Design sensitivity and finite element analysis of free surface flows with application to optimal design of casting rigging systems

摘要

A novel, fully-analytical design sensitivity formulation for transient, turbulent, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier-Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration.