1 Introduction

Most of the conventionally used solar thermal technologies are characterized by the presence of surface-based absorbers, wherein the solar radiation is firstly converted into heat by a solid surface using a selective coating and then transmitted to a working fluid by means of thermal conduction and convection. However, the solar-to-thermal conversion efficiency in such solar collectors is limited by the conductive and convective resistances between the absorber plate and the heat transfer fluid, which lead to high heat losses towards the environment. This issue can be addressed by allowing the incident solar radiation to directly interact with the heat transfer fluid, without heating any other component in the receiver. Indeed, with direct absorption solar collectors (DASCs) the conversion of solar radiation into heat occurs volumetrically inside the heat transfer fluid which acts as the absorber [1, 2].

Due to the recent advances in the field of nanotechnologies, increasing interest has been addressed to the use of the so-called nanofluids inside DASCs [3,4,5,6,7], particularly for their thermophysical [8, 9] and optical properties [10,11,12]. Many studies on nanofluids made of metallic nanoparticles (silver, copper, gold, metal oxide, …) for the direct absorption of solar radiation can be found in the literature [13, 14]. As concluded by Chen et al. [15], the presence of metallic nanoparticles in the base fluid leads not only to the enhancement of the thermodynamic properties of the base fluid (especially of the thermal conductivity), but also to improved optical properties in the 200–800 nm range of wavelengths. Zhang et al. [16] demonstrated that the addition of gold nanoparticles to the working fluid can improve the photo-thermal conversion efficiency of a volumetric receiver under simulated solar light by about 20% with respect to the base fluid, even at small mass concentrations (0.0007%-0.0028%). As nanofluids made of metallic particles can lead to corrosion or damage of the materials employed in the test apparatus and are affected by stability issues, increasing attention has been addressed to other promising solutions, such as nanofluids made of carbon nanoparticles [17]. The stability of multi-wall carbon nanotubes dispersed in ethylene glycol when subjected to thermal cycles and radiation flux at various nanoparticles concentrations was recently investigated by Li et al. [18]. They observed that the stability of the nanofluids was compromised due to intermittent heating cycles, but the ultrasonic process could easily reverse such tendency. Sani et al. [19] investigated the optical and thermal properties of nanofluids consisting of aqueous suspensions of Single-Wall-Carbon-NanoHorns (SWCNHs) at different concentrations. They demonstrated that the addition of such nanostructures to water significantly improves the absorption capability of the overall solution and this effect is even more and more significant with the increasing nanoparticles concentration. Mercatelli et al. [20] studied the absorption and scattering properties of three different Single-Wall-Carbon-NanoHorn suspensions concluding that a maximum of 95% of the total incident light could be absorbed by the nanofluids. Sani et al. [21] verified that SWCNHs suspensions can be very stable, as no settling or clustering phenomena were observed up to six months after the nanofluid preparation.

Many experimental and analytical studies have been performed to evaluate the effective potential of fluids made of SWCNHs inside direct absorption solar collectors. These works considered both concentrated and non-concentrated solar radiation. Moradi et al. [22] developed a model to predict the effect of nanoparticle concentrations on the efficiency of the solar collector under exposure to non-concentrated solar radiation. They found out that at high concentrations the absorption of the solar radiation is limited to a thin layer of nanofluid close to the glass cover, thus leading to a thermal efficiency comparable to that of traditional solar collectors. The same considerations can be formulated when considering concentrated solar radiation (Dugaria et al. [23]). In these analytical studies, thermal efficiency values equal to 80–90% for a mean reduced temperature equal to zero were expected from simulations involving SWCNHs-based nanofluids in DASCs. Experimental investigations confirmed such good values of efficiency. Bortolato et al. [24] evaluated the performance of SWCNHs with sodium dodecyl sulfate (SDS) as surfactant in a direct absorption solar collector under concentrated radiation. During the first hours of exposure to the concentrated solar radiation, the receiver thermal efficiency did not vary significantly and reached 87%. A continuous decrease in the efficiency of the solar collector was detected after about 8 h of tests, thus highlighting a stability issue probably caused by degradation of the polymeric surfactant. To further increase the stability of SWCNHs suspensions, Agresti et al. [25] proposed a surface oxidation of the SWCNHs particles with concentrated HNO3. In the work of Zanetti et al. [26], the stability of two surfactant-stabilized SWCNHs nanofluids (one containing SDS and the other one containing a mixture of SDS and polyvinylpyrrolidone PVP-10) and of a nanofluid of SWCNHs functionalized with polyethylene glycol (PEG) were investigated under exposure to non-concentrated solar radiation. The PEG-ylated SWCNHs nanofluid maintained an efficiency value of about 94–98% for 65 h of circulation, leading to a significant improvement in the test durability with respect to the other tested nanofluids.

