Abstract
In this work we consider the Navier–Stokes–Korteweg equations, a diffuse-interface model describing liquid–vapor phase transitions. A numerical scheme for this model is constructed based on functional entropy variables and a new time integration concept. The fully discrete scheme is unconditionally stable in entropy and second-order time-accurate. Isogeometric analysis is utilized for spatial discretization. The boiling problem is numerically investigated by making proper assumptions on transport parameters and boundary conditions. Compared with traditional multiphase solvers, the dependence on empirical data is significantly reduced, and this modeling approach provides a unified predictive tool for both nucleate and film boiling. Both two- and three-dimensional simulation results are provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson, D.M., McFadden, G.B., Wheeler, A.A.: Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139–165 (1998)
Dhir, V.K.: Boiling heat transfer. Annu. Rev. Fluid Mech. 30, 365–401 (1998)
Dunn, J.E., Serrin, J.: On the thermomechanics of interstitial working. Arch. Ration. Mech. Anal. 88, 95–133 (1985)
Gomez, H., Hughes, T.J.R., Nogueira, X., Calo, V.: Isogeometric analysis of the Navier-Stokes-Korteweg equations. Comput. Methods Appl. Mech. Eng. 199, 1828–1840 (2010)
Gomez, H., Hughes, T.J.R.: Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. J. Comput. Phys. 230, 5310–5327 (2011)
Hughes, T.J.R., Franca, L.P., Mallet, M.: A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics. Comput. Methods Appl. Mech. Eng. 54, 223–234 (1986)
Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)
Juric, D., Tryggvason, G.: Computation of boiling flows. Int. J. Multiphase Flow 24, 387–410 (1998)
Liu, J., Gomez, H., Evans, J.A., Landis, C.M., Hughes, T.J.R.: Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier-Stokes-Korteweg equations. J. Comput. Phys. 248, 47–86 (2013)
Liu, J., Landis, C.M., Gomez, H., Hughes, T.J.R.: Liquid-vapor phase transition: thermomechanical theory, entropy stable numerical formulation, and boiling simulations. Comput. Methods Appl. Mech. Eng. 297, 476–553 (2015)
Shakib, F., Hughes, T.J.R., Johan, Z.: A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 89, 141–219 (1991)
Acknowledgements
This work was partially supported by the Office of Naval Research under contract number N00014-08-1-0992.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Liu, J., Hughes, T.J.R. (2016). Isogeometric Phase-Field Simulation of Boiling. In: Bazilevs, Y., Takizawa, K. (eds) Advances in Computational Fluid-Structure Interaction and Flow Simulation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40827-9_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-40827-9_17
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-40825-5
Online ISBN: 978-3-319-40827-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)