A unified compressible two-phase, two-scale model with inter-scale mass transfer for separated-to-disperse transitions in atomizing flows

  • Haegeman, Ward (CMAP, École polytechnique)
  • Orlando, Giuseppe (CMAP, École polytechnique)
  • Kokh, Samuel (CEA, Maison de la Simulation)
  • Massot, Marc (CMAP, École polytechnique)

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We present a novel two-phase, two-scale compressible flow model that enables a unified description of both separated-interface and disperse-phase regimes [3]. The model is derived in a isothermal setting and is based on Hamilton’s Stationary Action Principle [2]. Mass transfer mechanisms between the large and small scales are activated when the interface curvature exceeds a grid-independent cutoff length scale, allowing the transition from a resolved large-scale interface representation to a sub-grid disperse phase. This approach ensures regularization of the large-scale interface while simultaneously modeling atomization through the generation of a spray of droplets at the small scale [3]. The resulting model is dissipative, in the sense that it satisfies the second law of thermodynamics. It extends the previous work in [1] with a refined modeling perspective and a revised framework that guarantees full thermodynamic consistency between scales. We further address the numerical simulation of the proposed model and introduce robust numerical strategies that ensure the preservation of physically admissible states. The performance and properties of the model and numerical scheme are demonstrated on a representative test case. Finally, preliminary results for extending the methodology to full thermodynamics will also be presented. [1] A. Loison, S. Kokh, T. Pichard, M. Massot. A unified two-scale gas-liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales. International Journal of Multiphase Flow, 177:104857, 2024. [2] W. Haegeman, S. Kokh, M. Massot, G. Orlando. A generic framework to derive systems of conservation laws with source terms and its application to heat conduction in fluid flows: An alternative to the method of moments in kinetic theory of gases?. ESAIM: Proceedings and surveys, 78:80-97, 2025. [3] W. Haegeman, G. Orlando, S. Kokh, M. Massot. A two-scale two-phase flow model for the separate-to-disperse phase transition in atomizing flows (in preparation).