The evaluation of the stability of SWCNHs nanofluids in real working conditions is still an open issue due to the limited experimental investigations performed in real systems; however, it represents an essential step to ascertain their reliability and applicability. In this paper, the stability and optical behaviour of a nanofluid obtained with functionalized SWCNHs is experimentally investigated under the effect of fluid circulation, variable temperature and exposure to non-concentrated solar radiation. A novel experimental technique based on the combined use of pyranometers positioned on the front and on the rear side of the solar receiver is employed to determine the absorption efficiency of the nanofluid.

2 Characteristics of the employed nanofluid

2.1 Nanofluid preparation

The nanofluid employed in the experimental apparatus is a suspension of functionalized SWCNHs (Single-Wall-Carbon-NanoHorns) nanoparticles in deionized water. The SWCNHs nanoparticles, provided by Carbonium S.r.l., are obtained by means of rapid condensation of carbon atoms without any catalyst and consist of aggregates of tiny graphene conically-shaped sheets of 3–5 nm diameter and 40–50 nm length. The SWCNHs aggregates, with diameter of about 50–100 nm, appear similar to “dahlia” flowers or buds and display large surface and high number of cavities.

For the preparation of the nanofluid, SWCNHs aggregates were functionalized with 750 Da polyethylene glycol chains (PEG-ylation). As highlighted in [26], the functionalization with PEG ensures a better stability of the SWCNHs suspension and a higher absorption compared to the oxidized non-PEG-ylated products. The oxidation of the SWCNHs aggregates was the first step of the PEG-ylation. 0.1 g of SWCNHs were mixed with 40 mL of sulphonitric mixture (H2SO4:HNO3 = 3:1 in volume) in an ice bath under continuous magnetic stirring. Then the reaction was continued in a water bath at 45 °C for 30 min. Three sonication cycles, each of 1 min with a working time of 0.3 s and a pause of 0.7 s, were performed with a 20 W tip sonicator. After the cycles, the reaction continued at 45 °C for 30 min under magnetic stirring. Then, the solution was cooled in an ice bath for 1 h and centrifuged to recover the oxidized material. The previous steps were repeated five times, for a total initial amount of 0.5 g of SWCNHs. The final products, ox-SWCNHs, were mixed with the addition of 1 mL of solvent and homogenised by sonication.

An acid–base titration allowed estimating that 30% of the carbon atoms were oxidized.

In the second step the PEG chains were covalently linked to the ox-SWCNHs using a reaction of amidation. The material was functionalized in small batches of 25 mg of ox-SWCNHs using 215 mg of PEG750-NH2. Both reactants were dried for 1 h at 50 °C and then for 3 h in a desiccator with P2O5. In a 25 mL flask the ox-SWCNHs were sonicated with 3 mL of anhydrous DMF for 5 min. Then about 20 mg of HOBt and 28 mg of EDC∙HCl were added as activators of the amidation reaction and the solution was cooled in an ice bath under magnetic stirring. Hence the PEG750-NH2, dissolved in anhydrous DMF, was added in three aliquots of 2 mL. The reaction continued for 17 h at ambient temperature under magnetic stirring. Then, diethyl ether was added and the solution centrifuged, in order to remove the DMF, the excess of PEG750-NH2 and reaction sub-products.

The absorbance spectra of a solution of the PEG-ylated SWCNHs (SWCNH-PEG) were monitored for about 40 days and allowed verifying the stability of the solution. The solution, diluted in deionized water to obtain the desired absorbance, allowed to get the volume of nanofluid necessary to completely fill the experimental setup (about 2 L).

2.2 Nanofluid optical characterization

The dilution of the solution must be calibrated to obtain the optimal absorption efficiency with the minimum expenditure for the nanofluid preparation. The criterion adopted for this choice imposes an optical efficiency of at least 90% considering the overall volume of the solar receiver employed in the present experimental tests. For the calculation of the optical efficiency of the nanofluid the absorbance spectrum is needed. The absorbance values of a reference nanofluid, serving as bases for calculations, are evaluated in the range from 200 to 1200 nm with a Cary5000 spectrometer (Varian) using a 0.2 cm quartz cell and applying the Lambert–Beer law:

$${A}_{\lambda }=L\cdot {\varepsilon }_{\lambda }\cdot C$$
(1)

where Aλ is the absorbance, L is the path length, ελ is the molar extinction coefficient and C is the concentration of nanoparticles in the solution. The absorbance values are then used to calculate the spectral transmittance of the nanofluid τλ:

$${\tau }_{\lambda }=\frac{1}{{10}^{{A}_{\lambda }}}$$
(2)

