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Abstract
The excitation of localized surface plasmon at the metal nanoparticles can significantly enhance the absorption of solar energy. However, the absorption peak is sharp at the resonant frequency. To achieve a broadband absorption, the blended nanofluid formed by SiO2/Ag nanoshells of different core size and shell thickness is employed. The blended nanofluid has a good solar absorption property, whose extinction spectrum matches the solar spectrum well. The transient temperature response of the nanofluid is simulated. It is found that the photothermal performance of the solar thermal collector is related to the geometric parameters and operation conditions of the solar collector, and the optical and thermophysical properties of nanofluid. As the flow velocity increases, the outlet temperature is gradually reduced. But, the collector efficiency is increased since less heat is lost to the environment via convection as nanofluid flows fast in the channel. In order to obtain a large outlet temperature at high velocity, it can be considered to elongate the channel length. Due to the strong extinction properties of the blended nanofluid, the required volume fraction can be significantly reduced, only 1/10 of that of Ag nanofluid for an equal temperature increases.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Solar energy is one of the most promising renewable energy resources and it is considered to be an ideal substitute of traditional energy for its clean, abundant, widely distributed characteristics. Among the various applications of solar energy, the photothermal conversion is most direct and simplest. Solar radiation is transformed to internal energy of the transport medium by a solar thermal collector. For conventional surface-based absorber, the working fluid is heated by the absorptive surface through conduction. Such surface-based thermal collectors are not suitable for high incident energy flux since the radiative heat loss is significant at high temperatures. An alternative way to reduce the radiative heat loss and improve the photothermal efficiency is the use of volumetric absorbers.
The idea of volumetric absorption using working fluid as absorber was proposed in the 1970s [1,2]. The working fluid directly absorbs solar energy can effectively reduce the conduction resistance and surface temperature [3]. So that, the radiative heat loss can be reduced compared with the collectors based on surface absorption. As the medium of light absorption and conversion, the working fluid is required to have strong optical absorption property. Water is tested to be the best base fluid among the four common liquids namely water, ethylene glycol, propylene glycol and therminol VP-1 [4,5]. However, the absorption is still extremely weak, only absorbing 13% of the incident energy. Adding some nanoparticles into the base fluid to form nanofluid can improve the light absorption significantly. In Moghadam and associates’ study, CuO-H2O nanofluid with mass flow rate of 1 kg/min increases the collector efficiency about 21.8% [6]. Using Cu-H2O nanofluid (25 nm, 0.1 wt%) as the absorbing medium, the efficiency of solar collector is found to be enhanced by 23.83% [7]. For Al2O3-H2O nanofluid, it is reported 28.3% enhancement in the collector efficiency for 0.2 wt% [8]. While for TiO2-H2O nanofluid, the collector efficiency is found to be enhanced by 15.7% [9]. Lenert et al. [10] optimize the efficiency of carbon-coated cobalt nanofluid-based solar absorber. The optimum system efficiency is predicted to exceed 35% when nanofluid volumetric absorber is optimized and coupled to a power cycle. The addition of nanoparticles causes scattering of incident radiation within the fluid and allows more light to be absorbed [5]. Hence, an improvement in collector efficiency is achieved.
