ORIGINAL ARTICLE Computation of casting solidification feed-paths using gradient vector method with various boundary conditions Mayur Sutaria & B. Ravi Received: 15 May 2012 /Accepted: 9 June 2014 /Published online: 15 July 2014 # Springer-Verlag London 2014 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 contin- uously tracked to generate complete feed-paths. The originat- ing points of the feed-paths indicate hot-spots that manifest as shrinkage defects. Mathematical models are proposed to han- dle 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. Keywords Feed-path . Gradient vector . Hot-spot . Interfacial heat flux . Shrinkage . Solidification 1 Introduction The emergence of metal casting as a near-net shape manufacturing process with good reproducibility and part quality relies on a clear understanding of the underlying solidification mechanism. During casting solidification, heat transfer occurs by all three modes: for example, conduction from the solidifying metal to the mould, convection from outer surface of the mould and radiation from open risers. The higher density of solid phase compared to liquid phase drives the feeding mechanism in castings. The volumetric contraction during solidification at any location is compensat- ed by movement of molten metal from adjacent hotter regions. The casting solidifies progressively from its outer surface toward the last solidifying points, called ‘hot-spots’, which are the most probable locations for shrinkage related defects illustrated in Fig. 1. Shrinkage defects can be minimized by designing an ap- propriate feeding system to ensure directional solidification from thin to thick sections in the casting, finally ending in feeders. Feeders must contain adequate amount of molten metal required for compensating the volumetric shrinkage and should be positioned within the ‘feeding distance’ to the hot-spots. Feeding distance is the length from the edge of the feeder to the farthest point in a simple- shaped casting that can be fed without shrinkage defect, as proposed by Bishop et al. [1]. Ravi and Srinivasan [2] extended this definition to complex-shaped castings by introducing the concept of ‘feed-path’. The feed-path at any given location inside a casting is the direction along which molten metal flows to an adjacent solidifying region to compensate its volumetric con- traction. It is along the local maximum temperature gradient, which in turn is normal to the solidification front. Feed-paths originating from a point inside the feeder imply proper feeding of the casting. If they originate from a point inside the part, M. Sutaria (*) : B. Ravi Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India e-mail: mayursutaria@gmail.com URL: www.iitb.ac.in M. Sutaria Department of Mechanical Engineering, Charotar University of Science and Technology, Changa, Anand 388421, Gujarat, India Int J Adv Manuf Technol (2014) 75:209–223 DOI 10.1007/s00170-014-6049-3