Numerical study of conduction and radiation heat losses from vacuum annulus in parabolic trough receivers

Abstract

Parabolic trough receiver is a key component to convert solar energy into thermal energy in the parabolic trough solar system. The heat loss of the receiver has an important influence on the thermal efficiency and the operating cost of the power station. In this paper, conduction and radiation heat losses are analyzed respectively to identify the heat loss mechanism of the receiver. A 2-D heat transfer model is established by using the direct simulation Monte Carlo method for rarefied gas flow and heat transfer within the annulus of the receiver to predict the conduction heat loss caused by residual gases. The numerical results conform to the experimental results, and show the temperature of the glass envelope and heat loss for various conditions in detail. The effects of annulus pressure, gas species, temperature of heat transfer fluid, and annulus size on the conduction and radiation heat losses are systematically analyzed. Besides, the main factors that cause heat loss are analyzed, providing a theoretical basis for guiding the improvement of receiver, as well as the operation and maintenance strategy to reduce heat loss.

Graphical abstract

Keywords

parabolic trough receiver / vacuum annulus / rarefied gas / DSMC (direct simulation Monte Carlo) / heat loss

1 Introduction

Parabolic trough solar technology is an important renewable energy technology which can bear the basic electrical load as it has the abilities of long-time thermal storage and lower cost [1–3]. A parabolic trough collector includes parabolic reflectors and parabolic trough receivers that are located in the focal line of the reflectors. The reflectors can concentrate sunlight onto the receiver all time to heat up the heat transfer fluids (HTF) which then transfers its heat to a stream generator. The high temperature steam then drives a stream turbine to generate electricity. Parabolic trough receiver is the key component to convert solar energy into thermal energy in the system [4,5]. It consists of an absorber tube with a solar selective coating and a glass envelope surrounding the absorber tube to form a vacuum-tight annulus space between the absorber tube and glass envelope. The annulus space is evacuated to reduce the conduction or convection heat loss and avoid the oxidization of the solar selecting coating. Getters are placed to adsorb gas molecules in the annulus space to keep long vacuum lifetime. Glass-to-metal seals and bellows are arranged between the glass envelope and the absorber tube to form the vacuum-tight and to accommodate for thermal expansion difference between the absorber tube and the glass envelope [2,5], as shown in Fig. 1.The parabolic trough receiver can also be used in the linear Fresnel solar power system which can provide the possibility of getting low levelized cost of electricity due to its simple construction and flat shape [6,7].

The power plant generally requires 25 years of operation, so the life of the receiver should be maintained for at least 25 years. However, the data from existing power plant indicates that receivers are often damaged during operation [8]. The data for the American 9 solar electric generating stations (SEGS) indicated that receiver failures is about 3.37% per year in the solar field. Of these failures, 55% were reported to involve broken glass and 29% involved vacuum failure [9,10].

The vacuum loss is usually resulted from the out gassing of materials, the gas permeation from the surfaces, the leak of air, and the failure of getters [11]. It has a negative impact on the power plant. The immediate effect is that it remarkably increases the heat loss of the receiver. Price et al. [12] presented that the heat losses from a receiver with hydrogen in the annulus space could be more than 4 times those of a good vacuum. When receiver was permeated with hydrogen, the plant revenue might be reduced by 20%. Furthermore, the cost of the receivers was about 20% of the material cost in the solar field, and it required additional labor to replace the failure receivers [13]. Therefore, in order to avoid the lower efficiency and higher costs caused by vacuum failure, it is necessary to analyze the effect of vacuum performance on the heat loss of receivers.

Many studies were conducted to analyze the effects of vacuum performance on heat loss. Ratzel et al. [14] studied techniques for reducing conductive heat loss and evacuation of annulus gas. Tang et al. [15] reported that the annulus gas pressure had an important influence on the heat loss based on a cross-sectional heat transfer model using the direct simulation Monte Carlo (DSMC) method. Roesle et al. [16] predicted the conduction heat transfer, including off-sun and on-sun configurations using the DSMC method too. Burkholder et al. [17] measured receiver heat losses for argon-hydrogen and xenon-hydrogen mixtures at a temperature of 350°C. The results showed that sufficient quantity of inert gas would reduce the hydrogen-induced heat loss in the annulus space. Recently, some papers have been published which have investigated additional techniques to analyze the relationship between partial pressure in the annulus and the heat loss of the parabolic tough receivers [18–21].

