1. Introduction

To satisfy the increasing world energy demand, the use of renewable energy is mandatory. A large fraction of total energy consumption, in developed countries like US, is used to produce heat (both, residential and industrial). Solar energy can be easily converted into heat and it represents the most versatile form of renewable energy to face the increasing demand for thermal energy worldwide. The key components of solar thermal panels are insulation and spectrally selective solar absorbers. A spectrally selective absorber should efficiently absorb the light in the solar spectrum (solar absorptance $\alpha$ = 1), while minimizing emission as thermal radiation (thermal emittance $\epsilon$ = 0). The optimal cut-off wavelength, from high absorbance to high reflectance (low emittance), is determined by the operating temperature: increasing the operating temperature requires lowering the cut-off wavelength [1]. Sun light concentration defines the relative importance of absorbance and emittance in determining the efficiency at a given temperature: at high light concentration absorptance is the key to improve efficiency, whereas without concentration emittance and absorptance are equally important [2]. However, due to the Stefan-Boltzmann law, the emittance becomes more important as the operating temperature increases and it is the essential parameter to control in order to operate a thermal panel at temperatures higher than 200°C with a good efficiency, without concentration [2]. Such importance of controlling the radiative emission process for improving energy conversion has been recently reviewed for several applications [3].

To estimate panel performance, the absorber emittance should be known at operating conditions; however, the emittance of selective solar absorbers is usually measured at 100°C in air [4]. The emittance is known to be temperature dependent for different reasons: there is an intrinsic dependence due to the relation between emissivity and thermal conductivity (lower conductivity implies higher emissivity) [5] and an extrinsic dependence due the shift of the black body emission towards shorter wavelengths, when the temperature increases [6].

The other key parameter to determine the solar thermal panel performance is thermal insulation. Recent evacuated flat-plate solar thermal panels make use of high vacuum to insulate the solar absorber from ambient, reducing convection power losses to a negligible level. They reach stagnation temperatures in excess of 300°C and are capable to operate efficiently at temperatures as high as 200°C [7], thus requiring precise determination of the properties of the selective absorber at such temperatures, under high vacuum.

2. Experimental set-up

To measure the thermal emittance and absorptance of selective solar absorbers, we use a calorimetric approach. The sample temperature variations are related to the absorbed power and the power losses through the following power balance equation:

A glass window placed above the absorber allows for an array of white LED lights [8] to supply a controllable amount of incident power to the absorber. The power per unit area provided by the LEDs on the absorber surface is calibrated using a class 1 thermopile pyranometer and it is precisely controlled measuring the current supplied to the LEDs as well as their temperature. To measure the temperature of the sample under investigation, a thermocouple fixed to a nickel-plated copper lug is tightened to the sample center using aluminum bolt and nut. The thermocouple wires having a negligible thermal conductivity. When illuminating the sample, the increase of the absorber temperature is governed by the power balance Eq. (1), where the losses are reduced to the electromagnetic radiation emitted according to the Stefan-Boltzmann law because of the set-up. At low temperatures the emitted power is negligible and therefore the temperature increase during heat up can provide a measure of the absorptance. On the other hand, measuring the temperature decrease during cool down provides an estimation of the emitted power and allows evaluating the emittance as well as its temperature dependence. The temperature of the glass window and of the high-vacuum vessel are also monitored and included in the calculations, taking into account their nominal reflectivity.

As a final check a fitting procedure of the complete sample temperature curve under illumination is performed to verify that the calculated parameters are consistent both for the heat up and cool down stages.

3. Results

The selective solar absorbers usually consist of a thin multilayered absorbing film (100-200nm thick) deposited on a high thermal conductivity, low emittance substrate (0.3-0.7mm) such as aluminum or copper. We investigate the Mirotherm selective solar absorber from Alanod, which is the same used in the TVP SOLAR MT-Power panels for mid-temperature applications. The manufacturer datasheet of such absorber reports an emittance at 100°C, ε_100°C = 0.05 ± 0,02 and an absorptance $\alpha$ = 0.95 ± 0.01 [9].

The power balance equation for the absorber in the previously described experimental set-up can be written with good approximation:

In this equation, m, c_p, α, A, P_in are constants already described before, $m_{th}$ is the total mass of thermocouple assembly (including lug, bolt and nut), ${\epsilon }_a$ is the absorber emittance, $\sigma$ the Stephan-Boltzmann constant, ${\epsilon }_{sub}$ the equivalent substrate emittance and finally T_a, T_g and T_v are the temperatures of the absorber, glass and vacuum vessel respectively. In the power balance equation the absorptance α is defined as the ratio between the absorpted power and the incident power whereas emittance ε is defined as the ratio between the emitted power and the power emitted by a black body at the same temperature. The absorptance α and the emittance ε are therefore numeric values as defined in [2] and they are also referred as spectrally averaged absorptivity and spectrally averaged emissivity as defined in [1].

In writing Eq. (2) we have made also the following assumptions: 1) the thin absorber film and the thermocouple assembly have the same specific heat of the substrate (their mass is less the 3% of the total mass), 2) the thermocouple is at the same temperature of the absorber (we will see in the following that the temperature difference is small and temperature derivatives after an initial transient are identical), 3) the power emitted by the thin absorber borders can be neglected (the total surface of the border is less than 1% of the absorber surface).

Figure 1 shows part of the data collected during the experiment: the LED illumination was set to the power level needed to direct 1000W/m² on the absorber surface. To obtain the emittance of the absorber we calculate the time derivative of the absorber temperature from the experimental data and we perform a best fitting procedure using Eq. (2) (see Fig. 2 left). During cool down P_in is zero and the only unknown parameter is the spectrally averaged emissivity. Since the substrate is aluminum and it faces a polished stainless steel (spectrally averaged emissivity = 0.1), an equivalent, temperature independent, spectrally averaged emissivity of 0.03 can be assumed and the only fitting parameter remaining is the selective coating thermal emittance ${\epsilon }_a$. Since the thermocouple assembly is not ideal (it has a finite mass and a finite thermal conductivity) the temperature derivative has inertia and it does not reach immediately the value predicted by Eq. (2); therefore, the experimental data with temperature higher than 310°C were excluded from the fitting procedure.

 

Fig. 1 Experimental data of temperatures and pressure versus time. A stagnation temperature of about 320°C is reached when the absorber is illuminated with 1000W/m². The internal pressure remains well below 1x10⁻⁵ mbar throughout the experiment.

Download Full Size | PDF

 

Fig. 2 Left: absorber temperature derivative (black dots) vs absorber temperature is fitted (red line) using Eq. (2), assuming P_in = 0 (cool down). Rigth: Mirotherm emittance versus temperature: black dots are obtained assuming emissivity constant in a 20 degrees interval, blue line is obtained fitting the whole set of cool down data using Eq. (2) with P_in = 0 and assuming a quadratic temperature dependence for the emittance. The red line, which overlaps with the blue line, is the quadratic fit of the black dots.

Download Full Size | PDF

Fitting the data measured during cool down confirms a temperature dependence for the emittance and therefore we used two different procedures to fit our data:

The two procedures are equivalent, and the emittance ${\epsilon }_a\left(T_a\right)$ calculated by the two methods at a given temperature are within the experimental errors as shown in right chart of Fig. 2. For Mirotherm we found the emittance having a quadratic temperature dependence in the form:

The results are in agreement with the specifications at temperatures below 100°C, whereas at the stagnation temperature the emittance increases up to 0.1, which is about twice the previous value. The emittance temperature dependence, can then be used to perform best fit analysis of the temperature derivative when the absorber is under illumination. This to evaluate the absorptance α.

Figure 3 shows a fit of the experimental data from 45°C up to stagnation temperature, assuming alpha to be temperature independent. The best fit procedure returns α = 0.85 (blue dashed line in the figure). Alternatively, the data can also be analyzed leaving both α and ${\epsilon }_a\left(T_a\right)$ as free fitting parameters. The results are reported as a continuous line in Fig. 3 (red curve), The two curves are identical within the experimental errors, giving a good confidence in the procedure used. However, we have to note that the $\alpha$ value obtained by both best fit analysis, is well below the specifications ($\alpha$ = 0.95 ± 0.01).

 

Fig. 3 Left: Absorber temperature derivative under 1000W/m2 illumination fitted using Eq. (2). Black dots: experimental data. Continuous red line: best fit from 45°C to 320°C with ${\epsilon }_a\left(T_a\right)$ and $\alpha$ as free fitting parameters. Blue dashed curve: ${\epsilon }_a\left(T_a\right)$ from cool down and only α as free fitting parameter. Right: absorptivity obtained by hemispherical reflectivity measurement using an integrating sphere. The Spectrally averaged absorptivity $\overline{\alpha }$ is 0.95 when averaged on the solar standard ASTM G173 and 0.96 when averaged on our white LED spectrum.

