# Energy Harvesting Using Thermocouple and Compressed Air

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### Experimental Chamber

^{−6}.

_{v}= 2.6 was used.

_{o}is the input pressure, p

_{v}is the output pressure, T

_{o}is the input temperature, T

_{v}is the output temperature, v

_{o}is the input velocity, v

_{v}is the output velocity, v

_{kr}is the critical velocity, ρ

_{o}is the input density, ρ

_{v}is the output density, M is the Mach number, $\varkappa $ is the gas constant = 1.4, A is the computational cross-section and A

_{kr}is the critical cross-section.

_{v}= 2.6 behind the nozzle, a ratio between p

_{v}and p

_{o}needs to be 1:4 according to Equation (4). Considering the output pressure behind the nozzle will be 1 atm, the chamber before the nozzle should be pressurized to 4 atm or more precisely 371,971 Pa [3].

_{p}is heat capacity at constant pressure, T is temperature of the gas flow.

_{z}denotes the decelerated state where the velocity is zero, S

_{kr}is the critical state where the velocity reaches V

_{kr}at the narrowest point in the nozzle, and S

_{m}denotes the limit state where the velocity reaches a theoretical maximum that cannot occur in practice. The temperature at that point would reach 0 K.

_{kr}and S

_{m}.

## 3. Results

_{o}= 371,971 Pa and p

_{v}= 101,325 Pa, the relationships 1 to 6 mentioned above give us following results as shown in Table 1:

_{o}= 347.2 m·s

^{−1}and is determined from relationship 8:

_{A}= 287.039 J·kg

^{−1}K

^{−1}is the gas constant for air and T

_{o}= 300 K [13], $\varkappa $ is the Poisson’s ratio = 1.4.

_{v}/v

_{o}= 0.6521, which gives the value of v

_{v}= 588.6 m·s

^{−1}when using relationships mentioned above.

_{o}= 4.32 kg·m

^{−3}can be calculated from ideal gas state Equation (9):

_{v}/p

_{o}= 0.0617. Then it is possible to determine the value of output density ρ

_{v}= 0.51 kg·m

^{−3}.

_{o}= 300 K allows calculation of the temperature in the output T

_{v}= 127.56 K.

_{v}, ρ

_{o}, ρ

_{v}, and T

_{v}were used as control values for results obtained using the Ansys Fluent system as shown in Table 2:

^{−1}the head of the cylindrical probe reaches the stagnation temperature T

_{stg}, which is higher than the static temperature T without any obstacle which we need for maximum cooling of the thermocouple probe. The following relationship applies:

_{v}= 2. This means the stagnation temperature is T

_{stg}= 17 °C (290 K), which can be seen in Figure 18. The stagnation temperature is 17 °C because the following temperature drop is caused by the cooled probe behind the shockwave as seen in Figure 17a.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Quantity | Symbol | Unit |

Mach Number | M | - |

Output Mach Number | M_{v} | - |

Input Velocity | v_{o} | m·s^{−1} |

Output Velocity | v_{v} | m·s^{−1} |

Critical Velocity | v_{kr} | m·s^{−1} |

Input Pressure | p_{o} | Pa |

Output Pressure | p_{v} | Pa |

Input Density | ρ_{o} | kg·m^{−3} |

Output Density | ρ_{v} | kg·m^{−3} |

Location of The Mach Disk | Z_{m} | mm |

Computational Cross-Section | A_{kr} | m^{2} |

Input Temperature | T_{o} | K |

Output Temperature | T_{v} | K |

Static Temperature | T | K |

Stagnation Temperature | T_{stg} | K |

Poisson’s Ratio | $\varkappa $ | - |

Universal Gas Constant | R | J·K^{−1}·mol^{−1} |

Cone Angle | c | ° |

Deflection Angle | a | ° |

Ray Angle | θ | ° |

Shock Angle | s | ° |

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**Figure 12.**Taylor–McCall theory [21].

**Figure 13.**Dependence of Mach number on a probe cone angle [4].

**Figure 19.**Shockwave forming before the probe head: (

**a**) conical shockwave, and (

**b**) perpendicular/detached shockwave.

Mach Number | Output Velocity/Critical Velocity | Output Velocity/Input Velocity | Output Temperature/Input Temperature | Output Pressure/Input Pressure | Output Density/Input Density | Output Density/Critical Density |
---|---|---|---|---|---|---|

M_{v} | v_{v}/v_{kr} | v_{v}/v_{o} | T_{v}/T_{o} | p_{v}/p_{o} | ρ_{v}/ρ_{o} | ρ_{v}/ρ_{kr} |

2.6 | 1.8571 | 0.6521 | 0.4252 | 0.05 | 0.1179 | 0.3453 |

Theoretical Value | Ansys Fluent Value | |
---|---|---|

Mach number (-) | 2.6 | 2.65 |

Density (kg·m^{−3}) | 0.5 | 0.49 |

Velocity (m·s^{−1}) | 598.6 | 600 |

Temperature (°C) | −146.6 | −148 |

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**MDPI and ACS Style**

Bayer, R.; Maxa, J.; Šabacká, P. Energy Harvesting Using Thermocouple and Compressed Air. *Sensors* **2021**, *21*, 6031.
https://doi.org/10.3390/s21186031

**AMA Style**

Bayer R, Maxa J, Šabacká P. Energy Harvesting Using Thermocouple and Compressed Air. *Sensors*. 2021; 21(18):6031.
https://doi.org/10.3390/s21186031

**Chicago/Turabian Style**

Bayer, Robert, Jiří Maxa, and Pavla Šabacká. 2021. "Energy Harvesting Using Thermocouple and Compressed Air" *Sensors* 21, no. 18: 6031.
https://doi.org/10.3390/s21186031