Energy Recovery System

\label{sec:trade_ERS} Since a battery was chosen, the main choice in the energy recovery system lies within the type of energy one intends to recover. From the design option tree only kinetic and thermal energy were identified as feasible. Below both are discussed and their potential is investigated. To determine whether an energy recovery system is beneficial, its added mass, cost and complexity must be compared with the reduction in mass it allows.

Kinetic energy could be extracted when throttling down. Momentum wheels could be spun up to store energy. Another option is regenerative braking on the electric motor. However during the flight the throttle setting is reduced only at cruise descent and landing approach, so this energy source is very limited and there would be a net mass increase. Furthermore at landing generators could be installed on the wheels to perform regenerative braking. This energy source would only be useful to reduce charging times, since it is only available after landing. Again it is a small source and there would be a net mass increase. From these arguments it can be concluded that there is no potential in recovering kinetic energy.

Thermal energy could be recovered by the use of thermoelectric generators (TEGs) or a Rankine cycle. TEGs convert a temperature difference directly in electricity using the Seebeck effect \cite{TEGbirdeye}. The Rankine cycle consists of a fluid flowing through an evaporator heated by the heat source, a turbine to expand the gas and extract power to drive a generator, and condenser. The fluid could be water, making it a steam cycle, or an organic fluid when hot reservoir temperature is rather low (below 350 degrees Celsius).

The Carnot efficiency gives the limit of thermal energy recovery, it is a function of temperature of the hot reservoir and cold reservoir. The cold reservoir is ambient air with an assumed temperature of around 40 degrees Celsius in worst case. The hot reservoir temperature is difficult to predict since it depends how the heat in the electric motor and batteries dissipates through radiation, convection and conduction. A value of 50% is assumed, corresponding to a hot reservoir temperature of 330 degrees Celsius, which is already very high for motors and batteries.

The efficiency of TEGs depends on the used materials in the junction and the temperatures of the heat source and ambient environment \cite{TEGbirdeye}. A maximum obtainable efficiency when looking at future developments and the considered hot and cold reservoir temperatures is around 16% \cite{TEGscope} \cite{TEGconv}. The efficiency of the Rankine cycle considered is assumed to be equal to the Carnot efficiency as best case, thus 50%. Losses within the system are not considered yet.

To calculate the battery mass saved the amount of recovered energy is needed. This is estimated by looking at the power level of motor and battery during race and cruise and using their power efficiency to determine the waste heat dissipated. From this the waste energy is calculated using the flight durations. These steps are shown in Table \ref{tab:wasteng}. Then the recovered energy is determined by using the conversion efficiency of the TEGs and Rankine cycle and using the energy density of the chosen batteries, the saved mass is stated as in Table \ref{tab:receng}.

\label{tab:wasteng}

bbbbbbb Component &Power (race, cruise) [kW] & Power efficiency [-] &Waste heat (race, cruise) [kW] & Waste energy (race, cruise) [Wh] & Total waste energy [Wh]
Motor & (140, 70) & 0.95 & (7, 3.5) & (350,1750) & 2100
Battery & (155, 77.5) & 0.90 & (15, 7.75) & (750,3875) & 4625

\label{tab:receng}

From Table \ref{tab:receng} it can be seen that when both possible heat sources, the motor and battery, are used 2.2 kg is saved in case of TEGs or 6.7 kg in case of a Rankine cycle system. These are rather modest savings and now the question is whether the added mass, cost and complexity from the recovery system is compensated by this saving.