Significant efforts have been made by materials scientists and metallurgists to understand the un... more Significant efforts have been made by materials scientists and metallurgists to understand the underlying physics involved in solidification of aluminum alloys to predict a variety of casting defects. Shrinkage porosity is one of the most important types of casting defects. Addressing porosity has been a formidable challenge due to many contributing (and interacting) phenomena responsible for its formation and growth. Shrinkage porosity occurs by nucleation and growth phenomena. Very few previous models for shrinkage prediction consider the pore * Ny Dimensionless Niyama criterion G Thermal gradient Secondary dendrite arm spacing Critical pressure drop for stable pore to exist Cooling rate Freezing range Dynamic viscosity of liquid Dimensionless number Liquid volume fraction Final pore volume fraction P e Local pressure in melt v V Volume of bubble A Area of liquid-gas interface γ Interfacial energy per unit area P i Pressure from the interior of bubble ∆P* Critical pressure difference to form a pore We Weber number Fr Froude number Number of entrapped oxides resulted from the collision , Parameters depending on alloy composition Collision surface area , Velocity of the free surfaces Average surface area of the broken oxides Surface area of the broken oxide film Distance of oxide movement Tensor of pulse flow velocity Kinematic viscosity Normal vector to the solid surface Volume fraction of solid phase Volume fraction of liquid phase Volume fraction of empty phase Temporal evolution of density of solid phase Temporal evolution of density of liquid phases Concentrations of the i th alloy component in solid phases viii CONTENTS
Significant efforts have been made by materials scientists and metallurgists to understand the un... more Significant efforts have been made by materials scientists and metallurgists to understand the underlying physics involved in solidification of aluminum alloys to predict a variety of casting defects. Shrinkage porosity is one of the most important types of casting defects. Addressing porosity has been a formidable challenge due to many contributing (and interacting) phenomena responsible for its formation and growth. Shrinkage porosity occurs by nucleation and growth phenomena. Very few previous models for shrinkage prediction consider the pore * Ny Dimensionless Niyama criterion G Thermal gradient Secondary dendrite arm spacing Critical pressure drop for stable pore to exist Cooling rate Freezing range Dynamic viscosity of liquid Dimensionless number Liquid volume fraction Final pore volume fraction P e Local pressure in melt v V Volume of bubble A Area of liquid-gas interface γ Interfacial energy per unit area P i Pressure from the interior of bubble ∆P* Critical pressure difference to form a pore We Weber number Fr Froude number Number of entrapped oxides resulted from the collision , Parameters depending on alloy composition Collision surface area , Velocity of the free surfaces Average surface area of the broken oxides Surface area of the broken oxide film Distance of oxide movement Tensor of pulse flow velocity Kinematic viscosity Normal vector to the solid surface Volume fraction of solid phase Volume fraction of liquid phase Volume fraction of empty phase Temporal evolution of density of solid phase Temporal evolution of density of liquid phases Concentrations of the i th alloy component in solid phases viii CONTENTS
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