Geometric optimization model for the solar cavity receiver with helical pipe at different solar radiation

Abstract

In consideration of geometric parameters, several researches have already optimized the thermal efficiency of the cylindrical cavity receiver. However, most of the optimal results have been achieved at a fixed solar radiation. At different direct normal irradiance (DNI), any single optimal result may not be suitable enough for different regions over the world. This study constructed a 3-D numerical model of cylindrical cavity receiver with DNI variation. In the model of a cylindrical cavity receiver containing a helical pipe, the heat losses of the cavity and heat transfer of working medium were also taken into account. The simulation results show that for a particular DNI in the range of 400 W/m² to 800 W/m², there exists a best design for achieving a highest thermal efficiency of the cavity receiver. Besides, for a receiver in constant geometric parameters, the total heat losses increases dramatically with the DNI increasing in that range, as well as the temperature of the working medium. The thermal efficiency presented a different variation tendency with the heat losses, which is 2.45% as a minimum decline. In summary, this paper proposed an optimization method in the form of a bunch of fitting curves which could be applied to receiver design in different DNI regions, with comparatively appropriate thermal performances.

Keywords

cylindrical cavity receiver / 3-D numerical simulation / geometric optimization / direct normal irradiation

Introduction

The concentrated solar power (CSP) technology is notably promising among the research filed of renewable energy. For reaching a target performance in the CSP system, the key is to convert the solar energy into thermal energy with high efficiency and safety. The CSP system would produce more electricity with higher performance components and less heat transfer losses. Cavity receiver is one of the most significant components in the CSP system for solar-to-electricity conversion.

In recent years, many researchers have studied heat transfer losses of the cavity receiver, considering the influences of aperture size, inclination magnitude, and wind speed, etc. Wu et al. [¹] have performed a 3-D study to investigate the influence of aperture position and aperture ratio on the convection loss of cavity receiver. Wu et al. [²] have revealed a negligible influence of rotation on convective loss at different rotation speeds by experiments. It is discovered that rotation affects convective loss only by at most 10% compared to a receiver inclination of 90%. Reddy and his colleagues [³–⁷] have researched the inclination and the aperture size. In Ref. [⁶], Sendhil Kumar and Reddy have numerically investigated the convection heat loss by varying the receiver inclinations form 0° to 90°. The convection heat loss of the receiver is maximum at 0° and decreases monotonically when the inclination increases to 90°. In Ref. [⁷], Reddy et al. have found that, for each operating conditions, there is no forced convection effect when the wind speed is lower than a specific value. Besides, the variation in heat loss caused by side-on wind is negligible at all receiver inclinations and higher wind speeds. Researchers from German Aerospace Center (DLR) [⁸,⁹] have investigated the influence of wind on convective heat losses of large scale cavity receivers used for solar thermal power tower with different inclination angles. The simulation shows that when no wind is present, the losses decrease considerably with the increasing inclination angle of the receiver. Additionally, an experiment analysis is presented to discuss the susceptibility of the receiver to inclination angle.

To minimize the heat losses is an effective method to improve the cavity receiver performance. Many researches focus on the geometric optimization of the receiver to reduce the heat losses. Ngo et al. [¹⁰,¹¹] have found that the use of plate fins attached to the inner aperture surface is a possible low cost means of suppressing the natural convection heat loss in a cavity receiver. Wang et al. [¹²] have conducted an experimental analysis on the thermal performance of a windowed volumetric solar receiver. Xu et al. [¹³] have designed a new tapered tube bundle receiver and investigated the geometric principle dish concentrators. To optimize the location of focal points, Prezenak et al. [¹⁴] have constructed a receiver model in the shape of a flat disk, within pipes wiggling across it. The CFD and MCRT simulation result indicate that a distance of 76 cm and a fluid flow of 0.6 m/s are optimal values to maximize the heat transfer.

