CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

Compressibility induced bubble size variation in bubble column reactors: Simulations by the CFD–PBE

Bubble column reactors can be simulated by the two fluid model (TFM) coupled with the population balance equation (PBE). For the large industrial bubble columns, the compressibility due to the pressure difference may introduce notable bubble size variation. In order to address the compressibility effect, the PBE should be reformulated and coupled with the compressible TFM. In this work, the PBE with a compressibility term was formulated from single bubble dynamics, the mean Sauter diameters predicted by the compressible TFM coupled with the PBE were compared with the analytical solutions obtained by the ideal gas law. It was proven that the mesoscale formulations presented in this work were physically consistent with the macroscale modeling. It can be used to simulate large industrial plants when the compressibility induced bubble size variation is important.     

Agglomeration and breakage of nanoparticles in stirred media mills—a comparison of different methods and models

The increasing industrial demand for nanoparticles challenges the application of stirred media mills to grind in the sub-micron size range. It was shown recently [Mende et al., 2003. Mechanical production and stabilization of submicron particles in stirred media mills. Powder Technology 132, 64-73] that the grinding behavior of particles in the sub-micron size range in stirred media mills and the minimum achievable particle size is strongly influenced by the suspension stability and thus the agglomeration behavior of the suspension. Therefore, an appropriate modeling of the process must include a superposition of the two opposing processes in the mill i.e., breakage and agglomeration which can be done by means of population balance models. Modeling must now include the influence of colloidal surface forces and hydrodynamic forces on particle aggregation and breakup. The superposition of the population balance models for agglomeration and grinding with the appropriate kernels leads to a system of partial differential equations, which can be solved in various ways numerically. Here a modified h-p Galerkin algorithm which is implemented in the commercially available software package PARSIVAL developed by CiT (CiT GmbH, Rastede, Germany) and the moment methodology according to [Diemer and Olsen, 2002a. A moment methodology for coagulation and breakage problems: Part I—analytical solution of the steady-state population balance. Chemical Engineering Science 57 (12), 2193-2209; Diemer and Olsen, 2002b. A moment methodology for coagulation and breakage problems: Part II—moment models and distribution reconstruction. Chemical Engineering Science 57 (12), 2211-2288] are used and compared to explicit data on alumina. This includes a comparison of the derived particle size distributions, moments and its accuracy depending on the starting particle size distribution and the used agglomeration and breakage kernels. Finally, the computational effort of both methods in comparison to the prior mentioned parameters is evaluated in terms of practical application.     

Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems

In this work the quadrature method of moments (QMOM) is implemented in a commercial computational fluid dynamics (CFD) code (FLUENT) for modeling simultaneous aggregation and breakage. Turbulent and Brownian aggregation kernels are considered in combination with different breakage kernels (power law and exponential) and various daughter distribution functions (symmetric, erosion, uniform). CFD predictions are compared with experimental data taken from other work in the literature and conclusions about CPU time required for the simulations and the advantages of this approach are drawn.     

CFD simulation of flow and mixing characteristics in a stirred tank agitated by improved disc turbines

To reduce the power consumption and improve the mixing performance in stirred tanks, two improved disc turbines namely swept-back parabolic disc turbine (SPDT) and staggered fan-shaped parabolic disc turbine (SFPDT) are developed. After validation of computational fluid dynamics (CFD) model with experimental results, CFD simulations are carried out to study the flow pattern, mean velocity, power consumption, pumping capacity and mixing efficiency of the improved and traditional impellers in a dished-bottom tank under turbulent flow conditions. The results indicate that compared with the commonly used parabolic disc turbine (PDT), the power number of proposed SPDT and SFPDT impellers is reduced by 43% and 12%, and the pumping efficiency is increased by 68% and 13%, respectively. Furthermore, under the same power consumption (0-700 W·m^-3), the mixing performance of both SPDT and SFPDT is also superior to that of Rushton turbine and PDT.     

