Development of a k-ε Model for Bubbly Two-Phase Flow

Abstract

An extension of the k-ε model for bubbly two-phase flow is proposed and tested against experimental data. The basic assumption made is that the shear-induced turbulence and bubble-induced turbulence may be linearly superposed. This assumption results in a model with two time constants that matches both homogeneous two-phase turbulence data (Lance and Bataille, 1991) and pipe data (Serizawa, 1986). The coefficients of the single-phase k-ε model have not been modified and only one additional coefficient is required: the virtual volume coefficient of the bubbles, which may be determined from first principles. This model not only agrees with the data trends, but it also predicts the turbulence suppression which has been measured for high Reynolds number bubbly air/water flows in pipes.

Numerical Investigation of Turbulent Bubbly Flow Under Breaking Waves

“…These bubbles are involved in intense interactions with mean flow and turbulence, producing a complex two-phase bubbly flow field. It is well known that the presence of bubbles can suppress liquid phase turbulence (Wang et al, 1987;Kataoka and Serizawa, 1989;Serizawa and Kataoka, 1990;Lopez de Bertodano et al, 1994). Other studies have also revealed that bubbles may alter the local vorticity field and consequently deform or displace the vortex structure (Sridhar and Katz, 1999;Watanabe et al, 2005).…”

The Geometric Conservation Based Algorithms For Multi-Fluid Flow At All Speeds

“…Many experimental and numerical studies involving the prediction of radial phase distribution in turbulent upward air-water flow in a pipe have appeared in the literature [61][62][63][64][65][66][67][68]. These studies indicated that the lateral forces that most strongly affect the void distribution are the lateral lift force and the turbulent stresses.…”

“…For two-phase flow, several extensions of the k-ε model that are based on calculating the turbulent viscosity by solving the k and ε equations for the carrier or continuous phase only have been proposed in the literature [50][51][52][53][54][55]. In a recent article, Cokljat and Ivanov [49] presented a phase coupled k-ε turbulence model, intended for the cases where a non-dilute secondary phase is present, in which the k-ε transport equations for all phases are solved.…”

Toward a Multiphase Local Approach in the Modeling of Flotation and Mass Transferin Gas-Liquid Contacting Systems

“…Nevertheless, from a practical point of view, second order modeling is still difficult to use and turbulence models based on turbulent viscosity concept, particularly two-equation models, remain widely used in industrial applications. Several two-equation models were developed for turbulent bubbly flows (Lopez de Bertodano et al, 1994;Lee et al, 1989;Morel, 1995;Troshko & Hassan, 2001). All of these models are founded on an extrapolation of single-phase turbulence models by introducing supplementary terms (source terms) in the transport equations of turbulent energy and dissipation rate.…”