1. Introduction
The overall efficiency of a concentrating solar power system depends on three main factors, the efficiency of the receiver, field efficiency (effective capacity to theoretical capacity) and the Carnot efficiency. With the use of nanofluids both receiver and Carnot efficiencies can be improved [
1,
2]. Nanofluid heat transfer fluid will also have significant impact of thermal storage performance [
3,
4].
In a conventional solar thermal receiver the solar radiation is directed onto a high-absorptive surface where it is converted to thermal energy [
5,
6,
7,
8,
9]. Spectrally selective surfaces are used to achieve both high absorptivity in the solar spectrum and low emissivity in the infrared [
10,
11,
12,
13,
14,
15]. The collected thermal energy is then transferred to a heat transfer fluid (HTF) to be used in a thermodynamic cycle. These surface based receivers, while being efficient at converting solar to thermal energy, suffer from two major drawbacks at high temperatures. First, the receiver surface being directly in contact with the environment has significant convective and radiative losses which increase with the temperature, also leading to a temperature difference between the surface and the fluid lowering the overall conversion efficiency. Second, the high temperatures cause significant thermal stress on the material causing it to degrade [
16]. An alternative concept to avoid these drawbacks is to use a direct absorption collector (DAC) in place of the surface collector [
17]. A DAC works by absorbing the solar radiation directly in the HTF, resulting in a more uniform distribution and a decrease in the temperature difference between the absorber and fluid. There exist numerous DAC designs, including the solar pond, trickle collectors, small particle collectors, volume trap collectors and black liquid collectors [
17,
18,
19,
20]. With the recent advancements in nanotechnology, small particle collectors have gained significant interest, with the small particles being of the nanometre scale the absorption of solar radiation can be significantly improved by low particle volume concentrations. Also due to their small size the particles are essentially fluidized, meaning they can pass through pumps, micro-channels and piping without any adverse effects [
21]. Nanofluids provide a number of advantages in DAC including:
The performance of the receiver can be tuned to suit conditions by altering the size, shape, solar concentration and material type of the nanoparticles, as the optical properties of the nanofluid are dominated by the nanoparticles [
21,
22].
DACs do not require a surface absorption plate, which results in a significantly simpler receiver design and reduced cost and labour, as surface-absorbing plates require complex manufacturing processes [
23]
Nanofluids also possess superior thermophysical properties, such as enhanced thermal conductivity, heat transfer coefficient and in some cases enhanced specific heat capacity [
23,
24,
25].
Tyagi et al. [
26] developed a two dimensional heat transfer analysis of direct sunlight incident on a thin flowing film of water/aluminium nanofluid. Using a finite difference method they found an increase in efficiency of approximately 10% of the volumetric receiver compared to a conventional flat-plate solar collector. Without performing any experimental work, this theoretical study only considered direct sun and neglected in-scattering effect [
26]. Otanicar et al. [
27] extended on Tyagi et al. [
26] work by investigating the properties of the base fluids, included size-dependent effects on the nanoparticle optical properties and verified the model experimentally. They found an increase in receiver efficiency of up to 5% by using nanofluids and that after a steep initial increase of the efficiency levels off as the volume fraction continues to increase [
27]. Taylor et al. [
28] conducted a conservative, simplified analysis of how a medium temperature (100–400 °C) nanofluid Concentrating Solar Power (CSP) system would perform compared to a conventional one. It was found that an efficiency improvement in the order of 5–10% was possible when using a nanofluid receiver. For a 100 MW nanofluid thermal plant, such an improvement in efficiency can equate to an addition of
$3.5 million to the yearly revenue [
21]. Experimental work was also conducted to validate the model; however, the results did not match well with the theoretical model. The discrepancies were attributed to the instability of the nanofluid (agglomeration and sedimentation) and the fact that more concentrated light will be absorbed in a thin upper layer of the nanofluid, which would be easily transferred back out of the receiver. Veeraragavan et al. [
29] developed a non-dimensional analytical model to account for the effect of heat loss, particle loading, solar concentration and channel height on receiver efficiency with a Therminol VP-1 graphite nanofluid. The total system efficiency was determined by combining the receiver efficiency with the Carnot efficiency to determine an optimum value of 35% at a dimensionless receiver length of 0.86 [
