Skip to main content

Numerical Simulation of Solidification and Melting Problems on Unstructured Grid

  • Conference paper
  • First Online:
Fluid Mechanics and Fluid Power – Contemporary Research

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

  • 4852 Accesses

Abstract

Solidification and melting problems are phase change kind of problems in which interface moves and it separates the phases. Natural convection and conduction are the main mechanism behind the physics of these problems. In the present study, Navier-Stokes equations along with continuity and energy equation are solved to predict the phase change pattern of pure metals (e.g. Gallium) and alloys (e.g. Steel). Here, enthalpy method is used to find the temperature distribution and to track the position of the solid-liquid interface with time. A coupled fully implicit method is used to solve the momentum and energy equation. Both isothermal and mushy region phase change problem is presented and verified with numerical results available in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Babu, A.B.: Numerical Simulation of Solidification and Melting Problems. Master Thesis. IIT Kanpur, India (2006)

    Google Scholar 

  2. Basu, B., Date, A.W.: Numerical modelling of melting and solidification problems-a review. Sadhana, Part 3(13), 169–213 (1988)

    Article  Google Scholar 

  3. Brent, A.D., Voller, V.R., Reid, K.J.: Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal. Numer. Heat Transf. 13, 297–318 (1988)

    Article  Google Scholar 

  4. Cruchaga, M.A., Celentano, D.J.: A finite-element thermally coupled flow formulation for phase-change problems. Int. J. Numer. Meth. Eng. 34, 279–305 (2000)

    Article  MATH  Google Scholar 

  5. Dalal, A., Eswaran, V., Biswas, G.: A finite-volume method for navier-stokes equation on unstructured meshes. Numer. Heat Transf., Part B 52, 238–249 (2008)

    Article  Google Scholar 

  6. Dantzig, J.: Modelling liquid-solid phase change with melt convection. Int. J. Num. Meth. Eng. 28, 1769–1785 (1989)

    Article  MathSciNet  Google Scholar 

  7. Gau, C., Viskanta, R.: Melting and solidification of a pure metal on a vertical wall. J. Heat Transf. 13, 297–318 (1988)

    Google Scholar 

  8. Hannoun, N., Alexiades, V., Mai, T.Z.: Resolving the controversy over tin and gllium melting in a rectangular cavity heated from the side. Numer. Heat Transf., Part B 44, 253–276 (2003)

    Article  Google Scholar 

  9. Ilegbusi, O.J., Mat, M.D.: Modelling flowability of mushy zone with a hybrid model utilizing coherency solid fraction. Mater. Sci. Eng., A 247, 135–141 (1998)

    Article  Google Scholar 

  10. Lazaridis, A.: A nemerical solution of the multidimensional solidification (or melting) problem. Int. J. Heat Mass Transf. 13, 1459–1477 (1970)

    Article  MATH  Google Scholar 

  11. Ben-David, O., Levy, A.: B.M.A.A.: 3d numerical and experimental study of gallium melting in a rectangular container. Int. J. Heat Mass Transf. 67, 260–271 (2013)

    Article  Google Scholar 

  12. Rady, M.A., Mohanty, A.K.: Natural convection during melting and solidification of pure metals in a cavity. Numer. Heat Transf., Part A 29, 49–63 (1996)

    Article  Google Scholar 

  13. Rhie, C.M., Chow, W.L.: Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J 21, 1525–1532 (1983)

    Article  MATH  Google Scholar 

  14. Voller, V.R., Cross, M., Markatos, N.C.: An enthalpy method for convection/diffusion phase change. Int. J. Num. Meth. Eng. 24, 271–284 (1987)

    Article  MATH  Google Scholar 

  15. Voller, V.R., Prakash, C.: A fixed grid numerical modelling methodology for convection-diffusion mushy region phase change problems. Int. J. Heat Mass Transf. 30(No.8), 1709–1719 (1987)

    Google Scholar 

Download references

Acknowledgements

This study is funded by a grant from the DAE-BRNS, Government of India.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amaresh Dalal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer India

About this paper

Cite this paper

Debraj Das, Amaresh Dalal (2017). Numerical Simulation of Solidification and Melting Problems on Unstructured Grid. In: Saha, A., Das, D., Srivastava, R., Panigrahi, P., Muralidhar, K. (eds) Fluid Mechanics and Fluid Power – Contemporary Research. Lecture Notes in Mechanical Engineering. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2743-4_42

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-2743-4_42

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2741-0

  • Online ISBN: 978-81-322-2743-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics