Introduction

Energy has always been a vital issue for man and human societies. Its availability affects human behavior whether in abundance or in scarcity. Consequently, new challenges will arise particularly for the environment and socio-economic balances. Awareness of the importance of these issues (global warming, depletion of resources, increased costs, etc.) should divert us towards a more rational use of energy, an optimization of implemented energy processes, and more widespread use of renewable energy systems. Among these renewable energies, solar energy has been used for millennia. Techniques for exploiting this resource have considerably improved in recent years involving state-of-the-art technology and making operating costs more attractive, particularly in the production of thermal energy. Thermal energy produced by solar energy is ecological without any greenhouse gas emissions. The present work focuses on solar air flat plate collector.

Solar air collectors suffer from poor thermal efficiency, due to low heat exchange between the absorber and the heat transfer fluid (Alta et al. 2010) as well as heat loss from its various parts (Saxena et al. 2015; Hernandez and Quinonez 2018; Karwa and Srivastava 2013), in particular at glazing (Koyuncu 2006; Youcef and Desmons 2006). One of the proposed solutions consists in generating zones of turbulence in the flow path by the using fins (Khatri et al. 2021; Ho et al. 2012; Mahmood et al. 2015; El-khawajah et al. 2011; Omojaro and Aldabbagh 2010) and roughness (Karwa and Srivastava 2013; Kumar and Prasad 2017). V ribs constitute another way to create roughness and to enhance heat transfer from the surface to the flowing air (Yadav et al. 2021; Kumar et al. 2020, 2021a; Mahanand and Senapati 2021; Patel & Langevar 2019; Thakur et al. 2017; Singh et al. 2011, 2012; Sahu and Prasad 2017; Kumar and Layek 2019). The presence of turbulences improves heat exchange and the fins or the ribs increase the heat exchange area. The different studies consider parameters in order to optimize configurations.

In order to increase the low heat transfer, other studies consider forced air solar heater based on air impinging on flat surface of absorber plate. According to authors (Zukowski 2015), the new configuration improves the energy conversion efficiency and reduces the pressure losses.

Other works suggest the use of thermal energy storage system (Tyagi et al. 2021; Saxena et al. 2020; Wadhawan et al. 2018; Fath 1995; Rasheed 2020; Duan et al. 2021), by means of sensible heat storage materials (Kumar et al. 2021b; Alkilani et al. 2011; Gautam and Saini 2020; Saxena and Goel 2013; Pradyumna and Debendra 2017; Saxena et al. 2013; Prasad et al. 2019; Kumar et al. 2016). A particular case was the use of granular carbon on the absorber in order to stabilize the exit temperature (Patel & Langevar 2019). Latent heat storage materials (PCM) was also used in order to reduce losses to the outside environment (Quanquan et al. 2022; El Khadraoui et al. 2016; Ke et al. 2021; Salih et al. 2020). PCM paraffin filling the vacuum tube of heat pipe was investigated with a purpose of improving the efficiency of the heat transfer. In the case, aluminum fins were used to contain the PCM paraffin and to extend the heat transfer area Wang & al. 2021).

In the present work, we are interested in geometry modification of the solar air flat plate collector in which the collector back made of an insulation panel will be replaced by a water-filled tank. The water tank that acts as a storage system in a solar water heater is used as a back-up system for the solar air collector. Generally, a field of solar collectors is used to respond to thermal energy needs expressed by a consumer for a given purpose (heating, drying, etc.). The modified solar flat plate air collector will avoid the realization complexity of storage tank separately, which is generally of a cylindrical shape, free more space, improve the thermal efficiency of the solar air heater (SAH), and generate a stabilized exit temperature.

The objective of this study is to analyze the energy contribution of the storage system to the performance of solar air collectors.

Physical model of the solar air heater

A solar collector benchmark is set up at the Renewable Energy Development Center. The benchmark is made of a solar air heater, a solar water heater, and a mixed solar collector (air-water). The daily follow-up of the recorded data from the benches, during test periods and their analysis showed the following (Bouhdjar et al. 2021):

  • A low thermal efficiency of the SAH; even the use of baffles placed in the flow vein to increase the exchange surface does not have a noteworthy effect on thermal efficiency.