24]. Lenert and Wang [
30] presented a combined modelling and experimental study to optimize the efficiency of liquid based solar receivers using carbon-coated absorbing nanoparticles. A transient one-dimensional heat transfer model and a cylindrical nanofluid volume receiver were used as the model and experiment respectively, and showed good agreement in results for varying optical thicknesses of the nanofluid. It was predicted that receiver-side efficiencies could exceed 35% when the receiver is optimized with respect to the optical thickness and solar exposure time [
30]. Luo et al. [
31] presented a simulation model and validated it with an experimental setup where the results were in accordance with each other. It was found that nanofluids could increase the collector efficiency by 2–25% compared to the base fluid [
31]. Parvin, Nasrin and Alim [
32] investigated the heat transfer performance and entropy generation of forced convection through a direct absorption collector. The heat transfer performance was enhanced by up to 31% and the collector efficiency was enhanced by more than two times [
32]. Kaluri et al. [
16] recently presented a three dimensional CFD model of a direct absorbing collector that took into account the effects of optical concentration, optical density of fluid, mass flowrate and thermal insulation on the receiver efficiency. An increase of up to 28% in receiver efficiency was observed.
There is a large amount of published literature on the thermophysical and rheological properties of low temperature nanofluids. These works mainly include aqueous and glycol based nanofluids with the temperatures generally less than 100 °C. There is also comprehensive literature on the possible mechanisms behind the changes in thermophysical and rheological properties, which have shown good agreement with the experimental works in some instances. Numerous works have also presented on empirical models with good results. Molten salt nanofluids have received very little attention in comparison. These have been shown to act differently to other nanofluids, as with the addition of nanoparticles in molten salt nanofluids show an increase in specific heat capacity while other nanofluids, including those that are aqueous and glycol based, show a decrease. Similarly, some research studies have been conducted on modelling CSP nanofluid receivers. However, these works have also been limited to low to medium temperature nanofluids, the majority of which are aqueous, and glycol based [
33]. There is yet to be any study, which focuses specifically on the use of molten salt nanofluids as the HTF in DAC systems. This study aims to address this issue by developing a computational model of a receiver in order to determine an optimal receiver design for DAC systems using molten solar salt (NaNO
3-KNO
3) nanofluids as the HTF. The model has been validated by comparing to the results found in the literature. Factors of the receiver to be taken into account are the thermal re-radiation of the HTF to the environment, convective and conductive heat transfer with the environment, forced convection due to wind, volume fraction of nanoparticles and height of receiver. This research is therefore significant because molten salt nanofluids have been shown as an HTF for high temperature applications.
The paper is structured as follows: a comprehensive literature is reviewed and the research gap is identified in the introduction above, details of the computational model, including governing equations, solution method, initial and boundary conditions, model validation, and results and discussion is presented next. Finally, conclusion of this new study has been presented at the end.
3. Results and Discussion
Due to the acceptable level of agreement between results of current study and Veeraragavan’s model [
29], this model can be considered validated. After validation, the model was further improved and several more factors were added. In order to increase the accuracy of the absorptive coefficient of the nanofluid, the model considered the refractive and absorptive indexes of both the base fluid and nanoparticles as wavelength dependent. It also considered initial and inlet temperatures that are significantly higher than that of the ambient temperature. Due to the considerations of these high temperatures, the heat transfer equation is altered to include re-radiation of the nanofluid. The radiative heat loss is defined using Stefan-Boltzmann’s law and the convective heat loss is dependent on the Nusselt number and by default the inlet velocity and base fluid properties. In addition to the convective heat transfer coefficient being dependent on the Nusselt number, this model also considered the thermal resistance of a cover plate; taking into account its thermal conductivity and thickness. Additionally, the nanofluid absorption coefficient is a combination of the base fluid absorption coefficient and the nanoparticle coefficient.
