Models for New Corrugated and Porous Solar Air Collectors under Transient Operation

1 Introduction

Solar air heaters are solar collectors which utilize air as working fluid. Widespread applications include space heating and drying processes. Among their advantages are simple maintenance and manufacturing, the fact that they do not freeze and are less prone to corrosion compared with solar water collectors. Solar air collectors can be glazed or unglazed, and their absorbers usually consist of materials having high solar absorbance and low emittance, i. e. selective characteristics.

Many researchers focused on the improvement of the thermal performance of solar air collectors. In order to enhance the heat transfer by convection from the absorber to the flowing air, several design solutions have been tested, such as corrugated absorber plate [1, 2], roughness geometry [3, 4] or fins welded over and under the absorber plate [5, 6]. The performance of a single-pass solar air heater with baffles was studied in [7]. The results show that increasing the number of fins and increasing the baffle width are effective at low mass flow rates. The thermal performance of a solar air collector with a fin fixed on the absorber has been studied in [8]. The authors found a bias error of 3.5 % between the theoretical and experimental results. The effect of geometrical parameters of circular transverse ribs on the heat transfer of a rectangular duct with heated plate has been studied in [9]. The thermal efficiency of a roughened duct is observed to be 5–9 % higher than that of a smooth duct.

There are two common absorber geometries of solar air collectors; the first one is the U-corrugated absorber and the second one is the V-corrugated absorber.

The convective heat transfer in U-corrugated solar collectors (see Figure 1) was studied numerically by Gao et al. [10]. The results show that, in order to efficiently suppress heat loss caused by natural convection, the height ratio should be greater than 2, the geometrical ratio should be greater than 1 and the angle of inclination should be less than 40°. The main objective of using U-corrugated absorbing plates is to enhance the turbulence and the heat transfer rate inside the air flow channel, both of which are crucial in improving the solar air collector efficiency [11, 12].

Figure 1:

Schematic view of the cross-sectional area in a U-corrugated solar air heater [10].

A large number of studies have also been carried out on the V-corrugated solar air collector. Ref. [13] developed a mathematical model for such a collector. This model was able to correctly predict the mean temperature of all components of the collector, the instantaneous air temperature at any section of the collector, the output air temperature and the thermal conversion efficiency. It has been found that the best solar air collector with V-corrugated absorber plate has a height of 50 mm from the center of the triangle and a 60° tilt angle for the sides. This is shown in Figure 2.

Figure 2:

Design of an air collector with V-corrugated absorber [13].

The authors of Ref. [14] carried out experimental studies on the heat transfer characteristics and the performance of solar air collectors with rectangular fins. Solar air collectors with longitudinal rectangular fins array exhibited high thermal efficiency, which is attributed to the additional surface area. The thermal performance of V-groove and cross-corrugated solar air collectors had been compared theoretically in Ref. [15], under a wide range of configurations and operating conditions. The results showed that the cross-corrugated collector is superior to the V-groove collector. The fabrication and performance evaluation of a V-groove solar air heater has been studied in [16]. The authors reported collector efficiency about 35 %.

Several studies have been performed on the performance of solar air collectors with porous absorbers. The authors of Refs. [17–19] investigated experimentally a single-pass solar air heater. The results showed that the efficiency of this solar air collector is higher than that of the solar air collector without porous media.

Trying to improve the thermal efficiency of solar thermal collectors, Munuswamy et al. [20] conducted numerical experiments on the effectiveness of nanoparticles in solar water collector systems. The authors of Ref. [21] studied theoretically and experimentally the performance of solar water heaters, in different operating conditions. The maximum thermal efficiency was about 45 %. Two flat plate collectors with the same surface area have been compared in [22]. The first one has internally grooved fins riser tubes and the second has plain riser tubes. The results show that the efficiency of the collector with finned tube is higher than that of the collector without riser tubes.

V-corrugated absorbers have been treated in several papers [13–16]. The novelty of this work is that it focuses on V-porous absorbers, which have been rarely considered in literature. The thermal performance of a collector with “V”-corrugated porous absorber is compared with that of a single-pass collector with “U”-corrugated absorber. The collectors are nearly identical since they differ only by the absorber type. The collectors are tested outdoor under the same meteorological and radiometric conditions. Transient mathematical models for these two types of solar air heaters are presented. The proposed models are of general interest as they can be easily used with different shapes of absorbers through changes in the criterial equation of the convection heat transfer coefficient. Validation is an important step in mathematical modeling development, and therefore comparisons with actual experimental results obtained at Bucharest – Romania (latitude 44°26′N, longitude 26°6′E) have been reported.