In the case of a nanofluid used for the absorption of the solar radiation, the spectral transmittance can be defined as the ratio of the spectral solar irradiance transmitted by the nanofluid Itrans,λ to the incident spectral solar irradiance Iinc,λ:

$${\tau }_{\lambda }=\frac{{\text{I}}_{trans,\lambda }}{{\text{I}}_{inc,\lambda }}$$
(3)

From the values of incident spectral solar irradiance Iinc,λ it is possible to define fλ:

$${f}_{\lambda }=\frac{{\text{I}}_{inc,\lambda }}{{\text{I}}_{inc}}$$
(4)

where Iinc is the total incident solar irradiance. Combining Eqs. (3) and (4), fλ can be also defined as follows:

$${f}_{\lambda }=\frac{{\text{I}}_{trans,\lambda }}{{\text{I}}_{inc}\cdot {\tau }_{\lambda }}$$
(5)

The optical efficiency of the nanofluid, also named “absorbed energy fraction”, can be defined applying Eq. (6):

$${\eta }_{opt,n}=1-\tau =1-\frac{\int {\text{I}}_{trans,\lambda }\cdot {\text{d}}\lambda }{\int {\text{I}}_{inc,\lambda }\cdot {\text{d}}\lambda }$$
(6)

where τ is the “transmitted energy fraction”. Combining Eq. (6) with Eqs. (4) and (5), the following expression of the optical efficiency of the nanofluid can be obtained:

$${\eta }_{opt,n}=1-\frac{\int {f}_{\lambda }\cdot {\tau }_{\lambda }\cdot {\text{d}}\lambda }{\int {f}_{\lambda }\cdot {\text{d}}\lambda }$$
(7)

Since \(\int {f_{\lambda } \cdot {\text{d}}\lambda } = 1\), Eq. (7) can be simplified as follows:

$${\eta }_{opt,n}=1-\int {f}_{\lambda }\cdot {\tau }_{\lambda }\cdot {\text{d}}\lambda$$
(8)

Considering the values of Iinc and Iinc,λ for the reference Air Mass 1.5 spectral distribution of the solar radiation [27] and the values of τλ obtained from the absorbance spectra, ηopt,n can be calculated.

Figure 1 shows the absorbed energy fraction as function of the optical length for four nanofluids having different absorbance spectra, obtained by triplicating (A400nm = 0.66), doubling (A400nm = 0.44), equalising (A400nm = 0.22) or halving (A400nm = 0.11) the absorbance values of a reference nanofluid. As shown in the figure, the absorbed energy fraction is higher than 90% for three of the considered nanofluids at 18 mm path length, which corresponds to the depth of the volumetric solar receiver employed in this study. The nanofluid having A400nm = 0.22 (which is also the reference one) is the most favourable one as it guarantees good optical efficiency at 18 mm path length (ηopt,n = 0.93), while avoiding further expenses for increasing the concentration of nanoparticles in the fluid.

Fig. 1
figure 1

Absorbed energy fraction of four nanofluids having different absorbance spectra as function of the path length (A400nm refers to the absorbance value at wavelength λ = 400 nm)

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Figure 2 reports the absorbance spectrum of the selected nanofluid as function of the wavelength. The UV–Vis-NIR spectrum of the resulting nanofluid shows a maximum at 263 nm, equal to 0.42.

Fig. 2
figure 2

Absorbance spectrum of the ox-SWCNHs-PEG nanofluid used for the tests (path length of the cuvette Lcuv equal to 2 mm)

