In this study, the shape optimization of the injector according to fuel and tip was conducted through analytical techniques. As an analysis condition, a flow rate of 0.08 kg / s was applied to the inlet and the outlet was given a condition of 0 Bar. The working fluid for each fuel was applied. As a result of the analysis, it can be seen that the pressure and velocity of model with the modified tip become higher than that of the base model in diesel. Compared with the base model in the case of gasoline, the modified model of the tip was found to have more stable injection when the pressure inside the combustion chamber and the straightness of the fuel were observed. Finally, in case of LPG injector, the same modified tip as gasoline was found to be the more stable injection. On the basis of this study result, the shape parameters of the injector can be inferred.

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.