At the same time, another issue proposed by recent studies is the geometric optimization of optical efficiency for cavity receiver. Researchers from the University of Birmingham [¹⁵,¹⁶] have focused on the effect of receiver geometry on the optical performance. The conical, cylindrical, and spherical geometries of cavity receiver have been considered by analyzing their optical behavior and thermal behavior. The cavity with a conical shape is found to have the highest optical efficiency. A spiral solar particle receiver (SSPR) has been proposed by Qiu et al. [¹⁷]. A dynamic thermal conversion model based on optical model has been used to indicate the overall efficiency and particle temperature of SSPR. Huang et al. [¹⁸] have used an analytical function to predict and optimize the performance of parabolic solar dish concentrator with a sphere receiver. A quick process is presented to optimize the system to provide the maximum cavity efficiency for different optical errors under typical condition. Cheng et al. [¹⁹] have built a new modeling method and unified code using Monte Carlo ray-tracing (MCRT) for concentrating solar collector and its applications.

For the thermal performance, diverse shapes of cavity receiver have been studied, including hemisphere cavity, rectangular cavity, and some other irregular shapes by numerical simulation or experimental investigation. Loni et al. [²⁰] have optimized the efficiency of a cylindrical cavity receiver by investigating the affecting parameters including the inlet temperature, receiver aperture area, cavity receiver depth, receiver tube diameter, and the mass flow rate of the thermal oil through the receiver. Qiu et al. [²¹] have proposed a comprehensive simulation model for an air tube-cavity cylindrical receiver and validated the model by experimental results. The influence of pipe inner radius and airflow direction are investigated to optimize the cavity design. Besides, Zou et al. [²²] have constructed a 3-D model for researching the effects of geometric parameters on the thermal performance of a cylindrical cavity receiver, which provided some successful examples of its design. However, the former model sets DNI as a constant, since the value of constant is suitable for Wuhan, the city where the designed receiver operates. Sun and Yan [²³] have estimated the wall temperature distribution and the thickness of oxide scale of the superheater tubes of a supercritical boiler over the length of the steam flow path for different periods of service, revealing that the distribution of the gas temperature field along the height of the heating surface has a great influence on the final wall temperature calculation results.

In actual conditions, the direct normal irradiance (DNI) from the sun is varied by the geographical environment. It is not precise enough to design the receiver in a constant DNI while it operates in different regions over the world. Hence, to develop a design method which can possess a high thermal efficiency for different DNI values is a crucial for utilizing solar power.

In this paper, a 3-D numerical model of cylindrical cavity receiver is developed to study the effect of influencing parameters, including aperture diameter, cavity length, and DNI, on the heating capability and thermal performance. Compared to pre-existing work from Li et al. [²⁴,²⁵] which focus on bending analysis of heat collection element of a parabolic-trough solar power plant, this work concentrates on analyzing the effect of geometric and environmental parameters on the thermal performance. Besides, the influence of the aperture diameter and cavity length has also been considered in order to find out the mutual effect of geometric parameters and the DNI. In addition, the optimization method for geometric design under different DNI conditions has also been proposed.

Geometric model and numerical procedure

Geometric model

As shown in Figs. 1 and 2, the designed cylindrical receiver consists of an enclosed bottom on the back, an aperture in the front, and a helical pipe inside. The pipe is made of silicon carbide (SiC), which can stand high temperature. The reason for this is that the SiC has a relatively high emissivity and absorptivity, and has a considerable heat transfer rate [²⁶]. With insulation of ceramic fiber outside, the dish receiver can effectively reduce the heat loss. The solar beams reflected by the dish concentrate into a spot, enter the cavity aperture, and then heat the pipe. The working fluid flows from the inlet to the outlet of the pipe, and heated by the helical pipe.

The constant wall temperature or constant heat flux boundary has been widely used in many previous studies, which is a reasonable assumption for numerical simulation [²⁷–³⁰]. Meanwhile, the calculation would be efficient with the simplified assumptions below, without any negative impact on simulation results: the temperature of the helical pipe is constant; the effect of wind is not considered; and the surfaces are considered smooth and uniform for the cavity receiver and helical pipe.

The cavity receiver is placed at the focus of the dish. The inclination of the cavity receiver (θ) is fixed at 45°. The aperture diameter (d_ap) equals 184 mm, 220 mm, 250 mm, 280 mm, and 300 mm, respectively. The cavity length (l) is in the range of 400 mm to 640 mm. The other requirements and ambient parameters are listed in Table 1.

Mathematical formulation

The solar beams are reflected by the dish mirror, concentrated, and then, enter the cavity receiver. Therefore, the energy balance of the cavity receiver can be determined by using Eqs. (1) and (2).

(1){{\displaystyle Q}}_{\mathrm{i}\mathrm{n}}={{\displaystyle Q}}_{\mathrm{u}\mathrm{s}\mathrm{e}}+{{\displaystyle Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}},

(2){{\displaystyle Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}={{\displaystyle Q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}+{{\displaystyle Q}}_{\mathrm{r}\mathrm{a}\mathrm{d}},

where Q_in is the solar energy entering the receiver, Q_use is the energy absorbed by the working fluid, Q_loss is the energy loss, Q_conv is the convection loss, and Q_rad is the radiation loss. The conduction loss represents less than 2% of the total heat loss if an effective insulation layer is covered around the receiver [³¹], which is not considered in the simulation procedure.

The energy entering the receiver is given by

(3){{\displaystyle Q}}_{\mathrm{i}\mathrm{n}}=I\times {{\displaystyle A}}_{\mathrm{m}}\times {{\displaystyle \tau }}_{\mathrm{i}}\times {{\displaystyle \tau }}_{\mathrm{s}}\times {{\displaystyle \rho }}_{\mathrm{r}},

where I (W/m²) is the symbol of DNI for convenience and conciseness, A_m (m²) is the area of the dish mirror, τ_i is the interception factor, τ_s is the shading factor and ρ_r is the reflectivity of the parabolic dish, which are presented in Table 2.

The convection heat loss (Q_conv) is expressed as

(4)Q_{\mathrm{conv}}=A_{\mathrm{cav}}{h}_{\mathrm{conv}}(T_{\mathrm{cav}}-T_{\mathrm{amb}}),

where A_cav is the area of cavity inner wall, h_conv is the heat transfer coefficient of nature convection, T_cav is the temperature of cavity inner wall, and T_amb is the ambient temperature. The Nusselt number of nature convection can be expressed as

(5)N{u}_{\mathrm{conv}}={\displaystyle \frac{h_{\mathrm{conv}}{d}_{\mathrm{cav}}}{\lambda }},

where d_cav is the inner diameter of the cavity receiver, and λ is the thermal conductivity.

The thermal efficiency (η) of the cavity receiver can be derived from the energy balance equation

(6)\eta ={\displaystyle \frac{Q_{\mathrm{use}}}{Q_{\mathrm{in}}}}.

Numerical procedure

The simulation procedure is performed by Fluent 17.0 using a pressure-based solver. The surface-to-surface (S2S) radiation model is incorporated to account for the radiation exchange among the surfaces of the improved receiver. This radiation model has proved to be accurately predictable for the simulation of radiation heat transfer [⁵]. The k–ε model is used as the viscous model.

The boundary conditions are set, as illustrated in Figs. 3 and 4. The pipe inside the cavity is in an isothermal condition with a constant temperature. With good insulation, the adiabatic condition is applied to the cavity surface, the cavity inner wall, and the pipe outside the cavity. Additionally, the pipe is extended to the boundary of the ambient wall to ignore the influence of the ambient. The working fluid flowed in the pipe is pressured air. The inlet condition is at a mass flow rate of 0.05 kg/s and a gauge pressure of 0.35 MPa. The outlet condition should be pressure outflow. The ambient boundary is a pressure inlet with an atmospheric pressure, which is demonstrated in Fig. 4.

