Optimization Methodology for Design of Three-Dimensional Rocket Nozzles

Several current rocket engine concepts such as the bell-annular tripropellant engine require unconventional three-dimensional rocket nozzles which must conform to rectangular or sector-shaped envelopes to meet integration constraints. While traditional nozzles typically utilize circular cross sections due to structural and thermal concerns, recent advances in materials and manufacturing technologies have opened the door to other possibilities. Three-dimensional nozzles exist outside the current experience database, therefore, development of efficient design methods for these propulsion concepts is critical to the success of the new single stage to orbit launch vehicle programs. Several approaches for optimizing rocket nozzles, including streamline tracing techniques and the coupling of computational fluid dynamics (CFD) analysis to optimization algorithms, are investigated. The relative strengths and weaknesses of four classes of optimization algorithms are evaluated: Quasi-Newton gradient based methods, genetic algorithms, implicit filtering schemes, and simplex methods. Orthogonal arrays are also investigated for their utility in the aerodynamic optimization process. Additionally, the performance of a streamline tracing technique, which provides a very computationally efficient means of defining a three-dimensional contour, is assessed.