Quantitative Characterization of Solidification Structure in Different Sections for Calculating the Permeability in Actual High-Carbon Steel Billet

Cao, Jianghai; Hou, Zibing; Liu, Qian; Guo, Zuoxing; Guo, Dongwei

doi:10.1007/s11663-021-02087-9

Cited by 3 publications

(2 citation statements)

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“…Considering the permeation and wall-preferring characteristics, similar to the porous structure of the mushy zone of dendrites, the fluid velocity can be approximated by Darcy's law [21], which is given by: [21] where in the above equation, K is the permeability, μ is the liquid viscosity, gL is the liquid fraction of the region, and Δp/L is the pressure term. Regarding the shape characteristics of dendrites, the permeabilities parallel to the primary (Πp) and secondary (Πn) dendritic arms are given by [21,22]: (3) [21,22] where λ1 and λ2 are the spacings between primary and secondary dendritic arms, respectively, and τ is the tortuosity, defined as the ratio of the actual streamline length to the straight-line distance between two points. Some studies have shown that the tortuosity of dendritic flow models is related to their geometric shape characteristics and can be calculated from their geometric fractal dimensions, which is constant about 1.8 [21,23].…”

Section: The Principle Of Treatment Of the Wall-attachment Effectmentioning

confidence: 99%

“…Regarding the shape characteristics of dendrites, the permeabilities parallel to the primary (Πp) and secondary (Πn) dendritic arms are given by [21,22]: (3) [21,22] where λ1 and λ2 are the spacings between primary and secondary dendritic arms, respectively, and τ is the tortuosity, defined as the ratio of the actual streamline length to the straight-line distance between two points. Some studies have shown that the tortuosity of dendritic flow models is related to their geometric shape characteristics and can be calculated from their geometric fractal dimensions, which is constant about 1.8 [21,23]. Therefore, as shown in Fig.…”

Section: The Principle Of Treatment Of the Wall-attachment Effectmentioning

confidence: 99%

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A novel prediction model of the freckle defects for single-crystal superalloy blades

Liu,

Wang

2024

J. Phys.: Conf. Ser.

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The freckle is a typical surface defect formed during the directional solidification of SC (single crystal) components of Ni-based superalloys. It generally appears as a long and narrow trail of equiaxed grains aligned roughly parallel to the direction of gravity, which breaks the integrity. Once appears, the freckle can never be avoided by further treatment. With the turbine blade requirements increasing, the state-of-the-art methods include adding more refractory elements into Ni-based SC superalloys, and the design of blades with a more complex geometric shape make the freckle defects grow easier at the special surface zones. This leads to a significant challenge in controlling grain defect formation in SC blades and vanes for freckles. The current consensus to freckle formation is described as the Rayleigh-Taylor instability (RTI) flow that occurred in the interdendritic zone. During solidification, the compositional segregation (CS) occurred as soon as the solid interface forwarding led to the density changes between the interdendritic melting phases and the residual liquids. For nickel-based superalloys, the enrichment of low-density solutes like Al, and Ti at the interdendritic zone will make the liquid lighter. However, the widely used Ra model can’t correctly match the freckle tendency of the components with complex shapes (called geometrical effects of freckles), especially for blades. Recent reports indicate that the freckles occur at the preferred positions in the casting. In this work, a novel model is designed to quantitatively discuss the geometrical effects on freckle formation and to combine existing Ra number models with solidification models to enable freckle predictions at a smaller scale. The proceeding of this work can make the design of complex blades easier.

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