# Study of the Radiation Flux Distribution in a Parabolic Dish Concentrator

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

^{2}and the lowest value of 4.5 MW/m

^{2}.

## 1. Introduction

## 2. Methodology

#### 2.1. Experimental Set

#### 2.2. Ray Tracing Simulation

^{2}, a standard sun shape, and a circumsolar ratio value of 0.02, which were determined experimentally by image analysis of the actual sun (Figure 5). A ray stability study is essential to eliminate the effect of the number of rays for the numerical resolution [32]. Therefore, variation of the maximum power regarding the number of rays was analyzed. The mesh size for the experimental images was 500 × 500, and for simulated images was set at 250 × 250.

#### 2.3. Global Optical Error of the System

#### 2.4. Generation of Effective Volumes

## 3. Results and Discussion

#### 3.1. Global Optical Error of the System

^{2}.

#### 3.2. Effective Volumes

^{2}, theoretical effective volumes present a length in the z-axis of ~2 cm and 1 cm in the x and y axes, while in experimental ones, lengths of less than 2 cm in the z-axis and 1 cm in the x and y-axes were observed.

^{2}with 7.6% and the largest at 4 MW/m

^{2}on the xz plane with 174%.

#### 3.3. Discussion

## 4. Conclusions

^{2}, and the lowest was 4.5 MW/m

^{2}. Higher flux theoretical effective volumes presented an oval shape; by decreasing the flux value, they are transformed into an ellipsoid. Higher flux experimental effective volumes also presented oval shapes by decreasing the flux value, a twist in the extreme sides was observed. This twist could be due to mechanical efforts, thermal efforts, or wind direction and speed; however, determining the origin is not important for this work because the determination of the global optical error of the system is done in the focal zone—high-intensity region—whereas this error might not be revealed at low-intensity regions.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Parabolic Dish Concentrating Solar System located at the Solar Platform of Hermosillo in Hermosillo, Sonora, Mexico.

**Figure 2.**(

**a**) The 8 bits CCD camera used with a photographic lens and a linear filter, (

**b**) front part of the RLFP (after the experiments) with dimensions of 0.25 × 0.15 m

^{2}, and (

**c**) back of the RLFP where inlets and outlets for coolant flow are shown.

**Figure 8.**Real concentrated solar radiation spot in the focal zone: (

**a**) Gray Scale and (

**b**) Real flux values (MW/m

^{2}).

**Figure 9.**Qualitative matching of the solar radiation distribution profiles (theoretical and experimental) when x = 0, y = [−3.3], varying the global optical error from 0 to 4 mrad with increments of 1 mrad.

**Figure 10.**Quantitative comparison of solar radiation distribution profiles varying the error from 2.0 to 3.0 mrad.

**Figure 11.**Experimental effective volumes of different flux values: (

**a**) 10, (

**b**) 9, (

**c**) 8, (

**d**) 7, (

**e**) 6, (

**f**) 5, (

**g**) 4.5, and (

**h**) 4 MW/m

^{2}.

**Figure 12.**Theoretical effective volumes of different flux values: (

**a**) 10, (

**b**) 9, (

**c**) 8, (

**d**) 7, (

**e**) 6, (

**f**) 5, (

**g**) 4.5, and (

**h**) 4 MW/m

^{2}.

Parabolic Dish Concentrator | RLFP | |
---|---|---|

Measurements | 1.65 × 1.65 m^{2} | 0.15 × 0.25 m^{2} |

Focal point | 1.5 m | - |

Reflectivity | 0.9 ^{1} | 0 |

Global optical error of the system | TBD | - |

Distance from the vertex | - | 1.5 m |

^{1}This value was provided by the technical data sheet of the parabolic dish concentrator.

Numbers of Rays (Millions) | Maximum Power (W) | Uncertainty (%) |
---|---|---|

0.01 | 3.36 × 10^{7} | 48.6 |

0.05 | 1.73 × 10^{7} | 37.5 |

1 | 1.08 × 10^{7} | 6.5 |

5 | 1.01 × 10^{7} | 1.5 |

10 | 9.94 × 10^{6} | −0.5 |

15 | 9.99 × 10^{6} | 0.2 |

20 | 9.96 × 10^{6} | 2.2 |

25 | 9.75 × 10^{6} | −1.1 |

30 | 9.85 × 10^{6} | 1.1 |

35 | 9.75 × 10^{6} | 0.5 |

40 | 9.70 × 10^{6} | −0.5 |

45 | 9.75 × 10^{6} |

Flux | XY Plane | XZ Plane | YZ Plane | ||||||
---|---|---|---|---|---|---|---|---|---|

(MW/m^{2}) | Real (cm ^{2}) | Theoretical (cm^{2)} | Difference (%) | Real (cm ^{2}) | Theoretical (cm^{2)} | Difference (%) | Real (cm ^{2}) | Theoretical (cm^{2)} | Difference (%) |

10 | 0.21 | 0.28 | 7.6 | 0.31 | 0.50 | 18.5 | 0.32 | 0.55 | 22.7 |

9 | 0.41 | 0.53 | 12.2 | 0.90 | 0.28 | 28.4 | 0.64 | 0.94 | 29.8 |

8 | 0.64 | 0.79 | 14.3 | 0.95 | 1.43 | 48.6 | 0.99 | 1.42 | 43.5 |

7 | 0.89 | 1.13 | 24.9 | 1.30 | 1.89 | 58.6 | 1.33 | 2.21 | 88.3 |

6 | 1.17 | 1.44 | 27.0 | 1.80 | 2.68 | 88.1 | 1.90 | 2.71 | 80.7 |

4 | 1.88 | 2.40 | 52.1 | 3.40 | 5.07 | 167.0 | 3.37 | 5.11 | 174.0 |

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**MDPI and ACS Style**

Cisneros-Cárdenas, N.A.; Cabanillas-López, R.; Pérez-Enciso, R.; Martínez-Rodríguez, G.; García-Gutiérrez, R.; Pérez-Rábago, C.; Calleja-Valdez, R.; Riveros-Rosas, D. Study of the Radiation Flux Distribution in a Parabolic Dish Concentrator. *Energies* **2021**, *14*, 7053.
https://doi.org/10.3390/en14217053

**AMA Style**

Cisneros-Cárdenas NA, Cabanillas-López R, Pérez-Enciso R, Martínez-Rodríguez G, García-Gutiérrez R, Pérez-Rábago C, Calleja-Valdez R, Riveros-Rosas D. Study of the Radiation Flux Distribution in a Parabolic Dish Concentrator. *Energies*. 2021; 14(21):7053.
https://doi.org/10.3390/en14217053

**Chicago/Turabian Style**

Cisneros-Cárdenas, Nidia Aracely, Rafael Cabanillas-López, Ricardo Pérez-Enciso, Guillermo Martínez-Rodríguez, Rafael García-Gutiérrez, Carlos Pérez-Rábago, Ramiro Calleja-Valdez, and David Riveros-Rosas. 2021. "Study of the Radiation Flux Distribution in a Parabolic Dish Concentrator" *Energies* 14, no. 21: 7053.
https://doi.org/10.3390/en14217053