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 multi-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 multi-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.

Comparison of macro- and microscopic solutions of the Riemann problem I. Supercritical shock tube and expansion into vacuum

“…For this study, the method of Fechter et al [16,18,19] was simplified to a one-dimensional front-tracking scheme. In the bulk phases, the solution was obtained by the DGSEM solver FLEXI .…”

“…We follow the ideas of a ghost fluid approach as proposed in Refs. [16,18,19,49] and use this solution to define the ghost states. The inner states at the interface U * liq and U # are taken as ghost states for the respective bulk phase.…”

“…To alleviate this numerical problem, similar to Ref. [18], a second contact wave was introduced as shown in Fig. 5.…”

On Riemann solvers and kinetic relations for isothermal two-phase flows with surface tension

“…It turns out that the use of a kinetic relation that has been derived by density functional theory in [26] gives excellent agreement with the measured data while other choices fail. Besides the obvious interest to understand Riemann problems from the analytic point of view, the Riemann problem is essential for all numerical methods that rely on some kind of interface tracking (see [9,13,14,15,16,22,31]). The tracking approach uses any finite volume or discontinuous Galerkin method as powerful tool to solve (1.1) numerically in the bulk sets.…”

Expansion rates of bubble clusters in superheated liquids

“…The simplifications include an estimation of the outer wave speeds (rarefaction and shock waves) as well as omission of the contact wave. The iteration procedure now simplifies to finding the interfacial mass flux where we use the kinetic relation [18] cent 9 m…”