# Analysis and Design of Fuel Cell Systems for Aviation

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## Abstract

**:**

## 1. Introduction

## 2. Model

^{®}(MathWorks, Natick, MA, USA) using the parameters given in Table 1.

## 3. Results and Discussion

#### 3.1. General Design Considerations

#### 3.2. Design for Passenger Aircraft

#### 3.3. Sensitivity Analysis for Future Aircraft

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CCL | Cathode catalyst layer |

EM | Electric motor |

FCS | Fuel cell system |

GDL | Gas diffusion layer |

MEA | Membrane electrode assembly |

PEMFC | Polymer electrolyte membrane fuel cell |

## List of Symbols

b | Tafel slope, V |

${c}_{\mathrm{h}}$ | oxygen concentration in the channel, mol cm${}^{-3}$ |

D | effective diffusion coefficient, cm${}^{2}$ s${}^{-1}$ |

${E}_{\mathrm{rq}}$ | required energy |

f | objective function |

$\Delta G$ | Gibbs free energy |

$\Delta H$ | reaction enthalpy |

${i}_{*}$ | volumetric exchange current density, A cm${}^{-3}$ |

j | local current density, A cm${}^{-2}$ |

${j}_{0}$ | cell current density, A cm${}^{-2}$ |

l | thickness, m |

m | mass, kg |

${P}_{\mathrm{rq}}$ | required power |

r | ratio, dimensionless |

${R}_{\mathsf{\Omega}}$ | ohmic resistance, $\mathsf{\Omega}$ |

${w}_{P}$ | weight parameter w.r.t power |

## Greek

$\eta $ | local overpotential, V |

${\eta}_{0}$ | cell overpotential, V |

${\rho}_{\mathrm{fc}}$ | specific power of the fuel cell, kW kg${}^{-1}$ |

${\varrho}_{\mathrm{tk}}$ | area-specific tank mass, kg m${}^{-2}$ |

${\sigma}_{\mathrm{t}}$ | proton conductivity in the catalyst, S m${}^{-1}$ |

$\upsilon $ | efficiency |

${\omega}_{{\mathrm{H}}_{2}}$ | specific energy of hydrogen, 33.3 kWh kg${}^{-1}$ |

## Subscripts and Superscripts

${}_{\mathrm{b}}$ | backing or gas diffusion layer |

${}_{\mathrm{c}}$ | converter |

${}_{\mathrm{fc}}$ | fuel cell |

${}_{\mathrm{m}}$ | membrane |

${}_{\mathrm{max}}$ | maximum |

${}_{\mathrm{oc}}$ | open circuit |

${}_{\mathrm{os}}$ | oversize |

${}_{\mathrm{rq}}$ | required |

${}_{\mathrm{s}}$ | storage |

${}_{\mathrm{t}}$ | cathode catalyst layer |

${}_{\mathrm{tk}}$ | tank |

## Appendix A. Mass of a Spherical Tank

## References

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**Figure 1.**Polarisation curve (blue) and power curve (red) of a plymer electrolyte membrane fuel cell. Dotted line marks the high current branch above the maximum power point.

**Figure 2.**Cell efficiency vs. normalized cell power. Dotted line marks the high current branch above the maximum power point.

**Figure 3.**Efficiency gain that is obtained from lowering the power as function of operating power. The dotted line marks the branch above the maximum power point. Analysis of 41 experimental polarization curves [23] is marked in grey: the dashed line marks the average and the grey solid line mark the 99% confidence interval.

**Figure 4.**Objective function of power vs. efficiency optimization for 4 different weights. Dotted: ${w}_{P}$ = 1, dash-dotted: ${w}_{P}$ = 0.37, dashed: ${w}_{P}$ = 0.18, solid ${w}_{P}$ = 0.

**Figure 5.**Mass of the fuel cell system and its components as function of working point current density for a reference flight mission with a power demand of ${P}_{\mathrm{rq}}=16.3$ MW and an energy demand of ${E}_{\mathrm{rq}}=63.7$ MWh, i.e., a medium haul flight [16]. Blue: total mass of the system; Red: mass of the fuel cell; Yellow: mass of the hydrogen fuel; Purple: mass of the empty tank; Green: mass of the tank system (tank+hydrogen). Dotted lines mark the branch above the maximum power point.

