Viscosity induced drag force

The model closes interaction phase Mkj with effective viscosity //eff, and it is considered that the slurry phase of FTS is in the turbulent zone. The effective viscosity can be considered as turbulence viscosity, which can usually be solved by standard model, where turbulence induced by bubbles is also taken into consideration. Interaction force between the phases consists of drag, lift, and virtual mass force. The main force of interaction between phases often is overlooked. Drag force, caused by gas, drives the serious movements and the type of which is written as Eq. (28) ... 

In a recent study Jakobsen et al. [71] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise equivalent simulations were performed. Additional simulations were run with three different turbulence closures for the liquid phase, and no shear stress terms for the gas phase. A standard k — e model [95] was used to examine the effect of shear induced turbulence, case (a). In an alternative case (b), both shear- and bubble induced turbulence were accounted for by linearly superposing the turbulent viscosities obtained from the A — e model and the model of Sato and Sekoguchi [138]. A third approach, case (c), is similar to case (b) in that both shear and bubble induce turbulence contributions are considered. However, in this model formulation, case (c), the bubble induced turbulence contribution was included through an extra source term in the turbulence model equations [64, 67, 71]. The relevant theory is summarized in Sect. 8.4.4. 

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