ABSTRACT
The invention relates to a sustainable painting system for aircraft that mimics the anatomy of a peregrine falcon, reduces the impact of aircraft against birds and flying insects, improves aerodynamics and harnesses solar and wind energy. The surfaces painted in matt black (1) and (6a), due to their composition and color, are negatively electrified due to friction with air by the triboelectric effect, and absorb electromagnetic radiation, heating up. The opposite occurs with the surfaces painted in glossy white (2) and (6b); which are positively electrified and cool down. This different electrification and heating of the surfaces produces electrical forces and transfers the energy to the air flow, so as to increase the lift, reduce drag and improve the aerodynamics of the vehicle. The appearance of a falcon, swallow or bat frightens birds and flying insects, respectively. The invention is mainly intended for aircraft, vehicles and wind turbines.
Electromagnetism
$$TECD(MBP)=-100\mu C/m^2$$ $$TECD(GWP)=+100\mu C/m^2$$
$$TECD=\frac{q}{S}$$
TECD: Triboelectric charge density
q: electric charge
S: surface
MBP: matte black paint
GWP: gloss white paint
The surfaces painted in matt black (1) and (6a), due to their composition, are negatively electrified due to friction with air by the triboelectric effect. The opposite occurs with the surfaces painted in glossy white (2) and (6b); which are positively electrified. This different electrification of the surfaces produces electrical forces, so as to increase the lift, reduce drag and improve the aerodynamics of the vehicle.
Electrochemistry
$$N: [He] 2s2\,2p3, N_2: 5+5=10, N\equiv N, 6+2=8$$
From the electronic configuration of the nitrogen atom, N. Each nitrogen atom contributes 5 valence electrons, for a total of 10. The dinitrogen molecule present in the air has a triple covalent bond that forms 6 shared electrons plus 2 of its own, adding up to 8 and reaching the noble gas structure.
$$2N_2\to 2N_2^+ +2e^-$$
We take two nitrogen molecules, one that travels through the extrados and another through the intrados, becoming positively ionized by triboelectricity or possibly already being positively ionized in the atmosphere, since air is the material with the greatest tendency to give up electrons by triboelectricity according to the triboelectric series.
$$GWP\to GWP^+ +e^-$$
The molecules of the bright white paint become positively electrified by giving up an electron
$$MBP +3e^- \to MBP^{3-}$$
The molecules in the matte black paint become negatively electrified, capturing three electrons to balance the electrochemical equations
MBP: matte black paint
GWP: gloss white paint
Solar radiation equation
$$P_{rs}=IS=constant$$
Prs: Power of solar radiation
I: maximum normal surface irradiance, approximately 1000 W/m2
S: Surface
Continuity equation
$$M_\infty<0.4$$
The most logical application of this innovation is to vehicles that move at relatively low speeds, where the power of solar radiation captured by the matte black painted surfaces is not small or negligible compared to the propulsive power of the vehicle. Therefore, the efficiency of the paint system will be greater the lower the speed of the vehicle, especially taking into account that the power of the aerodynamic resistance that must be overcome is proportional to the cube of the forward speed.
$$\rho=constant$$
Assumption of high Reynolds number and attached boundary layer, negligible mass forces and small Mach number (allowing compressibility effects to be neglected so that the air density can be assumed constant)
$$\nabla·\mathbf{v}=0$$
Obtained directly from the continuity equation for an incompressible fluid
Momentum equation
$$\rho\frac{D\mathbf{v}}{Dt}=-\nabla p+\nabla·\tau’+\rho \mathbf{F_m}+\rho \mathbf{F_e}$$
Fe: electrical forces
Both the paints that cover the vehicle and the air in contact with the surfaces are electrified; and they are designed to produce electrical forces that increase lift, decrease drag and improve aerodynamic flow. In addition, the accumulation of static charge is a phenomenon that occurs in aircraft, and which is solved in practice by means of static electricity discharge devices. However, in the case of this innovation, the aim is not to eliminate it but to take advantage of it.
$$\nabla·\tau’=-\nabla\times(\mu\nabla\times\mathbf{v})$$
According to the Navier-Stokes model and the divergence of the velocity being zero
$$\rho\frac{D\mathbf{v}}{Dt}=-\nabla p+\rho \mathbf{F_e}$$
Large Reynolds number and Froude number, it is justified to neglect the viscous terms and mass forces.
$$\frac{D\mathbf{v}}{Dt}=\frac{\partial \mathbf{v}}{\partial t}+\mathbf{v}·\nabla \mathbf{v}=\frac{\partial \mathbf{v}}{\partial t}+\frac{1}{2}\nabla(v^2)-\mathbf{v}\times(\nabla\times\mathbf{v})=-\frac{1}{\rho}\nabla p+\mathbf{F_e}$$
$$\frac{\partial \mathbf{v}}{\partial t}=0\hspace{20mm}\nabla\times\mathbf{v}\not=0$$
Stationary and non-irrotational flow. The flow is not assumed to be irrotational because the effect of solar radiation on surfaces can produce an increase in circulation around an aerodynamic profile.
$$\frac{1}{2}\nabla(v^2)-\mathbf{v}\times(\nabla\times\mathbf{v})=-\frac{1}{\rho}\nabla p+\mathbf{F_e}$$
Energy equation
$$\rho\frac{De}{Dt}=\nabla·(k\nabla T)-p\nabla·\mathbf{v}+\mathbf{\Phi_v}-\nabla·\mathbf{q_r}+Q_{rq}$$
$$\rho\frac{De}{Dt}=-\nabla·\mathbf{q_r}$$
The heat flux by radiation is due to solar radiation and cannot be ignored in this case, which is designed to take advantage of it. On the upper faces and on the extradoses, with matte black paint; being in the sun and due to the absorption of electromagnetic radiation, the surfaces heat up, radiating heat. This heat is transferred to the convective flow of the extrados, increasing its kinetic energy. On the contrary, on the lower faces and on the intradoses, with bright white paint; being in the shade and due to the reflection of electromagnetic radiation, the surfaces cool down, absorbing heat. This heat is absorbed from the convective flow of the intrados, decreasing its kinetic energy. An increase in circulation around the aerodynamic profiles is expected.
High Reynolds number assumption. Heat transfer effects by conduction are negligible. It is justified to neglect viscosity-dependent terms in the energy equation. Heat flux due to chemical reactions is zero. And the divergence of the velocity being zero
$$\rho c_p\frac{DT}{Dt}-\frac{Dp}{Dt}=-\nabla·\mathbf{q_r}$$
$$\rho c_p(\frac{\partial \mathbf{T}}{\partial t}+\mathbf{v}·\nabla \mathbf{T})-(\frac{\partial \mathbf{p}}{\partial t}+\mathbf{v}·\nabla \mathbf{p})=-\nabla·\mathbf{q_r}$$
$$\frac{\partial \mathbf{T}}{\partial t}=0\hspace{20mm}\frac{\partial \mathbf{p}}{\partial t}=0$$
Steady flow
$$\rho c_p\mathbf{v}·\nabla \mathbf{T}-\mathbf{v}·\nabla \mathbf{p}=-\nabla·\mathbf{q_r}$$
Equation of state
$$p=\rho RT$$
R=287 m2s-2K-1
Considering air as perfect gas
Literature: Meseguer Ruiz J., Sanz Andrés A., AERODINÁMICA BÁSICA, E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, 2005