Determining optimal parameters for the design of curvy ducts poses computational challenges. Visual exploration of the transformations of curvilinear duct design space and response parameters requires optimization tools beyond the inevitable computational fluid dynamics of analytical simulations. It is complex to fuse numerical optimization techniques, computational fluid dynamics (CFDs), and surface geometry generation codes into algorithms for optimizing duct shapes.

Nonlinear algorithms for solving unconstrained and constrained optimization problems exist [1]. There are polynomial and spline functions for curve fitting of duct shapes [2]. CFDs are functional for forecasting fluid flow patterns. However, the design of efficient CFD-oriented optimization algorithms for applications in the computer-aided design of wavy ducts remains an open quandary. The authors developed a novel methodology for gaining ideas about design spaces and locating optimal design parameters of duct products. To implement a reliable shape optimization tool, they combined a nonlinearly constrained sequential quadratic programming optimization code, a steady airflow CFD code, and a surface geometry code. A test to locate the optimum shape of an airfoil with minimized pressure losses of both skin friction and turning flow bends required significant central processing unit (CPU) hours. Tests of the steady airflow of an S-shaped duct, with constraints on packaging space and geometry robustness, utilized significant CPU time as design variables increased. Designing efficient algorithms for duct shape optimization is still a venture. Nevertheless, the authors offer exceptional insights on code integration and reusability; in particular, the use of outputs as inputs in disparate computational models is novel.