many scholars [15
] have studied the influence of various geometric parameters such as cavity diameter and cavity height on the thermal performance of the receiver. Additionally, the heat transfer ability of the heat transfer fluid (HTF) in heat transfer tubes should match the solar flux distribution as closely as possible. Hence, it is important to improve the structure and layout of the heat transfer tube to improve these problems caused by nonuniform heat flux distribution. Regarding tube structure, some have studied the influence of tube diameter [17
], and some scholars have investigated the influence of tube layout, such as the tube loop number [15
]. For example, Wang et al. [21
] employed an asymmetric outward convex corrugated tube as the metal tube of a parabolic trough receiver to enhance the tube receiver’s overall heat transfer efficacy and dependability.
The above studies were quantitative studies on the geometric parameters of the receiver and tubes. In addition, some scholars have carried out optimization research on the thermal performance of the receiver. Since uniform temperature distribution in solar dish receivers and high optical–thermal efficiency are crucial to improving the reliability and economy of a solar dish system, Li et al. [22
] designed a new solar receiver–Stirling heater configuration to obtain a uniform distribution over the tube walls. Moreover, phase change materials were employed to improve thermal uniformity. For example, a coupling heat transfer containing phase change was applied in a cavity receiver by Tao et al. [23
], and could reduce the temperature gradient; in particular, it enhanced the thermal conductivity of the phase change material. In addition, heat pipe technology [24
] has also been applied to achieve more uniformity in the temperature of receivers. The impact of metal foam inserts in the receiver tube of the parabolic trough collector was investigated by Wang et al. [25
] regarding heat transfer under non-uniform heat flux boundary conditions. Moreover, some studies have adopted optimization algorithms to improve the performance of the receiver. Zheng et al. [26
] found that the majority of optimization investigations on the porous configuration of heat transfer tubes have relied on a “parameter analysis” trial-and-error approach. In response to this, they put forward a new optimization methodology that combines computational fluid dynamics (CFD) and a genetic algorithm (GA) to optimize the receiver’s porous configurations. Shen et al. [28
] developed a gradually varied porous configuration to boost the thermal performance of the porous volumetric solar receiver. They employed an optimization technique involving GA and CFD to establish the optimal distribution of porosity. Guo et al. [29
] employed multi-parameter optimization of a parabolic trough solar receiver based on a GA. Du et al. [30
] proposed an optimization method that couples the GA and the heat transfer analysis of the porous volumetric solar receiver. In their work, the receiver with relatively lower flow resistance and relatively higher thermal efficiency was obtained using multi-objective optimization (MOO). Risi et al. [31
] considered solar thermal efficiency as an objective function with four design variables, and a GA was used for the optimization process. Moloodpoor et al. [32
] developed an effective approach to solving the governing equations of heat transfer in parabolic trough collectors and used integrated particle swarm optimization to optimize the system’s thermal characteristics. Zadeh et al. [33
] used the hybrid optimization algorithm including a GA and an SQP (sequence quadratic program), to improve the thermal performance of the solar parabolic trough collector, where the tube diameter, HTF velocity, etc., were set as design variables.
In summary, most current research is generally limited to optimizing the geometric parameters of the receiver and those of the tubes in it. However, a reasonable layout design of the fluid flow in the thermal cavity receiver is also crucial, which can be classified as a topology optimization problem. In recent years, there have been few studies on topology optimization of the heat transfer tube in a cavity receiver. Montes et al. [34
] optimized the fluid flow pattern of a solar central receiver by adjusting the width and diameter of each pass, as well as the number of tubes to achieve a more uniform temperature distribution at the outlets of all circuits. However, Montes et al.’s design procedure did not adopt an optimization algorithm. In this article, we consider developing a topology optimization method to optimize the topology of flow layout while optimizing the geometric parameters of the receiver, to further improve the thermal and flow performance of the receivers.
In this study, fluid flow, heat transfer, and heat loss analysis are considered together to describe the heat transfer process in the receiver. However, the mathematical model of heat loss analysis based on previous studies [32
] is highly nonlinear, and the conventional thermal–fluid coupling model based on the finite element method (or finite volume method) is also very computationally expensive. The optimization of thermal–fluid analysis coupled with the heat loss model in a receiver will be a nonlinear and computationally intensive process. The “ground structure method” was proposed by Dorn et al. [37
]. In this method, the initial design domain is discretized into enough units, and then some units are removed or added using optimization algorithms to realize topology optimization. Previous work [38
] adopted the network structure as the ground structure for thermal–fluid analysis and optimization, to reduce the computational cost. The network structure comprises a series of nodes and edges that connect those nodes. The original complex flow calculation can be simplified into one-dimensional flow, and the temperature field is calculated based on the finite difference method, which can greatly reduce the requirement for computing resources. In addition, many studies have taken the thermal performance of receiver as the optimization objective, while few optimizations have adopted flow dissipation as the objective. In this work, the MOO is performed, considering both thermal performance and flow energy dissipation under nonuniform heat flux, and a Pareto front is obtained. A GA is utilized as the optimizer tool, as it is an efficient metaheuristic optimization method to solve MOO problems [39
The remainder of this paper is organized as follows. In Section 2
, the net-based thermal–fluid model and heat loss model are introduced. In Section 3
, the objective function, design variables, and implementation of optimization by the GA are provided. In Section 4.1
, the relationship between heat loss and cavity temperature, and the relationship between thermal efficiency and receiver size, are discussed. In Section 4.2
, a comparative numerical example under uniform heat flux is carried out to verify the accuracy of the model in Section 2
. In Section 4.3
, the optimization results of the GA under inhomogeneous heat flux are obtained and compared with the helical channel as a reference design. Finally, the conclusions are presented in Section 5
In this article, a thermal–fluid model based on a channel network was adopted to describe the flow and heat transfer processes of a thermal receiver with low computational cost, and to develop a topology optimization method using a GA to optimize the performance of the receiver. The thermal–fluid model was verified through comparison with the numerical simulation. Two single-objective topology optimizations and a multi-objective topology optimization were implemented for the cavity receiver and the channels in it under inhomogeneous heat flux. The following conclusions can be drawn.
(1) The physical field results of the net-based thermal–fluid model under uniform heat flux were compared with those of the numerical simulation to verify the accuracy of the model. The relative discrepancies of the inlet pressure, average temperature, and maximum temperature of the solid domain between the two were 9.62%, 4.83%, and 4.02%, respectively.
(2) The heat loss model was coupled with the thermal–fluid model using linear fitting to achieve topology optimization and size optimization of the receiver. In the comparative example, the linear fitting result had a maximum deviation of 0.6% compared with the calculated result of the heat loss model.
(3) Single-objective optimizations of temperature uniformity () and thermal efficiency () and a multi-objective optimization (MOO) that considered , and the pressure drop were carried out using a GA. The optimization results provided better comprehensive performance than those of the reference design (helical channel) under the same conditions. Compared with the reference design, the temperature uniformity of the result was improved by 83%; the thermal efficiency of the result was improved by 3%; the MOO result illustrated a 72% and 0.2% improvement in temperature uniformity and thermal efficiency, respectively; and the pressure drop was reduced by 88%. Moreover, the topological characteristics of the optimization results were different from the conventional helical channel, and the optimization effect proved the effectiveness of the proposed topology optimization method.