However, the abovementioned models do not take into consideration the influences of gas species and pressure on conduction heat loss and radiation heat loss in annulus, respectively. Especially, related research has usually been conducted to study radiation or conduction heat loss by only focusing on one aspect. There is little discussion on which factor is dominating for the impact of heat loss which is valuable. Moreover, existing researches have been performed based on using the traditional organic biphenyl/diphenyl oxide(BP/DPO) as HTF, whose operating temperature is usually less than 393°C [22]. To improve the efficiency, some new higher temperature HTFs have been proposed. HELISOL 5 A [23], as a new type silicon oil, has a maximum operating temperature of 425°C. Molten salt raises the operation temperature to 550°C in the parabolic trough system [24,25]. Gas such as supercritical CO₂ as the HTF can further improve the temperature in the parabolic trough system [26–28]. On the one hand, different HTFs may decompose different gas species at higher temperatures. On the other hand, the gas absorption capacity of the getter will be reduced due to the higher temperature, in which the gas partial pressure may remarkably increase in the annulus. Therefore, the influence of different gas species and partial pressure in the annulus on conduction heat loss and radiation heat loss is worthy of study.

In this paper, the influences of gas species and pressure on the conduction heat loss and radiation heat loss in the annulus are discussed, respectively. Besides, a 2-D DSMC numerical model is established to simulate the conduction heat loss caused by residual gases. In addition, the radiation heat loss is also calculated. Moreover, the numerical model is verified by experimental data in existing literature, and the effects of annulus pressure, gas species, HTF temperature and annulus size on the conduction heat loss and radiation heat losses are analyzed systematically. Furthermore, the pure hydrogen, helium, argon and nitrogen at different pressure are simulated, and the gas pressure and species are found to have a great influence on conduction heat loss and radiation heat loss. The analysis of the formation mechanism of heat loss in different situations provides a theoretical basis for guiding the improvement of receiver, and the operation and maintenance strategy to reduce heat loss.

2 Physical model and numerical method

2.1 Physical model

The thermal resistances and heat flows of the parabolic trough receiver are shown in Fig. 2(a). The heat transfer process is described as the flux of concentrated solar radiation Q_solar drops on the outer surface of absorber tube through the glass envelop. The selective coating absorbs the solar radiation and converts it into heat. The inner surface of the absorber tube obtains the heat by conduction and then transfers it to the HTF through convection, resulting in the fact that the HTF obtains Q_obtain and the absorber transfers Q_cond,abs by conduction. In the annulus space, the inner surface of the glass envelope exchanges heat with the selective coating through not only radiation Q_r but also conduction Q_c. The calculation of Q_r is assumed that the glass envelope is opaque to infrared radiation and assuming gray surfaces. The heat transfer of rarefied gas in the annulus is defined as conduction heat transfer due to lower pressure in this paper. The conduction heat Q_cond,g transfers from the inner surface of the glass envelope to its outer surface. Finally, a quantity of heat is transferred to the environment from the out surface of the glass envelop by radiation and convection [29].

The energy balance of the receiver can be expressed by [30]

(1)Q_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}=Q_{\mathrm{o}\mathrm{b}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{n}}+Q_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}},

(2)Q_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}=Q_{\mathrm{r}}+Q_{\mathrm{c}}=Q_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d},\mathrm{g}}\mathrm{.}

The heat transfer model of vacuum annulus is shown in Fig. 2(b). Two surfaces are the outer surface of the absorber tube and the inner surface of the glass envelope. The vacuum annulus between the two surfaces is full of residual gases whose average pressure is represented as p. In the annulus of the receiver, the heat loss comes from conduction heat transfer and radiation heat transfer. In this paper, the conduction heat transfer caused by residual gases under various conditions is numerically modeled by using a 2-D DSMC model. The radiation heat transfer caused by the difference in temperatures between the outer absorber surface and the inner glass envelope surface is separately calculated.

The assumptions of the DSMC model include:

1)Steady-state equilibrium;

2)Temperatures of the absorber tube and the glass envelope are uniformon the axial and circumferential direction;

3)The receiver ends and metal bellow influences are ignored;

4)The gravity is ignored.

