Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 4
1,130
Views
35
CrossRef citations to date
0
Altmetric
Original Articles

New smoothed particle hydrodynamics (SPH) formulation for modeling heat conduction with solidification and melting

, &
Pages 299-312 | Received 12 Oct 2016, Accepted 20 Jan 2017, Published online: 05 Apr 2017

References

  • M. Passandideh Fard, Droplet Impact and Solidification in a Thermal Spray Process: Droplet-substrate Interactions, Proceedings of the 9th National Thermal Spray Conference & Exposition, Cincinnati, OH, 1996.
  • V. R. Voller and C. Prakash, A Fixed Grid Numerical Modelling Methodology for Convection-Diffusion Mushy Region Phase-Change Problems, Int. J. Heat Mass Transf., vol. 30, no. 8, pp. 1709–1719, 1987.
  • B. G. Thomas, I. V. Samarasekera, and J. K. Brimacombe, Comparison of numerical modeling techniques for complex, two-dimensional, transient heat-conduction problems, Metall. Trans. B, vol. 15, no. 2, pp. 307–318, 1984.
  • J. S. Hsiao and Benjamin T. F. Chung, An Efficient Algorithm for Finite Element Solution to Two-Dimensional Heat Transfer with Melting and Freezing, J. Heat Transf., vol. 108, no. 2, pp. 462–464, 1986.
  • A. J. Dalhuijsen and A. Segal, Comparison of Finite Element Techniques for Solidification Problems, Int. J. Numer. Methods Eng., vol. 23, no. 10, pp. 1807–1829, 1986.
  • L. B. Lucy, A Numerical Approach to the Testing of the Fission Hypothesis, Astronom. J., vol. 82, pp. 1013–1024, 1977.
  • R. A. Gingold and J. J. Monaghan, SmoothParticle Hydrodynamics: Theory and Application to Non-spherical Stars, Monthly Notices R. Astronom. Soc., vol. 181, no. 3, pp. 375–389, 1977.
  • J. P. Morris, P. J. Fox, and Y. Zhu, Modeling Low Reynolds Number Incompressible Flows Using SPH, J. Comput. Phys., vol. 136, no. 1, pp. 214–226, 1997.
  • P. Li-Fan Liu, H. Hsiu-Jen Yeh, and C. Synolakis, Advanced Numerical Models for Simulating Tsunami Waves and Runup. World Scientific Publishing Co., Hackensack, NJ, 2008.
  • B. Cartwright, P. H. L. Groenenboom, and D. McGuckin, Examples of ship motion and wash predictions by SmoothParticle Hydrodynamics (SPH), 9th Symposium on Practical Design of Ships and Other Floating Structures, Luebeck-Travemuende, Germany, 2004.
  • X. Y. Hu and N. A. Adams, A Multi-phase SPH Method for Macroscopic and Mesoscopic Flows, J. Comput. Phys., vol. 213, no. 2, pp. 844–861, 2006.
  • N. Grenier, D. L. Touze, M. Antuono, and A. Colagrossi, An ImprovSPH Method for Multi-phase Simulations, In 8th International Conference on Hydrodynamics, ICHD, 2008.
  • A. M. Tartakovsky, K. F. Ferris, and P. Meakin, Lagrangian Particle Model for Multiphase Flows, Comput. Phys. Commun., vol. 180, no. 10, pp. 1874–1881, 2009.
  • P. W. Cleary, J. Ha, J. Mooney, and V. Ahuja, Effect of Heat Transfer and Solidification on High Pressure Die Casting, Proc. 13th Australasian Fluid Mechanics Conference, Melbourne, pp. 679–682, 1998.
  • P. W. Cleary, J. Ha, M. Prakash, and T. Nguyen, 3D SPH Flow Predictions and Validation for High Pressure Die Casting of Automotive Components, Appl. Math. Model., vol. 30, no. 11, pp. 1406–1427, 2006.
  • P. W. Cleary, Extension of SPH to Predict Feeding, Freezing and Defect Creation in Low Pressure Die Casting, Appl. Math. Model., vol. 34, no. 11, pp. 3189–3201, 2010.
  • M. Zhang, H. Zhang, and L. Zheng, Application of Smoothed Particle Hydrodynamics Method to Free Surface, and Solidification Problems, Numer. Heat Transf. Part A: Appl., vol. 52, no. 4, pp. 299–314, 2007.
  • M. Y. Zhang, H. Zhang, and L. L. Zheng, Simulation of Droplet Spreading, Splashing and Solidification using SmoothParticle Hydrodynamics Method, Int. J. Heat Mass Transf., vol. 51, no. 13, pp. 3410–3419, 2008.
