Numerical modelling of sub-grid wave turbulence at the interface of horizontal multiphase flows

In the last decade, applications of Computational Fluid Dynamic (CFD) methods for nuclear applications received more and more attention, as they proved to be a valuable complementary tool for design and safety. The main interest towards CFD consists in fact in the possibility of obtaining detailed 3D complete flow-field information on relevant physical phenomena at lower cost than experiments.

Typically free surfaces manifest as stratified and wavy flows in horizontal flow domain where gas and liquid are separated by gravity.

Stratified two-phase flows are relevant in many nuclear applications, e.g. pipelines, main coolant lines, horizontal heat exchangers and storage tanks. Special flow characteristics as flow rate, pressure drop and flow regimes have always been of engineering interest. Wallis (1973) analyzed the onset of slugging in horizontal and near horizontal gas-liquid flows. Flow maps which predict transitions between horizontal flow regimes in pipes were introduced e.g. by Taitel and Dukler (1976) and Mandhane et al. (1974). The most important flow regimes are smooth stratified flow, wavy flow, slug flow and elongated bubble flow. Taitel and Dukler (1976) explained the formation of slug flow by the Kelvin-Helmholtz instability. They also proposed a model for the frequency of slug initiation (Taitel and Dukler, 1977).

CFD simulations for free surface flows require the modeling of the non-resolved scales. For modeling of interfacial transfers it is necessary to select the adequate interfacial transfer models and to determine the interfacial area. The numerical solution can resolve the statistically averaged motion of the free surface (including waves) which may not be too small relatively to the channel height and to the characteristic length of the spatial discretization. However, the detailed structure of interacting boundary layers of the separated continuous phases and surface ripples cannot be resolved. Instead, its influence on the average flow must be modeled.

Non-resolved small scale structures of the interface have influence on mass, momentum and heat transfer between the phases. The type of required models depends on the general modeling approach used. To model the momentum transfer e.g. in the frame of the two-fluid model the correlations for the interfacial drag are used. In the past due to the lack of appropriate models often drag correlations valid for bubbly flows or correlations developed for 1D codes were used to simulate the interfacial momentum transfer at the free surface. Such approaches use simplifications and therefore are not able to represent completely the phenomena.