# Study of PTC System with Rectangular Cavity Receiver with Different Receiver Tube Shapes Using Oil, Water and Air

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## Abstract

**:**

## 1. Introduction

## 2. Material and Method

- -
- Optical modeling of the rectangular cavity receiver at optimization dimensions.
- -
- Thermal modeling of the rectangular cavity receiver with smooth and corrugated tubes at optimization dimensions.
- -
- Investigation of different fluids, including air, water, and thermal oil in the solar system.
- -
- Investigation effect of different parameters on the thermal performance of the PTC system, including solar beam irradiation, inlet temperature, and volume flow rate.

#### 2.1. Optical and Thermal Modeling

#### 2.2. Thermal Modeling

- Internal Mixed Heat Loss

- External Heat Loss

- Smooth and Corrugated Tube Simulation

- Method to Determine the Optimum Structure of Receiver

#### 2.3. Validation

## 3. Result and Discussion

#### 3.1. Comparison between Two Kinds of Cavity Tube

^{2}to 1100 W/m

^{2}for smooth and corrugated tubes as the cavity tube, respectively. It should be mentioned that thermal oil with inlet temperature of 50 °C and flow rate of 50 mL/s was used as the solar heat transfer fluid. It can be seen that thermal performance of the cavity receiver for both types of the cavity tube improved with increasing solar beam irradiation.

^{2}and heat transfer fluid as 50 mL/s were assumed in this analysis. It should be mentioned that thermal oil was used as the solar heat transfer fluid. The results showed the absorbed heat and energy performance of the cavity receiver decreased with increasing heat transfer fluid inlet temperature. So, application of the heat transfer fluid is more efficient for achieving higher thermal performance.

^{2}and inlet temperature of heat transfer fluid equal to 50 °C were investigated in this analysis. As concluded, thermal performance of the cavity receiver, including the absorbed heat and thermal performance, increased with increasing heat transfer fluid inlet temperature. So, application of the heat transfer fluid with higher flow rate of the heat transfer fluid is more effective for achieving higher thermal performance.

^{2}to 1100 W/m

^{2}were presented in Figure 10a,b, respectively. Two types of tube, including smooth and corrugated tubes, were used as the cavity tube. Solar heat transfer fluid was investigated with inlet temperature of 50 °C and flow rate of 50 mL/s. As seen from Figure 10, the cavity surface temperature and outlet temperature of the cavity receiver for both types of the cavity tube enhanced with increasing solar beam irradiation.

^{2}and flow rate of 50 mL/s. Results shown in Figure 11 show increasing inlet temperature of the solar heat transfer fluid, as well as increasing cavity wall temperature and oil outlet temperature. On the other side, variation of the temperature of cavity walls and oil under changes of flow rate in the range of 0.001 mL/s to 600 mL/s are presented Figure 12a,b, respectively. The rectangular cavity receiver with smooth and corrugated tubes was investigated as the PTC receiver. It should be mentioned that the solar beam irradiation equal to 800 W/m

^{2}and inlet temperature of heat transfer fluid as 50 °C were assumed in this analysis. As seen in Figure 12, increasing the flow rate of the heat transfer fluid decreased temperature of the cavity walls and oil.

^{2}and flow rate of 50 mL/s. As seen from Figure 13, the pressure drop of the cavity receiver decreased with increasing oil temperature. In addition, variation of pressure drop under variation of flow rate in the range of 0.001 mL/s to 600 mL/s is presented in Figure 14. The rectangular cavity receiver with two types of the cavity tube, including smooth and corrugated tubes, was studied as the solar PTC receiver. This analysis was conducted under the solar beam irradiation of 800 W/m

^{2}. Thermal oil with inlet temperature of 50 °C was used. As Figure 14, the pressure drop increased with increasing volume flow rate of the heat transfer fluid. In Figure 13 and Figure 14, the cavity pressure drop increased with application of the rectangular cavity receiver with the corrugated tube. It can be recommended that lower pressure drop can be achieved with a smooth tube as the cavity tube.

#### 3.2. Comparison of Different Heat Transfer Fluids

^{2}to 1100 W/m

^{2}. Different fluids, including water, air, and thermal oil, were studied as the solar heat transfer fluid of a rectangular cavity receiver. The rectangular cavity receiver with the smooth tube was considered as the solar PTC receiver. Figure 15a,b depict the variation of absorbed heat and energy performance of the rectangular cavity receiver under changes of inlet temperature in the range of 50 °C to 230 °C, respectively. Three kinds of fluids were considered as the solar heat transfer fluids, including water, air, and thermal oil. The rectangular cavity receiver with a smooth tube was used as the solar PTC receiver. This analysis was conducted at the solar beam irradiation of 800 W/m

^{2}and flow rate of the heat transfer fluids equal to 50 mL/s. Results showed that thermal performance decreased with increasing inlet temperature of three investigated solar heat transfer fluids.

