# Exergy Analysis of a Pilot Parabolic Solar Dish-Stirling System

^{*}

## Abstract

**:**

## 1. Introduction

^{2}year, with about 2800 solar hours in a year [2]. The Kerman pilot system is shown in Figure 1.

^{2}concentrator area. A new solar dish configuration was developed by Ahmed [10], in which, compared to a usual dish, the focal point was located much closer to the dish, which enabled the rim angle value to reach up to 90°. A mathematical model was presented to assess the thermal efficiency of the solar dish-Stirling engine [11].

## 2. Methodology

#### 2.1. Solar Radiation Calculation

#### 2.2. The Collector Model

#### 2.3. The Stirling Engine Model

#### 2.4. The Energy and Exergy Efficiency and Performance

## 3. Results and Discussion

^{2}in the middle of May [26]. The analytical model was validated by comparing the predicted power output with the experimental data of the two projects, and the relative errors between measured data and results obtained from the model were calculated (Table 2). Results revealed that the predicted power outputs were in close agreement with the measured data.

#### 3.1. Energy Efficiency and Exergy Efficiency of the Collector

#### 3.2. Total Energy Efficiency and Exergy Efficiency of the System

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

A | area (m^{2}) |

a_{0},a_{1} | constants of atmospheric transmittance equation for beam radiation |

C | concentration ratio |

c_{p} | specific heat at constant pressure (J/(kg·K)) |

c_{v} | specific heat at constant volume (J/(kg·K)) |

d | diameter (m) |

Ex | Exergy |

f | focal distance (m) |

G | beam solar irradiance (W/m^{2}) |

G_{on} | extraterrestrial radiation incident on the plane normal to the radiation on the nth day of the year (W/m^{2}) |

G_{sc} | solar constant; =1367 (W/m^{2}) |

Gr | Grashof number |

h | convective heat transfer coefficient (W/(m^{2}·K)) |

k | thermal conductivity (W/(m·K)); constant of atmospheric transmittance equation for beam radiation |

L | Length (m) |

N_{s} | number of screens in regenerator |

Nu | Nusselt number |

n | day number of the year |

P | power output (W) |

p | pressure (Pa) |

Pr | Prandtl number |

$\dot{\mathrm{Q}}$ | heat transfer rate (W) |

R | gas constant (J/(kg·K)) |

Δr | beam spread (m) |

v | wind speed (m/s) |

w | piston speed (m/s) |

w_{s} | sound speed (m/s) |

X | regenerative losses coefficient |

x | direction |

y | adjusting coefficient |

Greek symbols | |

α | absorptivity |

γ | specific heat ratio |

δ | declination, thickness (m) |

ε | emissivity |

ε_{v} | engine volume ratio |

η | efficiency |

η_{I} | energy efficiency |

η_{II} | exergy efficiency |

θ | incident angle |

θ_{z} | zenith angle |

σ | Stefan–Boltzmann constant (W/(m^{2}·K^{4})) |

τ | ratio of the gas extreme temperatures (T_{H}/T_{L}) |

τ_{b} | atmospheric transmittance |

υ | viscosity of the working gas (m^{2}/s) |

φ | latitude |

ψ_{rim} | rim angle |

ω | hour angle |

Subscripts | |

amb | ambient |

ap | aperture |

CC | Carnot Cycle |

cav | receiver cavity |

coll | collector |

conc | concentrator |

d | dish |

eff | effective |

g | gas |

gen | generator |

H | gas at the source |

in | input |

insul | insulation |

L | gas at the sink |

m | mean |

Δp | refers to pressure losses |

rec | receiver |

S | sun |

SE | Stirling Engine |

u | useful |

X | refers to regenerative losses |

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**Figure 6.**Energy losses of main parts of (

**a**) the Kerman pilot; (

**b**) EuroDish project as a percentage of total energy losses.

**Figure 7.**Exergy loss of the main parts of (

**a**) the Kerman pilot; (

**b**) EuroDish project as a percentage of total energy loss.

**Table 1.**Wind speed (m/s), ambient temperature (°C), and horizontal beam solar irradiance (W/m

^{2}) at the Kerman site recorded on 15 June.

Time (h) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |

Wind Speed | 6.4 | 4.4 | 4.1 | 6.1 | 6.4 | 8 | 9.5 | 7.8 | 7.6 | 6.3 | 6.9 |

Ambient Temperature | 31 | 31.8 | 33.1 | 34.2 | 35.1 | 36 | 35.5 | 35.7 | 35.8 | 35.7 | 34.5 |

Beam Solar Irradiance | 374.9 | 579.8 | 755.2 | 885.1 | 959.1 | 971.3 | 921 | 811.9 | 652.7 | 456.9 | 245.7 |

**Table 2.**Comparison between numerical results and measured power output of the Kerman project and EuroDish project.

Project | Power Output (kW) | Relative Error (%) | |
---|---|---|---|

Measured | Analytic | ||

EuroDish | 7.55 | 7.66 | 1.44 % |

Kerman Pilot | 0.60 | 0.629 | 4.61 % |

Energy Input (kW) | Energy Output (kW) | Energy Loss (kW) | Exergy Input (kW) | Exergy Output (kW) | Exergy Loss (kW) | Energy Efficiency | Exergy Efficiency | |
---|---|---|---|---|---|---|---|---|

Concentrator | 6.92 | 6.31 | 0.61 | 6.43 | 4.50 | 1.93 | 0.91 | 0.70 |

Receiver | 6.31 | 2.78 | 3.53 | 4.50 | 1.98 | 2.52 | 0.44 | 0.44 |

Stirling Engine | 2.78 | 0.63 | 2.15 | 1.98 | 0.63 | 1.35 | 0.23 | 0.32 |

Collector | 6.92 | 2.78 | 4.14 | 6.43 | 1.98 | 4.45 | 0.40 | 0.31 |

Overall | 6.92 | 0.63 | 6.29 | 6.43 | 0.63 | 5.80 | 0.091 | 0.098 |

Energy Input (kW) | Energy Output (kW) | Energy Loss (kW) | Exergy Input (kW) | Exergy Output (kW) | Exergy Loss (kW) | Energy Efficiency | Exergy Efficiency | |
---|---|---|---|---|---|---|---|---|

Concentrator | 46.39 | 40.50 | 5.89 | 43.14 | 29.57 | 13.57 | 0.87 | 0.69 |

Receiver | 40.50 | 25.16 | 15.34 | 29.57 | 18.37 | 11.20 | 0.62 | 0.62 |

Stirling Engine | 25.16 | 8.11 | 17.05 | 18.37 | 8.11 | 10.26 | 0.32 | 0.44 |

Collector | 46.39 | 25.16 | 21.23 | 43.14 | 18.37 | 24.77 | 0.54 | 0.43 |

Overall | 46.39 | 8.11 | 38.28 | 43.14 | 8.11 | 35.03 | 0.17 | 0.19 |

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Gholamalizadeh, E.; Chung, J.D.
Exergy Analysis of a Pilot Parabolic Solar Dish-Stirling System. *Entropy* **2017**, *19*, 509.
https://doi.org/10.3390/e19100509

**AMA Style**

Gholamalizadeh E, Chung JD.
Exergy Analysis of a Pilot Parabolic Solar Dish-Stirling System. *Entropy*. 2017; 19(10):509.
https://doi.org/10.3390/e19100509

**Chicago/Turabian Style**

Gholamalizadeh, Ehsan, and Jae Dong Chung.
2017. "Exergy Analysis of a Pilot Parabolic Solar Dish-Stirling System" *Entropy* 19, no. 10: 509.
https://doi.org/10.3390/e19100509