# Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector

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## Abstract

**:**

## 1. Introduction

^{2}with solar spectrum air mass of 1.5) to 11% and thermal efficiency of 58%. Chow [8] compared air-cooled and water-cooled PVTs, and their overall thermal efficiencies were in the range of 45% to 70% for water-cooled and 55% for air-cooled collector. Reichl et al. [13] developed a CFD model for a CPC collector and compared the model with experimental results. The results showed that a steady 2D model matched well with experimental results. It also showed that the heat loss through the covering glass is 73%. Buonomano et al. [14] designed and developed experimental analyses on a PVT collector. The collector thermal and electrical efficiencies were 13% and 15%, respectively. Stylianou [7] developed a CFD model for a CPVT collector. The obtained results showed that the thermal efficiency varied from 45% to 55% and electrical efficiency varied from 8% to 11%. Tyto [15] worked on a numerical model to evaluate the performance of the Solarus PowerCollector under indoor and outdoor conditions and compared it numerically with experimental results. Li et al. [16] worked on a CFD simulation of a CCPC (crossed compound parabolic concentrator) to estimate natural heat transfer behavior and optical performance. Yi [17] performed a Computational Fluid Dynamics (CFD) simulation and determined the effects of natural convection, radiation and conduction heat transfer on the thermal performance of the Solarus PowerCollector. Campos et al. [18] studied the effects of HTF on the efficiency of a CPVT collector. Tiemessen [19] developed a CFD simulation model for the Solarus PowerCollector and compared with experimental results and modified the model to reduce the heat losses. The results showed that the most heat losses are by convection (78%) and the rest (22%) is by radiation.

## 2. Materials and Methods

#### 2.1. Description of the Collector and the Properties of its Components

^{2}and it is divided into two troughs, each one with one receiver with 2.29 m of length and 0.158 m of width. It is characterized by an overall thermal efficiency of around 52% and the linear loss coefficient is 3.47W/(m

^{2}K) [21].

^{2}= y/0.0017), therefore the focal length is 144.86 mm (and circle radius). The focal point of the parabolic is located right on the center of the circle (Figure 3). Figure 4 shows how solar radiation is reflected to the receiver and PV cells.

#### 2.2. CFD Model of the Collector

_{p}is the specific heat constant, u is the fluid velocity, P is the fluid pressure, T is the fluid temperature and q

_{c}can be defined by Fourier’s law—k∇T. Q and F are the heat generation and external forces, respectively.

#### 2.2.1. Simulation Procedure

^{®}v2019 R3 fluent [26]. Firstly, the geometry of the collector was defined in the software and meshed optimally. Secondly, from the experimental results, the specific setup, variable and solution method were defined. Finally, the results of the model were analyzed and then compared with experimental results. The simulation model solved the continuity, energy and momentum equations inside the collector. Flow field, heat transfer, temperature gradient inside the receiver, thermal and electrical yield, and radiation field were obtained from these set of simulations.

#### 2.2.2. Geometry and Mesh of the Collector

^{®}meshing tool (Figure 6). The collector has been meshed with a total number of 180,000 elements. The space around the receiver, the reflector and the surrounding edges were meshed carefully due to the strong temperature and velocity gradients.

#### 2.2.3. Solution Methods

^{7}), the laminar model was an excellent approximation to model the behavior of fluid inside the collector.

_{PV}is the temperature coefficient of the PV cell (0.4%/K for mono-crystalline cells) and is defined as the following:

_{0}is the standard temperature of 25 °C, and ƞ

_{0}is the efficiency of the PV cell operating at STC. ϒ

_{G}is the intensity of the PV cell and in this condition, is set to zero because the effect of solar radiation on the PV cell is negligible. The electrical power output by the PV cells as the volumetric heat absorption is calculated by Equation (5), as can be seen below.

#### 2.2.4. Material Parameter

#### 2.2.5. Radiation Model

^{-8}W/m2.K4), and σ

_{s}and κ are the scattering and absorption coefficients, respectively. T is the local temperature and Φ is the scattering phase function that describes the probability that a ray from one direction (s) will be scattered into a certain direction (s’). The numerical method used to solve the RTE equation was the Discrete Ordinate Method (DOM), as this model allows a specular surface to be defined. This method solves the radiation field inside the model for a finite number of discrete solid angle and direction vectors. The DOM method requires a directional discretization and, to avoid the ray effect, an angular discretization of 15 × 15 divisions (Theta divisions and Phi division) and 3 × 3 pixels (Theta pixels and Phi pixels) was specified [29]. All the surfaces were set as opaque with diffuse reflectivity, except for the glass and reflector. The glass was set as a semi-transparent surface and the reflector was set as a specular surface. The absorption and scattering coefficient were not considered for the air.

#### 2.2.6. Boundary Conditions

_{d}), the thermal conductivity of the fluid (k

_{f}) and the hydraulic diameter (D

_{h}), and is defined as [25]:

_{d}= 3.66 [25]. The thermal generation of the collector is calculated by Equation (8), where h

_{w,forced}is the heat transfer coefficient, T

_{f}is fluid temperature and T

_{w}is the temperature of the channels.