  • The use of a mixed solar collector (air-water) in order to reduce heat losses to the outside environment has had a positive impact on the instantaneous efficiency compared to the two other collectors combined (water collector and air collector), but it remains below the required threshold.

  • The set-up of a storage tank requires professional intervention and additional space.

Replacing the back insulation of the collector with a water tank as a back-up system avoids the aforementioned drawbacks. Moreover, the new configuration will not generate additional costs because the component is an integral part of the solar water heater and even allows a reduction in cost with a simple realization without the intermediary intervention.

The storage tank fed by water coming from the solar water heater will be adjusted to the shape of the air collector back. Thus, the data collected at the level of the solar water heater (outlet water temperature), available at the level of the test bench, will be used as a boundary condition for the solar flat plate air collector. The modified solar air heater (MSAH) considered in the study has a shape similar to the one set up in the test bench. Results from the later will be considered for validation.

Figure 1 shows a scheme of typical SAH and Fig. 2 shows a scheme of the MSAH.

Fig. 1
figure 1

Typical solar air heater (SAH)

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Fig. 2
figure 2

Modified solar air heater (MSAH)

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Figure 3 shows the test benches made of solar air heater and solar water heater designed and used for the experiment.

Fig. 3
figure 3

Pictures of solar collector setup: a solar flat plate air collector, b solar flat plate water collector

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Table 1 shows dimensions of the solar air heater and the modified solar air collector.

Table 1 Geometrical parameters of solar air heaters (conventional and modified)
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Mathematical model and boundary conditions

Governing equations

CFD methods consist of numerical solutions of mass, momentum, and energy conservation equations along with other equations such as species transport.

The following equations summarize the governing equations:

Continuity equation

$$\frac{\partial \rho }{\partial t}+\nabla .\left(\rho \overrightarrow{v}\right)=0$$
(1)

Momentum equation

$$\frac{\partial \left(\uprho \overrightarrow{v}\right)}{\partial t}+\nabla .\left(\rho \overrightarrow{v}\ \overrightarrow{v}\right)=\rho \overrightarrow{g}-\nabla p+\nabla .\left(\overline{\tau}\right)+\overrightarrow{F}$$
(2)

Energy equation

$$\frac{\partial \left(\uprho \textrm{E}\right)}{\partial t}+\nabla .\left(\overrightarrow{v}\ \left(\rho E+p\right)\right)=\nabla .\left({k}_{eff}\nabla T+\left(\overline{\tau_{eff}}.\overrightarrow{v}\right)\right)$$
(3)

where p is the static pressure, \(\overline{\tau}\) is the stress tensor, and \(\rho \overrightarrow{g}\) and \(\overrightarrow{F}\) are the gravitational body force and external body forces, respectively.

The k-ε model used for turbulent flows is expressed by:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial {x}_j}\left(\rho k{u}_j\right)=\frac{\partial }{\partial {x}_j}\left(\left(\mu +\frac{\mu_t}{\sigma_K}\right)\frac{\partial k}{\partial {x}_j}\right)+{G}_K+{G}_b-\rho \varepsilon +{S}_K$$
(4)
$$\frac{\partial }{\partial t}\left(\rho \varepsilon \right)+\frac{\partial }{\partial {x}_j}\left(\rho \varepsilon {u}_j\right)=\frac{\partial }{\partial {x}_j}\left(\left(\mu +\frac{\mu_t}{\sigma_{\varepsilon }}\right)\frac{\partial \varepsilon }{\partial {x}_j}\right)+{C}_{1\varepsilon}\left({G}_K+{C}_{3\varepsilon }{G}_b\right)-{C}_{2\varepsilon}\rho \frac{\varepsilon^2}{K}+{S}_{\varepsilon }$$
(5)

G k is the generation of turbulence kinetic energy due to the mean velocity gradients. It is defined by:

\({G}_k=-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\frac{\partial {u}_j}{{\partial x}_i};{G}_b\) is the generation of turbulence due to buoyancy; σk and σε are the turbulent Prandtl numbers for k and ε, respectively, and β is the thermal expansion coefficient which is approximated by \(\beta \approx {~}^{1}\!\left/ \!{~}_{T}\right..\)

Nusselt number

In solar heating system, the convective heat transfer coefficient between the absorber surface and the flowing air is low. Considering the heat transfer from the absorber to a region at the bulk temperature, we can easily express the Nusselt number from which we deduce the convection heat transfer coefficient.