^{2}and inlet temperature of heat transfer fluids equal to 50 °C were assumed in this analysis. As seen, amounts of the absorbed heat and energy performance of the PTC system with the rectangular cavity receiver enhanced with increasing flow rate. As seen from Table 3, Figure 15 and Figure 16, thermal performance of the rectangular cavity was improved using the application of water as the solar heat transfer fluid, which was followed by thermal oil and, finally, air, as the solar heat transfer fluid. As a result, water as the solar heat transfer fluid is appropriate for low-temperature application, whereas the thermal oil as the solar heat transfer fluid is suitable for high-temperature application.

^{2}to 1100 W/m

^{2}for three investigated heat transfer fluids, including water, thermal oil, and air, respectively. The linear rectangular cavity with smooth tube was used. The heat transfer fluids were evaluated under inlet temperature of 50 °C, and flow rate of 50 mL/s. As concluded from Figure 17, the temperature of cavity walls and heat transfer fluids for the three investigated solar heat transfer fluids increased with increasing solar beam irradiation. On the other hand, Figure 18a,b display variation of the cavity surface temperature and heat transfer fluid outlet temperature under changes of inlet temperature in the range of 50 °C to 230 °C for the three investigated heat transfer fluids, including water, thermal oil, and air, respectively. The rectangular cavity receiver with a smooth tube was used. The considered solar heat transfer fluid was studied as flow rate of 50 mL/s, and the solar beam irradiation was investigated equal to 800 W/m

^{2}, during these analyses. Results in Figure 18 show higher amounts of the cavity surface temperature and higher outlet temperature of the solar heat transfer fluid, using application of the solar heat transfer fluids with higher inlet temperature for the three investigated solar heat transfer fluids.

^{2}and inlet temperature of heat transfer fluids as 50 °C were investigated in this analysis. As presented in Figure 19, the temperature of cavity walls and heat transfer fluids decreased with increasing the flow rate of the heat transfer fluid. As concluded from Figure 17, Figure 18 and Figure 19 amounts of the temperature of cavity walls and air as the solar heat transfer fluid presented the highest amount, followed by thermal oil and, finally, water, which showed lowest amounts of the temperature of cavity walls and heat transfer fluids. It could be recommended that the rectangular cavity receiver with air is suitable as the heat source of a Brayton cycle, whereas the rectangular cavity receiver with water as the solar heat transfer fluid can be suggested for achieving the highest thermal performance in low-temperature application. Finally, thermal oil as the solar heat transfer fluid of the rectangular cavity receiver can be recommended as achieving the highest thermal performance in high-temperature application.

^{2}, and flow rate of 50 mL/s. As presented in Figure 20, the pressure drop has decreased with increasing inlet temperature of the heat transfer fluid for the three investigated heat transfer fluids. Figure 21 displays variation of pressure drop of the solar system with smooth tube under variation of flow rate in the range of 0.001 mL/s to 600 mL/s for the three investigated solar heat transfer fluids, including thermal oil, water, and air. It should be mentioned that this analysis was conducted for the solar system with inlet temperature of the solar heat transfer fluids equal to 50 °C and the solar beam irradiation of 800 W/m

^{2}. As concluded from Figure 21, the pressure drop increased with increasing volume flow rate of the heat transfer fluids for all of the investigated solar heat transfer fluids. As concluded from Figure 20 and Figure 21, the rectangular cavity receiver with thermal oil as the solar heat transfer fluid resulted in the highest pressure drop. On the other side, the rectangular cavity receiver with air as the solar heat transfer fluid showed the lowest pressure drop.

## 4. Conclusions

- -
- It can be seen that absorbed heat and energy performance of the cavity receiver for both types of the cavity tube, using different solar heat transfer fluids, improved with increasing solar beam irradiation, decreasing inlet temperature, and increasing flow rate of the heat transfer fluids. On the other side, the rectangular cavity receiver with corrugated tube showed higher amounts of the absorbed heat and energy performance compared to the smooth tube as the cavity tube. It can be recommended that higher thermal performance can be achieved with corrugated tube as the cavity tube.
- -
- The pressure drop of the cavity receiver using both types of the cavity tube decreased with increasing inlet temperature of the heat transfer fluid, as well as decreasing flow rate of all of the investigated solar heat transfer fluids. On the other side, the cavity pressure drop increased with application of the rectangular cavity receiver with the corrugated tube compared to the smooth tube. It can be recommended that lower pressure drop can be achieved with smooth tube as the cavity tube.
- -
- The thermal performance of the rectangular cavity improved using the application of water as the solar heat transfer fluid, which was followed by thermal oil and, finally, air, as the solar heat transfer fluid. It can be recommended that the rectangular cavity receiver with air, water, and oil is suitable as the heat source of a Brayton cycle, low-temperature application, and high-temperature application, respectively.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Area, m^{2} |