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3 Experimental test rig

An ad hoc experimental setup has been built at the Solar Energy Conversion Laboratory of the Department of Industrial Engineering of the University of Padova to check the stability of the SWCNHs based nanofluid and evaluate its absorption efficiency when exposed to the solar radiation. A sketch of the experimental setup is shown in Fig. 3. The experimental test rig consists of a primary loop and an auxiliary water circuit. In the primary loop, the nanofluid exiting the volumetric solar receiver is sent to a Coriolis mass flow meter by an inverter-controlled volumetric rotary vane pump (NUERT PR4ASXV). The nanofluid mass flow rate can be evaluated by two Coriolis mass flow meters (Endress + Hauser Cubemass C500 and Siemens SITRAN FC MASS2100), which are calibrated in two different measuring ranges (the first one from 0 kg h−1 to 90 kg h−1, the second from 25 kg h−1 to 400 kg h−1). Then, the nanofluid reaches a tube-in-tube heat exchanger, where the nanofluid is heated up or cooled down before entering the solar receiver. In the tube-in-tube heat exchanger water flows in the external annulus while the nanofluid streams in counter-current in the internal tube. The internal tube has an inner diameter equal to 8 mm and is made of stainless steel, while the external one, which encloses the annulus where water flows, is made of copper. The tube-in-tube heat exchanger is 0.5 m long. The water provided to the heat exchanger can be either heated up, by means of electrical resistances, or cooled down in a plate heat exchanger using groundwater of the building central plant.

Fig. 3
figure 3

Scheme of the experimental setup (T is the temperature sensor, P is the pressure transducer, CFM is the Coriolis mass flow meter)

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The volumetric solar receiver consists of two rectangular low-iron and anti-reflective glass sheets (dimensions 500 × 60 × 3 mm), embedded in two stainless steel frames, and three PEEK layers combined to form the channel for the nanofluid passage with 18 mm depth. The volumetric solar receiver has been employed in previous experimental campaigns (Bortolato et al. [24], Dugaria et al. [23], Zanetti et al. [26]). An absolute pressure transducer (STS ATM.1ST) is placed before the volumetric solar receiver to check that the nanofluid pressure does not exceed the maximum tolerable pressure for the glass layers. A ball valve is employed to remove the air trapped inside the loop and regulate the pressure of the system. The PVC pipes used for the connections are insulated and shielded to avoid the direct exposure of the nanofluid to the solar radiation. The nanofluid loop is mounted on a movable structure which allows to vary the azimuth and the tilt angle of the system in order to track the sun path and keep the receiver almost perpendicular to the solar radiation. Six PT-100 type RTDs (1/10 DIN accuracy class) are used to measure the temperatures of the nanofluid at the inlet and outlet of both the receiver and the heat exchanger and the water temperatures at the heat exchanger (inlet and outlet). An additional RTD is used to measure the ambient temperature. The RTDs have been calibrated against a Fluke® 1586A Super-DAQ Precision Temperature Scanner coupled to another four wires RTD (measuring chain accuracy equal to ± 0.01 K).

Solar irradiance measurements are also performed. Two secondary standard pyranometers (Kipp & Zonen CM11) are respectively positioned on the front and on the back of the receiver, to evaluate the global tilted irradiance (GTI) on two planes parallel to the receiver one. The two pyranometers display a sensibility of 5.1 × 10–6 V m2 W−1. When the receiver is exposed to the solar radiation, its double-glazing structure allows the radiation that is not absorbed by the nanofluid to pass through the rear glass and the transmitted irradiance GTItrans is thus measured by the pyranometer positioned on the back (Pyranometer B). Instead, the irradiance incident onto the receiver surface GTIinc is measured by the external pyranometer (Pyranometer A). In the experimental technique presented in this paper, the comparison between GTIinc and GTItrans allows to evaluate the absorption rate of the nanofluid. The pyranometers are placed as shown in Fig. 4. The rear pyranometer is enclosed within a reflective box which guarantees that the only source of light is the one coming from the nanofluid. Two more pyranometers (Kipp & Zonen CMP22 and DeltaOHM LP PYRA 02) are respectively used to measure the diffuse horizontal irradiance (DHI) and the global horizontal irradiance (GHI). The two pyranometers respectively present a sensibility of 8.95 × 10–6 V m2 W−1 and 11.87 × 10–6 V m2 W−1.

Fig. 4
figure 4

Positioning of the two pyranometers used for the determination of the optical efficiency

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The pressure and temperature sensors have been calibrated in situ and they are all connected to an Agilent Technologies 34970A data acquisition unit, which allows to acquire measurement data every 10 s. Samples of thirty consecutive measurements, corresponding to five minutes of acquisition, are considered for calculating the mean value of each measured parameter. The collected data are then reduced in Matlab® environment.

4 Experimental technique and data reduction procedure

The experimental campaign aims at evaluating the optical efficiency of the volumetric solar receiver with the varying operating conditions. The whole experimental campaign has been performed following the indications provided by ISO 9806:2017 Standard [28] for the identification of steady-state conditions. Such requirements concern the dispersion of the measures within the sample considered for calculating the average of each measured parameter. According to the Standard, the deviation of each measured value from the average must be lower than an imposed threshold which corresponds to:

  •  ± 0.1 °C for the nanofluid temperature at the inlet of the volumetric receiver;

  •  ± 0.4 °C for the nanofluid temperature at the outlet of the volumetric receiver;

  •  ± 1.5 °C for the ambient air temperature;

  •  ± 50 W m−2 for the global tilted irradiance incident on the volumetric receiver (GTIinc);

  •  ± 1% for the nanofluid mass flow rate.