2 Experimental equipment

Both solar air collectors consist of absorber, glazing, insulation and a wood collector frame on which these components were assembled. Both collectors have a single glass cover (1.5 m×0.75 m). The back and edges of both collectors are insulated with polystyrene in order to avoid heat losses. Two types of absorbers were used. The first one (the V-corrugated porous absorber) was made of soft steel with two layers of mesh wire while the second one (the U-corrugated absorber) was made of aluminum. The size of the two collectors is 1.52 m×0.7 m×0.0007 m and 1.4 m×1.13 m×0.00035 m, respectively. Table 1 presents the parameters of the collectors.

The two solar collectors were installed at the Polytechnic University of Bucharest (44°26′N, 26°6′E). The collectors’ slope was 55°, which is adequate for space heating during winter at the geographical location of Bucharest.

A Kipp and Zonen CMP3 Pyranometer was used for measuring solar irradiance at the level and inclination of the collectors. The pyranometer was connected to a computer and the measurements were recorded at time intervals of 10 s.

A photograph and schematic view of the experimental setup are shown in Figure 3. The experimental studies were conducted during September and October 2014 under clear sky conditions. Further details are as follows.

Figure 3:

(A) photograph and (B) schematic view of the solar air collectors: (1) air fan, (2) humidity transducer, (3) pressure transducer, (4) air inlet, (5) V-corrugated porous absorber, (6) fins, (7) thermal transducer, (8) pyranometer, (9) air outlet and (10) “U”-corrugated absorber.

2.1 Absorbers

The main component of solar air collectors is the absorber, which converts solar energy into heat and transfers it to the flowing air. The shape of the absorber is of significant importance. Moreover, increasing the absorber surface area increases the amount of heat transferred to the air [5, 6].

The absorbers of the collectors used in this study have different configurations and are made of different materials (see Figure 4). One collector is a single-passage air collector with the absorber made of aluminum (“U”-corrugated absorber). The other collector is an original through-pass air collector with the absorber consisting of a wire net made of soft steel (“V”-corrugated porous absorber). Both types of absorbers are painted black, to convert the maximum amount of solar energy into heat.

Figure 4:

“U”-corrugated absorber (left) and V-corrugated porous absorber (right).

The collector based on the V-corrugated porous absorber has a rectangular shape. Its casing is made of wood and has the length equal to 1.2 m and width equal to 0.8 m. A sketch of this collector is presented in Figure 5(a). The absorber material is a double-layered wire net of fine meshes, of about 0.1–0.2 mm, which can be seen as a porous material with large pores, of about 0.05–0.1 mm (Figure 5(b)). The wire net is placed in the casing so that the air flows over, under and through the net mesh. From this point of view, the collector can be seen as a combination of a single-passage air collector and a through-pass air collector. The effective surface of the porous absorber made of two wire nets is (2×0.7×1.523=2.1322 m²). The effective heat transfer area between the wire mesh and air has been calculated with the following formula:

(1)Aab=nWabPt⋅Lab+LabPt⋅Wab⋅π⋅Thab

Figure 5:

(a) Sketch of the solar collector based on V-corrugated porous absorber and (b) view of the V-porous absorber.

where W_ab is the width of one steel mesh (0.7 m), L_ab is the length of one steel mesh (1.523 m), Pt is the pitch of the steel mesh (0.00017 m), Th_ab is the diameter of the steel mesh wire (0.0001 m) and n is the number of wire nets (n=2; double-layered wire net). After calculations, the effective heat transfer area between the wire mesh and air is found to be 7.88 m². Both the “V”-corrugated porous absorber collector and the “U”-corrugated absorber collector have the same net aperture surface area (glass cover area) of 1.125 m² (1.5 m×0.75 m). However, the heat transfer area is larger for the collector with a V-corrugated porous absorber than that of the collector with a U-corrugated absorber.

