Sustainable aircraft design-A review on optimization methods for electric propulsion with derived optimal number of propulsors

The high environmental impact of conventional aircraft can be considerably reduced using hybrid- or fullyelectrical propulsion systems with distributed propulsors. It results in an increased efficiency for a higher number of propulsors, where different effects like boundary layer ingestion, propulsors-structure interactions, or component failures affect the overall design decisions. Hence, a distributed electric propulsion layout leads to an increasing demand for an overall integrated system design process in which optimization methods play an important role. In this review study, first, we give an overview of embedded propulsion, where boundary layer ingestion was heavily examined. Second, we present distributed propulsion and its combination with embedded propulsion. Third, we give a detailed overview of optimization methods in the conceptual and preliminary design stage. We illustrate the benefits of the usage of integrated optimization methods by presenting a study and answer the question of how many propulsors would be optimal for a distributed electric aircraft to maximize the overall efficiency in cruise. The formulated constrained optimization model is derived from the application of first principles, allometric scaling, and dimensional analysis. The solution of the optimization problem yields the design rule that the optimal number of propulsors increases with the aircraft mass to the power of 0.29. As uncertainty is always present in the design process and especially in earlier design stages, we explicitly present approaches to master this uncertainty by presenting an overview of sensitivity analysis methods.