Computation of casting solidification feed-paths using gradient vector method with various boundary conditions

Abstract

In the present work, a computationally efficient numerical approach called gradient vector method (GVM) is proposed to visualise feed-paths and to evaluate the design of feeding systems with various thermal boundary conditions. It involves the computation of liquid–solid interfacial heat flux vector using an analytically derived solution to phase change-heat transport equation. The resultant of flux vectors gives the direction of the highest temperature gradient, which is continuously tracked to generate complete feed-paths. The originating points of the feed-paths indicate hot-spots that manifest as shrinkage defects. Mathematical models are proposed to handle the effect of various boundary conditions like insulation or exothermic sleeves around feeders and chill blocks in mould. The accuracy of GVM in predicting the location of shrinkage porosity defect has been validated by pouring and sectioning benchmark castings. Computation of feed-paths using this method was found to be an order of magnitude faster than level-set method for casting solidification simulation. The implementation of the method in three dimensions and its application to an industrial casting are also presented.