The relevant parameters of the model are listed in Table 1. The annulus gases are argon, helium, nitrogen and hydrogen, respectively.

2.2 Numerical method

2.2.1 Conduction heat transfer

Different gas heat transfer regimes are classified using the concept of the Knudsen number K_n, as expressed in Eq. (3), which is an important parameter on behalf of pressure levels [31]:

(3)K_{\mathrm{n}}=\frac{\lambda }{L}\mathrm{.}

Four gas heat transfer regimes exist based on K_n, where K_n>10: free molecular; 10>K_n >0.1: transition; 0.1> K_n >0.01: temperature-jump; 0.01>K_n: continuum.

For continuum flow, continuum models can be used. When K_n is more than 0.01, the continuum models are not suitable anymore and the governing equation for the behavior of gas is the Boltzmann equation. In this paper, the DSMC method is employed to solve the Boltzmann equation. The DSMC method [32], based on molecular dynamics, can be used to solve the rarefied gas flow and heat transfer problem. In this paper, the DS2V software developed by Bird et al. [33] was employed to calculate the 2-D DSMC simulation. To simplify the simulation the movements and collisions of analog molecules (10¹³–10¹⁸/m³) are used to simulate the behavior of the real molecules (10¹⁸–10²²/m³). To avoid the non-real physical phenomena, the average collision time is longer than the appropriate time step Δt .The annulus space is meshed into many grid units. Each grid unit is 33% of the average free path where the molecules can collide. The transient properties of the simulation particles are sampled in a domain to get the macroscopic parameters within a set period [5]. The basic steps of the program are depicted in Fig. 3.

The ratio of the local mean separation of the collision partners to the local mean free path is a key verification parameter in DSMC simulation. To meet the criterion of the simulation, the ratio in each case is maintained less than 0.2 in this paper. The number of representative molecules is chosen according to the number of cells in the simulation.

1) Molecule-surface interaction

The Cercignani-Lampis-Lord (CLL) model is used for molecule surface interactions because it can obtain the results that are more consistent with the actual results when the flow temperature is higher and the surface is cleaner. It includes two adjustable parameters that play a decisive role in simulating the real gas flow accurately, the accommodation coefficient of the kinetic energy of the tangential velocity component α_t and the energy accommodation coefficient of the normal velocity component α_n. Both the scatter kernel of the tangential component and the scatter kernel of the normal velocity component are expressed in Eqs. (4) and (5) [34], respectively.

(4)\mathcal{R}(v_{\mathrm{i}},v_{\mathrm{r}})=\frac{1}{\sqrt{\mathrm{\pi }{\alpha }_{\mathrm{t}}}}\exp [-\frac{{(v_{\mathrm{r}}-{(1-{\alpha }_{\mathrm{t}})}^{1/2}{v}_{\mathrm{i}})}^2}{{\alpha }_{\mathrm{t}}}]\mathrm{.}

(5)\mathcal{R}(u_{\mathrm{i}},u_{\mathrm{r}})=\frac{2u_{\mathrm{r}}}{{\alpha }_{\mathrm{n}}}\exp [-\frac{u_{\mathrm{r}}^2+(1-{\alpha }_{\mathrm{n}})u_{\mathrm{i}}^2}{{\alpha }_{\mathrm{n}}}]I_0\left[\frac{2{(1-{\alpha }_{\mathrm{n}})}^{1/2}{u}_{\mathrm{r}}{u}_{\mathrm{i}}}{{\alpha }_{\mathrm{n}}}\right]\mathrm{.}

In this paper, it is assumed that α_t=α_n=α, and the value obtained by the formula of Song and Yovanovich [34] is tabulated in Table 2.

(6)\alpha =\exp \left[C_0\left(\frac{T_{\mathrm{s}}-T_0}{T_0}\right)\right]\left(\frac{M_{\mathrm{g}}^{*}}{C_1+M_{\mathrm{g}}^{*}}\right)+\{1-\exp \left[C_1\left(\frac{T_{\mathrm{s}}-T_0}{T_0}\right)\right]\}\left\{\frac{2.4\mu }{{(1+\mu )}^2}\right\}\mathrm{.}

2) Molecule- molecular interaction

The variable hard sphere (VHS) model is used for intermolecular interactions, which can be defined as expressed in Eq. (7). The characteristic of this model is that the scattering angle has the same probability after the collision, and the cross section varies with relative velocity, and can describe the relationship between viscosity and temperature accurately [31].

