# Design and Optimization of Ram Air–Based Thermal Management Systems for Hybrid-Electric Aircraft

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## Abstract

**:**

## 1. Introduction

_{2}emissions by the year 2050 set by the European Commission’s Strategic Research and Innovation Agenda [1]. Thermal management is one of the key challenges for the successful realization of such powertrains [2].

## 2. Models and Methods

- Coldplates to receive heat from the electric components and transfer it to the coolant.
- A compact HEX to reject the collected heat to ambiance.
- A diffuser to reduce cooling air speed and thereby the cold-side pressure loss of the compact HEX.
- Optionally, a puller fan to increase cooling air flow.
- A nozzle to recover some of the momentum of the cooling air and thereby reduce drag.
- Pipes to transfer the coolant.
- A pump to recover the pressure loss of the coolant.

#### 2.1. Coldplates

#### 2.2. Compact Heat Exchanger

- Rectangular microchannels.
- Offset-strip fins.
- Louvered fins.

#### 2.3. Diffuser, Nozzle, and Pipes

#### 2.4. Pump and Fan

#### 2.5. Aircraft Fuel Burn Sensitivities

_{WTP}is the shaft power of the WTP and P

_{MP}is the shaft power of the turboprop engine’s main propeller (MP). The design power of the electric system is determined by ${S}_{P}$ and ${P}_{MP}$ at the top of climb (TOC) of the aircraft design mission. This electric power remains constant unless the power of the gas turbine is lower than its TOC power of the design mission. In this case, ${P}_{WTP}$ is lowered accordingly to match the desired ${S}_{P}$. Further details about the propulsion system and aircraft are provided in [26]. The aircraft investigated in [26] and this study is visualized in Figure 4.

_{P}values (10%, 20%, and 30%). Regarding the additional mass of a TMS (${m}_{TMS}$), the operating empty mass (OEM) was gradually increased to include an assumed ${m}_{TMS}$ of up to 1000 kg. In the same manner, the wing profile drag was increased to include an assumed TMS drag (${D}_{TMS}$) of up to 1000 N since an integration into the wing was found to be reasonable. Consequently, every combination of ${m}_{TMS}$ and ${D}_{TMS}$ represents a new aircraft design. The resulting aircraft FB sensitivities for the three S

_{P}variations are similar in their relative FB changes (ΔFB values) to the FB of the respective baseline aircraft design. An exemplary FB sensitivity is presented in Figure 5.

_{P}= 30%, Figure 5 shows an increase in ΔFB of approximately 1.5% for a m

_{TMS}increment of 1000 kg and approximately 3.6% if D

_{TMS}is increased by 1000 N. These FB gradients of Δm

_{TMS}and ΔD

_{TMS}are almost independent of each other, which leads to a sensitivity plane with only minimal curvature.

## 3. System Sensitivity Analysis

_{P}= 30% is used for the sensitivity analysis. The trends shown in this section are also valid for the other ${S}_{P}$ values. The heat loads of the design and the off-design point are shown in Figure 6.

#### 3.1. One-Dimensional Sensitivities

#### 3.2. Multi-Dimensional Sensitivities

#### 3.3. Heat Exchanger Size

## 4. Design and Off-Design Optimization for the Application Case

#### 4.1. Design Point Optimization

#### 4.2. Off-Design Point Optimization

#### 4.3. Multi-Point Optimization

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HDTO | Hot-day takeoff | |

HEA | Hybrid-electric aircraft | |

HEX | Heat exchanger | |

ISA | International standard atmosphere | |

MP | Main propeller | |

NASA | National Aeronautics and Space Administration | |

OEM | Operating empty mass | |

PCHE | Printed circuit heat exchanger | |

PFHE | Plate fin heat exchanger | |

TMS | Thermal management system | |

TOC | Top of climb | |

VTOL | Vertical takeoff and landing | |

WTP | Wingtip propeller | |

Roman Symbols | ||

A | Area | m^{2} |

${A}_{R}$ | Diffuser area ratio | - |

$\overline{{A}_{R}}$ | Corrected diffuser area ratio | - |

b | Heat exchanger plate space | m |

B | Diffuser inlet blockage | - |

${c}_{p}$ | Specific heat capacity at constant pressure | $\mathrm{J}/\left(\mathrm{k}\mathrm{g}\mathrm{K}\right)$ |