**Figure 6.**Fuel cell oversize for minimum fuel cell system weight as function of the ratio of tank-to-fuel cell mass. Red: Stationary tank design. Blue: Advanced tank design of Winnefeld et al. [16].

**Figure 7.**Ragone plot of current and future fuel cell systems for aviation. Yellow: current fuel cells with 1.6 kW/kg incl. periphery, current electric engines with 5.2 kW/kg and simple stationary tanks. Red: current fuel cells+periphery and electric engines with LH2 tanks optimized for medium-haul flight. Blue: future lightweight, high-power fuel cells+periphery with 8 kW/kg, future electric engines with 10 kW/kg and optimized LH2 tanks. Green: current system of jet engine (Airbus A320) and kerosene tanks. Dotted lines mark time constants of 1 h (top), 10 h (middle), and 100 h (bottom).

Parameter | Value | Reference |
---|---|---|

GDL thickness ${l}_{\mathrm{b}}$ | 250 $\mathsf{\mu}$m | [13,18] |

CCL thickness ${l}_{\mathrm{t}}$ | 10 $\mathsf{\mu}$m | [13,18] |

Membrane thickness ${l}_{\mathrm{m}}$ | 25 $\mathsf{\mu}$m | [13,18] |

oxygen concentration ${c}_{\mathrm{h}}$ (p = 1 bar) | 7.36 × 10${}^{-6}$ mol cm${}^{-3}$ | [13] |

Cell open-circuit potential ${V}_{\mathrm{oc}}$ | 1.145 V | [13,18] |

CCL proton conductivity $\sigma $ | 0.03 S m${}^{-1}$ | [13] |

Tafel slope b | 0.03 V | [13] |

exchange current density ${i}_{*}$ | 0.817 × 10${}^{-3}$ A cm${}^{-3}$ | [13] |

effective diffusion coefficient of GDL ${D}_{\mathrm{b}}$ | 0.0259 cm${}^{2}$ s${}^{-1}$ | [13] |

effective diffusion coefficient of CCL D | 1.36 × 10${}^{-4}$ cm${}^{2}$ s${}^{-1}$ | [13] |

required energy for flight mission, ${E}_{\mathrm{rq}}$ | 63.7 MWh | [16] |

required power of current aircraft, ${P}_{\mathrm{rq}}$ | 27.6 MW | [19] |

required power of future aircraft, ${P}_{\mathrm{rq}}$ | 16.3 MW | [19] |

area-specific tank mass, ${\varrho}_{\mathrm{tk}}$ | 75 kg m${}^{-2}$ | [20] |

specific power of fuel cell+periphery (currently), ${\rho}_{\mathrm{fc}}$ | 1.6 kW kg${}^{-1}$ | [21] |

specific power of fuel cell+periphery (future), ${\rho}_{\mathrm{fc}}$ | 8 kW kg${}^{-1}$ | estimate |

specific power of electric motor (currently), ${\rho}_{\mathrm{em}}$ | 5.2 kW kg${}^{-1}$ | [22] |

specific power of electric motor (future), ${\rho}_{\mathrm{em}}$ | 10 kW kg${}^{-1}$ | estimate |

**Table 2.**Comparison of fuel cell system weight of current and future aircraft technology employing current and future fuel cell and electric motor (EM) technology.

Aircraft Tech., P${}_{\mathbf{rq}}$ | Current FCS | Future FCS |
---|---|---|

1.6 kW/kg FC | 8 kW/kg FC | |

5.8 kW/kg EM | 10 kW/kg EM | |

current, 27.6 MW | 25,028 kg | 10,900 kg |

future, 16.3 MW | 16,758 kg | 8197 kg |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kadyk, T.; Winnefeld, C.; Hanke-Rauschenbach, R.; Krewer, U.
Analysis and Design of Fuel Cell Systems for Aviation. *Energies* **2018**, *11*, 375.
https://doi.org/10.3390/en11020375

**AMA Style**

Kadyk T, Winnefeld C, Hanke-Rauschenbach R, Krewer U.
Analysis and Design of Fuel Cell Systems for Aviation. *Energies*. 2018; 11(2):375.
https://doi.org/10.3390/en11020375

**Chicago/Turabian Style**

Kadyk, Thomas, Christopher Winnefeld, Richard Hanke-Rauschenbach, and Ulrike Krewer.
2018. "Analysis and Design of Fuel Cell Systems for Aviation" *Energies* 11, no. 2: 375.
https://doi.org/10.3390/en11020375