(7)\frac{{\sigma }_{\mathrm{T}}}{{\sigma }_{\mathrm{T},\mathrm{r}\mathrm{e}\mathrm{f}}}={\left(\frac{d}{d_{\mathrm{r}\mathrm{e}\mathrm{f}}}\right)}^2={\left(\frac{c_{\mathrm{r}}}{c_{\mathrm{r},\mathrm{r}\mathrm{e}\mathrm{f}}}\right)}^{-2\xi }={\left(\frac{{\epsilon }_{\mathrm{t}}}{{\epsilon }_{\mathrm{t},\mathrm{r}\mathrm{e}\mathrm{f}}}\right)}^{-\xi }\mathrm{,}

where ξ is the negative power of ε_t in the dependence of collision cross-section σ_T on the transitional energy ε_t; and the ω in the dependence of viscosity μ on temperature can be obtained by inputting the viscosity and temperature.

3) Geometric model and boundary condition

The geometric model is demonstrated in Fig. 4. The size and temperature of the surfaces are presented in Table 1. The annular gap is the fluid domain. The argon, nitrogen, hydrogen, and helium are the gas molecules, respectively. The range of the molecular density is 2×10¹⁸–2.3×10²² m⁻³. The input parameters of the gases are given in Table 2 [31,33].

2.2.2 Radiation heat transfer

Radiation heat transfer occurs between the selective coating and the inner surface of the glass envelope. Several assumptions were made: diffuse reflections and irradiation and gray surfaces. In addition, it is assumed that the glass envelope is opaque to infrared radiation, which can be described as [30].

(8)Q_{\mathrm{r}}=\frac{2\times {10}^{-3}\mathrm{\pi }{R}_{\mathrm{a}\mathrm{b}\mathrm{s},\mathrm{o}}\sigma (T_{\mathrm{a}\mathrm{b}\mathrm{s},\mathrm{o}}^4-T_{\mathrm{g},\mathrm{i}}^4)}{\frac{1}{{\epsilon }_{\mathrm{s}}}+\frac{1-{\epsilon }_{\mathrm{g}}}{{\epsilon }_{\mathrm{g}}}\left(\frac{R_{\mathrm{a}\mathrm{b}\mathrm{s},\mathrm{o}}}{R_{\mathrm{g},\mathrm{i}}}\right)},

where ε_g is the emissivity of glass envelope, whose value is 0.86; and ε_s is the emissivity of solar selective coatings, whose values are related to temperature, which are 0.0756-5.9673\times {10}^{-5}{T}_{\mathrm{a}\mathrm{b}\mathrm{s},\mathrm{o}}+3.81\times {10}^{-7}{T}_{\mathrm{a}\mathrm{b}\mathrm{s},\mathrm{o}}^2[22].

3 Results

The DSMC model is validated against the experimental results measured by Burkholder [35]. The experiment system consists of the vacuum subsystem and the heat-loss test subsystem. The vacuum subsystem is able to vacuum the annulus by pumps and to put a certain pressure gas into the annulus by gas tank and flow controller. The heat loss measured by the heat loss bench is the total heat loss which includes the radiation heat loss and the conductive heat loss. A test was performed with no gas in the annulus to determine the radiation heat loss so that both radiation heat loss and conduction heat loss were acquired respectively.

The results of conduction heat losses of experimental value Q_c and model value Q_{\mathrm{c}}^{\prime }are shown in Fig. 5 and Table 3. Figure 5 indicates that the numerical results are in good agreement with the experimental results. For cases 1–6, the gas in the annulus is hydrogen, and the simulated results are slightly lower than the experimental results but the deviation is within 10%. For cases 7–10, the gas in the annulus is argon, in which the deviation is within 9%. The accommodation coefficient of the gas may cause difference between the simulated heat loss and the experimental heat loss. Because the heat loss is an averaged value in the axial direction of the receiver, the end loss of the receiver may also cause the error in the experimental heat loss when the receiver is tested. To reduce the deviation, more experimental cases are to be conducted. Therefore, more accurate accommodation coefficients can be obtained in the future. Although there exists deviation, the model results are consistent with experimental values, which shows that the model can accurately predict the conduction heat loss of different gases at different pressures and temperatures.