It can be found that the efficiency improvement of nanofluid-based volumetric absorber is dependent on the suspended nanoparticles. The metal nanoparticles have many unique properties, one of which is that the localized surface plasmon resonance (LSPR) supported at the particle surface [11,12]. LSPR effect arises from the collective oscillation of conduction electrons. At resonant frequency, the incident energy is trapped around the nanoparticle, leading to a significant enhancement of light absorption [13,14]. Zhang et al. [15] experimentally show that plasmonic Au nanoparticles have stronger absorption than the carbon-based nanoparticles. The required Au nanoparticle concentration is 2-4 order of magnitude lower than those of carbon based materials to reach a similar enhancement ratio. Therefore, the plasmon resonance effect supported by metal nanoparticles has great potential to improve the performance of direct solar thermal collector [16–21]. However, it should be noticed that the excitation of LSPR effect is frequency-dependent, leading to a sharp increase of light absorption at resonant wavelength. Obviously, the sharp absorption peak arose from the plasmon resonance effect doesn’t meet the need for broadband solar absorption. The resonant frequencies of metal nanoparticles, such as gold, silver, and aluminum, are usually located in the ultraviolet to short visible range [17]. It is desirable to tune the plasmon resonance peak in a wide range of wavelength for a broadband enhancement of absorption [22]. For core/shell nanoparticles, the resonant frequency can be tuned from visible to near-infrared by adjusting core and shell sizes [23–28]. Take SiO2/Au core/shell nanoparticle for an example, the plasmon resonant peak is shifted from 1190 to 730 nm as the Au shell thickness varies from 2.5 to 12.5 nm [12]. The plasmonic nanostructure could enable efficient and broadband solar absorption through several mechanisms [29]. Zhou et al. [29] fabricate an aluminium-based plasmonic absorbers by the self-assembly of aluminium nanoparticles into a three-dimensional porous membrane for solar desalination. The self-assembled aluminium nanoparticles are closely packed along the sidewalls of the nanopores, resulting in a strong plasmon hybridization effect [30] and excitations of high-density localized plasmon resonances [31]. In addition, the mixing of plasmonic nanoparticles with different sizes can also have a broadband absorption. Cole and Halas [32] present an optimization model to determine ideal distributions of nanospheres and nanoshells in a mixed component that would either absorb or scatter the AM 1.5 solar spectrum. And, the potential for light harvesting using plasmonic nanoparticles for solar energy applications is demonstrated.
In this paper, the blended nanofluid formed by SiO2/Ag plasmonic nanoshells with different core and shell sizes is employed as working fluid to induce plasmon resonance across a broad-range of wavelength. The localized surface plasmon resonance can be tuned by controlling the proportion of different nanoshells for a broadband solar absorption. The optical properties of the plasmonic nanoshells are simulated based on Mie theory, and the solar energy absorbed by the nanofluid is solved from the radiative transfer equation. Finally, the temperature rise within the nanofluid is calculated and the resultant photothermal performance is evaluated. The improvements in photothermal conversion will facilitate the development of a range of solar devices and applications, such as receivers with integrated storage for concentrated solar power systems [10], efficient solar thermal collectors [33], solar desalination system [29], and other solar equipment.
2. Model and method
The schematic of a direct solar thermal collector based on blended nanofluid is shown in Fig. 1. The SiO2 core is coated with Ag shell. The core radius is R and the shell thickness is t. The nanoshells with different core size and shell thickness are randomly suspended in water forming blended nanofluid. The height and length of the channel is H and L respectively. The top is covered with a transparent glass to prevent evaporation and heat loss of nanofluid. The glass cover has a good transmittance to sunlight. More than 90% of the sunlight can pass through it. In the calculation, the transmittance τg of the glass cove is assumed to be 0.9. The nanofluid directly absorbs the sunlight and converts to heat. It is assumed to have a uniform velocity profile.
2.1 Optical properties of base fluid
The fluid medium is the main part of volumetric absorber. Thus, the optical properties of the fluid medium have important influence on the efficiency of volumetric absorber. The absorption of nanofluid is contributed from both the base fluid and nanoparticles. For pure fluids, the scattering can be neglected. The attenuation of incident light is mainly caused by absorption. So that, the spectral absorption coefficient of base fluid can be calculated by [34]:
where κ is the imaginary part of refractive index of base fluid. In this study, water is chosen to be the base fluid due to its clean and non-toxic characteristics. Water is almost transparent to UV and visible light, only absorbs some near infrared radiation. The suspended nanoparticles can significantly improve the absorption properties of base fluid.2.2 Optical properties of nanoshells
The optical properties of individual nanoshell can be calculated by Mie theory. For spherical coated nanostructure, the extinction efficiency Qeλ can be expressed based on the Mie scattering coefficients of the core/shell nanoparticle as [35]:
where x is size parameter, given by x = πDnw/λ with the refractive index of water (nw), and the outer diameter of nanoshell (D), an and bn are Mie scattering coefficients of the core/shell nanostructure referred to [35]. When the particle size is very small and the volume concentration is not too high (less than 0.6%), the nanofluid can be assumed to be worked in the independent scattering regime [34]. For an efficient volumetric absorber, the nanofluid is always worked at very low volume fractions. The scattering is regarded as series of a single particle scattering, so that the intensities can be added simply. The extinction coefficient of the suspended nanoshells is obtained from the extinction efficiency Qeλ of each nanoshell and its volume fraction given by [35]:where fi is the volume fraction, and Di is the particle diameter. The total extinction coefficient of a nanofluid blended with different nanoshells can be calculated by a linear combination of that of base fluid and nanoshells. It can be expressed as [17]:The energy transfer in an absorbing, emitting, and scattering medium can be described by the radiative transport equation. When the nanoparticle volume concentration is less than 0.1%, the directional dependence of radiation can be neglected [20]. In this paper, the particle concentration is relatively weak and the particle sizes are in the nanometer scale. The level of scattering is remarkably reduced within the system [33]. This leads to a significant simplification in the radiative transport equation by dropping the scattering terms. Since the temperature rise within the nanofluid is not very high for low-flux solar radiation, the emission term is ignored. The simplified radiative transport equation as
where Iλ is the spectral radiation intensity, σeλ is the extinction coefficient.When the particle size is much smaller than the mean-free-path of the conduction electrons, the optical constants of materials are size dependent. And, the optical properties may be modified, leading to a broadening of the plasmonic effects [36]. The size-dependent dielectric function of Ag shell can be calculated by the modified Drude model [12,17,37]:
where εbulk is the bulk dielectric function, ωp is the plasma frequency and Γ∞ is the scattering rate of bulk Ag. These values are obtained from [38] as ωp = 7.27 × 104 cm−1 and Γ∞ = 145 cm−1. The scattering rate of thin Ag shell is related to the bulk value by Γ(t) = Γ∞ + vF/t with vF and t being the Fermi velocity and thickness of Ag shell, respectively. The optical constants of bulk Ag, SiO2, and water are obtained from [39].2.3 Energy balance equation
As Fig. 1 shows, the heat transfer model is considered as a two-dimensional transient-state case. The following energy balance equation is applied:
where ρ is the nanofluid density, cp is the specific heat, U is the fluid velocity, k is the thermal conductivity, and qr is the radiative heat flux given by.The top surface takes the natural convection boundary condition with a convective heat transfer coefficient hc of 10 W/m2/K commonly used for air. And the radiative heat loss to the environment from the top surface is evaluated from Stefan-Boltzmann law. The bottom wall is considered to be insulated. The inlet temperature of nanofluid and ambient temperature are kept constant at a value of 293.15 K. According to energy balance equation, the discrete equation is deduced by control volume integration method. The 2D domain is divided into uniform nodes of finite differences. Along the length, the space was divided into 1000 control volumes, each having a length dx of 0.001 m. And, the height H of 0.01 m, is also divided into 1000 control volumes with dy = 1e-5 m. The discrete equation is solved using Gauss-Seidel line iteration method [40]. The implicit scheme is adopted, so the choices of grid distance and time step are arbitrary. Finally, the collector efficiency can be evaluated by:
where is the mass flow rate of nanofluid, and are the average outlet and inlet temperatures respectively, A is the top cover area, G is the incident solar flux of 1000 W/m2. Since the volume fraction of plasmonic nanoparticles is very low (i.e., less than 0.6%), the thermophysical parameters of nanofluid, such as density ρ, specific heat cp, thermal conductivity k, are assumed to be uniform. They can be calculated by a linear combination of that of base fluid and nanoshells related to the volume fraction.3. Results and discussion
3.1 Optical properties
It is known that the optical properties of nanoshells can be well tuned by adjusting the core and shell sizes. With the core radius of 5 nm as an example, the effect of shell thickness on the extinction properties is shown in Fig. 2. The nanoshells have the same volume fraction, temporarily taken as 0.01%. Figure 2 shows the extinction coefficient of the suspended nanoshells, calculated from Eq. (3), the contribution from base fluid is not included. In the visible band, a strong extinction peak can be observed, which originates from the excitation of plasmonic effect. As the shell thickness increases, the resonant intensity is enhanced, but the peak is narrowed. The excitation of LSPR effect can help enhance light absorption, but, the enhancement is wavelength-dependent. Obviously, the nanoshells of single size are difficult to meet the broadband absorption of solar energy.
Fig. 2 Effect of shell thickness on extinction properties of nanoshells, the volume fraction of nanoshells is 0.01%.
