Jet Mixing in Direct-Chill Casting of Aluminum: Crater Effects and its Consequence on Centerline Segregation
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I.
INTRODUCTION
DIRECT-CHILL casting is the primary processing route for wrought aluminum products in the world today. Since its conception in the 1940s the process has undergone significant advancements in order to improve productivity and deter defect formation. One of the most persistent defects is macrosegregation, or the large-scale inhomogeneity of the concentration of solute elements throughout the casting. Of particular concern in hypoeutectic alloys is the formation of a severely solute-depleted centerline,[1] which is responsible for mechanical property variations in rolled plate products.[2,3] We have recently postulated the dominant role of the accumulation of solute-lean grains on the formation of this centerline region.[4] In order to prevent the preferential sedimentation of these grains, we have proposed the use of a turbulent jet to re-suspend excess grains[5] thereby mitigating centerline segregation. The results from the original study[5] examined only cross-sectional samples of the ingots and found a significant reduction of centerline segregation using a properly scaled jet under steady-state conditions. A subsequent examination along the length of the entire ingot showed that the region directly underneath the impinging jet exhibited similar centerline segregation to that observed in the standard case.[4] We postulate that the crater formed by the impinging turbulent jet at the bottom of the sump is a proxy for the relative amount of material (grains) re-suspended from the centerline. In SAMUEL R. WAGSTAFF and ANTOINE ALLANORE are with the Department of Materials Science & Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139. Contact e-mail: [email protected] Manuscript submitted June 29, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS B
the present work we develop an analytical model to describe the shape of the crater formed as the turbulent jet impinges on the bed of grains at the bottom of the ingot sump. This calls for an in-depth investigation of the re-suspension of sedimenting grains due to the relative roles of pressure and shear forces, whose independent values due to an impinging jet have been presented in detail in Appendix 1.
II.
SETTING OF THE MODEL
We model the crater shape formed by a jet impinging perpendicularly onto a granular bed. The equations derived in this model are applicable to all Newtonian suspension systems, but we investigate the case of a vertical jet impinging on the two-phase region of a solidifying metal casting. Figure 1 is a schematic of this condition, specifically referencing the case of aluminum DC casting as practiced at industrial scale and discussed in References 4 and 5. A. Stability Criterion and Zone of Erosion This section considers the forces exerted on the grains comprising the granular bed. This enables the determination of the zone of erosion and quantifies the movement of grains as a function of the fluid dynamic characteristics of the jet. Three forces act on a single grain reposing on a planar bed at
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