Development of a freckle predictor via rayleigh number method for single-crystal nickel-base superalloy castings

A Rayleigh number based criterion is developed for predicting the formation of freckles in Ni-base superalloy castings. This criterion relies on finding the maximum local Rayleigh number in the mush, where the ratio of the driving buoyancy force to the retarding frictional force is the largest. A critical Rayleigh number for freckle formation of approximately 0.25 is found from available experimental data on directional solidification of a Ni-base superalloy. If the Rayleigh number in a superalloy casting is below this critical value, freckles are not expected to form. Full numerical simulations of freckling in directional solidification of superalloys are conducted for a large variety of casting conditions, alloy compositions, and inclinations of the system with respect to gravity. For the vertical cases, the Rayleigh numbers at the starting points of the predicted freckles are in good agreement with the critical value established from the experiments. The simulations confirm that the same critical Rayleigh number applies to different superalloys. The simulations for inclined domains show that even a small amount of inclination (less than 10 deg) significantly lowers the critical Rayleigh number and moves the freckles to the side wall of the casting, where the mushy zone has advanced the most relative to gravity. In application of the Rayleigh number criterion to complex-shaped superalloy castings, the absence of freckles near upper and lower boundaries and in sections of insufficient cross-sectional area or height needs to be taken into account as well. The criterion can be used to study the tradeoffs between different superalloy compositions, applied temperature gradients, and casting speeds. Additional experiments, in particular for other superalloys and for a range of inclinations, are desirable to confirm the critical Rayleigh numbers found in the present study.