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Title: A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension

Abstract

The numerical approximation of non-isothermal liquid–vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface approach which treats the interface as a shock-wave like discontinuity. Any mixing of fluid phases is avoided by using the flow solver in the bulk regions only, and a ghost-fluid approach close to the interface. The coupling states for the numerical solution in the bulk regions are determined by the solution of local two-phase Riemann problems across the interface. The Riemann solution accounts for the relevant physics by enforcing appropriate jump conditions at the phase boundary. A wide variety of interface effects can be handled in a thermodynamically consistent way. This includes surface tension or mass/energy transfer by phase transition. Moreover, the local normal speed of the interface, which is needed to calculate the time evolution of the interface, is given by the Riemann solution. The interface tracking itself is based on a level-set method. The focus in this paper is the description of the two-phase Riemann solver and its usage within the sharp interface approach. One-dimensional problems are selected to validate the approach. Finally, themore » three-dimensional simulation of a wobbling droplet and a shock droplet interaction in two dimensions are shown. In both problems phase transition and surface tension determine the global bulk behavior.« less

Authors:
 [1];  [1];  [2];  [2]
  1. Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart (Germany)
  2. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart (Germany)
Publication Date:
OSTI Identifier:
22622289
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 336; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; DROPLETS; ENERGY TRANSFER; HEAT; INTERFACES; LIQUIDS; MASS; NUMERICAL SOLUTION; PHASE TRANSFORMATIONS; RESOLUTION; SHOCK WAVES; SURFACE TENSION; SURFACES; THREE-DIMENSIONAL CALCULATIONS; TWO-PHASE FLOW; VAPORS; VELOCITY

Citation Formats

Fechter, Stefan, E-mail: stefan.fechter@iag.uni-stuttgart.de, Munz, Claus-Dieter, E-mail: munz@iag.uni-stuttgart.de, Rohde, Christian, E-mail: Christian.Rohde@mathematik.uni-stuttgart.de, and Zeiler, Christoph, E-mail: Christoph.Zeiler@mathematik.uni-stuttgart.de. A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.02.001.
Fechter, Stefan, E-mail: stefan.fechter@iag.uni-stuttgart.de, Munz, Claus-Dieter, E-mail: munz@iag.uni-stuttgart.de, Rohde, Christian, E-mail: Christian.Rohde@mathematik.uni-stuttgart.de, & Zeiler, Christoph, E-mail: Christoph.Zeiler@mathematik.uni-stuttgart.de. A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension. United States. doi:10.1016/J.JCP.2017.02.001.
Fechter, Stefan, E-mail: stefan.fechter@iag.uni-stuttgart.de, Munz, Claus-Dieter, E-mail: munz@iag.uni-stuttgart.de, Rohde, Christian, E-mail: Christian.Rohde@mathematik.uni-stuttgart.de, and Zeiler, Christoph, E-mail: Christoph.Zeiler@mathematik.uni-stuttgart.de. 2017. "A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension". United States. doi:10.1016/J.JCP.2017.02.001.
@article{osti_22622289,
title = {A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension},
author = {Fechter, Stefan, E-mail: stefan.fechter@iag.uni-stuttgart.de and Munz, Claus-Dieter, E-mail: munz@iag.uni-stuttgart.de and Rohde, Christian, E-mail: Christian.Rohde@mathematik.uni-stuttgart.de and Zeiler, Christoph, E-mail: Christoph.Zeiler@mathematik.uni-stuttgart.de},
abstractNote = {The numerical approximation of non-isothermal liquid–vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface approach which treats the interface as a shock-wave like discontinuity. Any mixing of fluid phases is avoided by using the flow solver in the bulk regions only, and a ghost-fluid approach close to the interface. The coupling states for the numerical solution in the bulk regions are determined by the solution of local two-phase Riemann problems across the interface. The Riemann solution accounts for the relevant physics by enforcing appropriate jump conditions at the phase boundary. A wide variety of interface effects can be handled in a thermodynamically consistent way. This includes surface tension or mass/energy transfer by phase transition. Moreover, the local normal speed of the interface, which is needed to calculate the time evolution of the interface, is given by the Riemann solution. The interface tracking itself is based on a level-set method. The focus in this paper is the description of the two-phase Riemann solver and its usage within the sharp interface approach. One-dimensional problems are selected to validate the approach. Finally, the three-dimensional simulation of a wobbling droplet and a shock droplet interaction in two dimensions are shown. In both problems phase transition and surface tension determine the global bulk behavior.},
doi = {10.1016/J.JCP.2017.02.001},
journal = {Journal of Computational Physics},
number = ,
volume = 336,
place = {United States},
year = 2017,
month = 5
}
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  • This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensionalmore » tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.« less