Aa | Aperture area, m^{2} |

$\stackrel{\xb4}{A}$ | PTC aspect ratio, - |

a | Nominal cavity aperture, m |

cp | Specific heat capacity, kJ/kgK |

c2 | Constant parameter, - |

dtube | Tube diameter, mm |

D | Cavity height, m |

f | Focal distance, cm |

Fi-j | View factor, - |

g | Earth’s gravity, m/s^{2} |

$\stackrel{\xb4}{h}$ | Heat convection coefficient, W/m^{2}K |

I_{beam} | Direct beam solar irradiation, W/m^{2} |

k | Thermal conductivity, W/mK |

L | Parabola length, m |

$\dot{m}$ | Mass flow rate, mL/s |

m2 | Constant parameter, - |

Nu | Nusselt number, - |

$\dot{Q}$ | Heat rate, W |

${\dot{Q}}^{*}$ | Absorbed solar energy, W |

R | Thermal resistance, Km^{2}/W |

Re | Reynolds number, - |

Ra | Rayleigh number, - |

Pr | Prandtl number, - |

tins | Insulation thickness, m |

T | Temperature, °C |

Tam | Ambient temperature, °C |

T_{s,Ave} | Receiver surface average temperature, °C |

W | Aperture wide, m |

V_{wind} | Wind speed, m/s |

## Greek Symbols

$\stackrel{\xb4}{\beta}$ | Coefficient of thermal expansion (equal to approximately 1/T, for ideal gases) |

ΔP | Pressure drop, Pa |

ε | Emittance, - |

η_{glob} | Collector global efficiency, - |

η_{th} | Receiver thermal efficiency, - |

η_{opt} | Optical efficiency of the receiver, - |

η_{refl} | Concentrator reflectance, - |

θ | Cavity side angle, ° |

ν | Kinematic viscosity |

ρ | Density, kg/m^{3} |

σ | Stefan-Boltzmann constant, W/m^{2}K^{4} |

φ | Rim angle, ° |

## Subscripts and Superscripts

0 | at inlet |

ab | absorbed |

ap | aperture |

C | cold |

cond | conduction |

conv | convection |

ext | external |

f | fluid |

glob | global |

H | hot |

in | inlet |

int | internal |

ins | insulation |

loss | thermal losses |

n | element number |

net | useful production |

out | outlet |

outer | outer |

rad | radiation |

solar | solar energy |

total | total |

$\infty $ | environmental |

## Abbreviations

PTC | Parabolic trough concentrator |

## Appendix A. Thermal Properties of the Heat Transfer Fluid

**Figure A1.**Variation of density versus variation of Heat transfer fluid temperature for water, air, and oil as the heat transfer fluids.

**Figure A2.**Variation of thermal conductivity versus variation of Heat transfer fluid temperature for water, air, and oil as the heat transfer fluids.

**Figure A3.**Variation of heat capacity versus variation of Heat transfer fluid temperature for water, air, and oil as the heat transfer fluids.

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**Figure 3.**A schematic of the solar Parabolic Trough Concentrator (PTC) with rectangular cavity receiver.

**Figure 4.**A schematic of the cavity heat losses based on thermal resistance method: (

**a**) internal heat losses and (

**b**) external heat losses.

**Figure 5.**Investigated PTC system (

**a**) dimensions of designed parabola and (

**b**) built PTC system [38].

**Figure 6.**Comparison between the reported experimental results by Reference [38] and the results of the current research.

**Figure 7.**Influence of solar radiation on thermal performance of the system including: (

**a**) Variation of absorbed heat and (

**b**) Variation of energy performance with variation of solar beam irradiation for smooth and corrugated tube as the cavity tube.

**Figure 8.**Influence of inlet temperature on thermal performance of the system including: (

**a**) variation of absorbed heat and (

**b**) variation of energy performance with variation inlet temperature for smooth and corrugated tube as the cavity tube.

**Figure 9.**Influence of flow rate of solar working fluid on thermal performance of the system including variation of: (

**a**) absorbed heat and (

**b**) energy performance with variation volume flow rate for smooth and corrugated tube as the cavity tube.

**Figure 10.**Influence of solar radiation on temperature of the cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature with variation solar beam irradiation for smooth and corrugated tube as the cavity tube.

