Development and assessment of a target-$ω$ interfacial turbulence-damping model for stratified gas--liquid flow

Abstract

Interfacial turbulence damping is required in Reynolds-averaged simulations of stratified gas--liquid flows when strong interfacial velocity gradients are present. In this work, we develop a target-$ω$ interfacial damping formulation for the low-Reynolds-number Wilcox-type $k$--$ω$ model in a one-field RANS/VOF framework. A gas-side target value of the specific dissipation rate $ω$ is constructed from an effective interfacial wall coordinate determined from the local resolved flow. The constructed target-$ω$ provides a smooth transition between the viscous and logarithmic limits through power-law blending and requires no calibration of model constants against target data. \textcolor{black}{The formulation is first assessed against three gas-layer DNS cases at $Re_τ\simeq180$ with different interface velocities. The model reproduces the principal features of the mean velocity, turbulent kinetic energy and Reynolds shear-stress distributions, while showing substantially weaker sensitivity to the near-interface grid resolution than the Egorov-type formulation, although some grid dependence remains on the coarsest mesh. The assessment is then extended to the co-current Fabre stratified-flow experiment at a higher Reynolds number and to the counter-current Stäbler experiment}. In both cases, the present formulation provides generally good predictions of the gas-side mean flow and turbulence statistics without case-specific adjustment. For the Stäbler case, in which the liquid level develops as part of the coupled two-phase solution, the predicted mean liquid depth agrees closely with the measured value. These results indicate that the target-$ω$ formulation provides a consistent interfacial turbulence-damping treatment for resolved large gas--liquid interfaces over the range of conditions considered.