${c}_{p}^{*}$ | Ideal diffuser pressure recovery factor | - |

${c}_{v}$ | Specific heat capacity at constant volume | $\mathrm{J}/\left(\mathrm{k}\mathrm{g}\mathrm{K}\right)$ |

C | Absolute heat capacity | W/K |

${C}_{R}$ | Heat capacity ratio (${C}_{min}/{C}_{max}$) | - |

${C}_{R}^{*}$ | Side-specific heat capacity ratio (${C}_{h}/{C}_{c}$) | - |

$cmv$ | Core mass velocity | kg/(m^{2}s) |

${d}_{H}$ | Hydraulic diameter | m |

D | Drag | N |

f | Fanning friction factor | - |

$FB$ | Fuel burn | $\mathrm{k}\mathrm{g}$ |

g | Diffuser pressure recovery geometry factor | - |

j | Colburn factor | - |

${K}_{bt}$ | Bend loss coefficient | - |

${K}_{c}$ | Inlet loss coefficient | - |

${K}_{e}$ | Outlet loss coefficient | - |

${K}_{loss}$ | Nozzle pressure loss coefficient | - |

${K}_{spill}$ | Spillage coefficient | - |

L | Length | m |

m | Mass | kg |

Ma | Mach number | - |

${n}_{p}$ | Number of passes | - |

$ntu$ | Number of transfer units on one side | - |

$NTU$ | Number of transfer units | - |

p | Pressure | Pa |

P | Power | W |

$Pr$ | Prandtl number | - |

q | Area-specific heat flow rate | W/m^{2} |

Q | Heat flow rate | W |

${r}_{th}$ | Thermal insulance | m^{2}K/W |

${R}_{th}$ | Thermal resistance | $\mathrm{K}/\mathrm{W}$ |

$Re$ | Reynolds number | - |

${S}_{P}$ | Power split | % |

t | Channel width | m |

T | Temperature | K |

U | Overall heat transfer coefficient | W/(m^{2}K) |

v | Velocity | m/s |

V | Volume | m^{3} |

w | Mass flow rate | $\mathrm{k}\mathrm{g}/\mathrm{s}$ |

Greek Symbols | ||

α | Heat transfer coefficient | W/(m^{2}K) |

δ | Fin thickness | m |

Δ | Difference | - |

ϵ | Heat exchanger effectiveness | - |

η^{o} | Overall fin efficiency | - |

Φ | Aspect ratio | - |

Π | Pressure ratio | - |

ρ | Density | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ |

${\rho}_{A}$ | Area density | kg/m^{2} |

σ | Heat exchanger ratio of free flow to frontal area | - |

θ | Diffuser opening angle | deg |

Subscripts | ||

c | Cold | |

cond | Conductive | |

conv | Convective | |

corr | Corrected | |

cp | Coldplate | |

cs | Cross section | |

des | Design | |

f | Finned | |

h | Hot | |

i | Inlet | |

m | Mean | |

o | Outlet | |

od | Off-design | |

s | Static | |

spill | Spillage | |

tot | Total |

## Appendix A. Coldplate Model

#### Appendix A.1. Model Description

Parameter | Symbol | Unit |
---|---|---|

Inputs | ||

Inlet pressure | ${p}_{i,des}$ | $\mathrm{Pa}$ |

Inlet temperature | ${T}_{i,des}$ | K |

Effectiveness | ${\u03f5}_{des}$ | - |

Heat load | ${Q}_{des}$ | $\mathrm{W}$ |

Coldplate surface temperature | ${T}_{cp,des}$ | $\mathrm{K}$ |

Thermal insulance | ${r}_{th,des}$ | m^{2}K/W |

Area density | ${\rho}_{A}$ | kg/m^{2} |

Pressure drop | $\Delta {p}_{des}$ | $\mathrm{Pa}$ |

Outputs | ||

Design mass flow | ${w}_{des}$ | $\mathrm{k}\mathrm{g}/\mathrm{s}$ |

Outlet pressure | ${p}_{o,des}$ | $\mathrm{Pa}$ |

Outlet temperature | ${T}_{o,des}$ | $\mathrm{K}$ |

Area-specific heat load | ${q}_{des}$ | W/m^{2} |

Coldplate area | ${A}_{cp}$ | m^{2} |

Dry mass | ${m}_{dry}$ | $\mathrm{k}\mathrm{g}$ |

Number of transfer units | $NT{U}_{des}$ | - |

