Bubble column reactors turbulence models

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Ranade, V.V. (1997b), Modeling of turbulent flow in a bubble column reactor, Chem. Eng. Res. Des., 75, 14. 

In a recent study Jakobsen et al [66] 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... 

Luo H (1993) Coalescence, break-up and liquid circulation in bubble column reactors. Dr ing Thesis, the Norwegian Institute of Technology, Trondheim Luo H, Svendsen HF (1996) Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J 42(5) 1225-1233... 

More recently, Kawase and co-workers have presented semi-analytical framework for the estimation of the volumetric mass transfer coefflcient in bubble column reactors with and without an internal draft tube [51,62,67]. They have essentially combined the Higbie s penetration model with the isotropic turbulence to deduce the following expression for gas-liquid mass transfer with power law liquids ... 

The US DOE had a major effort to understand the many variables affecting the performance of a bubble column reactor. Dudukovic and Toseland [75] outlined the cooperative study by Air Products and Chemicals (APC), Ohio State University (OSU), Sandia National Laboratory (SNL), and Washington University in St. Louis (WU). The efforts of this group have developed valuable unique experimental techniques for the measurement of gas holdup, velocity, and eddy diffusivities in bubble columns. They have obtained data that allows improved insight in churn-turbulent flow and have assessed the impact of various effects (internals, solid concentration, high gas velocity, pressure, etc.). General ideal flow pattern-based models do not reflect bubble column reality to date the models are based on a combination where some parameters are evaluated from first principles and some from the database. 

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. 

A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactor... 

Bubble columns Loop reactors Stirred tanks Hydrocyclones Reasonable Reasonable Reasonable Reasonable Modeling of chum-turbulent flow regime Modeling of chum-turbulent flow regime Improved geometrical representation of impeller and baffles Improved geometrical representation of system... 

The given k — e turbulence model formulation has been used to determine the turbulence of the continuous phase in two-phase bubbly flow by several investigators on bubble columns (e.g., [65, 127]) and on stirred tank reactors (e.g., [49]). 

Based on these observations [93] proposed a modified model containing two time constants, one for the liquid shear induced turbulence and a second one for the bubble induced turbulence. The basic assumption made in this model development is that the shear-induced turbulent kinetic energy and the bubble-induced turbulent kinetic energy may be linearly superposed in accordance with the hypothesis of [128, 129]. Note, however, that [82] observed experimentally that this assumption is only valid for void fractions less than 1 %, whereas for higher values there is an amplification in the turbulence attributed to the interactions between the bubbles. The application of this model to the high void fraction flows occurring in operating multiphase chemical reactors like stirred tanks and bubble columns is thus questionable. 

Joseph, S. and Y.T. Shah. A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactors. ACS Symp. Series 27 (1984) 149-167. 

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