The semi-implicit pressure linked equation (SIMPLE) has been considered for pressure-velocity coupling, and PRESTO! is used for pressure spatial discretization [³²–³⁴]. The second order upwind is used for momentum, turbulent, and energy spatial discretization. A convergence criterion of 10^-4 is considered for the residuals of continuity, k–ε equations, whereas for energy equation, the convergence criterion is imposed as 10^-6.

The Boussinesq approximation is considered while solving the momentum equation. The properties of air are considered as the function of temperature. Polynomial or piecewise-polynomial relationships for specific heat capacity (C_p), dynamic viscosity (μ), and thermal conductivity (λ) with the temperature of air are chosen to get accurate results [³⁵].

(7)\begin{array}{l}{C}_{\mathrm{p}}=\mathrm{0.103409}\times {\mathrm{10}}^{\mathrm{4}}-\mathrm{0.284887}T+\mathrm{0.7816818}\times {\mathrm{10}}^{-\mathrm{3}}{T}^{\mathrm{2}}-\mathrm{0.4970786}\times {\mathrm{10}}^{-\mathrm{6}}{T}^{\mathrm{3}}\\ +\mathrm{0.1077024}\times {\mathrm{10}}^{-\mathrm{9}}{T}^{\mathrm{4}}(\mathrm{250}\le T\le \mathrm{2000}\mathrm{K}),\end{array}

(8)\begin{array}{l}\mu =-\mathrm{9.8601}\times {\mathrm{10}}^{-\mathrm{7}}+\mathrm{9.080125}\times {\mathrm{10}}^{-\mathrm{8}}T-\mathrm{1.17635575}\times {\mathrm{10}}^{-\mathrm{10}}{T}^{\mathrm{2}}+\mathrm{1.2349703}\times {\mathrm{10}}^{-\mathrm{13}}{T}^{\mathrm{3}}\\ -\mathrm{5.7971299}\times {\mathrm{10}}^{-\mathrm{17}}{T}^{\mathrm{4}}\mathrm{(250}\le T\le \mathrm{600}\mathrm{K}),\end{array}

(9)\begin{array}{l}\mu =\mathrm{0.48856745}\times {\mathrm{10}}^{-\mathrm{6}}+\mathrm{5.43232}\times {\mathrm{10}}^{-\mathrm{8}}T-\mathrm{2.4261775}\times {\mathrm{10}}^{-\mathrm{11}}{T}^{\mathrm{2}}+\mathrm{7.9306}\times {\mathrm{10}}^{-\mathrm{15}}{T}^{\mathrm{3}}\\ -\mathrm{1.10398}\times {\mathrm{10}}^{-\mathrm{18}}{T}^{\mathrm{4}}(\mathrm{600}\le T\le \mathrm{1150}\mathrm{K}),\end{array}

(10)\begin{array}{l}\lambda =-\mathrm{2.276501}\times {\mathrm{10}}^{-\mathrm{3}}+\mathrm{1.2598485}\times {\mathrm{10}}^{-\mathrm{4}}T-\mathrm{1.4815235}\times {\mathrm{10}}^{-\mathrm{7}}{T}^{\mathrm{2}}+\mathrm{1.73550646}\times {\mathrm{10}}^{-\mathrm{10}}{T}^{\mathrm{3}}\\ -\mathrm{1.06657}\times {\mathrm{10}}^{-\mathrm{13}}{T}^{\mathrm{4}}+\mathrm{2.47663035}\times {\mathrm{10}}^{-\mathrm{17}}{T}^{-\mathrm{5}}(\mathrm{250}\le T\le \mathrm{1150}\mathrm{K}).\end{array}

Grid independence analysis

The grid independence analysis has been conducted to investigate the effects of grid number on the simulation procedure. 20 geometric models with the grid number from 959736 to 1210924 are built and simulated by ANSYS 17.0. A cavity model with a cavity length of 480 mm and an aperture diameter of 280 mm is presented to show the grid independent analysis for the sake of brevity. Meanwhile, a repeated simulation is presented to verify the stability of the numerical procedure. The grid independency results have been tabulated in Table 3. It is seen that, for all the cases, the deviations are less than 1%. Hence, the grid is compact enough for the simulation.