  • M. Zhang, H. Zhang, and L. Zheng, Numerical Investigation of Substrate Melting, and Deformation During Thermal Spray Coating by SPH Method, Plasma Chem. Plasma Process., vol. 29, no. 1, pp. 55–68, 2009.
  • J. J. Monaghan, H. E. Huppert, and M. G. Worster, Solidification using SmoothParticle Hydrodynamics, J. Comput. Phys., vol. 206, no. 2, pp. 684–705, 2005.
  • C. Bonacina, G. Comini, A. Fasano, and M. Primicerio, Numerical Solution of Phase-change Problems, Int. J. Heat Mass Transf., vol. 16, no. 10, pp. 1825–1832, 1973.
  • J.-S. Hsiao, Numerical, and Analytical Analysis of Heat Transfer with Ablation in a Two-dimensional Region, Ph.D. Thesis, The University of Akron, 1983.
  • S. D. Giudice, G. Comini, and R. W. Lewis, Finite Element Simulation of Freezing Processes In Soils, Int. J. Numer. Anal. Methods Geomech., vol. 2, no. 3, pp. 223–235, 1978.
  • E. C. Lemmon, Phase-change Techniques for Finite Element Conduction Codes, Technical Report CONF-790710–2, Idaho National Engineering Lab., Idaho Falls (USA), 1979.
  • G.-R. Liu and M. B Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, 2003.
  • A. Farrokhpanah, B. Samareh, and J. Mostaghimi, Applying Contact Angle to a Two-dimensional Multiphase SmoothParticle Hydrodynamics Model, J. Fluids Eng., vol. 137, no. 4, pp. 041303, 2015.
  • A. Farrokhpanah, Applying contact angle to a two-dimensional SmoothParticle Hydrodynamics (SPH) model on a Graphics Processing Unit (GPU) platform, Master’s thesis, University of Toronto, 2012.
  • I. Aleinov and E. G. Puckett, Computing Surface Tension with High-Order Kernels, Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, pp. 4–8, 1995.
  • M. Rudman, A Volume-Tracking Method for Incompressible Multifluid Flows with Large Density Variations, Int. J. Numer. Methods Fluids, vol. 28, no. 2, pp. 357–378, 1998.
  • J. P. Morris, Simulating Surface Tension with SmoothParticle Hydrodynamics, Int. J. Numer. Methods Fluids, vol. 33, no. 3, pp. 333–353, 2000.
  • K. A. Rathjen and L. M. Jiji, Heat Conduction with Melting or Freezing in a Corner, J. Heat Transf., vol. 93, no. 1, pp. 101–109, 1971.
  • H. Budhia and F. Kreith, Heat Transfer with Melting or Freezing in a Wedge, Int. J. Heat Mass Transf., vol. 16, no. 1, pp. 195–211, 1973.
  • Y. Cao, A. Faghri, and W. S. Chang, A Numerical Analysis of Stefan Problems for Generalized Multi-Dimensional Phase-Change Structures using the Enthalpy Transforming Model, Int. J. Heat Mass Transf., vol. 32, no. 7, pp. 1289–1298, 1989.
  • C.-S. Keung, The Use of Sources and Sinks in Solving Two-dimensional Heat Conduction Problems with Change of Phase in Arbitrary Domains, Ph.D. Thesis, Columbia University, 1980.
  • S. Meng, R. Yang, J.-S. Wu, and H. Zhang, Simulation of Droplet Spreading on Porous Substrates using SmoothParticle Hydrodynamics, Int. J. Heat Mass Transf., vol. 77, pp. 828–833, 2014.
  • G. R. Johnson, R. A. Stryk, and S. R. Beissel, SPH for High Velocity Impact Computations, Comput. Methods Appl. Mech. Eng., vol. 139, no. 1, pp. 347–373, 1996.
  • J. J. Monaghan and J. C. Lattanzio, A Refined Particle Method for Astrophysical Problems, Astronomy Astrophys., vol. 149, pp. 135–143, 1985.
  • A. Ayasoufi, T. G. Keith, and R. K. Rahmani, Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-dimensional Heat Conduction with Melting and/or Freezing, J. Heat Transf., vol. 126, no. 6, pp. 937–945, 2004.
  • V. Alexiades and D. Solomon, Mathematical Modeling of Melting and Freezing Processes, Taylor & Francis, Washington, DC, 1992.
  • A. Ayasoufi and T. G. Keith, Application of the Conservation Element and Solution Element Method in Numerical Modeling of Heat Conduction with Melting and/or Freezing, Int. J. Numer. Methods Heat & Fluid Flow, vol. 13, no. 4, pp. 448–472, 2003.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.