U-A product | ${\left(UA\right)}_{des}$ | $\mathrm{W}/\mathrm{K}$ |

Parameter | Symbol | Unit |
---|---|---|

Inputs | ||

Inlet pressure | ${p}_{i}$ | $\mathrm{Pa}$ |

Inlet temperature | ${T}_{i}$ | $\mathrm{K}$ |

Outlet temperature | ${T}_{o}$ | $\mathrm{K}$ |

Heat load | ${Q}_{od}$ | $\mathrm{W}$ |

Outputs | ||

Off-design mass flow | ${w}_{od}$ | $\mathrm{k}\mathrm{g}/\mathrm{s}$ |

Outlet pressure | ${p}_{o}$ | $\mathrm{Pa}$ |

Coldplate temperature | ${T}_{cp,od}$ | $\mathrm{K}$ |

Area-specific thermal resistance | ${r}_{th,od}$ | m^{2}K/W |

Effectiveness | ${\u03f5}_{od}$ | - |

#### Appendix A.2. Coldplate Validation Design Inputs

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

${T}_{1,des}$ | $\mathrm{K}$ | 294 |

${\u03f5}_{des}$ | - | $0.47$ |

${Q}_{des}$ | $\mathrm{W}$ | 100 |

${T}_{cp,des}$ | $\mathrm{K}$ | 330 |

${r}_{th,des}$ | m^{2}K/W | 2.88 × 10^{−5} |

$\Delta {p}_{des}$ | $\mathrm{Pa}$ | 50 × 10^{3} |

## Appendix B. Compact Heat Exchanger Core Model

**Rectangular microchannels**. j and f are calculated according to the methods described for rectangular channels in [24]. Of the parameters in Table 1, ${d}_{H}$ and $\delta $ are used as known inputs, and the other parameters are calculated. The aspect ratio of the channels is also an input and defined as:$$\begin{array}{c}\hfill \mathsf{\Phi}=b/t\end{array}$$$$\begin{array}{c}\hfill {d}_{H}=\frac{4{A}_{cs}}{P}\end{array}$$$$\begin{array}{c}\hfill b={d}_{H}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\frac{1+\mathsf{\Phi}}{2}\end{array}$$In a similar fashion, using basic geometry and regarding the side-walls of the channels as fins results in:$$\begin{array}{c}\hfill {A}_{f}/A=\frac{\mathsf{\Phi}}{\mathsf{\Phi}+1}\end{array}$$$$\begin{array}{c}\hfill \beta =\frac{A}{V}\end{array}$$$$\begin{array}{c}\hfill \beta =\frac{4\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(1+\mathsf{\Phi})}{{d}_{H}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}(1+\mathsf{\Phi})+2\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\mathsf{\Phi}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\delta}\end{array}$$**Offset-strip fins**. The model for this core is entirely based on [33]. j and f correlations were directly adapted and used within the given limits. For offset-strip fins, the fin length (${L}_{f}$) is required as an additional input parameter. The missing geometries were derived from Figure 1 in [33]. If offset-strip fins could be realized without additional material on the top or bottom b, ${A}_{f}/A$, and $\beta $ could be calculated from (A28), (A29), and (A30), respectively. With enhanced manufacturing techniques, it may become possible. Hence, for this model, the additional material thickness on the top and bottom is neglected.**Louvered fins**. The correlation for j was directly implemented from [34] and for f from [35]. b is used as a direct input for this model. ${A}_{f}/A$ and $\beta $ were calculated with (8.76–8.84) from [17]. Additional input parameters to be considered here are louver angle, louver pitch, and louver cut length, which should be selected carefully within the valid ranges given in [34,35].

