Skip to main content
SpringerLink
Log in

Solidification modelling

  • Published:
Bulletin of Materials Science Aims and scope Submit manuscript

Abstract

The modelling of solidification of a metal/alloy in a mold cavity is increasingly becoming popular with numerous attempts being made to understand the phenomena that occur at the level of the casting (macro level) and that which occur at the microscopic level (micro level). In this paper, an attempt has been made to describe the phenomena occurring at both the macro and the micro levels.

At the macro level, the effect of fluid flow on various thermal and solidification parameters has been studied. The results were compared with simulations carried out considering conduction alone and with experimental results. The relative importance of including fluid flow on solidification simulation of a casting has been brought out.

At the micro level, an algorithm based on the macro-micro model to take the melt superheat into account while numerically predicting the grain size and dendritic arm spacing at different locations of an Al-7% Si alloy sand casting has been developed. The results are compared with the experimental values.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

u,v :

velocity components inx andy directions

K :

permeability

μ :

dynamic viscosity

p :

pressure

S x, Sy :

source terms in Navier-Stokes equation

f t :

fraction liquid

R :

resistance function

ΔH(t) :

change in enthalpy as a function of time

C 1,C 2,C, D :

constants

N max :

maximum number of nuclei per unit volume

R g :

grain radius

T pour :

pouring temperature

ΔT max :

undercooling corresponding to the maximum of dN/dΔT

N act :

actual number of nuclei present per unit volume

ΔT act :

actual maximum undercooling experienced

{ie560-1}:

range in the gaussian curve

ΔT :

undercooling

References

  • Braaten M E 1985Development and evaluation of iterative and direct method for the solution of equations governing recirculative flows, Ph D Dissertation, University of Minnesota, Minnesota, USA

    Google Scholar 

  • Bradley F J and Fung C A 1990Proc. of F Weinberg int. symp. on solidification processing (eds) J E Lait and I V Samarasekera (London: Pergamon Press) p. 333

    Google Scholar 

  • Brown S G R and Spittle J A 1991 inModelling of casting, welding and advanced solidification processes (Warrendale, PA: TMS) p. 395

    Google Scholar 

  • Burden M H and Hunt J D 1974J. Cryst. Growth 22 99, 109

    Article  CAS  Google Scholar 

  • Campbell J 1991Mater. Sci. Technol. 7 885

    CAS  Google Scholar 

  • Cole G S and Bolling G F 1972AFS Trans. 80 211

    CAS  Google Scholar 

  • Comini G and Del Giudice S 1985Num. Heat Trans. 8 133

    Article  Google Scholar 

  • Crivelli L A and Idelsohn S R 1986Int. J. Numer. Meth. Eng. 23 99

    Article  Google Scholar 

  • Dalhuijsen A J and Segal A 1986Int. J. Numer. Meth. Eng. 23 1807

    Article  Google Scholar 

  • Daming Xu and Qingchun Li 1990Num. Heat Trans. A20 203

    Google Scholar 

  • Flood S C and Hunt J D 1987J. Cryst. Growth 82 543, 552

    Article  CAS  Google Scholar 

  • Gandin Ch-A, Rappaz M and Tintillier R 1993Met. Trans. A A24 467

    Article  Google Scholar 

  • Grest G S, Anderson M P and Srolovitz D J 1986 inComputer simulation of microstructural evolution (ed.) D J Srolovitz (Warrendale, PA: TMS) p. 21

    Google Scholar 

  • Harlow F H and Welch J E 1965Phys. Fluids 8 2182

    Article  Google Scholar 

  • Hirt C W, Nichols B D and Romero N C 1980SOLA — A numerical solution algorithm for transient fluid flows (Los Alamos: Los Alamos Scientific Laboratory)