The collector with “U”-corrugated absorber has three straight baffles to divert the flow and raise the turbulence coefficient (Figure 6(a) and (b)). A gap is maintained between the glass cover and the absorber plate. The air passes through the air channel (under the absorber plate) to collect heat from the absorber, which is an aluminum sheet painted black with a thickness of 0.35 mm. The absorptance and thermal conductivity coefficients of the plate are 95 % and 205 W/(m K), respectively.

Figure 6:

(a) Sketch of the solar collector based on U-corrugated absorber and (b) view of the “U” absorber with baffles.

2.2 Thermal transducers

Thirty-two thermal transducers were used, distributed evenly on the bottom surface of the absorber (see Figure 7), at identical positions along the direction of air flow for each collector. Inlet air temperatures were measured by two thermal transducers. Four thermal transducers were fixed at the end section of each collector to measure the outlet air temperatures. The thermal transducers were mounted in the same position in the entrance area of both collectors, in order to obtain the inlet temperature distributions. All thermal transducers were connected to a computer. Measurements were recorded at 10-s time intervals.

Figure 7:

Thermal transducers for both solar thermal air collectors.

3 Analysis of experimental data

The useful heat flux supplied by the collector to the air is computed by using the following equation:

where Ta,out−Ta,in is the air Spara temperature increase between collector inlet and outlet and m˙a (kg/s) is the mass flow rate of air, given by

where V˙a is the volumic flow rate of air exiting the collector via the duct of diameter d, va is the air speed and ρa is the density of air. The specific heat of air, Cpa [kJ/(kg K)], is assumed to vary linearly with temperature (°C) by [23]

The solar energy flux absorbed by the solar collector absorber is given by

where GT (W/m²) is the total solar irradiance incident on the tilted collector surface, Ac (m²) is the collector surface area and (τα) is the effective transmittance–absorptance product, which is evaluated by using the following equation:

The thermal efficiency of solar air collectors is defined as the ratio of the useful heat flux supplied by the collector and the total energy flux absorbed by the absorber [24]:

The ambient temperature, the solar irradiance, the outlet air temperature and the outlet air velocity have been measured. The heating characteristic of the collector, the air flow rate, the heat flux and finally the solar energy conversion efficiency into thermal energy were computed.

In steady-state operation conditions, the flux of useful heat delivered by a solar collector is equal to the flux of energy absorbed by the working fluid (the air) minus the flux of heat losses from the absorber surface to the surroundings. The useful output flux of the solar air collectors can be written as

The solar energy flux absorbed by the absorber per unit surface area, S (W/m²), is calculated by [24]

The performance of the two collectors has been compared, by using measurement data. The solar air collector with V-corrugated porous absorber is more effective or less effective than the solar air collector with U-corrugated absorber, depending on the radiative regime. For instance, the efficiency of the collector based on V-porous absorber is higher near the noon of clear days. However, in the beginning and at the end of clear days, the collector based on porous absorber is less effective that the collector with U-corrugated absorber (see Table 2).

4 Models

Two models for unsteady-state operation have been developed; the first one is for the solar air collector with “V”-corrugated porous absorber and the second is for the solar air collector with “U”-corrugated absorber.

The absorber temperature depends on the coordinate in the direction of air flow. Three nodes for each type of solar air collector have been considered (i. e. the mean value of temperature in glass cover, absorber and flowing air, respectively). The governing equations are obtained by applying the energy balance for each node. The energy balance equations are written under the following assumptions:

1. There is no temperature gradient along the thickness of the glass cover.

2. The air does not absorb solar radiation.

3. Thermal losses through the collector backs and sides are mainly due to conduction across the wood (3 cm thickness) and those caused by wind and thermal radiation are neglected.

4. The air flow properties depend on temperature.

5. The inlet air temperature is equal to the ambient temperature.

6. All air channels are assumed to be free of leakage.

7. The collectors are facing south (toward the midday sun in Bucharest).

5 Model solution procedure

The initial temperature distribution in the components of the collector is needed when solving the sets of three first-order differential equations presented in Sections 4.1 and 4.2, respectively. The instantaneous boundary conditions, including solar irradiance, ambient temperature and the mass flow rate of the working fluid (air), should be also known.

The model has four input parameters, namely ambient temperature, solar irradiation, inlet temperature and wind velocity. The collector properties are also inputs for the model. All these parameters are read from the input data files. The models calculate the outlet temperature and compare it with the measured outlet temperature. In addition, the models calculate the absorber temperature, glass cover temperature, mean air temperature and the thermal efficiency of the collectors.