Validation of numerical simulation

The Nusselt number of convection loss is a credible criterion in describing the natural convection process in a cavity. This procedure is widely used by many researchers in numerical validation. The 3-D numerical simulation proposed in the present study has been validated by the numerical model proposed by Wu et al. [¹] and the theoretical model proposed by Zou et al. [³⁶].

Table 4 compares the results of a cavity length of 560 mm across five different aperture diameters. It is observed that the present numerical procedure is in reasonable agreement with the two models, with a maximum deviation of 7.3% with the model of Wu et al. [¹], and 5.8% with the model of Zou et al. [³⁶].

Results and discussion

Effects of variable DNI

The simulation results of cavities at a cavity length of 540 mm and variable aperture diameters are presented here. The temperature of the pipe inside the cavity is taken from the data calculated by the mathematical model of Zou et al. [³⁶], which is given in Table 5.

Figure 5 presents the temperature contours of the receiver at a fixed aperture diameter of 184 mm. It is apparently seen that the enhancement of DNI can dramatically increase the temperature inside the cavity. The outlet temperatures (T_out) of the working fluid at a DNI of 400 W/m², 600 W/m², and 800 W/m² are 917 K, 1062 K, and 1197 K respectively. Meanwhile, the corresponding average temperatures (T_pipe) of the pipe are 929.1 K, 1077 K, and 1216 K respectively. T_pipe is over 1000 K when DNI is more than 600 W/m². The excessively high concentrated flux at an unexpected location, or hot point is likely leading to a material molten or lifetime shortening [³⁷]. Therefore, a high temperature tolerant material should be used to avoid melting or failure.

Figure 6 depicts the variation of heat loss of the receiver with DNI at an aperture diameter of 184 mm. The combined heat loss consists of radiation loss and convection loss. It is observed that the radiation heat loss varies greatly with the increasing DNI while the convection loss varies steadily with the increasing DNI. The radiation loss is predominant for the combined loss, which is from 70.1% in 400 W/m² to 74.6% in 800 W/m². This can be attributed to the increase of T_cav. When the temperature deviation between T_cav and T_amb is increasing, the convection loss and radiation loss increase concurrently. The radiative loss is notably higher than the convection loss because the Stefan-Boltzmann laws includes the fourth power of temperature. Consequently, the radiation loss increases faster than the convection loss at increasing DNI.

Figure 7 presents the variation of cavity thermal efficiency with DNI. The result shows that the cavity receiver efficiency decreases slightly with increasing DNI. The efficiency drops by 2.180% at an aperture diameter of 184 mm, which is the minimum thermal efficiency drop of all aperture diameters when DNI increases from 400 W/m² to 800 W/m². Besides, the maximum efficiency drops by 2.447% at an aperture diameter of 280 mm. As can be observed in Table 6, compared with the outlet temperature (T_out) and energy losses (Q_loss), the thermal efficiency of the cavity is insensitive to the variation of DNI. The reason for this is that the thermal efficiency is a function of using the thermal power (Q_loss) divided by the total input power (Q_in), which is presented in Eqs. (1) and (6). In spite of the fact that an increasing DNI leads to the growing of Q_in, Q_use displays a slower increase due to a sharper growing rate of the total heat loss (Q_loss). As a difference value of Q_in and Q_use, Q_loss is dominated by cavity temperature, which could be rapidly growing by increasing DNI. Hence, the thermal efficiency is decreased with the increase of DNI. The increment of Q_use and Q_loss are counteracted, which leads to the insensitivity of the cavity thermal efficiency to variable DNI.

Mutual effects of DNI and geometric parameters

The effect of DNI with respect to thermal efficiency is intensively investigated. The influence of the aperture diameter and cavity length has also been considered in order to see the mutual effect of geometric parameters and the DNI parameter. Furthermore, the 3-D model assisted the researchers to visualize the phenomenon that the DNI and the geometric parameters influence the thermal efficiency.

The effects of cavity length and aperture diameter on thermal efficiency at a DNI of 400 W/m² are exhibited in Fig. 8. In each black line in Fig. 8, one of the geometric parameters (cavity length and aperture diameter) is variable and the other is constant. From Fig. 8(a), it is obviously found that the thermal efficiency first increases and then decreases with the increase of l when d_ap is 184 mm, 220 mm, and 250 mm respectively. When d_ap is 280 mm or 300 mm, the thermal efficiency increases monotonously with the increase of cavity length. The reason for this is that the tendency of heat loss is opposite to the thermal efficiency. The stagnant zone inside the cavity is enlarged by the stretching of l, which can reduce the convection effects and free convection heat transfer coefficient. For instance, when d_ap is 184 mm, the convection loss decreases from 510 W to 452 W, as l varies from 400 mm to 480 mm. When l is stretched from 480 mm to 640 mm, the heat transfer area of cavity (A_cav) is increased from 0.915 m² to 1.113 m². The convection loss is increased from 452 W to 479 W because of the enlarged heat transfer area. Meanwhile, a deeper cavity is more close to a black body, which can reduce the radiation energy escaping from the cavity. The radiation loss is decreased as l varies from 400 mm to 640 mm. In Fig. 8(b), for each cavity length, the thermal efficiency decreases monotonously with the increase of aperture diameter due to more heat losses.

Figure 9 shows the results of the effect of DNI and aperture diameter. In this case, the cavity length is a constant of 560 mm. It is clearly observed from Fig. 9(a) that the lowest DNI (400 W/m²) has the highest thermal efficiency, reaching about 90.69% and 78.19% for the aperture diameter of 184 mm and 300 mm. With increasing DNI, the thermal efficiency keeps reducing, for each different aperture diameter representing the same trends, as the black lines shown in Fig. 9. The highest DNI (800 W/m²) achieves the lowest thermal efficiency, as low as 88.51% and 75.88% for an aperture diameter of 184 mm and 300 mm.

Figure 10 shows the results of the effect of DNI and cavity length. In this case, the aperture diameter is a constant of 180 mm. In general, the lowest DNI demonstrates the highest thermal efficiency of each different cavity length. For instance, in a cavity length of 400 mm, the lowest DNI and the highest DNI have a thermal efficiency of 89.86% and 87.39%, respectively. Moreover, each cavity length displays a monotonous decreasing of thermal efficiency with the increase of DNI.

As shown in Fig. 9(b), for each constant DNI, it is observed from the black lines that the thermal efficiency reduces with an increasing aperture diameter, which has a good agreement with the study in Ref. [²²]. The main reason for this has been discussed in Ref. [²²]. As for Fig. 10(a), the results also present the same expected curves as that of the former study, which first rise and then fall. The explanation of those trends has also been given previously [²²].

Optimization of cylindrical cavity receiver

Optimization method

In the design of the cavity receiver, a small aperture size is targeted which attributes to a high thermal efficiency and a low heat transfer loss. The aperture diameter is evaluated to a suitable size which must be larger than the spot diameter. For a determined aperture diameter, there exists an optimum cavity length, which is able to achieve the highest thermal efficiency.

As shown in Fig. 11, each point reveals the highest thermal efficiency for a given aperture diameter and its optimal cavity length. A bunch of fitting curves consisted of countless geometric points were proposed to show the tendency of optimized geometric design. It is clearly found that three curves at different DNI values have the same tendency, which reveals that the cavity length is increased with the increase of aperture diameter. When aperture diameter is larger than 250 mm, the slope of the curve at a DNI of 800 W/m² is dramatically larger than that of the curve at 400 W/m².

