Revisiting the linear forcing of turbulence in single-phase and two-phase flows
Résumé
This paper presents a comprehensive framework for addressing the challenges associated with turbulence linear forcing in incompressible single-phase and two-phase flows. By examining existing literature on linear forcing techniques for single-phase flows, which typically yield constant turbulent production, kinetic energy, or dissipation rates, we derive a general method based on constant energetics. This method ensures that any constant power of kinetic energy multiplied by any constant power of dissipation rate remains unchanged over time. A linear stability analysis of
this forcing method is performed, demonstrating its relevance and suitability in practical scenarios. Then, a novel solution is proposed for addressing numerical dissipation by measuring and including it in the linear forcing term. This methodology is adapted to the general method proposed for
constant energetics and validated on a single-phase flow. Finally, we investigate the linear forcing of turbulence in two-phase flows. Removing the mean contribution of the capillary forces prevents the exponential growth of kinetic energy. The paper also explores the impact of capillary forces
on the energetics budgets and their implications for turbulent forcing. The framework is validated through turbulent emulsion and mono-disperse droplet-laden turbulence scenarios, demonstrating its feasibility across various two-phase flow applications.
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