The system of three first-order differential equations was solved by using the Runge–Kutta fourth-order method. The software package used to code the model is MATLAB version R2012a.

6 Models validation

The models were validated by comparing the simulation results with measured data. The experiments were undertaken simultaneously for both solar air collectors, in Bucharest, during September and October 2014. Figure 8 shows the time variation of solar irradiance and ambient temperature during 3 days.

Figure 8:

Variation of ambient temperature and solar irradiance during 3 days in Bucharest, Romania.

These two collectors were tested in the same experimental facility and under the same meteorological conditions. Thus, the comparison is considered to be a true assessment of the performance. The experiments show that most of the time the collector based on the V-corrugated porous absorber is more effective than the collector based on the “U”-corrugated absorber. The air flow passing throughout the holes of the porous collector contributes to increase the heat transfer surface area per unit volume and, therefore, to increase the thermal efficiency, in comparison with the “U”-corrugated collector. The efficiency of the collector based on V-corrugated porous absorber is higher near the noon of the clear days while in the beginning and at the end of the clear days, the collector based on V-corrugated porous absorber is less effective than the collector with U-corrugated absorber (see Table 2). This may be explained in part by the lower optical efficiency of the porous absorber at large incidence angles, due to the cylindrical shape of the mesh fibers.

Measurement and simulation results for the glass temperature, absorber temperature, ambient temperature and outlet air temperature are shown in Figure 9. Generally, the simulated values follow the same trend as the measured values. The deviation from the measured temperature is larger at the start of the experiments and later on it becomes smaller. For instance, the difference between the simulated and measured outlet air temperature for the collector with V-corrugated porous absorber is about −7° in the early morning of 29 September 2014 but reduces to nearly 0° after 7 min of operation (Figure 9). Rather similar results were obtained for the same collector on 10 October 2014. The initial large difference between simulations and measurements is explained by the thermal inertia of the collector, which is stronger when the air flow starts. Similar results are obtained in case of the collector with U-corrugated absorber, but in that case, the initial simulated temperature is higher than the measured temperature (see Figure 9). Also, the time interval needed for the difference between the simulated and measured temperature to become nearly 0 is about 18 min (see results for 10 October 2014). This may be explained in part by the larger thermal inertia the collector based on U-corrugated absorber than that of the collector based on V-corrugated porous absorber.

Figure 9:

Time variation of several calculated and measured temperatures during days in September and October 2014. Collectors based on both V-corrugated porous absorber and U-corrugated absorbers are considered. The air flow rate is 0.33 kg/s.

Two statistical indicators, namely the relative root mean square error (rRMSE) and the relative mean bias error (rMBE), were used to assess the model performance. They are defined as follows:

where C_i and M_i are the calculated and measured values, respectively, and n is the number of observations.

Results are presented in Table 3. There is good agreement between simulation results and measurements. Generally, the model developed for the collector based on the U-corrugated absorber works slightly better than that of the collector based on the V-corrugated porous absorber.

It is interesting to compare the results obtained by using the simple steady-state model eq. (8) and the results obtained by using the model based on time-dependent differential equations, proposed in this paper. Eq. (8) has been used in the following way. Constant values have been used during the day for the optical efficiency (τα) and for the overall heat loss coefficient UL. Next, experimental values during 29 September were used for solar irradiance G, ambient temperature Tamb and useful heat flux Q˙u, respectively. Thus, eq. (8) was solved in the only unknown temperature Tma. Figure 10 shows the value of the mean air temperature Tma obtained by this procedure based on the steady-state eq. (8) (which is denoted “measured”) and the value Tma obtained by using the model proposed in this paper (which is denoted “calculated”). Both series of temperature Tma are associated with the beginning of the operation and correspond to a constant air mass flow rate 0.33 kg/s. Generally, the steady-state model provides temperature values smaller by a few degrees than the dynamic model. The steady-state model works better in case of the collector based on a V-corrugated porous absorber.

Figure 10:

Mean air temperature Tma obtained by using the steady-state eq. (8) (denoted “measured”) and the models proposed in this paper (denoted “calculated”) for both solar air collectors. Results correspond to the beginning of the operation. A constant air mass flow rate 0.33 kg/s has been considered on 29 September 2014.