3.1. Effect of Receiver Length and Height on the Efficiencies
The influence of the parameters like receiver length, receiver height, inlet velocity, solar concentration and volume fraction w investigated. The volume fraction was set at 0.00001, height of the receiver was 0.05 m, solar concentration was 10×, ambient temperature was assumed at 297 K and the inlet velocity was set at 0.0001 m/s. To determine the overall power plant efficiency the product of the receiver and power generation system efficiencies are considered.
This total efficiency represents the maximum achievable efficiency that such a power plant system can theoretically reach. The receiver length was varied between 0.0595 m and 1m for the parameters previously stated and the results are shown in
Figure 9.
It can be seen from the results that as the receiver length is increased the receiver efficiency decreases while the Carnot efficiency increases, resulting in a decreasing total efficiency. The Carnot efficiency increases as the longer the receiver is, the longer the heat transfer fluid is exposed to the solar radiation and the greater amount of radiation it is exposed to, resulting in a higher outlet temperature. However, the longer the receiver is the larger the surface area and the hotter the fluid is resulting in greater losses. The plot shows that there does not exist a length where optimal total efficiency is achieved. This result is in contrast with the findings of Veeraragavan et al. [
29] who showed that such a length does exist. The discrepancy between the results can be attributed to the higher heat losses in this model due to the use of Boltzmann’s law instead of the linear heat loss coefficient of radiation and high inlet temperature. To check this, the heat loss coefficient for both radiative and convective losses was set to 10W/m
2K [
21] and the inlet temperature set to ambient. It can be seen in
Figure 10 that with these altered parameters, there is a length for which the total efficiency is optimised.
This implies that for high temperature receivers an optimal length cannot be determined from the overall system efficiency. Instead, other factors need to be considered to determine the optimal length. Effect of receiver height on the efficiencies for a certain length and fixed parameters of the HTF were investigated as shown in
Figure 11.
As the depth of the HTF increases with the height of the receiver, larger portion of the incident radiation is absorbed by the bottom surface of the receiver than that of the HTF at shallow depth. This the phenomenon alters gradually with the increase of the receiver height. Therefore, peak Carnot efficiency is achieved at a very low receiver height, while the receiver efficiency is still increasing to a moderate receiver height before levelling off. For total efficiency there is an optimum height for a certain receiver length.
From
Figure 12 it can also be seen that the peak efficiency decreases with an increase in receiver length, which is in agreement with the results depicted in
Figure 11. The peak total efficiencies (receiver efficiency × Carnot efficiency) for different heights and lengths of a receiver are presented in
Table 3. As the parametric sweep was conducted with a receiver height step of 0.00495, so, the actual peak may fall within ±0.00495 m of the reported values.
Figure 13 shows the temperature distribution at various heights.
3.2. Effect of Inlet Velocity on the Efficiencies
Setting the previously defined lengths and their associated optimal heights, the effect of HTF inlet velocity was then investigated.
Figure 14 depicts that there is initially a sharp increase in receiver efficiency which then plateaus off quickly. There is then negligible change in total efficiency as the inlet velocity increases. This is a result of the Carnot efficiency decreasing and the receiver efficiency increasing with the inlet velocity. These two balance out and result in an almost constant total efficiency. The Carnot efficiency decreases because the average outlet temperature drops due to the HTF being exposed to the radiation for a less amount of time. The increase in receiver efficiency with inlet velocity is due to the total heat loss being dominated by surface to ambient radiation losses. Even though the convective heat transfer coefficient is increased as the fluid is exposed to the radiation for shorter period of time, causing the temperature to be lower which results in less radiative losses, eventuating in higher receiver efficiency.
To further analyse the effect that the fluid velocity has on the receiver, the dominating effects of surface to ambient radiation need to be considered. To do this the exposure time of the heat transfer fluid is to be kept constant and the inlet velocity varied. This is done by increasing the receiver length so that in all cases the fluid is exposed to the radiation for the same amount of time, arbitrarily chosen as 2500 s. Four cases were considered, a length of 0.25 m at inlet velocity of 0.0001 m/s, length of 0.5 m at inlet velocity of 0.0002 m/s, length of 1m at inlet velocity of 0.0004 m/s and a length of 5 m at inlet velocity of 0.002 m/s.
