Finite Element Method for Multiphase Flow Instabilities | #Sciencefather #Researcherawards


Introduction

The study introduces a comprehensive finite element framework designed to model compressible, turbulent multiphase flows with heat transfer, addressing major limitations in conventional finite volume–based Volume of Fluid (VOF) approaches. By integrating a reconstruction-free VOF formulation with the dynamic Vreman large eddy simulation (LES) turbulence model, the method captures interfacial dynamics more accurately in high-speed two-fluid scenarios. Unlike traditional VOF studies that often omit thermal effects, this framework embeds energy transport directly into the multiphase formulation, enabling simultaneous prediction of flow evolution, turbulence, and heat exchange. Its capability to handle conjugate heat transfer without prescribing interfacial heat fluxes represents a major advancement over finite volume methods, which typically require explicit thermal boundary conditions that reduce accuracy. The framework’s effectiveness is demonstrated through instability growth validation, high-temperature flow over a cold cylinder, and compressible spray breakup, showing clear improvements in predictive reliability and physical realism.

Finite Element Framework for Compressible Multiphase Flows

The developed finite element methodology advances the modeling of compressible multiphase flows by enabling robust coupling between flow variables, material properties, and interfacial behavior. The formulation inherently accommodates large density ratios, surface tension effects, and turbulent fluctuations without relying on geometric interface reconstruction. By expressing governing conservation equations in a weak finite element form, the approach allows higher numerical stability and reduced dissipation, especially in flows involving strong shocks, rapid interface deformation, or atomization. Its adaptability to unstructured meshes provides additional advantages for complex geometries relevant to engineering and scientific applications.

Heat Transfer Modeling and Conjugate Thermal Interaction

A key innovation of this research is the incorporation of heat transfer directly within the VOF-based multiphase system, enabling accurate prediction of temperature evolution and thermal gradients across fluid phases. The finite element formulation naturally handles conjugate heat transfer, eliminating the need to impose heat flux values at solid–fluid boundaries and improving numerical consistency. This capability enhances predictive performance in systems where two-way thermal coupling plays a crucial role, such as metal cooling, phase change, or high-temperature turbulent flows. Validation using flow over a cold cylinder demonstrates improved agreement with experimental pressure coefficients and thermal distributions.

Turbulence Resolution Using Dynamic Vreman LES Model

The implementation of the dynamic Vreman large eddy simulation (LES) model ensures accurate resolution of subgrid-scale turbulence effects within compressible multiphase environments. This turbulence model effectively captures energy dissipation and coherent structure formation without requiring case-specific tuning. The integration within a finite element framework enhances stability in regions of strong shear, shock–interface interaction, or high-speed breakup processes. By combining LES turbulence modeling with VOF-based multiphase tracking, the approach provides deeper insight into the mechanisms governing instability growth and flow transitions.

Validation Through Instability Growth, Conjugate Cooling, and Spray Breakup

The study demonstrates the versatility of the proposed methodology by applying it to three benchmark cases that collectively validate flow dynamics, heat transfer, and multiphase breakup capabilities. The accurate prediction of two-fluid instability growth rates confirms the method’s effectiveness in capturing interfacial evolution. Conjugate cooling over a metal cylinder further validates thermal predictions through experimental correlation. The compressible spray injection and breakup simulation highlights the method's ability to capture atomization, ligament formation, and droplet dispersion under turbulence-driven conditions.

Performance Comparison with Finite Volume Methods

A direct comparison with traditional finite volume methods (FVM) shows that the finite element method (FEM) significantly improves accuracy in the spray injection and breakup case. With identical mesh resolution, FEM reduces the root mean square error (RMSE) from 6.96 mm to 4.85 mm and the mean absolute percentage error (MAPE) from 26.0% to 12.7%, demonstrating enhanced robustness in predicting interfacial deformation and heat transfer. These improvements highlight the advantages of variational formulations in handling complex multiphase flows and turbulent thermal interactions, reinforcing FEM’s potential as a superior tool for predictive multiphase flow simulation.

Global Particle Physics Excellence Awards


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#Sciencefather, #Reseacherawards, #FiniteElementMethod, #MultiphaseFlow, #TurbulentFlow, #VOFModel, #HeatTransfer, #ConjugateHeatTransfer, #LESModeling, #VremanModel, #CompressibleFlow, #SprayBreakup, #ScientificComputing, #ComputationalFluidDynamics, #ThermalModeling, #InterfaceTracking, #HighSpeedFlows, #InstabilityAnalysis, #Atomization, #NumericalSimulation, #EngineeringResearch, #FlowVisualization,

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