4 Discussion

4.1 Fields distribution

When the annulus is filled with residual gas, the density distribution and temperature distribution have typical rarefied gas heat transfer characteristics. When T_abs,o = 623 K, T_g,i = 343 K, and argon is 10 Pa, the field distribution of annulus is exhibited in Fig. 6. There exists a uniform stratified distribution along the radial direction. Figure 7 shows that the temperature increases linearly from the glass envelope to the absorber tube. The density increases linearly with the increase of the radius due to the temperature change. The law of field distribution remains the same at different pressures, gas species, and temperatures.

4.2 Effects of annulus pressure on heat loss

The relationship between the annulus pressure P and the heat loss is numerically investigated. The annulus is filled with hydrogen whose pressure ranges from 0.01 Pa to 10000 Pa. T_abs,o is uniform at 350°C and T_g,i changes with pressure from approximately 60°C to 135°C. R_g,i is 59.5 mm and R_abs,o is 35 mm.

The effect of annulus pressure on the conduction heat loss obtained by DSMC simulation is displayed in Fig. 8. The Knudsen number decreases linearly as the pressure increases. It can be found that within the order of 0.1 Pa, K_n is larger than 10, which means that the annulus space is in the free molecular region. In this region, the heat conducts through discrete free molecules and the conduction heat loss can be negligible because of high vacuum degree and a smaller number of molecules. In the region of 0.1–10 Pa, K_n is between 0.1 and 10, which means that the annulus is in the transition region and conduction heat loss begins to increase significantly. In the region of 10–100 Pa, K_n is between 0.01 and 0.1, which means that the annulus is in the temperature jump region. The conduction heat loss presents a nearly linear growth first from 10 Pa to 100 Pa. Then, it increases little. Finally, as the pressure continues rising to approximately 100 Pa, K_n is less than 0.01 and it flattens out as the heat transfer of the rarefied gas reaches the maximum.

The effect of annulus pressure on radiation heat loss obtained by Eq. (8) is shown in Fig. 9. According to Eq. (8), the radiation heat loss is related to the emissivity of the glass envelope and solar selective coatings, which is 86% and 10.1% when T_abs,o= 350°C, respectively. It can be found that the radiation heat loss slowly decreases with the increase of vacuum pressure from 0.1 Pa to 1 Pa, and then fast drops from about 145 W/m to 125 W/m with the pressure from 1 Pa to 1000 Pa. When the pressure is higher than 1000 Pa, the radiation heat loss decreases a little. The reason for the decrease of the radiation heat loss is that the glass temperature increases as the pressure increases which reduces the radiation heat transfer between the absorber tube and the glass envelope.

A comparison of the effect of annular hydrogen pressure on conduction heat loss, radiation heat loss, and total heat loss is presented in Fig. 10. The total heat loss remarkably rises from 150 W/m to 800 W/m with annulus pressure increasing, resulting in a 5-fold increase in the total heat loss. It is observed from Fig. 10 that there are three stages for the variation of the heat loss with pressure. When p<1 Pa, the total heat loss is mainly caused by the radiation heat loss and slowly increases with the increase of the conduction heat loss. When 1 Pa<p<100 Pa, the conduction heat loss and the total heat loss increase very fast, while the radiation heat loss slowly decreases. When 100 Pa<p<10000 Pa, the total heat loss slightly increases with the pressure increasing. When the annulus pressure reaches about 5 Pa, the magnitude of the conduction heat loss is similar to that of the radiation heat loss. For the third stage, the proportion of conduction heat loss continues to increase and reaches up to 85% of the total heat loss. It should be noticed that although the radiation heat loss slowly decreases with the pressure rising, the decrease of the radiation heat loss is less than the increase of the conduction heat loss.

4.3 Effects of gas compositions on conduction heat loss

According to Refs. [2,5], nitrogen, hydrogen, argon, and helium are four main gases in the annulus. The comparison of the conduction heat loss of the four gases in the annulus are simulated when T_abs,o is uniform at 350°C, R_g,i is 59.5 mm, R_abs,o is 35 mm, and the ambient temperature is 22°C. The results suggest that hydrogen and helium have a great influence on the heat loss while nitrogen and argon have less influence. Based on the results of numerical simulations, the correlation functions between conduction heat loss and pressure are obtained for hydrogen, helium, nitrogen, and argon respectively.