    Google Scholar 

  • Hirt C W and Nichols B D 1981J. Comput. Phys. 39 201

    Article  Google Scholar 

  • Hughes T J R 1978Int. J. Numer. Meth. Eng. 12 1359

    Article  Google Scholar 

  • Hwang W S and Stoehr R A 1983J. Metals 35 22

    Google Scholar 

  • Jaisuk Yoo and Rubinsky B 1986Int. J. Numer. Meth. Eng. 23 1785

    Article  Google Scholar 

  • Kannan K S, Madhusudana K, Venkataramani R, Ganesh N and Prabhakar O 1990Indian J. Technol. 28 460

    CAS  Google Scholar 

  • Mackinnon R J and Carey G F 1987Int. J. Numer. Meth. Eng. 24 393

    Article  Google Scholar 

  • Madhusudana K, Venkataramani R and Prabhakar O 1989Solidification simulation — CADCAST, User Manual, DST Project No. III-4(38)/85-ET, IIT, Madras

  • Madhusudana K 1993Finite element analysis of solidification in castings, PhD thesis, IIT, Madras

    Google Scholar 

  • Morgan K, Lewis R W and Zienkiewicz O C 1978Int. J. Numer. Meth. Eng. 12 1191

    Article  Google Scholar 

  • Narayanaprabhu K, Prasannakumar T S and Ramachandran T 1989 inPrinciples of solidification and materials processing (eds) R Trivediet al 2 p. 761

  • Ohnaka I 1990Int. conf. on CAMSE-90 (Computer applications to materials science and engineering), Tokyo, 8

  • Oldfield W 1966Trans. ASM 59 945

    CAS  Google Scholar 

  • Patankar S V 1980Numerical heat transfer and fluid flow (New York: Hemisphere Publishing Company)

    Google Scholar 

  • Ramachandran N, Gupta J P and Jaluria Y 1982Int. J. Heat Mass Trans. 25 187

    Article  CAS  Google Scholar 

  • Rappaz M 1989Int. Mater. Rev. 3 93

    Google Scholar 

  • Rappaz M and Gandin Ch-A 1993Acta Metall. 41 345

    Article  CAS  Google Scholar 

  • Rolph III W D and Bathe K J 1982Int. J. Numer. Meth. Eng. 18 119

    Article  Google Scholar 

  • Salcudean M and Guthrie R I L 1979Met. Trans. AIME B10 423

    Article  Google Scholar 

  • Samonds M, Lewis R W, Morgan K and Symberlist R 1985 inComputational techniques in heat transfer (eds) R W Lewis, K Morgan, S Johnson and W R Smith (Swansea: Pineridge Press)1

    Google Scholar 

  • Sharma D G R and Prabhakar O 1990 Report No. III-4(39)/85-ET, DST, New Delhi

  • Smith T G and Wilkes J O 1975Comput. Fluids 51

  • Srinivasan M N 1982Indian J. Technol. 20 123

    CAS  Google Scholar 

  • Stefanescu D M, Upadhya G and Bandhyopadhyay D 1990Met. Trans. A A21 997

    Article  Google Scholar 

  • Venkataramani R, Gowrishankar N and Prabhakar O 1992Met. Mater. Process. 4 151

    CAS  Google Scholar 

  • Voller V R, Cross M and Markatose N C 1987Int. J. Numer. Meth. Eng. 24 271

    Article  Google Scholar 

  • Voller V R and Prakash C 1987Int. J. Heat Mass Transfer 30 1709

    Article  CAS  Google Scholar 

  • Voller V R and Swaminathan C R 1990Int. J. Numer. Meth. Eng. 30 875

    Article  Google Scholar 

  • Zhu P and Smith W 1992Acta Metall. 40 683

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Metallurgical Engineering, Indian Institute of Technology, 600 036, Madras, India

    O Prabhakar

Authors
  1. O Prabhakar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prabhakar, O. Solidification modelling. Bull. Mater. Sci. 16, 543–560 (1993). https://doi.org/10.1007/BF02757655

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02757655

Keywords

Search

Navigation