It can be observed that the resonant wavelength and intensity can be tuned as the nanoshell size varies. When the shell thickness is thin, the resonant peak is narrowed and blue-shifted with the increase of shell thickness. But, when the shell size is much larger than the core size, the extinction spectrum is almost unchanged as shell thickness increases further (as shown in Fig. 2). For a fixed shell thickness (e.g. t = 3 nm), the effects of core size on the extinction properties are shown in Fig. 3. As the core size increases, the resonant peak is broadened and red-shifted. In order to induce plasmon resonance across a broadband wavelength, it is desired to mix the nanoshells of different sizes in base fluid forming blended nanofluid. Due to the size effect of dielectric constants, the nanoshells of thinner shell thickness exhibit a gentler extinction spectrum. They are suitable to absorb the light of longer wavelengths.
For the nanoshells, the shift of resonant wavelength can be predicted by the effective medium theory [41]. The resonance occurs at a wavelength at which, where and meaning the ratio of the shell’s volume to that of the whole nanoparticle [42]. When R increases, |εAg| should increase due to the decrease of fs. So that, for a fixed core size, the blue shift of resonant wavelength can be expected as the shell thickness increases. According to this principle, we choose four types of nanoshells. The geometric parameters of the nanoshells are summarized in Table 1. The total volume fraction of blended nanofluid is temporarily taken as 0.01%. Figure 4 shows the extinction coefficient of blended nanofluid as well as the contributions of each type of nanoshells. The extinction spectrum of the blended nanofluid matches the solar spectrum well in the visible region where the solar irradiance is strongest.
Table 1. Geometric parameters of four types of nanoshells and their relative proportion toward the total volume fraction
Fig. 4 Extinction properties of the blended nanoshells and the contributions of each type of nanoshells.
3.2 Thermal properties
According to the energy balance equation (Eq. (7)), the temperature distribution within the nanofuid can be calculated. Take the channel of L = 1 m, H = 0.01 m as an example, Fig. 5 shows the variation of outlet temperature with time. At the initial time, the temperature within the nanofluid is uniform. When irradiated by sunlight, the temperature difference between the top and bottom nanofluids gradually increases since the top nanofluid can absorb more light than the bottom nanofluid. It can be observed that the outlet temperature increases gradually and then tends to be stable for half an hour irradiation. So, the temperature profile within the blended nanofluid (geometric parameters as Table 1 shows) shown in Fig. 6 is calculated at t = 1800 s.
As the nanofluid flows along the thermal collector, it is heated by solar energy. The temperature is gradually decreased as depth increases since the incident energy decays exponentially with depth from Eq. (5). At the bottom, the temperature varies a little as the nanofluid flows. Light is almost absorbed by the upper nanofluid. The temperature rise in the bottom nanofluid is mainly contributed from the heat conduction from upper nanofluid. When the nanofluid volume fraction is large, the collector height can be reduced properly. On the contrary, for dilute nanofluid, an equal solar absorption can be achieved by increasing the collector height. The effect of collector height and nanofluid volume fraction will be discussed in the following. To evaluate the collector efficiency, the average temperature is used.
According to Eq. (8), the collector efficiency is affected by the nanofluid thermophysical properties, flow velocity, and collector geometric parameters. Figure 7 shows the average temperature at outlet and the corresponding collector efficiency across the 1-m-long channel at t = 1800 s. It can be observed that the outlet temperature is almost irrelevant to the inlet velocity when U0 < 0.0005 m/s. And then, the outlet temperature drops rapidly as the velocity increases. The heat transfer model studied in this paper is a transient model. For nanofluid of different inlet velocity, the time needed to achieve stability is also different. From Fig. 5, we know that the heat transfer almost reaches to steady state at t = 1800 s for that case. But for U0 of other values, the lower inlet velocity, the longer time needed to achieve stability. For U0 < 0.0005 m/s, the nanofluid is still in the initial stage of solar heating at t = 1800 s. At this initial stage, the temperature rise rates are almost the same under different flow velocity. After reaching steady state, the outlet temperature is decreased since the mass of fluid is increased with the velocity increasing. But, the amount of energy carried by the nanofluid is constant as velocity increases. When nanofluid flows fast in the channel, less heat is lost to the environment via convection. So that, the collector efficiency is increased with velocity. The outlet temperature and collector efficiency have the opposite trends. To obtain a large outlet temperature at high velocity, it can be considered to elongate the channel length.