The convection heat transfer is expressed by:

$${q}_p=h\left({T}_{abs}-{T}_B\right)$$
(6)

and from Eq. (6), we deduce the Nusselt number

$$\textrm{Nu}=\frac{\textrm{h}{D}_h}{\uplambda}=\frac{{\textrm{q}}_P{D}_h}{\left({\textrm{T}}_{abs}-{T}_B\right)\uplambda}$$
(7)

where

qP:

is the heat flux

Dh:

is the hydraulic diameter

Tabs:

is the absorber mean temperature

TB:

is the bulk temperature of fluid and

λ:

is the thermal conductivity of fluid

Thermal efficiency

The performance of the flat solar collector varies with the geometry of the collector, internal and external parameters such as solar irradiation, ambient temperature, mass flow rate, etc.

The thermal efficiency of the modified solar air heater is defined as follows (Abuska 2018):

$$\eta =\frac{\dot{m_a}{C}_{pa}\left({T}_{fo}-{T}_{fi}\right)}{I{A}_c+\dot{m_w}{C}_{pw}\left({T}_{fwo}-{T}_{fwi}\right)}$$
(8)

where

\({\dot{m}}_a,{\dot{m}}_w\):

is the mass flow rate for air and water, respectively

Cpa, Cpw:

is the specific heat for air and water, respectively

Tfo, Tfi:

is the outlet and inlet temperatures for air

Tfwo, Tfwi:

is the outlet and inlet temperatures for water

I:

is the solar irradiance and

Ac:

is the collector area

Boundary conditions

Boundary conditions are defined from the weather conditions at the experimentation site (Bouzaréah, Algeria), solar irradiance as heat source, ambient temperature as inlet air temperature and water inlet temperature (secondary heat transfer fluid), and the latter is the water outlet temperature of the solar water heater. Weather conditions correspond to a clear sky day (Fig. 4).

Fig. 4
figure 4

Solar irradiance, ambient temperature, and water inlet temperature; a on the day of 02/01/2022 (natural flow), b on the day of 05/07/2021 (forced flow)

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On the second of January, 2022, solar air heater was operating under natural flow and on the fifth of July, 2021, solar air heater was operating under forced flow. On both days, water from the solar water heater, used as a second heat transfer fluid for the SAH, was operating under forced flow with a mass flow rate of 0.019kg/s.

We observe that solar radiation evolves regularly during the time interval (10–15h30). The maximum radiation recorded is 950W/m2 and the minimum is a little higher than 600W/m2, for the natural flow. On the other hand, radiation during the day in which the flow considered is forced varies from 600 to 900 W/m2. The same observation applies to the air inlet temperature (Tfi), which is generally stable throughout the time interval and evolves at 295 K average for the natural flow and just over 300K for the forced flow. However, the water outlet temperature (To) evolves in an upward and regular manner throughout the test interval with recorded values ranging between 307.9K for the minimum and 319.9K for the maximum, in the case of the natural flow and they are between 325K and 336.9K for the forced flow.

During the day of 02/01/2022, boundaries conditions are as follows:

The collector inlet pressure and the inlet temperature are those of the ambient environment:

$${P}_{ri}=0,{T}_{inlet}={T}_{\infty }$$
(9)

Pressure outlet is the duct exit

$${P}_{ro}=0$$
(10)

Sidewalls and bottom wall are adiabatic

$$u=0,v=0,\frac{\partial T}{\partial y}=0$$
(11)

Incident solar irradiance on the transparent cover is given in Fig. 4.

$$u=0,v=0,q=I$$
(12)

The physical properties of the air are assumed constant at bulk temperature.

During the day of 05/07/2021, the boundary conditions are:

The air mass flow is measured at the collector inlet, and the temperature is the ambient temperature:

$${\dot{m}}_a=0.075\ \left({~}^{ kg}\!\left/ \!{~}_{s}\right.\right),{T}_{inlet}={T}_{\infty }$$
(13)

The water mass flow rate is identical for all tests.

