Classification and resolution adaptive drag modelling of gas-liquid interfaces with a multifield two-fluid model

Reliable techniques for the numerical simulation of gas-liquid flows at industrial scales are of great interest for safety analysis and efficiency optimisation, e.g. in nuclear power or metal processing industries. This type of simulation is hard to carry out due to the immense range of scales, which is spanned by interfacial and turbulent structures. For this purpose, hybrid morphology-adaptive numerical frameworks are being developed in the recent years, combining different well established numerical methods for individual flow regimes. The present work follows the approach of Meller et al. (Int J Numer Meth Fluids. 2021; 93: 748-773), who utilise the Euler-Euler approach to statistically describe multiphase structures in dispersed flow regimes, such as bubbly flows, as a basis. At the same time, regimes with resolved gas-liquid interfaces, such as large rising gas bubbles or horizontal interfaces in stratified flows, are captured by means of a Volume-of-Fluid-like method (Tekavčič et al., Nucl Eng Des. 2021; 379: 111223). A fully morphology-adaptive numerical framework needs to comprise transitions between the aforementioned regimes. Hence, the limits of both underlying basic numerical approaches need to be pushed towards and beyond an overlapping region of grid resolution with adequate predictive power, such that the whole spectrum of length scales is covered, forming the basis of morphology transitions.
For this purpose, the present work focuses on the extension of the Volume-of-Fluid methodology towards reliable resolved simulations of gas-liquid interfaces with very coarse grid resolutions. By means of the underlying two-fluid model, an interfacial slip velocity in the interface region becomes generally possible and can be chosen physically motivated. The flow in the vicinity of the interface needs to be classified. For this purpose, the latter is categorised to be of shear type, stagnant type or in between the two. Furthermore, a dimensionless grid spacing is evaluated based on the shear stress across the interface, similarly to the y+ value for the cell thickness of wall-bounded flows. Besides that, interface curvature is considered in relation to grid spacing. From these information, a degree of under-resolution of the interface is determined, which subsequently serves as a criterion for the drag modelling framework. On this basis, interfacial drag coupling is manipulated, such that interfacial slip can take place in the direction tangential to the interface, whenever required. While the interfacial drag formulation of Štrubelj and Tiselj (Int J Numer Methods Engng. 2011; 85: 575-590) is used in case of proper resolution, the closure formulations of Porombka and Höhne (Chem Eng Sci. 2015; 134: 348-459) or Marschall (Technical University of Munich, PhD Thesis, 2011) are considered for portions of the computational domain, where interfaces are classified to be under-resolved. The functionality of the described procedure is validated in cases of 2D and 3D rising gas bubbles, considering their shape and rising velocity. Moreover, gas and liquid velocity profiles of a stratified flow serve as a validation in an additional flow regime.
In this way, the numerical prediction of the gas-liquid interface is improved, pushing the limit of spatial resolutions with adequately reliable predictions towards extremely coarse computational grids, which is the prerequisite for efficient numerical simulations in large-scale applications.