The transient temperature characteristics in the initial stage of 0-1800 s are simulated. Figure 8 shows the average temperatures at the outlets of the channels with different lengths. As expected, the outlet temperature increases with channel length. At the initial time, the temperature rise rate is almost the same for channels of different lengths. But, with the increase of length, the time needed to achieve steady state also increases.
In addition to the channel length, the channel height is another important factor that significantly influences the performance of solar thermal collector. Figure 9 shows the transient temperature responses at outlets of channels with different heights. Since the solar irradiation decays exponentially along the depth, the light that can transmit to the bottom is very limited. For nanofluid of strong absorption, increasing the channel height has little influence on the enhancement of solar absorption. While channel height increases, the amount of nanofluid that needs to be heated per unit time is increased. Correspondingly, the temperature rise rate and outlet temperature are reduced with the increase of channel height. The optimal height is related to the absorption properties of nanofluid. One of the main factors is the concentration of nanofluid. For large concentration, the collector of just a small height can have a good solar absorption. While for nanofluid of poor absorption, the amount of energy absorbed can be improved by increasing the collector height.
Figure 10 shows the effect of volume fraction on the photothermal properties. As a contrast, the transient temperature responses of Ag nanofluid flowing across the same collector channel are also presented (dashed lines). For nanofluids of the same volume fraction, the temperature rise rate of blended nanofluids is greater than that of Ag nanofluids under the same operation condition, especially at low volume fractions. This is due to the stronger absorption of blended nanofluid. The extinction spectrum of the blended nanofluid is more consistent with the solar spectrum. With the increase of volume fraction, the temperature rise rate of Ag nanofluid is gradually increased, and then tends to be stable. But for blended nanofluid, the volume fraction has little effect on the temperature response. As shown in Fig. 10, for blended nanofluid, the outlet temperature is just increased by 1.5 K as volume fraction increased from 0.001% to 0.005%. Further increasing the volume fraction to 0.01%, the temperature response curve remains almost unchanged, as the solid black and blue lines show in Fig. 10. It is known that the optical properties of nanofluid are related to the volume fraction. However, when the volume fraction is too large, the sunlight is absorbed almost by the nanofluid in upper layer, which leads to the increase of convection and radiative heat loss. For blended nanofluid, the temperature rise rate is reduced as volume fraction increased to 0.05%.The blended nanofluid has much stronger photothermal performance even at very low volume fraction. As shown in Fig. 10, the temperature rise rate of blended nanofluid at volume fraction of 0.005% is even higher than that of Ag nanofluid at volume fraction of 0.05%. Compared to the conventional nanofluid, the required volume fraction can be significantly reduced when blended nanofluid is used as working fluid.
Fig. 10 Effect of the volume fraction on the temperature responses of blended nanofluid (solid lines) and Ag nanofluid (dashed lines).
The factors affecting the photothermal performance include the geometric parameters and operating conditions of the solar thermal collector, the optical and thermophysical properties of nanofluid. For the best performance, the geometric parameters and the operation condition need to be carefully designed according to the needs of a specific application. The optimization of these parameters will be performed in future research.
4. Conclusions
The plasmonic nanofluid is employed as the working fluid of volumetric solar collector. In order to broaden the sharp absorption peak associated with the surface plasmon, the blended nanofluid formed by the SiO2/Ag nanoshells of different core size and shell thickness is employed. By tuning the proportions of different nanoshells, the extinction spectrum of blended nanofluid can match the solar spectrum well. The transient temperature response of the nanofluid is simulated according to the energy balance equation. There are many factors affecting the photothermal performance, such as the geometric parameters and operation conditions of solar thermal collector, optical and thermophysical properties of nanofluid. As the flow velocity increases, the outlet temperature is decreased. For large flow velocity, the channel length could be elongated to achieve a higher outlet temperature. For nanofluid of strong absorption, increasing the channel height has little influence on the enhancement of solar absorption. The temperature rise rate of blended nanofluid is much higher than that of Ag nanofluid due to the strong absorption of blended nanofluid. The required volume fraction can be significantly reduced when blended nanofluid is used as working fluid.
Funding
National Natural Science Foundation of China (NSFC) (51506044); Fundamental Research Funds for the Central Universities (2018B15614).
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