_{sky}) and a forced convective heat loss to the ambient because of wind (T

_{amb}). The heat transfer coefficient caused by wind and sky temperature is calculated as described by Kalogirou [4]:

_{wind}) with ambient temperature was defined for the collector box boundary conditions.

#### 2.3. Experimental Test Method and Equipment Description

- KippZonen CMP3 and CMP6 pyrometers were used to measure solar direct and diffuse radiation.
- PT100 thermal resistances were used to measure the inlet and outlet fluid temperature and ambient temperature.
- K-type thermocouples were used for measuring the PV cells’ temperature.
- 2 Omega FMG80 flowmeters were used to measure the flow rate in each trough.
- A PicoLog USB TC08 datalogger was used to collect the data from the K-type thermocouples.
- A datalogger CR1000 from Campbell Scientific was used to visualize/store the parameters obtained by the PT100 ambient and water flow temperature sensors, the CMP3 and CMP6, and flowmeters.

- Back side sensor 1: Temperature over the cell (second cell).
- Top side sensor 2: Temperature on the receiver (fourth cell).
- Top side sensor 3: Temperature under the cell (fourth cell).
- Top side sensor 4: Temperature over the cell (fourth cell).

## 3. Results and Discussion

#### 3.1. Experimental Results

#### 3.2. Validation of the CFD Model

#### 3.3. CFD Results

#### 3.3.1. Collector Tilt Angle Variation

#### 3.3.2. HTF Temperature Variation

_{m}-T

_{amb}). T

_{m}is mean HTF temperature and T

_{amb}is the ambient temperature. At higher HTF temperature, the thermal efficiency of the collector decreases and that is due to the decreasing temperature gradient between the receiver and HTF.

^{2}. The collector heat loss coefficient (U) is calculated as 4.89 W/m

^{2}.K.

_{m}₋T

_{amb}= 16.5)) to 105 °C. This 63 °C increase in the temperature of the cells caused a 25% decrease in efficiency. This shows the importance of cooling and thermal potential. The collector reaches a maximum of 52% in thermal and 13.3% in electrical efficiency. According to these results, the effect of HTF on thermal production was more pronounced than on electrical production. This is shown by a steeper curve slope for the thermal efficiency line than for the electrical efficiency line.

#### 3.3.3. Collector Modification

_{amb}= 18.6 °C, T

_{m}= 35.1 °C). This result shows that, as expected, a glass cover is fundamental for any collector that has been expected to work at 10 °C above ambient temperatures.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol | Description, (Unit) | Acronyms | |

κ | Absorption coefficient, (1/m) | CPC | Compound Parabolic Collector |

T_{amb} | Ambient temperature, (°C) | CFD | Computational Fluid Dynamics |

A | Area, (m^{2}) | CPV | Concentrating Photovoltaic |

L | Characteristic length of the collector, (m) | CPVT | Concentrating Photovoltaic-Thermal |

ρ | Density, (kg/m3) | CT | Concentrating Thermal |

L, W | Dimensions of the PV, (m) | DOM | Discrete Ordinate Method |

Ƞ_{0} | Efficiency of the PV cell operating at STC, (--) | DHW | Domestic Hot Water |

Ƞ_{cell} | Efficiency of the PV cell, (--) | HTF | Heat Transfer Fluid |

E | Electrical production of the PV cell, (W) | MCRT | Monte Carlo Ray Tracing |

ϵ | Emissivity, (--) | PVT | Photovoltaic-Thermal |

F | External forces, (N) | RTE | Radiative Transfer Equation |

K_{f} | Fluid Conductivity, (W/m.K) | STC | Standard Test Condition |

P | Fluid Pressure, (Pa) | UDF | User-Defined Function |

T_{f} | Fluid temperature, (°C) | ||

u | Fluid velocity, (m/s) | ||

Q | Heat generation, (W/m^{3}) | ||

U | Heat loss coefficient, (W/m^{2}.K) | ||

T^{’} | Highest operating temperature of the PV cells, (°C) | ||

D_{h} | Hydraulic diameter, (m) | ||

ϒ_{G} | Intensity of the PV cell, (--) | ||

T_{m} | Mean water temperature, (°C) | ||

Nu_{d} | Nusselt number, (--) | ||

$\overrightarrow{\mathrm{r}}.\overrightarrow{\mathrm{s}}$ | Position and direction vector, (m) | ||

I | Radiation intensity, (W/m^{2}) | ||

Ra | Rayleigh number, (--) | ||

n | Refraction index, (--) | ||

σ_{s} | Scattering coefficient, (1/m) | ||

Φ | Scattering phase function, (--) | ||

T_{sky} | Sky temperature, (°C) | ||

G | Solar radiation, (W/m2) | ||

C_{p} | Specific Heat Capacity, (J/kg.K) | ||

T_{0} | Standard temperature, (25 °C) | ||

σ | Stefan–Boltzmann constant, (5.669 *10^{-8} W/m^{2}.K^{4}) | ||

β_{PV} | Temperature coefficient of the PV cell, (%/K) | ||

T_{pv} | Temperature of PV cell, (°C) | ||

T_{w} | Temperature of the receiver channels, (°C) | ||

k | Thermal Conductivity, (W/m.K) | ||

Q_{th} | Thermal production of the collector, (W) | ||

β | Tilt angle, (degree) | ||

t | Time, (s) | ||

V_{cell} | Volume of the PV cell, (m^{3}) | ||

h_{w forced} | Water convection heat transfer, (W/m^{2}.k) | ||

h_{wind} | Wind convection heat transfer, (W/m^{2}.k) | ||

V | Wind speed, (m/s) |

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**Figure 2.**Top view of the concentrated photovoltaic-thermal collector (CPVT) collector. The water connections are marked in blue and the electrical connections in red [20].