Application of in situ adaptive tabulation to CFD simulation of nano-particle formation by reactive precipitation

Reactive precipitation involves four fundamental processes: mixing-limited reaction, nucleation, growth, and aggregation. A novel algorithm, in situ adaptive tabulation (ISAT), has been implemented in a code for micromixing simulations, which is often applied together with computational fluid dynamics (CFD), using full probability density function (PDF) methods to incorporate these fundamental processes in the formation of nano-particles by reactive precipitation in a plug-flow reactor. The quadrature method of moments is applied to solve population balance equations for turbulent aggregation of the growing particles. The various performance issues (error control, accuracy, number of records, speed-up) for ISAT are discussed. Based on a large number of simulations, an error tolerance of 10⁻⁴-10⁻⁵ is found to be satisfactory for carrying out time-evolving full PDF simulations of nano-particle formation by reactive precipitation. Our results show that CFD simulation of reactive precipitation requires a much smaller computational effort when the ISAT algorithm is implemented than when direct integration is used. Finally, the effects of initial species concentrations, micromixing time, and turbulent shear rate on the reactive precipitation of barium sulfate are studied.     

CFD simulation and PIV measurement of the flow field generated by modified pitched blade turbine impellers

The hydrodynamics generated by modified pitched blade turbine (m-PBT) impellers with down-pumping mode were systematically investigated through particle image velocimetry (PIV) measurements and computational fluid dynamics simulations. The simulated mean axial velocity, mean radial velocity, and turbulent kinetic energy by the standard k–? turbulent model were validated against the measured PIV data. This shows that the standard k–? turbulent model predicts mean velocity well, but underestimates turbulent kinetic energy near the blade. The flow field and power consumption as well as pumping number for the m-PBT and the standard PBT impeller were predicted. The simulation results demonstrate that a few simple changes of the blade shape influence the velocity distribution, i.e., increasing the magnitude of mean velocity in the vicinity of impeller, and that the m-PBT impeller has a higher pumping efficiency than the standard one.     

Investigation of aggregation, breakage and restructuring kinetics of colloidal dispersions in turbulent flows by population balance modeling and static light scattering

Quantitative modeling of aggregating colloidal systems is the underlying problem in many industrial processes, such as micro and nanoparticle processing, crystallization or flocculation. Population balance models with various aggregation and breakage kernels have been proposed in order to describe aggregating systems, but they have been rarely validated against appropriate experimental data. Typically, model parameters are fitted against a single measured moment of the cluster distribution which can usually be equivalently described using several variations of the set of parameters underlying the relevant aggregation, breakage and restructuring kernels. In order to discriminate among alternative models we propose an approach based on measurement and quantitative modeling of multiple moments of the cluster mass distribution, such as those obtained from static light scattering measurements. This approach is applied to aggregation processes in turbulent conditions in order to test alternative kernels for aggregation, breakage, and restructuring kinetics. We present a detailed study on the sensitivity of measurables from static light scattering with respect to commonly used aggregation and breakage kinetic models. In particular, we analyze the dynamic and steady state behavior of two measurables: the average radius of gyration and the average zero angle intensity which represent two independent moments of the cluster mass distribution. In addition, we discuss the effect of cluster structure and mass distribution on the average structure factor and the apparent fractal dimension measured by static light scattering, in order to assess what structural information can be reliably extracted from such measurements.     

Implementation of the population balance equation in CFD codes for modelling soot formation in turbulent flames

The simulation of soot formation in turbulent diffusion flames is carried out within a CFD code, by coupling kinetics and fluid dynamics computations with the solution of the population balance equation via the Direct Quadrature Method of Moments, a novel and efficient approach based on a quadrature approximation of the size distribution of soot particles. A turbulent non-premixed ethylene-air flame is used as the test case for validation of the model. Simplified kinetic expressions are employed for modelling nucleation, molecular growth and oxidation of particles, along with a Brownian aggregation kernel. A recently proposed approach for modelling the evolution of fractal dimension is used with a monovariate population balance to predict the morphological properties of aggregates.