Commun. Comput. Phys., 12 (2012), pp. 1129-1147.


Dynamic Modeling of Phase Crossings in Two-Phase Flow

S. Madsen 1*, C. Veje 1, M. Willatzen 1

1 Alsion 2, Mads Clausen Institute, University of Southern Denmark, DK-6400 Sonderborg, Denmark.

Received 19 May 2011; Accepted (in revised version) 11 November 2011
Available online 17 April 2012
doi:10.4208/cicp.190511.111111a

Abstract

Two-phase flow and heat transfer, such as boiling and condensing flows, are complicated physical phenomena that generally prohibit an exact solution and even pose severe challenges for numerical approaches. If numerical solution time is also an issue the challenge increases even further. We present here a numerical implementation and novel study of a fully distributed dynamic one-dimensional model of two-phase flow in a tube, including pressure drop, heat transfer, and variations in tube cross-section. The model is based on a homogeneous formulation of the governing equations, discretized by a high resolution finite difference scheme due to Kurganov and Tadmore. The homogeneous formulation requires a set of thermodynamic relations to cover the entire range from liquid to gas state. This leads a number of numerical challenges since these relations introduce discontinuities in the derivative of the variables and are usually very slow to evaluate. To overcome these challenges, we use an interpolation scheme with local refinement. The simulations show that the method handles crossing of the saturation lines for both liquid to two-phase and two-phase to gas regions. Furthermore, a novel result obtained in this work, the method is stable towards dynamic transitions of the inlet/outlet boundaries across the saturation lines. Results for these cases are presented along with a numerical demonstration of conservation of mass under dynamically varying boundary conditions. Finally we present results for the stability of the code in a case of a tube with a narrow section.

AMS subject classifications: 76T10, 80A20, 65M06

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Key words: Two-phase flow, heat exchange, flow boiling, central difference.

*Corresponding author.
Email: sma@mci.sdu.dk (S. Madsen), veje@mci.sdu.dk (C. Veje), willatzen@mci.sdu.dk (M. Willatzen)
 

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