A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

Journal Article · Tue Nov 18 00:00:00 EST 2025 · Fluids

DOI:https://doi.org/10.3390/fluids10110302· OSTI ID:3012222

Mahamud, Rajib ^[1]; Waters, Jiajia ^[2]; Bujack, Roxana Barbara ^[2]

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1. Idaho State Univ., Pocatello, ID (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 3012222
• Report Number(s): LA-UR--25-31624; 10.3390/fluids10110302
• Journal Information: Fluids, Journal Name: Fluids Journal Issue: 11 Vol. 10; ISSN 2311-5521
• Publisher: MDPI
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
VOF
conjugate heat transfer
dynamic Vreman
large eddy simulation
vector field topology