[Paper Review] Riemann Solvers for Phase Transition in a Compressible Sharp-Interface Method

Steven Jöns, Claus‐Dieter Munz|arXiv (Cornell University)|Jul 5, 2022

Gas Dynamics and Kinetic Theory4 citations

TL;DR

This paper proposes exact and approximate Riemann solvers for compressible two-phase flows with phase transition, using classical irreversible thermodynamics to model interfacial mass and heat fluxes via Onsager coefficients. The solvers are integrated into a level-set ghost fluid method, validated against molecular dynamics data and applied to shock-droplet interactions, demonstrating that phase transition significantly alters droplet deformation and wake structure.

ABSTRACT

In this paper, we consider Riemann solvers with phase transition effects based on the Euler-Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coefficients for evaporation and condensation. We use the proposed Riemann solvers in a sharp-interface level-set ghost fluid method to couple the individual phases with each other. The Riemann solvers are validated against molecular dynamics data of evaporating Lennard-Jones truncated and shifted fluid. We further study the effects of phase transition on a shock-drop interaction with the novel approximate Riemann solvers.

Motivation & Objective

• To develop thermodynamically consistent Riemann solvers for two-phase compressible flows with phase transition.
• To address the non-uniqueness and hyperbolicity issues in the two-phase Riemann problem via kinetic relations and irreversible thermodynamics.
• To enable accurate coupling of phases in a sharp-interface method by incorporating interfacial mass and heat fluxes.
• To validate the solvers against molecular dynamics simulations of evaporating Lennard-Jones fluids.
• To assess the impact of phase transition on complex shock-droplet interactions in 2D flows.

Proposed method

• Models phase transition using classical irreversible thermodynamics with Onsager coefficients for evaporation and condensation.
• Derives an exact Riemann solver using a kinetic relation to resolve non-uniqueness in the two-phase Riemann problem.
• Develops two approximate Riemann solvers based on HLL/HLLC: one iterative (HLLP) and one purely algebraic (HLLP0).
• Integrates the Riemann solvers into a level-set ghost fluid method to enforce interfacial jump conditions.
• Uses a modified mesh-velocity approach to track the interface and compute ghost states via Riemann solutions.
• Employs a source-term-free formulation with interfacial heat fluxes from both phases, ensuring energy conservation.

Experimental results

Research questions

• RQ1 How can the two-phase Riemann problem with phase transition be solved uniquely and thermodynamically consistently?
• RQ2 What is the impact of using exact vs. approximate Riemann solvers on the accuracy of shock-droplet interaction simulations?
• RQ3 How do Onsager coefficients derived from irreversible thermodynamics affect interfacial flux predictions?
• RQ4 To what extent does phase transition alter droplet deformation and wake structure in shock-droplet interactions?
• RQ5 How sensitive are the results to mesh resolution and the choice between iterative and non-iterative Riemann solvers?

Key findings

• The exact Riemann solver and both approximate solvers (HLLP and HLLP0) show good agreement with molecular dynamics data for evaporating Lennard-Jones fluids.
• The HLLP0 solver, being algebraic, achieves similar results to the iterative HLLP solver with slightly lower computational cost.
• Phase transition leads to a significant cooling effect in the droplet wake, visible as lower temperatures and reduced cold vapor in the absence of evaporation.
• Shock-droplet interaction simulations show distinct differences in droplet deformation and vortex structures when phase transition is included.
• Underresolved meshes lead to a slight overprediction of interfacial fluxes, indicating sensitivity to mesh resolution.
• The absence of phase transition results in stronger bow shocks and faster wave speeds, highlighting the cooling and stabilizing role of evaporation.