**Figure 11.**Influence of inlet temperature on temperature of the cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature with variation inlet temperature for smooth and corrugated tube as the cavity tube.

**Figure 12.**Influence of flow rate on temperature of the cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature with variation volume flow rate for smooth and corrugated tube as the cavity tube.

**Figure 13.**Variation of pressure drop with variation inlet temperature for smooth and corrugated tube as the cavity tube.

**Figure 14.**Variation of pressure drop with variation volume flow rate for smooth and corrugated tube as the cavity tube.

**Figure 15.**Influence of inlet temperature on thermal performance of the solar system including variation of: (

**a**) absorbed heat and (

**b**) energy performance versus variation of inlet temperature for different solar heat transfer fluids.

**Figure 16.**Influence of flow rate on thermal performance of the solar system including variation of: (

**a**) absorbed heat and (

**b**) energy performance with variation volume flow rate for different solar heat transfer fluids.

**Figure 17.**Influence of solar radiation on temperature of cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature versus solar beam irradiation for different solar heat transfer fluids.

**Figure 18.**Influence of inlet temperature on temperature of cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature versus variation of inlet temperature for different solar heat transfer fluids.

**Figure 19.**Influence of flow rate on temperature of cavity and working fluid including variation of: (

**a**) cavity surface temperature and (

**b**) outlet temperature with variation volume flow rate for different solar heat transfer fluids.

**Figure 20.**Variation of pressure drop with variation inlet temperature for different solar heat transfer fluids.

**Figure 21.**Variation of pressure drop with variation volume flow rate for different solar heat transfer fluids.

The optical error1 | 0–35 mrad |

The tracking error2 | 1° |

The sun-shape | pillbox |

The half-angle width | 4.65 mrad |

Number of ray intersections | 10,000 |

The reflectance of the cavity walls (black cobalt coating) | 15% |

Description | Dimension |
---|---|

Parabola length (L) | 2 m |

Parabola aperture (w) | 70 cm |

Focal distance (f) | 17.5 cm |

Aperture area (A_{a}) | 1.4 m^{2} |

Rim angle ($\phi $) | 90° |

Thickness (mean value) | 0.8 mm |

**Table 3.**Variation of the absorbed heat and energy performance versus different solar beam irradiation for different heat transfer fluids.

I_{beam} (W/m^{2}) | 600 | 650 | 700 | 750 | 800 | 850 | 900 | 950 | 1000 | 1050 | 1100 |
---|---|---|---|---|---|---|---|---|---|---|---|

Absorbed Heat (W) | |||||||||||

Oil | 312.43 | 339.21 | 365.99 | 392.76 | 419.53 | 446.29 | 473.06 | 499.82 | 526.57 | 553.33 | 580.07 |

Water | 414.90 | 450.48 | 486.07 | 521.65 | 557.24 | 592.82 | 628.41 | 663.99 | 699.57 | 735.15 | 770.74 |

Air | 8.99 | 9.79 | 10.60 | 11.42 | 12.23 | 13.05 | 13.87 | 14.69 | 15.52 | 16.35 | 17.18 |

Energy Performance | |||||||||||

Oil | 0.521 | 0.522 | 0.523 | 0.524 | 0.524 | 0.525 | 0.526 | 0.526 | 0.527 | 0.527 | 0.527 |

Water | 0.691 | 0.693 | 0.694 | 0.696 | 0.697 | 0.697 | 0.698 | 0.699 | 0.700 | 0.700 | 0.701 |

Air | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.016 | 0.016 | 0.016 |

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## Share and Cite

**MDPI and ACS Style**

Rafiei, A.; Loni, R.; Najafi, G.; Yusaf, T.
Study of PTC System with Rectangular Cavity Receiver with Different Receiver Tube Shapes Using Oil, Water and Air. *Energies* **2020**, *13*, 2114.
https://doi.org/10.3390/en13082114

**AMA Style**

Rafiei A, Loni R, Najafi G, Yusaf T.
Study of PTC System with Rectangular Cavity Receiver with Different Receiver Tube Shapes Using Oil, Water and Air. *Energies*. 2020; 13(8):2114.
https://doi.org/10.3390/en13082114

**Chicago/Turabian Style**

Rafiei, Alireza, Reyhaneh Loni, Gholamhassan Najafi, and Talal Yusaf.
2020. "Study of PTC System with Rectangular Cavity Receiver with Different Receiver Tube Shapes Using Oil, Water and Air" *Energies* 13, no. 8: 2114.
https://doi.org/10.3390/en13082114