A permeability length scale for cross flow through model structures
- PDF / 336,248 Bytes
- 2 Pages / 597.28 x 785 pts Page_size
- 55 Downloads / 227 Views
The authors wish to acknowledge the AISI Direct Steelmaking Project funded 77 pct by the Department of Energy for partial support of the research and to NSF (MSM 8713961) for support and to the Center for Iron and Steelmaking Research and to its member companies for supporting Y. Zhang. The authors also wish to thank Dr. I. Jimbo for his assistance in the X-ray experiments. REFERENCES 1. Y. Zhang and R.J. Fruehan: Metall. Mater. Trans., 1995, vol. 26B, pp. 000-00. 2. Y. Zhang and R.J. Fmehan: Metall. Mater. Trans., 1995, vol. 26B, pp. 000-00. 3. K. Ogino, S. Hara, and H. Kawai: Process Technology Conference Proceedings, ISS/AIME, Toronto, 1988, p. 23-29. 4. S. Hara, M. Ikuta, M. Kitamura, and M. Ogino, Tetsu-to-Hagan~, vol. 69, 1983, p. 1152-1159 (in Japanese).
The first hurdle to model the permeability is to assign a length scale to the dendrites. It is well established that growth rate, temperature gradient, and composition of material are the main factors that affect the dendrite morphology.E12] In dendritic alloys, behind the paraboloid tip, rodlike branches called secondary arms grow in preferred orientation. Also, as time progresses, tertiary arms may grow, even though their growth ceases as they encounter the diffusion field of branches of neighboring dendrites. In the present analyses, flows through transverse sections of columnar-dendritic alloys are modeled as flows through arrays of circles, rhombi, cruciforms, and schematic dendrites. Cruciforms and rhombi were also used by McCarthy,tU] who calculated permeabiiities with the lattice gas automata technique. Here, a goal is to show that an appropriate length scale of the solid is Sv z, where Sv is the surface area-to-volume ratio of the solid. The numerical method of calculating permeabilities with direct simulations is presented in Reference 9. In this work, simulations of the flows through regular model structures were carried out. The volume fraction of liquid in the porous media generated by these arrays was adjusted by changing the lengths of the arms in the cases of schematic dendrites and cruciforms, whereas in the rhombi the lengths of sides were altered and in the circles the diameters were varied. In all cases, the dendrite arm spacing was maintained constant. Simulations were done by generating quadrilateral meshes using finiteelement analyses. Using a Navier-Stokes (NS) finite element solver, velocities and pressures were calculated at each node and based on the output from the NS solver, a post processor was used to calculate the average pressure gradient and the nondimensional permeability. Figure 1 shows quadrants of the domains used for analyzing the flows. Velocity vectors around the model struc-
A Permeability Length Scale for Cross Flow Through Model Structures M.S. BHAT, D.R. POIRIER, and J.C. HEINRICH Modeling of macrosegregation caused by convection and the partitioning of solutes within the mushy zone of solidifying dendritic alloys is becoming realizable. El4] However, the fact that not enough experimental data on permeability ar
Data Loading...
