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Minimum fuel consumption of fuel-cell-powered airplanes driven by fixed-pitch propellers

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Abstract

Electric airplanes powered by fuel cells are a promising alternative for green aviation. However, many technological obstacles still have to be overcome for this type of aircraft to be commercially viable. For example, the relatively low output power capacity of fuel cells still constrains the application of these devices to power heavier aircraft. These limitations make performance optimization an even more important subject. This article presents a novel formulation for the analysis of electric current, fuel and oxidizer consumption of fuel-cell-powered airplanes driven by fixed-pitch propellers. Due to its simplicity, lighter weight and lower cost, the fixed-pitch propeller is widely used on aircraft with small flight speed variation. Also, since the efficiency of this type of propeller is known to vary with airspeed, a dedicated method is necessary. A parametric description of the relevant aircraft systems is developed, and expressions for instantaneous and total consumption are formulated. Optimal conditions for these performance metrics are investigated, and analytical solutions are derived and presented in closed form. The formulation employs a parametric model for the fixed-pitch propeller and eliminates the need to determine the motor and propeller rotation speed. A numerical approach for method validation is used, and simulations are provided to give the reader a quantitative insight into the problem. The results show that the optimal speeds for minimum fuel consumption of fuel-cell-powered aircraft driven by fixed-pitch propellers can be higher than what is predicted by traditional methods. Mathematical proofs are provided to show that this can happen.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. The propeller polar is usually written with the power coefficient \(C_P\) as a function of \(C_T\) but, being an affine function, it can be inverted and employed in the form presented.

  2. Aircraft and systems data kindly provided by the engineering team at CENIC Engineering, in São José dos Campos, Brazil.

Abbreviations

\(\alpha\) :

Angle of attack

\(\gamma\) :

Flight path angle

V :

True airspeed

T :

Propeller thrust

W :

Aircraft weight

L :

Aerodynamic lift

D :

Aerodynamic drag

\(C_{L}\) :

Lift coefficient

\(C_{D_{0}}\) :

Zero lift drag coefficient

k :

Lift-dependent drag constant

\(\rho\) :

Air density

h :

Altitude

g :

Gravitational acceleration

S :

Wing reference area

\(\eta _{fc}\) :

Fuel cell efficiency

\(\eta _p\) :

Propeller efficiency

\(\eta _m\) :

Electric motor efficiency

\(\eta\) :

Propulsion system total efficiency

\(Q_p\) :

Propeller torque

\(Q_m\) :

Electric motor torque

\(R_{fc}\) :

Fuel cell internal resistance

\(R_m\) :

Motor internal resistance

i :

Electric current

\(i_0\) :

Motor no-load current

F :

Faraday constant

\(K_V\) :

Motor speed constant

\(K_Q\) :

Motor torque constant

\(C_{el }\) :

Electric charge

\({\dot{m}}\) :

Instantaneous consumption (mass flow)

m :

Total consumption (mass)

s :

Traveled distance

\(U_0\) :

Fuel cell open-circuit voltage

\(C_T\) :

Propeller thrust coefficient

\(C_Q\) :

Propeller torque coefficient

n :

Propeller rotation frequency

J :

Propeller advance ratio

\(a_p\) :

Propeller polar angular coefficient

\(b_p\) :

Propeller polar independent term

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  1. EMBRAER, 12247-820, São José dos Campos, Brazil

    Guilherme N. Barufaldi & Mauricio A. V. Morales

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  1. Guilherme N. Barufaldi
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Barufaldi, G.N., Morales, M.A.V. Minimum fuel consumption of fuel-cell-powered airplanes driven by fixed-pitch propellers. CEAS Aeronaut J 14, 295–309 (2023). https://doi.org/10.1007/s13272-023-00653-2

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