Figure 15 summarises the results and shows that even when the exposure time is constant an increase in velocity results in a decrease in the overall efficiency. This shows that an increase in velocity and by default an increase in Nusselt number results in a higher heat loss coefficient and therefore a decrease in system efficiency.
3.3. Effect of Solar Concentrations on the Efficiencies
Setting the volume fraction to 0.00001, the inlet velocity to 0.0001 and the receiver height to 0.0908 m, the solar concentration was then varied for different receiver lengths. The solar concentration was varied from 10×–25× for different receiver lengths as illustrated in
Figure 16. The efficiencies are seen increasing with solar concentration but decreasing indefinitely with receiver length.
Given that the adjusted Carnot efficiency gives rise to an optimal efficiency for the volume fraction, the receiver length was re-investigated with the adjusted Carnot efficiency as shown in
Figure 17.
It can be seen from the plot that a peak in the adjusted efficiency occurs for the receiver length, implying that there exists a length that provides the best trade-off of receiver efficiency for average temperature rise. It can also be seen that the trade-off becomes more pronounced and the optimal receiver length decreases with an increase in solar concentration. Therefore, to achieve the best balance between the receiver efficiency and the temperature rise, short receivers with high solar concentrations are desirable. From this model the suggested optimal design for a solar salt and graphite nanofluid receiver is that consisting of a solar concentration of 25×, volume fraction of 0.00001, inlet velocity 0.0001 m/s, receiver length of 0.406 m and a receiver height of 0.0908 m. These parameters result in an average outlet temperature of 835 K, peak temperature of 870 K, receiver efficiency of 43.9% and a total system efficiency of 28.3%
It should be noted that the model begins to break down at higher concentrations and longer receiver lengths because the viscosity equation results in a negative value due to the high temperatures in those situations. As solar salt begins to break down at 873 K, the maximum temperature should also be considered in the model. To investigate even higher solar concentrations without the viscosity equation breaking down, the inlet velocity is increased while keeping the receiver length constant, allowing for suitable temperatures to be achieved for high concentrations.
Table 4 shows the solar concentrations investigated and their respective inlet velocities.
The effect that solar concentration has on the total efficiency of the system is illustrated in
Figure 18. It can be seen that the total efficiency continually increases with solar concentration and even exceeds efficiencies of 40%. It can also be seen that for higher concentrations, the relationship between the receiver length and total efficiency changes from that of a linear to more of a quadratic relationship, resulting in an optimal length. The reason behind this change can be attributed to the fact that the receiver efficiency becomes less of a dominating factor and the Carnot efficiency has a larger impact on the total efficiency.
However, this plot does not show the peak temperature of the nanofluid. This is shown in
Table 5 and it can be seen that after a length of approximately 0.604–0.6535 m, the peak temperature exceeds the upper limit for solar salt. This critical length can be altered to suit operational conditions by varying the inlet velocity; increasing the velocity allows for a longer length and vice versa. From
Figure 18, it appears that the more efficient receivers are those with the shortest length. However, in reality, efficiency is not the only factor to be considered. Referring to
Table 5 and
Figure 19, the shortest receiver lengths result in the lowest outlet temperature, where in the worst case is only 10 K higher than the inlet temperature. This implies that not enough emphasis is paid to the rise in temperature, as it seems that the most efficient receivers are those with the lowest temperature rise.
Considering the adjusted Carnot efficiency,
Figure 20 shows which lengths provide the best balance between the receiver efficiency and temperature rise for different concentrations. As no optimal point exists for the receiver length range in question, from the trends presented, it is deduced that the optimal lengths lie beyond those considered range, and the efficiencies increase with increasing of solar concentration. This trend is also represented in
Table 5 and
Figure 19, which show that the average outlet temperature is lower for high concentrations, with all having similar peak temperatures; meaning that the temperature difference between the average outlet temperature and the peak temperature increases with increasing solar concentration. This is due to the solar radiation being exponentially attenuated by the nanofluid, resulting in the majority of the radiation being absorbed in the upper thin layer of the nanofluid. So an increase in the intensity of the radiation results in an increase in the temperature difference between the peak temperature and average outlet temperature. This is made more evident when comparing solar concentrations of 30× and 100× at conditions where the highest peak temperature is reached without exceeding the upper limit. For a concentration of 30×, a receiver length of 0.5545 m is needed and results in an average outlet temperature of 684 K and a peak temperature of 867 K, resulting in a Carnot efficiency of 57.2%, a receiver efficiency of 49.9% and a total efficiency of 28.5%. In comparison a concentration of 100× results in a receiver length of 0.505 m, an average outlet temperature of 602 K and a peak temperature of 867K, resulting in a Carnot efficiency of 51.2%, a receiver efficiency of 82.8% and a total efficiency of 42.4%.