The Standard requires also a minimum value of 700 W m−2 for GTIinc and an incidence angle of the solar rays upon the receiver surface lower than 2.5°. Moreover, the ratio of the mean value of the diffuse irradiance on the receiver surface DTI, obtained from Eq. (9), to the incident irradiance GTIinc must be lower than 0.3:

$${\text{DTI}}={\text{DHI}}\cdot \frac{1+\mathrm{cos}\beta }{2}$$
(9)

In Eq. (9) β is the tilt angle, which can be evaluated using Eq. (10) considering the receiver perpendicular to the solar rays, and DHI is the average of thirty values measured by the pyranometer.

$${\text{cos}}\beta =\mathrm{cos}\phi \cdot \mathrm{cos}\delta \cdot \mathrm{cos}\omega +\mathrm{sin}\phi \cdot \mathrm{sin}\delta$$
(10)

In Eq. (10), ϕ is the latitude, δ is the declination of the solar rays (evaluated using Cooper [29] correlation) and ω is the solar hour angle.

If all the aforementioned conditions imposed by the Standard are respected, it is possible to calculate the optical efficiency of the receiver, which is defined as the ratio of the radiation absorbed by the fluid to the incident radiation on the receiver aperture area:

$${\eta }_{opt,r}=\frac{{\text{GTI}}_{abs}}{{\text{GTI}}_{inc}}$$
(11)

The radiation absorbed by the nanofluid in the receiver GTIabs is calculated with Eq. (12):

$${\text{GTI}}_{abs}={\text{GTI}}_{inc}\cdot {\tau }_{glass}-\frac{{\text{GTI}}_{trans}}{{\tau }_{glass}}$$
(12)

where τglass is the average transmittance of the glazed area of the receiver, equal to 0.93. The optical efficiency can be also referred to the nanofluid, representing the capability of the working fluid to absorb the solar radiation independently from the system. In such case the efficiency correponds to the absorbed energy fraction (Eq. 6), and can be obtained modifying Eq. (11) as follows:

$${\eta }_{opt,n}=\frac{{\text{GTI}}_{abs}}{{\text{GTI}}_{inc}\cdot {\tau }_{glass}}$$
(13)

where at the denominator the incident radiation is multiplied by the transmittance of the glass to account for the solar irradiance attenuation due to the presence of the front glass.

Since Pyranometer B has been embedded inside a box which is partially shielded from the solar radiation, it has a reduced field of view compared to Pyranometer A. This reduction in the field of view should be taken into account also in the value of the incident irradiance GTIinc. A corrected incident irradiance can be evaluated following the isotropic model of Liu Jordan neglecting the reflected component:

$${\text{GTI}}_{inc,corr}={\text{DNI}}+F\cdot {\text{DHI}}$$
(14)

where DNI is the direct normal irradiance calculated using the isotropic model of Liu and Jordan (Eq. 15), DHI is the measured diffuse horizontal irradiance and F is the correction factor accounting for the different fields of view between the rear and the front pyranometers. It is worth mentioning that the correction factor has been applied only to the diffuse component of the solar irradiance since the field of view related to the direct component is the same for pyranometers A and B.

$${\text{DNI}}=\frac{{\text{GTI}}_{inc}-{\text{DHI}}\cdot \frac{1+\mathrm{cos}\beta }{2}-\rho \cdot {\text{DHI}}\cdot \frac{1-\mathrm{cos}\beta }{2}}{\mathrm{cos}\theta +\rho \cdot \mathrm{cos}{\theta }_{h}\cdot \frac{1-\mathrm{cos}\beta }{2}}$$
(15)

In Eq. (15), ρ is the reflectivity of the surrounding ground (equal to 0.1), θ and θh are respectively the angles of incidence of the sun rays on the receiver surface and on the horizontal plane. Since the incidence angle of the solar rays upon the receiver is small, the cosine of the incidence angle is equal to 1 and the term θh coincides with the inclination angle β.

