DOI QR코드

DOI QR Code

NUMERICAL ANALYSIS OF THE SHOCK WAVES IN COMPRESSIBLE SOLIDS AND LIQUIDS USING A SIX-EQUATION DIFFUSE INTERFACE MODEL

6-방정식 확산경계 모델을 이용한 압축성 고체 및 액체에서 충격파 해석

  • Yeom, Geum-Su (School of Mechanicals Automotive Engineering, Gunsan Nat'l Univ.)
  • 염금수 (군산대학교 기계자동차공학부)
  • Received : 2011.04.23
  • Accepted : 2012.09.17
  • Published : 2012.09.30

Abstract

In this paper, the shock waves in compressible solids and liquids are simulated using a six-equation diffuse interface multiphase flow model that is extended to the Cochran and Chan equation of state. A pressure relaxation method based on a volume fraction function and a pressure-correction equation are newly implemented to the six-equation model. The developed code has been validated by a shock tube problem with liquid nitromethane and an impact problem of a copper plate on a solid explosive. In addition, a new problem, an impact of a copper plate on liquid nitromethane, has been solved. The present code well shows the wave structures in compressible solids and liquids without any numerical oscillations and overshoots. After the impact of a solid copper plate on liquid, two shock waves (one propagates into liquid and the other into solid) are generated and a material interface moves to the impacting direction. The computational results show that the shock velocity inside the liquid linearly increases with the impact velocity.

Keywords

References

  1. 1996, Abgrall, R., "How to Prevent Pressure Oscillations in Multicomponent Flow Calculations: a Quasi Conservative Approach," J. Comput. Phys., Vol.125, pp.150-160. https://doi.org/10.1006/jcph.1996.0085
  2. 1981, Hirt, C.W. and Nichols, B.D., "Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries," J. Comput. Phys., Vol.39, pp.201-255. https://doi.org/10.1016/0021-9991(81)90145-5
  3. 1999, Fedkiw, R., Aslam, T., Merriman, B. and Osher, S., "A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)," J. Comput. Phys., Vol.152, pp.457-492. https://doi.org/10.1006/jcph.1999.6236
  4. 1999, Saurel, R. and Abgrall, R., "A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows," J. Comput. Phys., Vol.150, pp.425-467. https://doi.org/10.1006/jcph.1999.6187
  5. 2001, Saurel, R. and LeMetayer, O., "A Multiphase Model for Compressible Flows with Interfaces, Shocks, Detonation Waves and Cavitation," J. Fluid Mech., Vol.431, pp.239-271. https://doi.org/10.1017/S0022112000003098
  6. 2009, Saurel, R., Petitpas, F. and Berry, R.A., "Simple and Efficient Relaxation Methods for Interfaces Separating Compressible Fluids, Cavitating Flows and Shocks in Multiphase Mixtures," J. Comput. Phys., Vol.228, pp.1678-1712. https://doi.org/10.1016/j.jcp.2008.11.002
  7. 2010, Zein, A., Hantke, M. and Warnecke, G., "Modeling Phase Transition for Compressible Two-Phase Flows Applied to Metastable Liquids," J. Comput. Phys., Vol. 229, pp.2964-2998. https://doi.org/10.1016/j.jcp.2009.12.026
  8. 2001, Kapila, A.K., Menikoff, R., Bdzil, J.B., Son, S.F. and Stewart, D.S., "Two-Phase Modeling of Deflagration -to-Detonation Transition in Granular Materials: Reduced Equations," Phys. Fluids, Vol.13, pp.3002-3024. https://doi.org/10.1063/1.1398042
  9. 2008, Saurel, R., Petitpas, F. and Abgrall, R., "Modelling Phase Transition in Metastable Liquids: Application to Cavitating and Flashing Flows," J. Fluid Mech., Vol.607, pp.313-350.
  10. 2012, Yeom, G.S. and Chang, K.S., "New HLLC-Type Riemann Solver for the Compressible Six-Equation Two -Fluid Model," Comput. Fluids, accepted for publication.
  11. 1979, Cochran, G. and Chan, J., "Shock Initiation and Detonation Models in One and Two Dimensions," Lawrence Livermore National Laboratory Report.
  12. 1998, Saurel, R. and Massoni, J., "On Riemann -Problem-Based Methods for Detonations in Solid Energetic Materials," Int. J. Numer. Meth. Fluids, Vol.26, pp.101-121. https://doi.org/10.1002/(SICI)1097-0363(19980115)26:1<101::AID-FLD629>3.0.CO;2-0
  13. 1999, Toro, E.F., Riemann Solver sand Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer-Verlag, Berlin.
  14. 1999, Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P., Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York.
  15. 2007, Saurel, R., Franquet, E., Daniel, E. and LeMetayer, O., "A Relaxation-Projection Method for Compressible Flows. Part I: The Numerical Equation of State for the Euler Equations," J. Comput. Phys., Vol.223, pp.822-845. https://doi.org/10.1016/j.jcp.2006.10.004
  16. 2001, Shyue, K.M., "A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with Mie-Gruneisen Equation of State," J. Comput. Phys., Vol.171, pp.678-707. https://doi.org/10.1006/jcph.2001.6801
  17. 2011, Tian, B., Toro, E.F. and Castro, C.E., "A Path-Conservative Method for a Five-Equation Model of Two-Phase Flow with an HLLC-type Riemann Solver," Comput Fluids, Vol.46, pp.122-132. https://doi.org/10.1016/j.compfluid.2011.01.038