Outflow conditions are considered at the duct exit

$$\frac{\partial u}{\partial x}=0,\kern0.5em \frac{\partial v}{\partial x}=0,\kern0.5em \frac{\partial T}{\partial x}=0$$
(14)

Sidewalls and bottom wall are adiabatic

$$u=0,v=0,\frac{\partial T}{\partial y}=0$$
(15)

Validation of the numerical simulation

The validation of the code requires its implementation on an existing experimental model of the benchmark according to the operating conditions, namely solar radiation and ambient temperature.

Figures 5, 6, and 7 show SAH outlet temperatures, Nusselt number, and instantaneous efficiency, respectively. Outlet air temperatures obtained from simulation and from experiment follow the same trend during the entire time interval in both flow regimes (Fig. 5). A 0.9% average deviation for the forced flow case and 0.95% average deviation for the natural one are observed. The average deviation for Nusselt numbers is 8.58% for natural flow and 15% for the forced flow (Fig. 6). Figure 7 shows system performances calculated by simulation model and the ones obtained from experiment data analysis. The curves have the same trend and average differences of about 13% for forced flow and 8.4% for the natural flow are observed.

Fig. 5
figure 5

Experimental data and simulation result for outlet temperatures, a for natural flow (on 02/01/2022), b for forced flow (on 05/07/2021)

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Fig. 6
figure 6

Experimental data and simulation results for Nusselt number, a for natural flow (on 02/01/2022), b for forced flow (on 05/07/2021)

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Fig. 7
figure 7

Experimental data and simulation result for the instantaneous efficiency, a for natural flow (on 02/01/2022), b for forced flow (on 05/07/2021)

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Nevertheless, comparing the results for the two flow regimes (natural and forced), it can be seen that temperatures recorded with a natural flow far exceed the ones obtained with a forced flow. In natural flow regime, the crossing time being much longer allows a lasting contact between the fluid and the absorber plate. This leads to a further temperature increase. However, the efficiency is much higher for a forced flow since it is proportional to the amount of energy transported by the heat transfer fluid. Forced flow means a high flow rate and therefore a larger airflow mass and therefore a greater amount of energy transported. The same situation is noticed for the Nusselt number, which characterizes the enhancement of heat transfer through a fluid as result of convection.

Due to the successful comparison between the experimental data and numerical simulation results, the code is considered valid.

Results and interpretation

Using the previously validated Fluent CFD code, a numerical simulation was performed on a typical SAH and on the modified SAH previously described in which a storage water tank replaces the collector back insulation. The storage tank is fed from a solar water heater. The water tank acts also as insulator for the air collector. As mentioned previously, the SAH is operating under natural fluid flow in one case and in forced fluid flow at a rate of 0.075kg/s in another case. As for the water coming from the solar water heater to the storage tank on the back of the SAH, the mass flow rate is equal to 0.019kg/s.

Figure 8 shows outlet air temperatures for both configurations of solar air heaters (MSAH, SAH). An improvement of the outlet temperature is obtained with the MSAH. Temperature increase is around 3K for forced flow. However, with natural flow, the temperature is lower in the same MSAH compared to the SAH. In natural flow, higher temperature is obtained with the modified air collector compared to the same collector in a forced flow regime. More energy is transferred from water to the air. Also for the Nusselt number, there is no improvement with the modified model (Fig. 9), for the case of a natural air flow.

Fig. 8
figure 8

Outlet temperatures in both configurations (SAH and MSAH), a for natural flow (on 02/01/2022), b forced flow (on 05/07/2021)

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Fig. 9
figure 9

Nusselt number for both configurations (SSAH and MSAH), a for natural flow (on 02/01/2022), b forced flow (on 05/07/2021)

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The instantaneous efficiency of the SAH in forced flow hardly exceeds 30%. However, with the MSAH, a substantial improvement is obtained with the efficiency exceeding 45%, and this represents a 57% increase compared to the typical SAH (Fig. 10). It can be observed on the efficient curve that the performance of the SAH follows the same trend as solar radiation, the only used heat source. However, for the MSAH, the efficiency does not follow the same path as solar irradiance. Due to the energy supplied by storage tank, it continues increasing even after sunset.

