# Assessment of Aircraft Surface Heat Exchanger Potential

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Aircraft Correlations

#### 2.1. Aircraft Component Geometries

- Fuselage
- Wing
- Nacelles
- Horizontal tail
- Vertical tail

#### 2.2. Surface Area Correlations

- Maximum Take-Off Weight ($MTOW$)
- Maximum number of seats (${n}_{max}$)
- Maximum payload ($MPL$)
- Design range (${R}_{des}$)

#### 2.3. Propulsive Power

## 3. Surface Heat Transfer

#### 3.1. Modeling

#### 3.2. Sensitivities

#### 3.2.1. Transition Location

#### 3.2.2. Wing Aspect Ratio

- In general, ${\alpha}_{x}$ decreases along x because of the increasing thickness of the thermal boundary layer (${\delta}_{T}$). Therefore, higher $AR$ favours heat transfer because for the same area, the average chord length is lower (cf. Figure 5 bottom graphs).
- The front section of the wing is laminar, which results in small ${\alpha}_{x}$. A higher $AR$ increases the span and, thus, the laminar portion of the plate’s total area (cf. Figure 5 top two graphs). The ${x}_{c}$ depends on $Ma$. For low $Ma$ the transition occurs further downstream, which means that this second effect contributes more.

#### 3.2.3. Wing Taper Ratio

#### 3.2.4. Fuselage Slenderness Ratio

#### 3.3. Drag

- Transition delay of initially laminar flow
- Drag alteration of fully turbulent flow

- Heating/cooling of the whole wetted surface area
- Strategic heating/cooling of a part of the wetted surface area

## 4. Surface Cooling Potential

#### 4.1. Area Reduction Assumptions

#### 4.2. Cooling Potential for Typical Operating Points

#### 4.3. Hot Day Take-Off Performance

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SRIA | Strategic Research and Innovation Agenda |

TMS | Thermal Management System |

ISA | International Standard Atmosphere |

TO | Take-off |

HTO | Hot Day Take-off |

CL | Climb |

CR | Cruise |

ACOC | Air Cooled Oil Cooler |

SACOC | Surface Air Cooled Oil Cooler |

APU | Auxilliary Power Unit |

MTOW | Maximum Take-off Weight |

MPL | Maximum Payload |

Roman Symbols | |

A | Area |

$dT$ | Temperature deviation |

T | Temperature |

$alt$ | Altitude |

$Ma$ | Mach number |

Q | Heat rate |

n | Number |

R | Range |

${r}^{2}$ | Coefficient of determination |

H | Degree of Hybrdization |

P | Power |

F | Thrust |

v | Velocity |

$Nu$ | Nusselt Number |

$Re$ | Reynolds Number |

$AR$ | Aspect Ratio |

l | Length |

d | Diameter |

x | Coordinate in flow direction |

c | Coefficient |

D | Drag Force |

$TR$ | Temperature Ratio |

${C}_{Q}$ | Ratio of Heat Rates |

Greek Symbols | |

$\sigma $ | Standard deviation |

$\delta $ | Boundary layer thickness |

$\Delta $ | Difference |

$\eta $ | Efficiency |

$\alpha $ | Heat transfer coefficient |

$\lambda $ | Wing taper ratio |

$\mathsf{\Lambda}$ | Slenderness ratio |

$\rho $ | Density |

$\mu $ | Dynamic Viscosity |

Subscripts | |

$wet$ | wetted |

$rq$ | required |

$exp$ | exposed |

$sim$ | simplified |

$act$ | actual |

$max$ | maximum |

$des$ | design |

$tot$ | total |

$av$ | available |

$trans$ | transmission |

$ec$ | electric |

$rad$ | radiation |

$surf$ | surface |

c | critical |

$min$ | minimum |

f | friction |

h | heated |

u | unheated |

$amb$ | ambient |

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**Figure 6.**Theoretical impact of wall heating/cooling on a smooth flat plate turbulent boundary layer density, skin friction coefficient, skin friction drag force and boundary layer $99\%$ thickness compared to an unheated wall. Valid for $R{e}_{x}={10}^{6}-{10}^{8}$.

**Figure 7.**${Q}_{av}$ in multiple operating points for aircraft equipped with surface heat exchangers.

**Figure 8.**Comparison of Q

_{av}and Q

_{rq}for hybrid electric aircraft in hot day take-off conditions. (

**a**) Ratio of Q

_{av}to Q

_{rq}for different T

_{surf}. (

**b**) Required T

_{surf}to achieve C

_{Q}= 1.

Component | ${\mathit{A}}_{\mathit{sim}}\left({\mathbf{m}}^{2}\right)$ | ${\mathit{A}}_{\mathit{act}}\left({\mathbf{m}}^{2}\right)$ | ${\mathbf{\Delta}}_{\mathit{A},\mathit{wet}}(\%)$ |
---|---|---|---|

Fuselage | 478.0 | 412.9 | +15.8 |

Wing | 202.4 | 208.7 | −3.0 |

Nacelles | 55.8 | 52.4 | +6.4 |

Horizontal tail | 48.4 | 49.6 | −2.4 |

Vertical tail | 42.2 | 43.3 | −2.7 |

Total | 826.8 | 766.9 | 7.8 |

x | a | c | ${\mathit{r}}^{2}$ |
---|---|---|---|

$MTOW$ | 0.748 | −0.689 | 0.986 |

${n}_{max}$ | 0.940 | 0.887 | 0.963 |

$MPL$ | 0.855 | −0.668 | 0.965 |

${R}_{des}$ | 0.995 | −0.417 | 0.859 |

Component | ${\mathit{A}}_{\mathit{wet},\mathit{i}}/{\mathit{A}}_{\mathit{wet},\mathit{tot}}(\%)$ | $\mathit{\sigma}(\%)$ |
---|---|---|

Fuselage | 49 | 3.80 |

Wing | 31 | 3.55 |

Nacelles | 7 | 1.49 |

Horizontal Tail | 8 | 1.21 |

Vertical Tail | 5 | 0.83 |

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

${A}_{exp}$ | 200 m${}^{2}$ |

$AR$ | 12 |

$\lambda $ | $0.29$ |

$R{e}_{x,c}$ | $5\times {10}^{5}$ |

${T}_{surf}$ | 320 K |

Opearting Point | $\mathit{Ma}$ (-) | $\mathit{alt}$ (m) | ${\mathit{dT}}_{\mathit{ISA}}$ (K) |
---|---|---|---|

TO | $0.2$ | 0 | 0 |

HTO | $0.2$ | 0 | $+20$ |

CL | $0.5$ | 5000 | 0 |

CR | $0.8$ | 10,000 | 0 |

${\eta}_{trans}$ | $0.5$ |

${\eta}_{ec}$ | $0.9$ |

${H}_{P}$ | $1.0$ |

$M{a}_{TO}$ | $0.2$ |

© 2019 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**

Kellermann, H.; Habermann, A.L.; Hornung, M.
Assessment of Aircraft Surface Heat Exchanger Potential. *Aerospace* **2020**, *7*, 1.
https://doi.org/10.3390/aerospace7010001

**AMA Style**

Kellermann H, Habermann AL, Hornung M.
Assessment of Aircraft Surface Heat Exchanger Potential. *Aerospace*. 2020; 7(1):1.
https://doi.org/10.3390/aerospace7010001

**Chicago/Turabian Style**

Kellermann, Hagen, Anaïs Luisa Habermann, and Mirko Hornung.
2020. "Assessment of Aircraft Surface Heat Exchanger Potential" *Aerospace* 7, no. 1: 1.
https://doi.org/10.3390/aerospace7010001