Grid fins shape design of a launch vehicle based on sequential approximation optimization

This paper performed the optimization of grid fins shape of a launch vehicle based on Sequential Approximation Optimization (SAO) and Computational Fluid Dynamics (CFD) simulation coupling. An efficient and reliable method is proposed for determining the width of Gaussian functions based on a logical relationship between the width and local density. The performance of the proposed method is evaluated using five classical test functions. The proposed method for width determination generates almost no excessive calculation costs, and improves the accuracy, reliability, and stability of the Radial Basis Function (RBF) surrogate model notably. Based on the improved RBF surrogate model, a framework and detailed procedure for the SAO algorithm is presented, and the performance of the proposed SAO algorithm is tested, with obtained results showing that the proposed SAO algorithm reduces the calling times of the original model and improves the optimization efficiency remarkably. The objective function is strictly deduced and reflects the momentum loss caused by aerodynamic drag directly. Three constraints are imposed to ensure the static stability and controllability of the launch vehicle. Finally, grid fins shape optimization problem of the launch vehicle is solved, with the objective function and constraints calculation tasks accomplished automatically by batch mode CFD simulations. The global optimal solution is obtained after 54 calling times of the original model, and 92 h (3.84 days) of computation on a 96-core cluster. Once the baseline shape is replaced with the optimized shape, it is detected that (1) taking the minimum fuel as an objective function, the take-off mass is 2.07% lighter than the take-off mass of the baseline shape, (2) taking the maximum payload mass as an objective function, the payload mass is 14.3% heavier than the payload mass of the baseline shape.