Here, a distinct procedure was adopted to optimize the shape of the NACA 0012 airfoil profile for Reynolds number, Mach number, and angle of attack equal to 2e6, 0.15, and 10.24 deg, respectively. The airfoil shape was appropriately parameterized, and mesh morphing tools were used to bypass the remeshing process. Computational fluid dynamic (CFD) simulations were carried out for all combinations of selected parameters. Response surfaces were constructed for the drag and lift coefficients of the airfoil based on several statistical criteria. Subsequently, the Pareto front was used to solve the multi-objective optimization problem. Eventually, three single-objective types of optimization problems were studied. A 10 % reduction in drag coefficient was estimated for the drag minimization problem, a 22 % improvement in lift coefficient was found in case of lift maximization problem, and a 6 % reduction in drag coefficient was determined in the lift constrained drag minimization problem.

在这里，采用了不同的程序来优化NACA 0012翼型轮廓的形状，以使雷诺数，马赫数和攻角分别等于2e6、0.15和10.24度。机翼形状已进行了适当的参数设置，并使用网格变形工具绕过了重新网格化过程。对所选参数的所有组合都进行了计算流体动力学（CFD）模拟。基于几个统计标准，为翼型的阻力和升力系数构建了响应面。随后，使用Pareto前沿来解决多目标优化问题。最终，研究了三种单目标类型的优化问题。对于阻力最小化问题，阻力系数降低了10％，