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Computation of casting solidification feed-paths using gradient vector method with various boundary conditions

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Abstract

In the present work, a computationally efficient numerical approach called gradient vector method (GVM) is proposed to visualise feed-paths and to evaluate the design of feeding systems with various thermal boundary conditions. It involves the computation of liquid–solid interfacial heat flux vector using an analytically derived solution to phase change-heat transport equation. The resultant of flux vectors gives the direction of the highest temperature gradient, which is continuously tracked to generate complete feed-paths. The originating points of the feed-paths indicate hot-spots that manifest as shrinkage defects. Mathematical models are proposed to handle the effect of various boundary conditions like insulation or exothermic sleeves around feeders and chill blocks in mould. The accuracy of GVM in predicting the location of shrinkage porosity defect has been validated by pouring and sectioning benchmark castings. Computation of feed-paths using this method was found to be an order of magnitude faster than level-set method for casting solidification simulation. The implementation of the method in three dimensions and its application to an industrial casting are also presented.

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References

  1. Bishop HF, Myskowski ET, Pellini WS (1955) A simplified method for determining riser dimensions. AFS Trans 63:271–281

    Google Scholar 

  2. Ravi B, Srinivasan MN (1996) Casting solidification analysis by modulus vector method. Int Cast Met J 9(1):1–7

    Google Scholar 

  3. Chvorinov N (1940) Theory of solidification of castings. Giess 27:177–225

    Google Scholar 

  4. Heine RW (1968) Feeding paths for risering castings. AFS Trans 76:463–469

    Google Scholar 

  5. Bishop HF, Pellini WS (1950) The contribution of risers and chill-edge effects to soundness of cast steel plates. AFS Trans 58:185–197

    Google Scholar 

  6. Bishop HF, Myskowski ET, Pellini WS (1951) The contribution of risers and chill-edge effects to soundness of cast steel bars. AFS Trans 59:171–180

    Google Scholar 

  7. Myskowski ET, Bishop HF, Pellini WS (1952) Application of chills to increasing the feeding range of risers. AFS Trans 60:389–400

    Google Scholar 

  8. Myskowski ET, Bishop HF, Pellini WS (1953) Feeding range of joined sections. AFS Trans 61:302–308

    Google Scholar 

  9. Kotschi RM (1988) Casting design. Met Handb (now ASM Handbook) 15(Casting):598–613

  10. Wifi AS, Gomaa AH, Essa YE, Abd-Elsalam AF (1999) Numerical and experimental determination of the feeding distance of aluminum alloys in gravity die casting using an optimized riser shape. Mater Manuf Process 14(4):601–619

    Article  Google Scholar 

  11. Carlson KD, Ou S, Hardin RA, Beckermann C (2002) Development of new feeding-distance rules using casting simulation: Part I. Methodology. Metall Mater Trans B 33(5):731–740

    Article  Google Scholar 

  12. Ou S, Carlson KD, Hardin RA, Beckermann C (2002) Development of new feeding-distance rules using casting simulation: Part II. The new rules. Metall Mater Trans B 33(5):741–755

    Article  Google Scholar 

  13. Goodman TR (1958) The heat-balance integral and its application to problems involving a change of phase. Trans ASME J Heat Transf 80:335–342

    Google Scholar 

  14. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Clarendon, Oxford

    Google Scholar 

  15. El-Genk MS, Cronenberg AW (1979) Solidification in a semi-infinite region with boundary condition of the second kind: an exact solution. Lett Heat Mass Transf 6(4):321–327

    Article  Google Scholar 

  16. Zubair SM, Chaudhry MA (1994) Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions. Wärme- und Stoffübertragung (now Heat Mass Transf) 30(2):77–81

  17. Garcia A, Clyne TW, Prates M (1979) Mathematical model for the unidirectional solidification of metals: II. Massive molds. Metall Mater Trans B 10(1):85–92

    Article  Google Scholar 

  18. Clyne TW, Garcia A (1980) Assessment of a new model for heat flow during unidirectional solidification of metals. Int J Heat Mass Transf 23(6):773–782

    Article  Google Scholar 

  19. Feltham DL, Garside J (2001) Analytical and numerical solutions describing the inward solidification of a binary melt. Chem Eng Sci 56:2357–2370

    Article  Google Scholar 

  20. Tadayon MR, Lewis RW (1998) A model of metal–mould interfacial heat transfer for finite element simulation of gravity die castings. Cast Met 1:24–29