The slope of a DNI of 800 W/m² is sharper, because the proportion of radiation heat loss in total heat losses keeps increasing. As described in the theoretical model [³⁶], the radiation heat loss would be reduced by increasing the cavity length in a certain range. Thus, in this case, the optimal cavity length was presented in a large value in the region of high DNI values, as well as the slope of the design curve.

The formula of the fitting curves is given in Eq. (11) to present the correlation between cavity length and aperture diameter:

(11)l=(a_{\mathrm{1}}+a_{\mathrm{2}}{d}_{\mathrm{ap}})/(\mathrm{1}+a_{\mathrm{3}}{d}_{\mathrm{ap}}+a_{\mathrm{4}}{d}_{\mathrm{ap}}^2),

where a₁, a₂, a₃, and a₄ are quantities as shown in Table 7. The range of cavity length (l) and aperture diameter (d_ap) are 400 mm≤l≤640 mm and 184 mm≤d_ap≤300 mm respectively. From Fig. 11, it is seen that the tendencies of points and lines are in good accordance. Utilizing regression coefficients, the effect of fitting curves is presented. The fitting results are presented in Table 7. It is shown that the coefficient of variation (R²) for a DNI of 400 W/m², 600 W/m², and 800 W/m² (0.993, 0.999, and 0.999 respectively) approximates to 1, which indicates that this formula is appropriate for calculating the optimized geometric parameters of a cylindrical cavity receiver.

Application of fitting curves

DNI is widely used to evaluate the solar resource of one region [³⁸,³⁹]. One primary factor for the site selection of a CSP plant is the annual average DNI of the region [⁴⁰]. The annual average DNI is used to evaluate the output of a CSP plant, and it is also used to design a CSP plant to enable it to have the best performance, and even the DNI is variable [⁴¹,⁴²].

Thus, the value of DNI could present the value of irradiance intensity. In this optimization scheme, 400 W/m², 600 W/m², and 800 W/m² represent the low, the medium, and the high level of irradiance intensity, respectively. According to the data provided by system advise model (SAM), three regions in China, Wuhan, Beijing, and Lhasa, as three different irradiance intensity regions, are used as the example to design a cylindrical cavity receiver.

The optimization design of the cylindrical cavity receiver for these three regions is given in Table 8. For these three regions, those curves which are derived from the results of this study and the optimization method could be used to calculate the optimized cavity length at a certain aperture diameter. Finally, a cylindrical cavity receiver would achieve the highest thermal efficiency with optimal geometrical parameters in its determined region.

Conclusions

In this study, a 3-D numerical simulation using a cylinder cavity receiver was conducted to investigate the effects of both geometric parameters and variable DNI on thermal performance. The results of this study can provide a novel approach for improving the geometric design of the cylindrical cavity receiver.

Based on the numerical results, it is concluded that the radiative loss is the primary among the total heat transfer losses, where the ratio of the total is 70.1% if DNI= 400 W/m², whereas 74.6% if DNI= 800 W/m². Compared to T_out and other kinds of heat losses, the thermal efficiency of cavity is insensitive to the variation of DNI, where the minimum and maximum efficiency drop by 2.180% and 2.447% at an aperture diameter of 184 mm and 280 mm respectively.

The thermal efficiency is monotonously decreased with the increase of DNI and aperture diameter. The thermal efficiency would first increase and then decrease with the increase of l when d_ap is 184 mm, 220 mm, and 250 mm respectively. When d_ap is 280 mm or 300 mm, the thermal efficiency would increase monotonously with the increase of cavity length.

For a determined level of DNI, there exists a corresponding optimal result of geometric structure, which is capable of achieving the highest thermal efficiency. An optimization method is given for the design of cavity receiver in different regions.

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