Note that in order to provide the same conditions for the air motion in both collectors (i. e. the same energy consumption, when the same mass flow rate is provided in both collectors), a metal network was placed at the inlet section of the collector with U-corrugated absorber. The network characteristics were the same as the ones used in the collector with V-corrugated porous absorber. By adding a number of metal network sheets and by monitoring the power consumption of the fans, one obtains the same flow conditions for the internal air motion, or, in other words, the same pressure losses across both collectors. Moreover, for both collectors, pressure losses were monitored by pressure transducers placed at the same distance from the outlet (see Figure 3).

The mass flow rate is included in the models as an input parameter but the energy needed to generate this mass flow is not considered in the energy balance and efficiency calculations. The use of a porous material would indeed enhance the thermal coefficients and thus would raise the efficiency of the solar collectors. However, this would also increase the drag force such that more energy may be required to maintain the constant mass flow rate, which leads to a decrease of the efficiency.

It is useful to estimate the approximation induced by neglecting the energy needed to move the air inside the collectors. We have selected a time period of 20 min starting at 12 pm hour on 29 September. The useful heat collected by the collector based on the porous absorber is 604,052 J. The fan power is 18 W. During a 20-min interval, the electrical energy consumed by the fan is 21,600 J (electrical energy). This energy is 21,600/604,052=3.57 % of the useful thermal energy provided by the air solar collector. To find how much thermal energy is consumed into a power plant to produce this amount of electrical energy, one multiplies the value of the electrical energy by 3.5, which is the average performance factor for the power plants in Romania. The result is 75,600 J (thermal energy). This thermal energy is 75,600/604,052=12.5 % of the useful thermal energy provided by the air solar collector. Therefore, neglecting the electrical energy needed to vehiculate the air in the collector is a quite reasonable assumption.

A typical space distribution of the air temperature along the air channels is shown in Figures 11 and 12 for both types of solar air collectors, for two irradiance levels. Average air temperatures were computed for the four lines of thermal transducers. The average temperature is a function of the position inside the air channel (four positions were considered here, namely X₁=19.5 cm, X₂=56.5 cm, X₃=93.5 cm and X₄=140.5 cm, as shown in Figure 3).

Figure 11:

Space variation of the average air temperature in the collector with “V”-corrugated porous absorber.

Figure 12:

Space variation of the average air temperature in the collector with “U”-corrugated absorber.

The average air temperature increases as the air is moving along the air channel, as expected. Also, the average temperatures exhibit a slight tendency to decrease near to the air heater outlet. This tendency was attributed to the end divergence and cooling effects and to mixing of the outgoing hot air with the ambient air due to recirculation.

In most experiments, the temperature variation across the collector is less than 5° for both collectors. However, this temperature variation can be as high as 10° in the V-corrugated porous collector at high values of the incident radiation (Figure 11). The model is based on the average temperature inside the collector. Thus, the underestimation at collector inlet is well compensated by the overestimation at collector outlet, as shown by the good agreement between the computed and the experimental results (see Table 3).

Notice that the temperature difference between the average measured temperature and the average temperature calculated by eq. (18) (in Appendix A) is between 1.5 and 2°. The air temperature variation is affected by the absorber type and by the level of the solar irradiance. Figures 11 and 12 show that the temperature tends to increase with increasing solar irradiance.

7 Conclusions

The operation of solar air collectors in real-world conditions, involving fluctuating incident solar irradiance, is inherently dynamic. Explicit time-dependent models of solar air collectors with and without porous absorber, suitable for dynamic system simulation, have been presented. Two specific air heaters have been considered: a V-corrugated porous collector and a “U”-corrugated collector. Note that V-corrugated absorbers have been treated in previous papers but the V-corrugated porous absorbers modeled here have not been very often considered in literature. A series of experiments have been performed under different weather conditions in Bucharest, Romania.

The results show that there is good agreement between the theoretical results and experiments. The rRMSE was about 10.36 % and 8.43 % for the solar air collectors with “V”-corrugated porous absorber and “U”-corrugated absorber, respectively.

An experimental comparison of the thermal performances of the two collectors was carried out under a wide range of configurations and operating conditions. The collector based on V-corrugated porous absorber has higher efficiency than the collector with U-corrugated absorber in the middle of clear days. Around sunrise and sunset the collector with U-corrugated absorber is more effective.