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**Figure 2.**Coldplate model validation for thermal resistance (

**left**) and pressure loss (

**right**) with data from [16].

**Figure 8.**Two-dimensional sensitivity analysis of the hot-side hydraulic diameter with the cold-side pressure ratio (

**left**) and the hot-side hydraulic diameter with the cold-side hydraulic diameter (

**right**).

**Figure 9.**Heat exchanger size sensitivity in three dimensions: hot-side length, cold-side length, and stack height over hot- and cold-side hydraulic diameter.

**Figure 11.**Off-design optimization at takeoff for a TMS designed for ${T}_{cp,des}=380\phantom{\rule{3.33333pt}{0ex}}\mathrm{K}$ and ${S}_{P}=30$%.

**Figure 12.**Multi-point optimization for a TMS for ${T}_{cp,des}=380\phantom{\rule{3.33333pt}{0ex}}\mathrm{K}$ and ${S}_{P}=30$%.

Name | Symbol | Unit |
---|---|---|

Colburn factor | j | - |

Fanning friction factor | f | - |

Hydraulic diameter | ${d}_{H}$ | $\mathrm{m}$ |

Plate space | b | $\mathrm{m}$ |

Area density | $\beta $ | m^{2}/m^{3} |

Fin thickness | $\delta $ | $\mathrm{m}$ |

Fin thermal conductivity | ${\lambda}_{f}$ | $\mathrm{W}/\left(\mathrm{m}\phantom{\rule{3.33333pt}{0ex}}\mathrm{K}\right)$ |

Ratio finned to total heat transfer area | ${A}_{f}/A$ | - |

Parameter | Symbol | Unit | Default Value |
---|---|---|---|

Coldplate surface temperature | ${T}_{cp}$ | $\mathrm{K}$ | 370 |

Heat capacity ratio HEX cold to hot side | ${C}_{R}^{*}$ | - | $1.0$ |

Coldplate coolant inlet temperature | ${T}_{1}$ | $\mathrm{K}$ | 275 |

Pressure ratio HEX cold side | ${\mathsf{\Pi}}_{c}$ | - | $0.95$ |

Hydraulic diameter HEX cold side | ${d}_{H,c}$ | mm | $10.0$ |

Coldplate effectiveness | ${\u03f5}_{cp}$ | - | $0.4$ |

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**MDPI and ACS Style**

Kellermann, H.; Lüdemann, M.; Pohl, M.; Hornung, M.
Design and Optimization of Ram Air–Based Thermal Management Systems for Hybrid-Electric Aircraft. *Aerospace* **2021**, *8*, 3.
https://doi.org/10.3390/aerospace8010003

**AMA Style**

Kellermann H, Lüdemann M, Pohl M, Hornung M.
Design and Optimization of Ram Air–Based Thermal Management Systems for Hybrid-Electric Aircraft. *Aerospace*. 2021; 8(1):3.
https://doi.org/10.3390/aerospace8010003

**Chicago/Turabian Style**

Kellermann, Hagen, Michael Lüdemann, Markus Pohl, and Mirko Hornung.
2021. "Design and Optimization of Ram Air–Based Thermal Management Systems for Hybrid-Electric Aircraft" *Aerospace* 8, no. 1: 3.
https://doi.org/10.3390/aerospace8010003