DESIGN SENSITIVITY AND FINITE-ELEMENT ANALYSIS OF FREE-SURFACE FLOWS WITH APPLICATION TO OPTIMAL-DESIGN OF CASTING RIGGING SYSTEMS

A novel, fully-analytical design sensitivity formulation for transient , turbulent, free surface flows is derived and implemented in the cont ext of finite element analysis. The time-averaged, turbulent form of t he Navier-Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free su rface movement. The design derivatives of-these governing equations ar e computed and solved to find the analytical sensitivities of the flui d position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sen sitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example app lication for using sensitivity information in design. The analytical s ensitivity routine is coupled to a numerical optimizer to yield an aut omated method for optimal design of the casting rigging system. The re sults produce runner shapes which eliminate mold-gas aspiration. (C) 1 998 John Wiley & Sons, Ltd.