# Effect of Structural Materials on Monopropellant Thruster Propulsion Performance in Micro Scale
## 4 Results and Discussion  
### Heat Loss  
The result of the simulation exhibited varying fluid temperatures as the working fluid flowed through the chamber inlet to the nozzle exit. Varying heat loss was also observed when investigating the temperature distribution across the microthruster chamber and the nozzle. Figure 5 summarizes temperatures at four different locations in the microthruster: the chamber inlet, nozzle inlet (chamber outlet), nozzle throat, and nozzle exit. These temperatures depended on the structural materials considered, as well as the propellant weight percentages. In regard to further investigations, additional temperature-related \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid** & **No. of Elements in Fluid Domain** & **No. of Elements in Solid Domain** & **Thrust (mN)** & **Average Temperature \({}^{*}\)** \\ \hline Coarse & 394,000 & 81,503 & 74.13 & 509.84 \\ Intermediate & 936,400 & 116,419 & 74.19 & 510.00 \\ Dense & 1,736,000 & 399,672 & 74.24 & 510.10 \\ \hline \hline \end{tabular} \({}^{*}\) outside surface.  
\end{table} 
Table 4: Result of grid-independent study (90 wt% hydrogen peroxide, material: glass). Figure 4: Microthruster boundary conditions for the simulation. (**a**) Fluid domain—left side view. (**b**) Fluid domain—right side view. figures follow. To determine the structural effect on the performance of a microthruster, we chose thermal diffusivity as a thermal performance indicator of the materials. Thermal diffusivity is a measure of the ability of a material to transfer heat by conduction relative to the amount of heat stored per unit volume of a material. Accordingly, with a high thermal diffusivity, heat moves rapidly, as heat conduction occurs more quickly than storing heat in a material. The thermal diffusivity (\(\alpha\)) is obtained from the following equation:  
\[\alpha=\frac{k}{\rho c_{p}} \tag{10}\]  
where \(k\) is thermal conductivity, \(\rho\) is density, and \(c_{p}\) is specific heat at constant pressure. Heat transfer coefficients at the fluid-solid interface are plotted in Figure 6 with respect to thermal diffusivity. The heat transfer coefficient of the microthruster using 85 wt% hydrogen peroxide decomposed gas mixture ranges from 246.14 to 284.80 W/m\({}^{2}\cdot\)K, depending on the thermal diffusivity. It was from 261.80 to 300.89 W/m\({}^{2}\cdot\)K for 90 wt% and from 281.91 to 320.32 W/m\({}^{2}\cdot\)K for 95 wt%. As expected, the heat transfer coefficient increased when heat transfer occurred through the high-thermal-diffusivity material and the high-temperature working fluid (i.e., high-enthalpy propellant). However, there were different slopes representing varying sensitivity with respect to thermal diffusivity. The variation in the heat transfer coefficient was larger for the range of relatively small thermal diffusivity below 3.7 mm\({}^{2}\)/s, compared to that for the range above. In order to identify the heat loss in the chamber affecting the temperature at the nozzle inlet, the amount of the heat loss in the chamber was defined as temperature variation in a chamber, and it involved a comparison between the chamber inlet and outlet temperatures, (T\({}_{\text{chamber inlet}}-\) T\({}_{\text{nozzle inlet}}\))/T\({}_{\text{chamber inlet}}\), which equals nozzle inlet temperature variation compared to adiabatic case, (T\({}_{\text{nozzle inlet}}\) adiabatic \(-\) T\({}_{\text{nozzle inlet}}\))/T\({}_{\text{nozzle inlet}}\), and is provided in Figure 7 for the nozzle inlet. When the thermal diffusivity was below 3.7 mm\({}^{2}\)/s, heat loss ranged from 8.12 to 10.72% for 85 wt% hydrogen peroxide, from 8.69 to 11.53% for 90 wt%, and from 8.93 to 11.98% for 95 wt%. Above a thermal diffusivity of 3.7 mm\({}^{2}\)/s, heat loss rose to 11.13, 11.98, and 12.47% for 85, 90, and 95 wt%, respectively.