# Thermodynamic Analysis of the Dryout Limit of Oscillating Heat Pipes

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## Abstract

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## 1. Introduction

- Channel size
- Vapor inertia limit
- Heat flux limit
- Sonic limit
- Viscous limit

Name | Equation | Normalized | d (mm) |
---|---|---|---|

Khandekar and Groll [11] | $E\ddot{o}\approx \frac{{d}^{2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}({\rho}_{l}-{\rho}_{v})}{\sigma}\approx 4$ | ${d}_{max}=2\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}La$ | 3.44 |

Triplett et al. [10] | ${d}_{max}=\sqrt{\frac{\sigma}{g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}({\rho}_{l}-{\rho}_{v})}}$ | ${d}_{max}=La$ | 1.72 |

Brauner and Maron [12] | ${d}_{max}=\sqrt{6}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\sqrt{\frac{\sigma}{g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}({\rho}_{l}-{\rho}_{v})}}$ | ${d}_{max}=\sqrt{6}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}La$ | 4.21 |

Xu and Zhang [20] | ${d}_{max}=1.83\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\sqrt{\frac{\sigma}{g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}({\rho}_{l}-{\rho}_{v})}}$ | ${d}_{max}=1.83\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}La$ | 3.14 |

Taft and Williams [19] | ${r}_{max}=\sqrt{\frac{\sigma \phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}Bo}{g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}({\rho}_{l}-{\rho}_{v})}}$ | ${d}_{max}=1.84\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}La$ | 3.16 |

## 2. Experimental Setup

#### Results of the Measurement

## 3. Thermodynamic Considerations on the Working Principle of OHPs

- ${\nu}_{OHP}<{\nu}_{crit}$: the entire fluid can become liquid
- ${\nu}_{OHP}={\nu}_{crit}$: there are always two-phases, because the isochoric is equal to the vapor pressure curve
- ${\nu}_{OHP}>{\nu}_{crit}$ : the entire fluid can become gaseous

## 4. Model to Determine the Dryout Threshold

#### Determination of the Dryout Threshold

## 5. Optimal Filling Ratio

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PHP | pulsating heat pipe |

OHP | oscillating heat pipe |

GaN | gallium nitride |

SiC | silicon carbide |

FR | filling ratio |

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**Figure 1.**The change of the threshold value (maximum diameter) as a function of temperature for acetone. The OHP can only operate if the fluid inside the channel consist of altering liquid and vapor parts. Therefore the diameter must be smaller than the threshold value.

**Figure 2.**Representation of the OHP with 26 meandering channels. The thermocouples for the temperature measurement are placed in the middle of the condenser and the heater. On the right side is the heater (red) with an area of 50 $\mathrm{m}\mathrm{m}$× 25 $\mathrm{m}\mathrm{m}$. The condenser (blue) is on the left side and has an area of 50 $\mathrm{m}\mathrm{m}$× 10 $\mathrm{m}\mathrm{m}$.

**Figure 3.**Experimental setup to determine the dryout limit, consisting of an OHP module with evaporator, adiabatic and condenser section. The heat input is increased stepwise from 15 W to 90 W to observe the dryout threshold.

**Figure 4.**Results for OHP filled with 53% acetone. Temperature of the heater vs. increasing heat input from 15 W to 90 W. The OHP dries out at 90 W and 89.6 ${}^{\circ}\mathrm{C}$.

**Figure 5.**Thermal resistance of the OHP vs. heating input from 15 W to 90 W, filled with 53% acetone. At the dryout limit the thermal resistance is rising from 0.41 (K/W) at 75 W to 0.9 (K/W) at 90 W.

**Figure 6.**Characteristic PVT-Diagram of a pure fluid modified from [28].

**Figure 8.**Vapor quality vs. temperature for different filling ratios for acetone; For a Filling Ratio (FR) of 10% the whole fluid becomes vapor (x = 1) at 203 ${}^{\circ}\mathrm{C}$. FR 34.7% ends in the critical point and for a FR of 50% the whole fluid becomes liquid (x = 0) at 230 ${}^{\circ}\mathrm{C}$.

**Figure 9.**Measurement from Shi and Pan [23]: Thermal resistance vs. heating input charged with acetone. For the FR of 35%, the OHP dries out between 40 ${}^{\circ}\mathrm{C}$ and 75 ${}^{\circ}\mathrm{C}$. When the OHP is charged with 50%, the OHP dries out between 60 ${}^{\circ}\mathrm{C}$ and 95 ${}^{\circ}\mathrm{C}$. For FR 70% and FR 85%, the dryout limit is not reached.

**Figure 11.**Specific volume vs. dryout temperature for acetone as given by our proposed compact theory. Due to the expected temperature of the heater, the minimum filling mass of the OHP is given to avoid a dryout.

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**MDPI and ACS Style**

Schwarz, F.; Danov, V.; Lodermeyer, A.; Hensler, A.; Becker, S.
Thermodynamic Analysis of the Dryout Limit of Oscillating Heat Pipes. *Energies* **2020**, *13*, 6346.
https://doi.org/10.3390/en13236346

**AMA Style**

Schwarz F, Danov V, Lodermeyer A, Hensler A, Becker S.
Thermodynamic Analysis of the Dryout Limit of Oscillating Heat Pipes. *Energies*. 2020; 13(23):6346.
https://doi.org/10.3390/en13236346

**Chicago/Turabian Style**

Schwarz, Florian, Vladimir Danov, Alexander Lodermeyer, Alexander Hensler, and Stefan Becker.
2020. "Thermodynamic Analysis of the Dryout Limit of Oscillating Heat Pipes" *Energies* 13, no. 23: 6346.
https://doi.org/10.3390/en13236346