Optimization for boiling heat transfer determination and enhancement in pressure die casting

Boiling in cooling channels has recently been demonstrated to be an effective mechanism for heat extraction in pressure die casting. Boiling heat transfer can be enhanced by cooling channel shape optimization. The occurrence of boiling presents a non-linear thermal problem which, when combined with shape optimization, necessitates the solving of non-linear equations for each channel configuration. In this paper a methodology is presented that involves the use of optimization for the combined determination of channel shapes and heat transfer coefficients. It is shown in the paper how this approach results in the accurate determination of boiling heat transfer coefficients on the final optimized cooling channel configuration. The non-linear thermal problem is calculated at very little computational cost over that required for a comparable linear problem. Focus in the paper is on the application of the methodology to the pressure die casting process. The approach adopted is founded on a design sensitivity analysis using the material derivative adjoint variable method. The thermal model for the pressure die casting process is founded on the boundary element method and the optimization is performed using a conjugate gradient scheme. Geometrical constraints are enforced using buffer elements superimposed on to the boundary element mesh. Numerical and experimental trials are performed to demonstrate the potential of the new optimization methodology.