2D shape optimization under proximity constraints by CFD and response surface methodology - Immonen, Eero (Applied Mathematical Modelling, 2017)
•CFD-based shape optimization is considered in 2 dimensions.•Shape deformations are subject to complex geometric proximity constraints.•Gregory splines are used to convert the proximity constraints to interval bounds.•Shape optimization is carried out by multivariate polynomial response surfaces.•The NACA 0012 airfoil, containing a rectangular fuel tank, is used as a test case. In this paper we consider two-dimensional CFD-based shape optimization in the presence of obstacles, which introduce nontrivial proximity constraints to the optimization problem. Built on Gregory’s piecewise rational cubic splines, the main contribution of this paper is the introduction of such parametric deformations to a nominal shape that are guaranteed to satisfy the proximity constraints. These deformed shape candidates are then used in the identification of a multivariate polynomial response surface; proximity-constrained shape optimization thus reduces to parametric optimization on this polynomial model, with simple interval bounds on the design variables. We illustrate the proposed approach by carrying out lift and/or drag optimization for the NACA 0012 airfoil containing a rectangular fuel tank: By identifying polynomial response surfaces using a large batch of 1800 design candidates, we conclude that the lift coefficient can be optimized by a linear model, whereas the drag coefficient can be optimized by using a quadratic model. Higher order polynomial models yield no improvement in the optimization.