# Electrohydrodynamic Propeller as One of the Alternatives to Replace Conventional Propulsion Systems
## 3 EHD Propulsion System Prototype Design
#### Experimental Results  
The first tested system was the system comprised of the emitter and the Type 1 collector in a single stage (Figure 9). When the emitter with a conductor diameter of 0.08 mm was  
Figure 8: Type 3 collector. Figure 6: Type 2 emitter. Figure 7: Type 2 collector. used, the shortest distance between the electrodes was determined by the structure of the electrodes, which was 8 mm when the front sides of their frames touched each other. With media accelerators, the velocity of the output medium is measured due to the fact that the holder represents a fixed placement-attachment to the base. In terms of the above-described predominant mechanism of propulsion, contributed primarily by an ion drift, the resulting electrohydrodynamic force may be defined as follows:  
\[\overline{F}_{\mathrm{EHD}}=\frac{\textit{1}\cdot\textit{d}}{\mu_{\mathrm{m}}} \ (\mathrm{N}) \tag{16}\]  
Due to relatively low velocities achieved in the present experiment, the air was not considered to be a pressurisable medium. While taking the Mach number into account, it may be stated that the following equation applies:  
\[M_{\mathrm{Mach}}=\frac{\overline{w}_{\mathrm{max}}}{\overline{a}}\ll 0.3\ (1) \tag{17}\]  
wherein \(\overline{w}_{\mathrm{max}}\) is the maximum velocity of the flowing medium (m\(\cdot\)s\({}^{-1}\)); \(\overline{a}\) is the velocity of a sound wave propagation in the air (ca 343 m\(\cdot\)s\({}^{-1}\) in this experiment). The real density of humid air may be expressed using the equation of state of an ideal gas, as follows:  
\[\rho_{\mathrm{air}}=\frac{\textit{p}\cdot M_{\mathrm{air}}}{\textit{R}\cdot \textit{T}}\ (\mathrm{kg}\cdot\mathrm{m}^{-3}) \tag{18}\]  
wherein \(p\) is the determined absolute pressure (Pa); \(M_{\mathrm{air}}\) is the molar mass of humid air (kg\(\cdot\)kmol\({}^{-1}\)); \(R\) is the universal gas constant (8314.463 kJ\(\cdot\)kmol\({}^{-1}\cdot\)K\({}^{-1}\)); and \(T\) is the thermodynamic temperature of air (K). Based on the Avogadro law, the molar mass of humid air may be expressed as follows:  
\[M_{\mathrm{air}}=x_{\mathrm{da}}\cdot M_{\mathrm{da}}+x_{\mathrm{ms}}\cdot M_ {\mathrm{ms}}=(1-x_{\mathrm{ms}})\cdot M_{\mathrm{da}}+x_{\mathrm{ms}}\cdot M_ {\mathrm{ms}}\ (\mathrm{kg}\cdot\mathrm{kmol}^{-1}) \tag{19}\]  
wherein \(x_{\mathrm{da}}\) is the molar fraction of dry air (1); \(M_{\mathrm{da}}\) is the molar mass of dry air (28.966 kg\(\cdot\)kmol\({}^{-1}\)); \(x_{\mathrm{ms}}\) is the molar fraction of water vapour (1); and \(M_{\mathrm{ms}}\) is the molar mass of water vapour (18.016 kg\(\cdot\)kmol\({}^{-1}\)). The molar fraction of water vapour is calculated as follows:  
\[x_{\mathrm{ms}}=RH\cdot\frac{p_{\mathrm{sat}}}{p}\ (1) \tag{20}\]  
wherein \(RH\) is the relative humidity (1) and \(p_{\mathrm{sat}}\) is the saturated vapour pressure (Pa). The Tetens equation may be used to calculate the saturated vapour pressure for temperatures above 0 \({}^{\circ}\)C, as follows:  
\[p_{\mathrm{sat}}=0.611\cdot\mathrm{e}^{\frac{172\cdot t}{t+2\cdot t}}\ ( \mathrm{kPa}) \tag{21}\]  
Figure 9: One-stage system of the emitter and the Type 1 collector. A theoretical velocity of air at the outlet from the collector, provided that the \(\overline{F}_{\text{EHD}}\) force is evenly distributed over the \(S\) surface area, may be calculated as follows:  
Figure 6:0  
wherein \(S\) is the surface area represented by a cross-sectional area of the flow in the collector (m\({}^{2}\)). A theoretical power of the equipment is then calculated as follows:  
Figure 6:1  
The real force, produced by an ion drift, will be much lower due to the effects of a non-homogeneous electric field, diffusion of cations into the surrounding neutral environment, as well as non-flexible collisions between ions and neutral molecules, at which the kinetic energy decreases and is transformed into a different energy form. Nevertheless, the total mobility is preserved. In an ideal case, the negative effects of humidity on electric mobility are not considered.