Download Full Size | PDF

Another way to estimate α is from the equilibrium temperature under illumination. At equilibrium we have $\frac{d{T}_a}{dt}= 0$ and $T_g=T_v$, and Eq. (2) becomes:

$\alpha P_{in}=\epsilon \sigma \left(T_a^4-T_g^4\right)$ with $\epsilon ={\epsilon }_a\left(T_a\right)+ {\epsilon }_{sub}$ and the ratio α/ε can be calculated. Using our experimental data, we obtain α/ε = 6.5. From this value, considering the absorber emittance at 318°C we find α = 0.84 in agreement with our best fit, but still below specifications.

To verify that our sample was in agreement with manufacturer specifications, we performed the measurement of the hemispherical reflectivity ρ using an integrating sphere equipped with a halogen lamp. The results have been normalized using a calibrated mirror having a reflectance of 5%. In the right part of Fig. 3 we report the absorptivity (1-ρ): the solar spectrally averaged absorptivity $\overline{\alpha }$ is equal to 0.95, in agreement with manufacturer datasheet.

According to Eq. (2) the temperature derivative has its maximum value when illumination starts (the absorber temperature is equal to ambient temperature and there are no losses). In Fig. 3 the initial experimental data do not reach the maximum temperature derivative value until 45°C and they are excluded from the best fit calculations. In fact, when illumination starts (or ceases) and the absorber temperature begins to increase (or decrease), a thermal gradient appears on the substrate to transfer heat to the thermocouple. Such temperature gradient also appears as time delay between the heating of the selective absorber and its temperature reading via the thermocouple assembly.

To estimate such delay and to verify that it does not introduce an error in the measured temperature derivative nor in the stagnation temperature, we have simulated our system using COMSOL multiphysics. The simulation set-up was as close as possible to our experimental conditions (the absorber is inserted in a stainless steel vacuum vessel with a glass on the upper side and there is air flow around the vessel). All surfaces have been set to the right emissivity values in the two spectral regions: the solar region [λ<2.5μm] and the infra-red region [λ>2.5μm]. In order to reproduce our experimental results, we introduce in the model the absorber temperature dependent emissivity reported in Eq. (3), whereas the small thermal conductance of the four stainless steel springs that suspend the absorber and the thermocouple wires thermal conductance are neglected. The power radiated by the thin absorber side was also verified to be negligible.

In Fig. 4 we report some results of our simulations: the presence of bolt and nut used to tighten the thermocouple to the absorber introduces a temperature reduction in the absorber center of about 0.5°C at 318°C. This temperature reduction is due to the increase of losses introduced by the bolt and nut radiating surfaces.

 

Fig. 4 Left: stationary simulation of the temperature of the absorber, with the bolt and nut to keep the thermocouple in thermal contact. The presence of the thermocouple assembly introduces a small error of about 0.5°C in the stagnation temperature. Right: time dependent simulation of the temperature derivative with (blue dots) and without (black squares) thermocouple.

Download Full Size | PDF

In the time dependent simulations, it is also possible to observe the difference introduced by the presence of the thermocouple. The simulation including the thermocouple assembly (blue dots) reproduces the experimental data in the whole temperature range, including the initial delay, while the simulation of the absorber alone, without thermocouple (black squares in Fig. 4), does not show any delay and it follows Eq. (2). It should be noted that the two curves overlap at temperature higher than 40°C indicating that, after the thermal gradient is established, the two derivatives are identical. These simulations support our choice to exclude the initial experimental data from the best fit analysis and confirm the reliability of the temperature derivative values measured with our thermocouple assembly. Both simulations, were performed using an incident illumination of 1000W/m² and α = 0.85, in agreement with our experimental data.

Whereas the change in emittance with temperature was expected, the measured reduced value for α is quite surprising. The difference cannot be simply ascribed to the different optical spectra between the Sun and the LEDs used in the experiment because the spectrally averaged absorptivities are very similar (0.95 vs 0.96). Moreover, COMSOL simulations performed using the whole solar spectrum show that α = 0.95 overestimates both, the measured stagnation temperature and the temperature derivative too.

4. Conclusions

We have reported the measurement of total absorptance and emittance of a selective solar absorber using a calorimetric method. The measurement is performed under high vacuum and allows determining the temperature dependence of the emittance at high temperature. The emittance value is in agreement with the manufacturer’s specification at temperature below 100°C, whereas it more than doubles at stagnation temperature. Surprising the absorptance α has been estimated to be about 10% lower than specification value. The measured α value of 0.85 resisted multiple independent checks and it indicates that the calorimetric method could be more appropriate to measure the coefficients required for calculating panel performances.

Such lower α value is probably due to a dissipation mechanism which was not taken into account in our calorimetric method and need to be further investigated.

Non-optical total measurements using a calorimetric method are therefore of great importance to better predict the overall performances of new high-vacuum insulated solar thermal panels working at high temperature, without concentration.