On the interfacial roughness scale in turbulent stratified two-phase flow: 3D lattice Boltzmann numerical simulations with forced turbulence and surfactant

• Published in: International journal of multiphase flow 2015-03, Vol.69, p.102-114
• Main Authors: Skartlien, R., Sollum, E., Fakharian, F., Palmer, T.L.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Fluid flow; Interfacial closure relations; Interfacial elasticity; Marangoni stress; Roughness; Scale models; Surfactant; Surfactants; Three dimensional; Turbulence; Turbulent flow; Two-phase turbulence modeling
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/j.ijmultiphaseflow.2014.11.003

•Simulations of turbulent, stratified two-phase flow with surfactant were conducted.•An energy based roughness scale model for the interface was developed.•The addition of surfactant lead to an increased roughness scale.•Interfacial dilatational elasticity and Marangoni stresses were important. Numerical 3D simulations of turbulent, stratified two-phase shear flow with a surfactant laden interface were used to test and develop a phenomenological interfacial roughness scale model where the energy required to deform the interface (buoyancy, interfacial tension, and viscous work) is proportional to the turbulent kinetic energy adjacent to the interface. The turbulence was forced in the upper and lower liquids in the simulations, to emulate the interfacial dynamics without requiring (prohibitively) large simulation domains and Reynolds numbers. The addition of surfactant lead to an increased roughness scale (for the same turbulent kinetic energy) due to the introduction of interfacial dilatational elasticity that suppressed horizontal motion parallel to the interface, and enhanced the vertical motion. The phenomenological roughness scale model was not fully developed for dilatational elasticity in this work, but we proposed a source term that represents surfactant induced pressure fluctuations near the interface. This source term should be developed further to account for the relation between surfactant density fluctuations and turbulence adjacent to the interface. We foresee that the roughness scale model can be used as a basis for more general interfacial closure relations in Reynolds averaged turbulence models, where also mobile surfactant is accounted for.