To further investigate the effects of solar concentration, it was varied for each volume fraction and the inlet velocities adjusted such that the peak temperature of the receiver equaled that of solar salt’s upper temperature limit. For a volume fraction of 0.0005 the total efficiency and the adjusted efficiency with respect to solar concentration are depicted in
Figure 21a,b respectively.
Figure 21 shows that while the system efficiency increases indefinitely with solar concentration, the adjusted efficiency is peaked approximately at 100× concentration. This better represents the increasing temperature difference between peak and outlet with solar concentration, implying that the best trade-off between receiver efficiency and average temperature rise occurs at a solar concentration of 100×. At higher volume fraction (e.g. 0.0001), most of the energy was absorbed close to the surface so there was a lot of convection and radiation losses due to the high temperature. At lower volume fraction (e.g. 0.00001), the energy was absorbed throughout the receiver with less losses but also resulted in a lower temperature rise in the fluid. However, further increase in volume fraction (e.g. 0.0005) resulted in higher total efficiency. Higher absorption of heat due to higher volume fraction was much higher than the loss to the environment.
The same simulations were conducted for different volume fractions and the results are illustrated in
Figure 22. With increasing solar concentration, each volume fraction shows a similar trend in
Figure 22a in a sense that the total efficiency increases indefinitely, and the adjusted efficiency is peaked between 50× and 100× concentration at first then starts to decrease. In addition, it can be seen from
Figure 22b that the peak solar concentration decreases with decreasing volume fraction such that it is about 100× for a volume fraction of 0.0005 and then approximately 50× for the remaining volume fractions. This can be attributed to the fact that, similar to solar concentration, a decrease in volume fraction results in an increase in the temperature difference between the peak and average outlet temperatures. So with the decreasing volume fraction and increasing solar concentration both increasing the temperature difference. This results in a lower adjusted efficiency and by extension reducing the peak solar concentration.
Figure 23 illustrates temperature profile at two different solar concentrations. It can be seen that the lower concentration has a more even temperature distribution compared to the higher concentration.
4. Conclusions
Nanofluid volumetric flow receivers have been studied for high-temperature concentrating solar thermal applications using sodium nitrate + potassium nitrate salts, NaNO3-KNO3, also commonly known as solar salt base fluids doped with graphite. A 2D CFD model is developed to investigate the effects of design and operating parameters on the receiver efficiency, temperature rise and system efficiency. Parameters taken into consideration included receiver length, inlet velocity and solar concentration. The model has been evaluated using three types of heat losses from the nanofluid: surface to ambient radiation loss, convective loss and re-emission loss.
The model shows that the receiver efficiency increases with increasing solar concentration, decreasing receiver length and decreasing nanoparticle volume fraction and, by extension, increasing receiver height. It also showed that the temperature rise across the receiver increases with an increase in receiver length, decrease in inlet velocity and an increase in solar concentration. When the receiver is connected to a power generation cycle, the total system efficiency is found to be in excess of 40% when solar concentrations are greater than 100×.
The reason behind the high concentration receivers resulting in a higher efficiency is that the increase in receiver efficiency outweighs the decrease in Carnot efficiency, as the receiver efficiency is found to exceed 90% in certain cases. It was also revealed that an optimal receiver length exists which increases with increasing solar concentration, and is also dependent on the inlet velocity. In addition, adjusted total efficiency resulted in a peak for solar concentration, which decreased with decreasing volume fraction, implying that each receiver configuration has an optimal solar concentration.
This study provides a comprehensive model of a direct absorption high temperature nanofluid solar receiver which can be used to determine an optimal receiver design given the operating conditions of the system.