Packing of sedimenting equiaxed dendrites

Abstract

The packing of free-floating crystal grains during solidification has a strong impact on the phase-change process as well as on the structure and the defects in the solidified material. The packing fraction is affected by the particular dendritic morphology of the grains and by their low inertia resulting from the small density difference between solid and liquid. Understanding the grain packing phenomenon during metal alloy solidification is not experimentally possible since packing is coupled to many other phenomena. We therefore investigate the packing of equiaxed dendrites on a model system, consisting of fixed-shape nonconvex model particles sedimenting in conditions hydrodynamically similar to those encountered in solidifying metals. We perform numerical simulations by a discrete-element model and experiments with transparent liquids in a sedimentation column. The combination of experiments and simulations enables us to determine the packing fraction as a function of (i) the grain morphology, expressed by a shape parameter, and (ii) the hydrodynamic conditions, expressed by the particle Stokes number.

Packing dynamics of spherical and nonconvex grains sedimenting at low Stokes number

“…In the case of the spheres, the widest grain length is simply the grain diameter. More details of the setup and grain characteristics are given in [14]. In this way, the grain-to-fluid density ratio remains close to unity with a Stokes number of St = o(10 −3 ) for both grain collections, which are conditions typically achieved in metal casting processes.…”

“…As far as we know, the packing of nonconvex grains by sedimentation in the presence of a viscous fluid has been exclusively addressed in Ref. [14], where the packing fraction for nonconvex dendritic grains ranges from approximately 0.39 up to 0.63 depending on the grain geometry and the hydrodynamic conditions of the packing.…”

Effect of Diffusion Length in Modeling of Equiaxed Dendritic Solidification under Buoyancy Flow in a Configuration of Hebditch–Hunt Experiment

“…A more complex morphology of the solid dendrites makes them easier to form a packed structure. [31] A widely used packing condition is that is higher than . However, even if ≥ , grains cannot be made rigid when they are in the middle of a non-rigid domain, as a group of them could still sediment or float up or be dragged.…”

Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification

“…Very recent studies based on this method have shown that the detailed structure of the mushy zone, such as the intermetallic precipitates, influences the permeability significantly [185,186]. Another interesting study was recently made on the packing behavior of settling equiaxed dendrites [187]. A so-called packing limit (volume fraction at packing point), usually taking the value (0.637) for random close packing of equal spheres, is often used to calculate the packing equiaxed grain (characterized by the shape of grain envelope).…”

“…On the other hand, plenty of closure laws need to be further refined. The aforementioned studies, such as on the hydrodynamic interactions between fluid and solid phases during solidification [181][182][183][184][185][186][187][188][189][190], are to be reinforced through rigorous scientific work. -Dedicated laboratory benchmark experiments for model evaluation.…”