    Google Scholar 

  21. Chow P, Bailey C, Cross M, Pericleous K (1995) Integrated numerical modelling of the complete casting process. Model Cast Weld Adv Solidif Process VII:213–221

    Google Scholar 

  22. Lee SL, Ou CR (2001) Gap formation and interfacial heat transfer between thermoelastic bodies in imperfect contact. Trans ASME J Heat Transf 123:205–212

    Article  Google Scholar 

  23. Lewis RW, Ransing RS (1998) A correlation to describe interfacial heat transfer during solidification simulation and its use in the optimal feeding design of castings. Metall Mater Trans B 29(2):437–448

    Article  Google Scholar 

  24. Prasanna Kumar TS, Kamath HC (2004) Estimation of multiple heat-flux components at the metal/mold interface in bar and plate aluminum alloy castings. Metall Mater Trans B 35(3):575–585

    Article  Google Scholar 

  25. Lewis RW, Manzari MT, Ransing RS, Gethin DT (2000) Casting shape optimization via process modeling. Mater Des 21(4):381–386

    Article  Google Scholar 

  26. Tavakoli R, Davami P (2007) Unconditionally stable fully explicit finite difference solution of solidification problems. Metall Mater Trans B 38(1):121–142

    Article  MathSciNet  Google Scholar 

  27. Bahmani A, Hatami N, Varahram N, Davami P, Shabani MO (2012) A mathematical model for prediction of microporosity in aluminum alloy A356. Int J Adv Manuf Technol. doi:10.1007/s00170-012-4102-7

    MATH  Google Scholar 

  28. Viswanathan S, Duncan AJ, Sabau AS, Han Q, Porter WD, Riemer BW (1998) Modeling of solidification and porosity in aluminum alloy castings. AFS Trans 106:411–417

    Google Scholar 

  29. Sutaria M, Gada VH, Sharma A, Ravi B (2012) Computation of feed-paths for casting solidification using level-set-method. J Mater Process Technol 212:1236–1249

    Article  Google Scholar 

  30. Joshi D, Ravi B (2009) Classification and simulation based design of 3D junctions in castings. AFS Trans 117:7–22

    Google Scholar 

  31. Voller VR, Cross M (1981) Accurate solutions of moving boundary problems using the enthalpy method. Int J Heat Mass Transf 24:545–556

    Article  MATH  Google Scholar 

  32. Welch SWJ, Wilson J (2000) A volume of fluid based method for fluid flows with phase change. J Comput Phys 160:662–682

    Article  MATH  Google Scholar 

  33. Chen S, Merriman B, Osher S, Smereka P (1997) A simple level set method for solving Stefan problems. J Comput Phys 135:8–29

    Article  MathSciNet  MATH  Google Scholar 

  34. Sutaria M, Ravi B (2012) Gradient vector method for computing feed-paths and hot-spots during casting solidification. Proceeding of 37th International MATADOR Conference, The University of Manchester, Manchester

  35. Garcia A, Prates M (1978) Mathematical model for the unidirectional solidification of metals: I. Cooled molds. Metall Mater Trans B 9(4):449–457

    Article  Google Scholar 

  36. Stefanescu DM (2009) Science and engineering of casting solidification, 2nd edn. Springer, New York

    Google Scholar 

  37. Campbell J (2003) Castings. Butterworth-Heinemann, Oxford

    Google Scholar 

  38. Patil S, Ravi B (2005) Voxel-based representation, display and thickness analysis of intricate shapes. 9th International Conference on Computer Aided Design and Computer Graphics (CAD/CG 2005), Hong Kong

  39. Jeyarajan A, Pehlke RD (1978) Application of computer-aided design to a steel wheel casting. AFS Trans 86:457–464

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, Maharashtra, India

    Mayur Sutaria & B. Ravi

  2. Department of Mechanical Engineering, Charotar University of Science and Technology, Changa, Anand, 388421, Gujarat, India

    Mayur Sutaria

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  1. Mayur Sutaria
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  2. B. Ravi
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Correspondence to Mayur Sutaria.

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Sutaria, M., Ravi, B. Computation of casting solidification feed-paths using gradient vector method with various boundary conditions. Int J Adv Manuf Technol 75, 209–223 (2014). https://doi.org/10.1007/s00170-014-6049-3

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  • DOI: https://doi.org/10.1007/s00170-014-6049-3

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