For hydrogen:

(9)Q_{\mathrm{c}}=1.17+358.31\times (1-E^{-P/9.22})+312.47\times (1-E^{-P/46.03}).

For helium:

(10)Q_{\mathrm{c}}=-0.25+106.76\times (1-E^{-P/11.73})+405.35\times (1-E^{-P/58.12}).

For nitrogen:

(11)Q_{\mathrm{c}}=-0.25+40.67\times (1-E^{-P/8.54})+40.67\times (1-E^{-P/8.54}).

For argon:

(12)Q_{\mathrm{c}}=0.25+36.23\times (1-E^{-P/9.39})+38.80\times (1-E^{-P/2.07}).

These correlation functions can intuitively analyze the conduction heat loss of different gases.

4.4 Effects of emittance of selective coating on radiation heat loss

The relationship among radiation heat loss, temperature of the glass envelope, and the emittance of selective coating operating at 673 K is shown in Fig. 11 which clearly reveals that the radiation heat loss and the temperature of glass envelope rise with the increase of emittance of selective coating. The heat loss reduces from 390 W/m to 189 W/m when the emittance reduces from 0.18 to 0.08. Therefore, the emittance of the coating is a key factor influencing the heat loss of the receiver.

Combined with Section 4.3, it can be obtained that the emittance, gas species, and pressure are three key factors for the total heat loss. The conduction heat loss caused by hydrogen deserves special attention. If there is hydrogen permeation, the conduction heat loss will be the main factor for the total heat loss. 10 Pa hydrogen increases conduction heat loss by 300 W/m and 200 Pa hydrogen increases it by 650 W/m when the temperature of the absorber tube is 350°C.

4.5 Effects of HTF temperature on heat loss

The relationship between absorber temperature and heat loss, which includes the conduction heat loss and the radiation heat loss is numerically investigated. The results show that the conduction heat loss increases with the increase of absorber temperature. For receivers using the traditional synthetic oil BP/DPO as HTF, such as Therminol VP-1, Diphyl, or Dowtherm A, the operating temperature is usually 623 K. In this case, HTF decomposes and produces hydrogen, which permeates into the vacuum annulus through the absorber tube. The hydrogen will stop permeating into the annulus as it is equilibrium with the partial pressure of hydrogen in the HTF. Some scholars believe that the partial pressure of hydrogen in annulus can reach about 133 Pa [9]. Thus, the conduction heat loss is approximately 650 W/m at 133 Pa.

To improve the efficient of the solar power system, a type of silicon oil HELISOL 5A is proposed by Wacker, whose operating temperature can reach 698 K [23]. For 10 Pa hydrogen, the rise in HTF temperature from 623 K to 698 K obviously leads to a rise in conduction heat loss by approximately 100 W/m. Hilgert et al. [23] found that HELISOL 5 A produced less hydrogen operating at 425°C than BP/DPO operating at 400°C for long-term. Even though, the hydrogen produced cannot be ignored. Therefore, there may also exist the phenomenon of high heat loss caused by hydrogen in the annulus.

When molten salt is used as HTF in the solar field, whether molten salt produce hydrogen or not is unknown, hydrogen will still exist by outgassing of absorber tube. The outgassing experiment was conducted to accurately analyze the residual gas in the receiver [2,5]. The results indicate that when the receiver is heated up to 663 K for 2 h, H₂ is the main gas which is about 1.5 Pa in the annulus. The production of hydrogen is mainly due to material outgassing. Especially, the outgassing rate remarkably increases with the increase of the temperature, and gases are increasingly accumulated in the annulus with time [2]. Even 1.5 Pa of hydrogen has a conduction heat loss of more than 100 W/m at 823 K. Therefore, more hydrogen getters are still needed to maintain annulus pressure and reduce conduction heat loss when using higher temperature HTF.

Figure 12 shows that the calculated radiation heat loss agrees well with the experimental results [17]. The radiation heat loss increases sharply with the temperature increasing. Therefore, when the operating temperature is higher, the conduction heat loss and the radiation heat loss are higher. Moreover, the high temperature will increase the amount of outgassing of materials and the gas permeation, which may cause more residual gases [5,17]. Thus, no matter the HTF is silicon oil HELISOL 5 A or molten salt, more getters are needed to avoid getter saturation for high-temperature operating.

