Hybrid optimization design of natural-laminar-flow (NLF) supercritical airfoil and infinite swept wing

Using modern optimization techniques, the design of natural-laminar-flow(NLF) airfoil and wing design in transonic and high Reynolds number flows have been made great progresses. Traditionally, there are two approaches: inverse design and direct optimization. The former one requires a well-prescribed target pressure distribution which can only be given by experienced experts, while the latter sometimes yields unexpected pressure distribution which is impractical. To avoid the above weaknesses, we propose the hybrid optimization strategy combining inverse design and direct optimization. The optimization strategy is expressed as a multiple-objective direct optimization problem with a weighted objective of two sub-objectives from inverse design and direct optimization, respectively. In this paper, the objective function related to inverse design is to minimize the sum of squares of pressure difference values from the target over the forepart of the airfoil upper surface; the objective function related to direct optimization is to minimize the total drag. To demonstrate the performance of the proposed strategy, two cases are carried out. For case 1, a fine-design of NLF airfoil LSC72613 is conducted at Ma=0.72, Re=20million, α=0.52°. For case 2, an infinite wing with 25° swept angle is designed at Ma=0.78, Re=20million, α=0.7°. A surrogate-based optimizer, SurroOpt, is utilized for both cases. The in-house flow solvers PMNS2D/3D are used to simulate the flow around aerodynamic configurations and to evaluate the aerodynamic performances on the basis of Reynolds-averaged Navier-Stokes (RANS) equations. The computational fluid dynamics (CFD) solvers feature automatic transition prediction with linear-stability-theory-based eN method. Results show that the optimized airfoil and wing maintain long laminar flow region by keeping suitable favourable pressure gradient on the upper surface, while a relative weak shock wave is obtained.