Conversions between kinetic and surface energy in periodically forced multiphase turbulence

Abstract

In multiphase flows, kinetic and interfacial energies coexist, and their mutual conversion can potentially influence the overall energy balance. However, in statistically steady flows these energy reservoirs remain constant, making such conversions undetectable. For them to be observed, a degree of unsteadiness must be introduced, here provided by the deliberate use of a fluctuating time-periodic input of kinetic energy into the system. The main focus of the present work is on the dynamical cycle connecting energy injection, conversion, and dissipation which we explore using {direct} numerical simulations of multiphase homogeneous isotropic turbulence, subjected to periodic forcing. The database includes various Reynolds and Weber numbers and volume fractions in the dense regime. To interpret and replicate the observed dynamics, we reformulate the \textit{Ka-Pi-bara} model of \cite{Bos2026} (an extension of the $k$--$\epsilon$ model) in terms of total energy (the sum of kinetic and surface energy), which we further enhance by adding equations for the surface energy and its destruction. This model accurately captures a key feature of turbulence: non-equilibrium effects, seen as the phase lag between kinetic energy and its rate of dissipation, which are found to operate also in multiphase flows. Linearizing the model highlights the various relevant time scales of the system and provides predictions of how different observables are coupled and respond to the energy input.

References in corpus (13)

• Droplet-turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions
• Modulation of homogeneous and isotropic turbulence in emulsions
• The "zeroth law" of turbulence: Isotropic turbulence simulations revisited
• The temporal evolution of the energy flux across scales in homogeneous turbulence
• Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy driven bubbly flows
• Response maxima in modulated turbulence
• Effects of Fluctuating Energy Input on the Small Scales in Turbulence
• Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence
• Energy transfer in simple and active binary fluid turbulence {\bf {-}} a false friend of incompressible MHD turbulence
• On the unsteady behavior of turbulence models
• Temporal large-scale intermittency and its impact on the statistics of turbulence
• Scale-by-scale kinetic energy budgets in multiphase turbulence
• Scale-by-scale energy transfers in bubbly flows