4.6 Effects of annulus size on heat loss

The relationship between dimensionless diameter R_g,o/R_abs,o and the heat loss, which includes conduction heat loss, radiation heat loss, and total heat loss, are numerically investigated. R_abs,o is 35 mm, and the dimensionless diameter R_g,o/R_abs,o ranges from 1.2 to 2.36. When the annulus is filled with hydrogen and the annulus pressure is selected as 0.1 Pa, 1 Pa, 10 Pa, and 50 Pa, the temperature of the inner surface of the glass envelope T_g,i is 333 K, 343 K, 373 K, and 408 K respectively. T_abs,o is uniform at 350°C. The emissivity of the glass envelope is 0.86 and that of the selective coating is 0.1 at 623 K.

The effects of dimensionless diameter on conduction heat loss are shown in Fig. 13. The conduction heat loss obviously decreases when the dimensionless diameter increases. The reason for this is that it can decrease the heat flux but increase the surface area for the heat transfer to the environment as the annulus gap between the absorber tube and glass envelope increases. Therefore, the conduction heat loss decreases as the dimensionless diameter increases. Another rule is that the higher the annulus pressure is, the more sensitive the effects are. When the dimensionless diameter increases from 1.2 to 2.36, the conduction heat loss of 0.1 Pa hydrogen is reduced by only about 5 W/m, while for 10 Pa hydrogen, the conduction heat loss decreased by 400 W/m. Therefore, when the annulus gap increases properly, the conduction heat loss can be reduced in the case of poor vacuum performance.

The effects of dimensionless diameter on radiation heat loss are shown in Fig. 14. The radiation heat losss lightly increases as the dimensionless diameter increases. Combining Figs. 13 and 14, when the vacuum performance is good, the effect caused by dimensionless diameter can be ignored, because the reduction of conduction heat loss is similar to the increase of radiation heat loss. When the receiver loses vacuum, it can greatly reduce the total heat loss by reducing the conduction heat loss to increasing the dimensionless diameter properly. Since vacuum failure is very common in power plants, increasing annular gap is one of the ways to reduce the total heat loss and maintenance cost, especially at higher operating temperatures.

5 Conclusions and future work

The present paper demonstrates the results of a numerical simulation of heat transfer model for rarefied gas flow and conduction heat transfer in the annulus of the receiver, and the calculation of the radiation heat transfer. The simulation demonstrates that there is a similar deviation of less than 10% as that of the experiment, proving the accuracy and reliability of the model. The effects of annulus pressure, gas species, HTF temperature, and annulus size are analyzed systematically. The radiation heat loss and conduction heat loss are discussed separately, which is essential to the understanding of the formation mechanism of heat loss in different situations. Based on the simulation, the following findings can be obtained:

There are two key factors which affect the heat loss of the receiver: the emittance of the selective coating, which mainly affects the radiation heat loss, and the gas species and pressure, which influence the conduction heat loss. Both have a significant impact on the total heat loss.

Decreasing emittance can significantly reduce the radiation heat loss. When the emittance is reduced from 0.18 to 0.08 at an operating temperature of 673 K, the radiation heat loss is reduced by 51.5%.

The total heat loss is mainly caused by the radiation heat loss when P<1 Pa. The conduction heat loss and total heat loss increase very fast as the pressure increases, while the radiation heat loss slowly decreases, and finally the total heat loss slowly increases when P>100 Pa.

The correlation functions between the conduction heat loss and pressure for hydrogen, helium, argon, and nitrogen are obtained. Hydrogen and helium have a great influence on conduction heat loss.

The radiation heat loss and conduction heat loss increase significantly with the increase of the HTF temperature.

When the ratio R_g,o/R_abs,o increases, the conduction heat loss significantly decreases while the radiation heat loss slightly increases. Increasing the annular gap is an efficient way to reduce the total heat loss, especially for poor vacuum in the annulus of the receiver.

In the future, the heat loss of the receiver with different gases and pressures will be tested, and more accurate accommodation coefficients for different residual gases should be obtained. In addition, residual gas analysis for the receiver with different HTF such as molten salt or gas will be performed in the laboratory to obtain the data of the actual residual gas in the annulus.

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