A model of blind zone for in situ monitoring the solid/liquid interface using ultrasonic wave

• A mathematical model is designed for calculating ultrasonic blind zone.
• Blind zone is related with ultrasonic source location and interface concavity.
• Numerical computation simulation verifies the accuracy of model.

To in situ monitor a solid/liquid interface to control metal qualities, the paper analysis blind models of the ultrasonic propagation in the solidifying molten metal with a solid/liquid interface in the Bridgman type furnace, and a mathematical calculation model of blind zone with different source locations and surface concavities is built. The study points out that the blind zone I is caused by ray bending in the interface edge, and the blind zone II is caused by totally reflection which is related with initial ray angle, critical refraction angle of solid/liquid media. A serial of simulation experiments are operated on the base of the model, and numerical computation results coincide with model calculated results very well. Therefore, receiver should locate beyond these blind zones in the right boundary to obtain time of flight data which is used to reconstruct the solid/liquid interface.