Fig. 10
figure 10

Instantaneous efficiency for both configurations (SAH and MSAH), a for natural flow (on 02/01/2022), b forced flow (on 05/07/2021)

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The temperature rise with the forced flow regime results from the use of hot water coming from the solar water collector, which comes as additional energy supplier to the solar air collector. This increase coupled with a forced flow improves the performance of the MSAH, as confirmed by the performance curve given in Fig. 10.

The new configuration makes the system operate over a longer time with a stabilized exit temperature.

As far as the comparison of the flow régime, the efficiency is better with the one of forced flow, as given by the validation curves. This due to a minimizing losses to the outside environment but with a slight improvement because of the absorber cooling, if the flow rate increases, and consequently decreasing a heat exchange rate between the absorber and the heat transfer fluid. With the MSAH, the flow rate can be increased further with no risk at lowering further the absorber temperature due to a significant heat exchange from the heat transfer fluid of the water collector. The latter will continuously be renewed by hot water coming from the solar water collectors. The consequence of this system is to stabilize the exit air temperature for any purpose whether it be for drying or building heating.

We studied also the effect of different flow rates for air and water in order to analyze which of the heat transfer fluids will have the most impact on the collector performance. Initially, the air flow rate is fixed at 0.075 kg/s and the water flow rate takes different values (0.013, 0.019, and 0.027 kg/s). In another simulation, the water flow rate is fixed at 0.019 kg/s and the air flow rate takes different values (0.005, 0.019 and 0.075 kg/s).

Figure 11 shows the outlet temperatures for MSAH model for different flow rates. The impact of the air flow rate (primary heat transfer fluid) far outweighs the water flow rate (secondary heat transfer fluid). The temperature difference between the two heat transfer fluids (air and water) can reach 21K. Increasing the flow rate of the secondary fluid (water) will have slight influence on the outlet temperature of the heat transfer fluid (air) because the quantity of energy transported by the latter will be smaller compared to the one of high airflow. The energy evacuated would be more important when increasing the flow rate as confirmed by the efficiency curve as long as it is partly proportional to the flow rates (Fig. 12).

Fig. 11
figure 11

Outlet temperature, a variable water flow, b variable airflow

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Fig. 12
figure 12

Instantaneous efficiency, a variable water flow, b variable airflow

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Similar result is obtained for the Nusselt number. The increase in the flow rate of the secondary fluid does not improve the temperature gradient at the absorber surface as long as the main heat transfer fluid (air) is fixed at 0.019kg/s. However, if the flow rate of the primary heat transfer fluid (air) is increased while fixing that the one of secondary fluid (water), Nusselt number is improved. Increasing the main fluid flow (air) beyond a threshold does not improve Nusselt number. With the highest flow rate for the main fluid flow (0.075 kg/s), Nusselt number is lower than the one obtained with a lower flow rate (0.019kg/s) (Fig. 13).

Fig. 13
figure 13

Nusselt number, a variable water flow, b variable airflow

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Conclusion

Typical solar air collector is considered. Some modifications are made on the initial solar air heater configuration replacing the back insulation with water storage tank. In order to assess the thermal efficiency of the two configurations, a numerical study using fluent CFD code was applied. The developed numerical model has been validated through experimental results. Different flow rates were considered for the two heat transfer fluids which are air as a primary heat transfer fluid and water as the second heat transfer fluid. From simulation results, we conclude that:

  • Forced flow gives better performance rather than natural flow.

  • Thermal efficiency of the modified model is better than that of the typical one for forced flow regime.

  • For the considered flow rates, best efficiency is obtained when the air flow rate is increased.

  • The increase of the water flow rate has a slight influence on the solar air heater efficiency.

Results show that modification made on a typical solar flat plate air collector has a considerable impact on the solar air heater thermal performance. Modified solar air collector might deliver heat or temperature according to the need whether in drying or building heating through a regulation system. Moreover, its construction will not require additional cost since the storage tank is an equipment, which is part of a solar system, and is moved to the solar air collector. Performance, flexibility and cost make the new solar air collector model more attractive for the development of solar energy system.