[Paper Review] Meshfree One-Fluid Modelling of Liquid-Vapor Phase Transitions

Pratik Suchde, Heinrich Kraus+2 more|arXiv (Cornell University)|Mar 19, 2022

Numerical methods in engineering4 citations

TL;DR

This paper presents a meshfree one-fluid approach for simulating liquid-vapor phase transitions, particularly vaporization at free surfaces and superheated interfaces, without explicitly modeling the phase interface. By varying material properties with temperature and enriching strong-form generalized finite difference methods to capture discontinuities, the method accurately models large property jumps and complex topological changes, showing strong agreement with experimental data in jet impingement and Leidenfrost effect scenarios.

ABSTRACT

We introduce a meshfree collocation framework to model the phase change from liquid to vapor at or above the boiling point. While typical vaporization or boiling simulations focus on the vaporization from the bulk of the fluid, here we include the possibility of vaporization from the free surface, when a moving fluid comes into contact with a superheated surface. We present a continuum, one-fluid approach in which the liquid and vapor phases are modeled with the same constitutive equations, with different material properties. The novelty here is a monolithic approach without explicit modeling of the interface between the phases, neither in a sharp nor diffuse sense. Furthermore, no interface boundary conditions or source terms are needed between the liquid and vapor phases. Instead, the phase transition is modeled only using material properties varying with temperature. Towards this end, we also present an enrichment of strong form meshfree generalized finite difference methods (GFDM) to accurately capture derivatives in the presence of jumps in density, viscosity, and other physical properties. The numerical results show a good agreement with experimental results, and highlight the ability of our proposed framework to model phase changes with large jumps.

Motivation & Objective

• Address the challenge of simulating complex liquid-vapor phase transitions in metal cutting processes where boiling occurs at free surfaces and interfaces with solid tools.
• Overcome limitations of conventional sharp and diffuse interface methods in handling topologically complex, evolving interfaces with multiple free boundaries.
• Develop a monolithic, one-fluid framework that avoids explicit interface tracking or source terms by embedding phase change solely in temperature-dependent material properties.
• Enable accurate simulation of large property jumps (density, viscosity) across phase boundaries using enriched strong-form meshfree methods.
• Validate the method against experimental data for fluid jet impingement on hot surfaces and demonstrate capability for modeling the Leidenfrost effect.

Proposed method

• Employ a one-fluid, monolithic formulation where liquid and vapor phases are governed by the same constitutive equations with temperature-dependent material properties.
• Model phase transition via a smeared latent heat over a narrow temperature range around the boiling point, eliminating the need for explicit interface tracking.
• Use a meshfree generalized finite difference method (GFDM) in a strong form to approximate spatial derivatives in the Navier-Stokes and energy equations.
• Enrich the test function space with discontinuous functions to improve accuracy in regions with sharp gradients in density, viscosity, and other properties.
• Implement a Lagrangian framework to naturally handle moving boundaries and free surfaces without remeshing.
• Apply pressure interpolation with enhanced stability in phase change regions to maintain numerical robustness.

Experimental results

Research questions

• RQ1 Can a one-fluid, interface-free approach accurately simulate liquid-vapor phase change in complex geometries with free surfaces and moving boundaries?
• RQ2 How does a temperature-dependent material property model compare to conventional interface-based methods in capturing boiling dynamics and volume expansion?
• RQ3 To what extent can enriched strong-form meshfree methods capture large gradients in physical properties without explicit interface resolution?
• RQ4 Can the proposed method reproduce experimental results for fluid jet impingement on hot surfaces, including temperature evolution and vapor layer formation?
• RQ5 Is the model capable of simulating the Leidenfrost effect and other complex vaporization phenomena without explicit interface tracking?

Key findings

• The method successfully captures vaporization at free surfaces and complex interface topologies, such as those formed during jet impingement on hot plates, without explicit interface tracking.
• Numerical results show good qualitative and quantitative agreement with experimental data for temperature history at the rear surface of a heated plate, including initial oscillations and stabilization trends.
• The simulated wetting area and vapor ring formation around the impingement point closely match experimental observations, though minor asymmetries suggest room for improvement in heat transfer modeling.
• The method accurately models large jumps in density and viscosity across the phase change region due to the enriched test function space in the strong-form GFDM.
• First simulations demonstrate the capability to model the Leidenfrost effect, indicating potential for broader application in high-temperature fluid dynamics.
• The approach enables stable simulations in Lagrangian frameworks without remeshing, even under large deformations and topological changes of the fluid domain.