**Figure 10.**Measurement A: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 2.2 L/min.

**Figure 11.**Measurement B: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 1 L/min.

**Figure 12.**Measurement C: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 2.2 L/min.

**Figure 13.**Simulated temperature distribution over the cells on both sides of the receiver (outer part) for measurement A.

Photovoltaics | Solar Thermal | Concentration | |
---|---|---|---|

CPV | ☑ | ☑ | |

CT | ☑ | ☑ | |

PVT | ☑ | ☑ | |

CPVT | ☑ | ☑ | ☑ |

Features | Values/Units |
---|---|

Collector production (nominal) | 1350W thermal, 270W electrical |

Collector total area | 2.2 m^{2} |

Receiver area | 0.362 m^{2} |

Concentration ratio | 1.52 |

Reflector reflectivity | 96% for the full spectrum and 92% for the visible spectrum |

Receiver channel area | 8 channels with 154 mm^{2} (one channel) |

Silicone thickness | 1 mm on both side of PV cells |

Solar cell efficiency | 18.7% (STC) |

Solar cell Temperature coefficient | 0.4%/C |

Glass transmittance | 95% |

Thermal Conductivity (W/m.K) | Density (kg/m ^{3}) | Specific Heat Capacity (J/kg.K) | |
---|---|---|---|

Front Glass | 1 | 2500 | 720 |

Reflector | 200 | 2700 | 901 |

Receiver | 210 | 2700 | 901 |

Silicon | 0.2 | 970 | 1550 |

PV cell | 124 | 2320 | 678 |

Collector Box | 0.033 | 500 | 100 |

Measurement | Ambient Temperature (°C) | Inlet Water Temperature (°C) | Outlet Water Temperature (°C) | Direct Radiation (W/m^{2}) | Diffuse Radiation (W/m^{2}) | Incident Angle (⁰) | Solar Altitude(⁰) | Solar Azimuth (⁰) | Flow Rate (L/min) | Duration of Measurement (min) |
---|---|---|---|---|---|---|---|---|---|---|

A | 18.6 | 33.6 | 36.6 | 978.3 | 93.1 | 18.5 | 48.5 | 199.4 | 2.2 | 10 |

B | 19.1 | 42.9 | 46.2 | 922.8 | 77.2 | 26.4 | 56.3 | 231.9 | 1 | 5 |

C | 20.1 | 46.3 | 48.4 | 946.0 | 77.2 | 17.9 | 47.8 | 189.4 | 2.2 | 10 |

D | 20.8 | 44.7 | 47.5 | 892.9 | 76.4 | 28.1 | 58.1 | 235.7 | 1.2 | 5 |

E | 21.6 | 36.2 | 39.0 | 757.8 | 145.5 | 21.4 | 51.4 | 200.9 | 2.1 | 3 |

F | 23.1 | - | - | 422.5 | 114.6 | 29.2 | 59.2 | 231.8 | 0 | 3 |

**Table 5.**Performance of the different collector variations studied (T

_{amb}= 18.6 °C, T

_{m}= 35.1 °C).

Back Side Cell Temperature (°C) | Top Side Cell Temperature (°C) | Thermal Power (w) | Electrical Power (w) | |
---|---|---|---|---|

Measurement A (base case) | 42.4 | 42.2 | 511 | 142.2 |

Reflector insulation | 42.6 | 42.4 | 528 | 142.1 |

Copper receiver | 42.3 | 42.1 | 512 | 142.3 |

No front glass | 38.2 | 36.5 | 150 | 145.2 |

No HTF | 105.7 | 105.2 | 0 | 103.6 |

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**MDPI and ACS Style**

Nasseriyan, P.; Afzali Gorouh, H.; Gomes, J.; Cabral, D.; Salmanzadeh, M.; Lehmann, T.; Hayati, A. Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector. *Energies* **2020**, *13*, 1669.
https://doi.org/10.3390/en13071669

**AMA Style**

Nasseriyan P, Afzali Gorouh H, Gomes J, Cabral D, Salmanzadeh M, Lehmann T, Hayati A. Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector. *Energies*. 2020; 13(7):1669.
https://doi.org/10.3390/en13071669

**Chicago/Turabian Style**

Nasseriyan, Pouriya, Hossein Afzali Gorouh, João Gomes, Diogo Cabral, Mazyar Salmanzadeh, Tiffany Lehmann, and Abolfazl Hayati. 2020. "Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector" *Energies* 13, no. 7: 1669.
https://doi.org/10.3390/en13071669