An assessment study on the correction factor F is analytically and experimentally performed. The aim is to find the value of F in order to refer the incident solar irradiance GTIinc to the field of view of the rear pyranometer (Pyranometer B), otherwise the two pyranometers would measure different values of irradiance, even in the absence of the glazed surface and the nanofluid. The correction factor F is analytically evaluated as the ratio of the solid angle subtended by the rectangular shape of the receiver glasses (field of view of Pyranometer B) to the solid angle related to the field of view of Pyranometer A (solid angle of a semisphere), according to the following equation:

$${F}_{an}=\frac{2}{\pi }\cdot {\mathrm{sin}}^{-1}\left(\frac{a\cdot b}{\sqrt{\left({a}^{2}+4{d}^{2}\right)\cdot \left({b}^{2}+4{d}^{2}\right)}}\right)$$
(16)

where a, b and d respectively represent the two sides of the glass rectangle and the distance between Pyranometer B and the receiver. A correction coefficient F equal to 0.23 is obtained from the calculation. In order to evaluate F experimentally, some tests have been performed in the same solar receiver exposed to the solar radiation and without nanofluid inside. The experimental value of the correction factor is determined with Eq. (17) as the ratio of the diffuse irradiance measured by Pyranometer B (rear) to the diffuse irradiance measured by Pyranometer A (front):

$${F}_{\mathrm{exp}}=\frac{{\text{DHI}}_{Pyr.B}}{{\text{DHI}}_{Pyr.A}}$$
(17)

The experimental values of F are displayed in Fig. 5a) as a function of the direct normal transmittance Kn which is defined as the ratio of the direct normal irradiance to the corresponding extra-terrestrial irradiance [30]:

Fig. 5
figure 5

a) Experimental and analytical values of the correction factor F as a function of the direct normal transmittance Kn; b) effect of the correction factor F on the incident irradiance GTIinc,corr

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$${K}_{n}=\frac{\text{DNI}}{{\text{I}}_{extra}}$$
(18)

The analytical value of F is in good agreement with the experiments only at low values of Kn when the isotropic diffuse component is relevant. On the contrary, at high values of Kn the experimental data are highly scattered probably due to the strong influence of the circumsolar diffuse component. The present experiments have been performed at high values of Kn and this poses the problem of which F value should be considered in Eq. (14). However, as shown in Fig. 5b), the influence of factor F on the corrected incident irradiance is less significant at high DNI values (i.e. high Kn). For this reason, a mean value of F equal to 0.6 is adopted for the calculations.

The uncertainty related to the measured parameters has been evaluated according to the JCGM guidelines [31]. The standard uncertainty of a measured parameter is obtained with the following equation:

$$u=\sqrt{{u}_{A}^{2}+{u}_{B}^{2}}$$
(19)

where the Type A uncertainty uA is related to the standard deviation of the sample and the Type B uncertainty uB comes from manufacturers’ specifications and sensors calibration. The Type B uncertainties of the employed sensors are reported in Table 1. In the case of the pyranometers several Type B uncertainty contributions must be considered, as reported in Table 2. The combined uncertainty of the parameters that are not directly measured, such as the optical efficiency, is evaluated applying the law of uncertainty propagation. The expanded uncertainty is obtained multiplying the combined standard uncertainty to the coverage factor k = 2, with 95% level of confidence. The expanded uncertainty of the optical efficiency ranges from 11% to 13%.

Table 1 Type B experimental uncertainty of measured parameters (95% confidence)
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Table 2 Type B uncertainty contributions of the employed pyranometers
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5 Experimental results

All the experimental tests have been performed in Padova, Italy (45 deg 24′ 23’’ N, 11 deg 52′ 40’’ E). Tests are conducted by varying the temperature of the nanofluid at the inlet of the volumetric solar receiver from about 25 °C to 45 °C, while the mass flow rate is increased from 5 kg h−1 to about 320 kg h−1.

The optical efficiency of the volumetric solar receiver is evaluated and monitored with time to investigate the stability of the nanofluid. Indeed, recently SWCNHs nanofluids showed a degradation of their absorption rate after a certain utilization time [24, 26] and the reason for this phenomenon is still an open issue. If the optical efficiency remains almost constant over time of operation, the nanoparticles suspension stability is assured and thus, no degradation in the absorption properties of the nanofluid occurs. A sample of few millilitres of nanofluid is collected at the end of each day of test to detect any changes in the absorbance spectrum during the experimental campaign. In particular, the reduction in the absorbance value is symptomatic of the nanofluid degradation due to particles clustering and deposition. Moreover, the effect of the changing nanofluid mass flow rate and temperature on the optical efficiency is examined.

