Two-Dimensional Shape Optimization of Hypersonic Vehicles Considering Transonic Aerodynamic Performance

Abstract

For the success of hypersonic vehicles, their shape must be optimized to achieve a high lift-to-drag ratio as well as a low aerodynamic heating rate in the hypersonic regime. In addition, the transonic lift-to-drag ratio must also be optimized to realize quick acceleration to the hypersonic cruise speed. The three-dimensional lift-to-drag ratio can be improved even by the two-dimensional section shape (i.e., airfoil) optimization in the region where the sweep back angle is small. Here, prior to three-dimensional shape optimization, a study is done to optimize airfoils of hypersonic vehicles based on these three parameters. At optimization, the hypersonic lift-to-drag ratio is maximized while the transonic lift-to-drag ratio and the aerodynamic heating rate are constrained. The optimum lift coefficient for hypersonic cruise at the maximum lift-to-drag ratio is investigated. The relation between the leading edge radius, which determines the aerodynamic heating rate, and the hypersonic lift-to-drag ratio is also investigated. Results show that to improve the hypersonic lift-to-drag ratio, the airfoil thickness around the leading edge should be small as long as an appropriate compromise with the transonic lift-to-drag ratio is achieved. Results also show that the optimum lift coefficient for hypersonic cruise is much lower than that for typical supersonic vehicles. Small cruise lift coefficient suggests that the wing loading of a hypersonic vehicle should be small. The leading edge radius should be determined by a compromise between the hypersonic lift-to-drag ratio and leading edge heating. Airfoil optimization can provide an appropriate initial guess of the three-dimensional optimum shape. By using an appropriate initial guess, the computation time of the three-dimensional shape optimization is expected to be reduced.