# Effect of Structural Materials on Monopropellant Thruster Propulsion Performance in Micro Scale
## 4 Results and Discussion
### Chamber Pressure and Thrust  
The amount of thrust produced by thrusters is significantly affected in micro scale by viscosity and heat loss, and thus it is one of the most appropriate performance indicators for microthrusters. Thrust can be obtained from the following equation:  
\[F=\int_{S_{exit}}\rho u_{a}(\mathbf{u}\cdot\mathbf{n})dA+\int_{S_{exit}}(P_{e}-P_{\infty} )dA \tag{12}\]  
where \(\rho\) is density, \(u_{a}\) is the velocity component in an axial direction, \(\mathbf{u}\) is a velocity vector, \(S_{exit}\) is the area of the fluid outlet, \(A\) is the control surface, \(\mathbf{n}\) is a unit vector normal to a plan \(A\), \(P_{e}\) is the pressure at the fluid outlet, and \(P_{\infty}\) is the ambient pressure. The first term represents the momentum thrust induced by the momentum change of the fluid through the nozzle exit, and the second term represents the pressure of the thrust generated by the pressure difference in the nozzle exit and the ambient. In this work, a mass flow rate of \(7\times 10^{-5}\) kg/s was specified at the fluid inlet, which was consistent in all simulations. The inlet pressure changed at each time step, and the ultimate pressure distribution was determined as the simulation solution was converged. The average chamber pressure was obtained from an arithmetic mean of the pressures at the chamber inlet and nozzle inlet, which is shown in Figure 12, with respect to thermal diffusivity. The average chamber pressure in the adiabatic simulation was 799.12, 850.73, and 901.40 kPa for 85, 90, and the 95 wt% hydrogen peroxide decomposed gas mixtures, respectively, while a chamber pressure for the materials considered was lower than that of the adiabatic case due to thermal loss. This phenomenon was attributable to the greater heat loss via the higher-thermal-diffusivity materials, which resulted in further temperature reductions and molecules with less kinetic energies, which in turn exerted less pressure on the chamber wall. There was a varying amount of pressure degradation, depending on the propellant weight percentages and thermal diffusivities, as shown in the figure. At a low thermal diffusivity, of around 0.39 mm\({}^{2}\)/s, the chamber pressure was approximately 96% of the pressure in the case of the adiabatic. The chamber pressure decreased as the thermal diffusivity increased, and it reached approximately 93% of the adiabatic pressure in the case of the 95 wt% propellant, and approximately 94% in regard to the 85 wt%, indicating a larger pressure degradation for the high-weight-percentage propellant. From the results, it was determined that there was a degradation of chamber pressure due to thermal loss, the amount of which differed depending on the thermal diffusivities. In addition, a greater degradation of chamber pressure was observed with respect to thermal diffusivity, in relation to the high-enthalpy propellant. It was also found that in a low thermal diffusivity range, below 3.7 mm\({}^{2}\)/s, the variation in pressure was larger compared to that in a higher thermal diffusivity range. The amounts of thrust produced by the microthrusters with different thermal diffusivity materials, using 85, 90, and 95 wt% hydrogen peroxide, are compared in Figure 13. The thrust generated in the case of the adiabatic was 72.03, 77.16, and 82.12 mN for 85, 90, and 95 wt% hydrogen peroxide, respectively. The simulated thrust amount for 90 wt% hydrogen peroxide was greater than the targeted theoretical performance of the microthruster considered in the previous study [20], as shown in Figure 1, which reported the MEMS fabrication process of the H\({}_{2}\)O\({}_{2}\) monop propellant microthruster and experimental performance tests aiming to produce 50 mN class thrust.