Figure 6 shows the values of incident solar irradiance on the receiver surface GTIinc (given by Pyranometer A) and solar irradiance transmitted by the nanofluid across the glasses of the solar receiver GTItrans (given by Pyranometer B). The irradiance values are reported versus the circulation and exposure time, i.e. the time during which the nanofluid has been simultaneously circulated in the loop and exposed to the solar radiation. Since the nanofluid stability was found to be penalized by recirculation at high mass flow rates (≈330 kg h−1) during a previous experimental campaign ([26]), it has been decided to perform these preliminary tests at small mass flow rate (5–14 kg h−1), with the temperature of the nanofluid at the inlet of the volumetric solar receiver varying between 25 °C and 45 °C. In these conditions the nanofluid temperature increase in the receiver varied between 1.1 K and 2 K. As shown in Fig. 6, the incident solar irradiance ranges from 800 W m−2 and 1100 W m−2, as the experimental tests were performed in different days. The transmitted solar irradiance shows a slightly increasing trend, from about 37 W m−2 at the beginning of the tests to 59 W m−2 after 84 h of circulation/solar exposure.

Fig. 6
figure 6

Measured values of incident and transmitted solar irradiance versus the circulation and exposure time

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It must be underlined that, in the time interval from about 50 h to 58 h, the nanofluid was still exposed to the solar radiation and circulated in the test rig, but the corresponding experimental data points were discarded due to non-compliance with ISO 9806:2017 Standard requirements.

During the same experimental tests, the optical efficiency of the solar receiver ηopt,corr,r and of the nanofluid ηopt,corr,n is calculated from the measured GTItrans value and using Eq. (14) for GTIinc,corr:

$${\eta }_{opt,corr,r}=\frac{{\text{GTI}}_{abs}}{{\text{GTI}}_{inc,corr}}$$
(20)
$${\eta }_{opt,corr,n}=\frac{{\text{GTI}}_{abs}}{{\text{GTI}}_{inc,corr}\cdot {\tau }_{glass}}$$
(21)

In a previous work (Zanetti et al. [26]) it was shown that the optical efficiency of the nanofluid is a clear indicator of the nanofluid stability, although its decrease may not be significant for small variation of nanoparticles concentration. In particular, about 10% decrease in the optical efficiency was observed for various SHCNHs-based nanofluids with loss in nanoparticles concentration up to 60%. After that, i.e. with loss in concentration higher than 60%, the rate of optical efficiency degradation increases.

In Fig. 7 the temporal evolution of the optical efficiency of the receiver and the nanofluid is reported. After a little decrease during the first 16 h, the optical efficiency of the solar receiver ηopt,corr,r remains almost constant, varying between 88 and 86%. The initial decrease in the optical efficiency may be related to settling of the nanofluid in the experimental setup and the deposition of the residual solid particulate which was present in the solution before charging the circuit. After about 58 h, a refill of nanofluid in the experimental setup is required to compensate for the nanofluid samples collection. The nanofluid additional charge corresponds to about 1% of the total volume. Even after the nanofluid recharge, the optical efficiency of the solar receiver shows a slightly decreasing trend, reaching a constant value of 86%. The optical efficiency of the nanofluid ηopt,corr,n displays a similar behaviour, with a constant value of 93% after 84 h of tests. It can be observed that the measured optical efficiency of the nanofluid coincides with the one calculated in Sect. 2.2 using the absorbance spectra.

Fig. 7
figure 7

Optical efficiency values of the volumetric solar receiver ηopt,corr,r (Eq. 20) and of the nanofluid ηopt,corr,n (Eq. 21) versus the circulation and exposure time

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The absorbance spectra of the tested nanofluid at the beginning of the experimental campaign and after 84 h of tests are reported in Fig. 8. As shown in the figure, the shape of the absorbance spectra of the two nanofluid samples is similar, while the spectral absorbance values are found to decrease with time. Indeed, after 84 h of tests the spectral absorbance of the nanofluid at 400 nm wavelength is nearly halved compared to the initial solution. Such decrease can be related to the gradual reduction of nanoparticles concentration in the solution, according to the Lambert–Beer law (Eq. 1).

