Optimal Robust Design of Hybrid Rocket Engines

Hybrid rocket engines are flexible, safe, reliable, and low-cost and can be used in many aerospace applications. The engine design and operation are contingent on the type of designated mission and engine design is strictly related to trajectory optimization. In real-world applications, uncertainties affect propulsion system performance: mission goals and constraints may be not fulfilled by an engine designed using a deterministic approach. Uncertainty of the coefficient and mass flux exponent in the classical regression rate correlation are here taken into account, as they are the ones that more remarkably deviate delivered propulsion system performance from expected nominal values. The upper-stage of a small launcher is considered. The engine has a partially regulated pressure-fed system. First, the deterministic optimal design is obtained by means of a nested direct–indirect optimization procedure, and launcher performance are evaluated considering non-nominal regression rate correlations. The height of the attainable orbit results to be strongly jeopardized when the regression rate is larger than that of the nominal case (large oxidizer residual). In contrast, when regression rate is smaller than nominal, residual propellant consists of fuel and a less severe performance degradation occurs. Some improvements in the off-design behavior can be obtained if the engine design is optimized for values of the regression rate correlation coefficient that are larger than the nominal ones. Results shows that robustness of deterministic solutions is not adequate (e.g., insertion within 100 km from the desired orbit altitude). An evolutionary optimization code is then used to define the optimal robust design. The fitness of each individual of the population is evaluated as a linear combination of payload and an index that quantifies the effective reaching of the target orbit under uncertainty (based either on the worst case scenario or on the average performance). Results show that close matching of the required performance (e.g., within 10 km from the desired orbit altitude) can be obtained with a moderate (below 5 %) penalty on the payload.