Fluid flow in casting rigging systems: Modeling, validation, and optimal design
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INTRODUCTION
IN sand casting, molten material is poured into a forming cavity, via a delivery system of ducts and channels, with the fluid displacing the air within. Figure 1 shows a typical arrangement of components in a sand casting mold. The shapes and sizes of the sprue, runners, and ingates are critical to the entire process, because they determine, among other things, the rate, uniformity, and smoothness with which material is delivered to the mold cavity. The volume of material in the rigging system also represents an additional cost in the process. The uniformity and smoothness of the material flow have implications for the quality of the final part. Therefore, the design of the rigging system to achieve quality and production goals is of prime importance. Traditionally, runner and gating systems for foundry castings have been designed using generic design rules, such as those compiled by the American Foundrymen’s Society.[1] Originally developed 5 decades ago, these rules provide guidelines for the sizing of sprues, runners, and ingates. The objective of these designs is to provide smooth, nonagitated delivery of metal into the mold, while avoiding defects due to events like premature solidification and gas aspiration in the runners. The design rules currently used are based primarily on Bernoulli’s equation, along with empirical data[2,3] for simple shapes. These rules produce satisfactory results for many castings. However, the many, sometimes conflicting, requirements for a sound casting suggest that computer simulation and modeling can provide valuable insight into rigging system design. The volume-of-fluid (VOF) method[4] has made it computationally feasible to model mold filling in realistic geROBERT M. McDAVID is Senior Project Engineer, Automated Analysis Corp., Peoria, IL, 61602. JONATHAN A. DANTZIG, Professor, is with the Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801. Manuscript submitted September 16, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
ometries. The main advantage of the VOF method is that large surface deformations commonly encountered in mold filling are readily handled. This feature is in contrast to deformable grid techniques,[5,6] which perform best when free-surface movements are relatively limited. Zhang et al.[7] modeled the filling process by assuming that the flow is inviscid and irrotational. In this case, the VOF equation can be used in conjunction with Bernoulli’s equation to simulate mold filling. Although this formulation has the advantage of being less computationally intensive than solving the full Navier–Stokes equations, numerical and physical modeling studies[8,9] have shown that viscous effects can also be important in mold filling. At the large Reynolds numbers typically encountered in metal casting, the flow can be assumed to be inviscid in the core. However, near the walls of the metal delivery system, viscous effects predominate. Since defects due to mold erosion, gas aspiration, turbul
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