Fig. 8
figure 8

Absorbance spectra of the ox-SWCNHs-PEG nanofluid at the beginning of the experimental campaign and after 84 h of tests (path length of the cuvette Lcuv equal to 2 mm)

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During the 84 h of tests, the nanofluid temperature is varied using the tube-in-tube heat exchanger, while the mass flow rate is kept in the range 5–14 kg h−1. To better understand if the reduction in the optical efficiency and spectral absorbance values is linked to the nanofluid temperature variation at the volumetric solar receiver, additional experimental tests are conducted when varying temperature at low mass flow rate (ṁn = 10 kg h−1) for 4 days (around 20 h of tests). Figure 9a) displays the optical efficiency of the solar receiver as a function of the mean temperature of the nanofluid in the solar receiver (average between inlet and outlet). As shown in the figure, a mild decrease of the optical efficiency ηopt,corr,r is observed when increasing the temperature of the nanofluid: at 25 °C mean fluid temperature the optical efficiency of the solar receiver is equal to 0.87, at 45 °C it reaches ηopt,corr,r = 0.85. Such a reduction, although very little (-2.3%), may be explained considering that solutions made of PEG can be degraded if subjected to several heating cycles due to the dissociation of water molecules from PEG clustering [32]. This phenomenon may alter the absorption characteristics of the nanofluid, with the subsequent decrease of the optical efficiency of the system. The nanofluid stability was not further investigated at higher temperatures.

Fig. 9
figure 9

Effect of nanofluid temperature (a) and mass flow rate (b) on the optical efficiency of the volumetric solar receiver ηopt,corr,r under exposure to the solar radiation

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With the aim to study the effect of the recirculation on the nanofluid stability, Fig. 9b) reports the optical efficiency of the solar receiver as a function of the nanofluid mass flow rate. Tests have been conducted with mass flow rate varying between 35 kg h−1 and 315 kg h−1 for a total amount of time equal to 20 h. No significant dependence of ηopt,corr,r on the nanofluid mass flow rate variation can be detected: from about 35 kg h−1 to 315 kg h−1 the optical efficiency decrease is less than 1%.

The effect of the exposure to the solar radiation on the nanofluid optical characteristics has been also evaluated. Some periods of testing under solely circulation without exposure have been performed and the value of the absorptance has been recorded after intermediate time periods. These tests have been conducted at a fixed nanofluid mass flow rate of 310 kg h−1, which is close to the one chosen in previous experimental campaigns [24, 26], allowing to a transition flow regime in the receiver. Table 3 reports the resulting optical efficiency of the receiver ηopt,corr,r and the absorbance of the nanofluid at wavelength λ = 400 nm. Both the optical efficiency ηopt,corr,r and the absorbance values display a slightly decreasing trend. In particular, the optical efficiency of the solar receiver decreases by about 1% over more than 60 h of tests. These results show that the mere exposure to the solar radiation cannot be considered as the main responsible for the change in the optical behaviour of the nanofluid and the decrease of its stability. Such experimental result agrees with the main findings of the study by Zanetti et al. [26], where the degradation of the optical properties of the SWCNHs nanofluid was found to be linked to circulation rather than exposure to the solar radiation.

Table 3 Optical efficiency of the solar receiver ηopt,corr,r and absorbance of the nanofluid at wavelength λ = 400 nm during experimental tests at 310 kg h−1 nanofluid mass flow rate and discontinuous exposure to the solar radiation
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6 Conclusions

In this paper, a novel experimental technique to evaluate the optical absorption rate of solar radiation by a nanofluid circulating in a volumetric solar thermal receiver during real time operation has been presented. Two pyranometers are positioned on the front and on the back of the receiver to measure the solar radiation incident onto and transmitted by the nanofluid. The absorbed energy fraction measured with the present technique is consistent with the theoretical one, calculated from the absorbance spectrum of the nanofluid and the reference spectral distribution of the solar radiation.

Experimental tests have been conducted using a suspension of Single-Wall-Carbon-NanoHorns functionalized with polyethylene glycol chains (SWCNH-PEG) in deionized water as direct absorber.

The effects of exposure to non-concentrated solar radiation, temperature variation (from 25 °C to 45 °C) and circulation (at mass flow rate from 5 kg h−1 to about 320 kg h−1) on the stability and absorption efficiency of the nanofluid have been addressed. It was found that the optical performance of the SWCNH-PEG nanofluid is slightly influenced by the fluid temperature (around -2% in the tested range). However, the nanofluid efficiency for temperatures higher than 50 °C should be investigated in the future. With regard to the mass flow rate, in the time interval of the present tests we found a very small decrease (around 1%) when increasing the mass flow rate of the circulating fluid by ten times. On the whole, a limited decrease of the optical efficiency of the nanofluid was found after more than 80 hours of operation, reaching a value of 93% from the initial value of 95%. Therefore, based on the present results, the use of SWCNH-PEG in direct absorption solar collectors represents a promising solution. Since the time interval considered in the present study is limited (around 84 hours), the stability of the nanofluid needs to be studied in the future for longer periods of circulation.