Modeling of Mixing and Reaction in Turbulent Multi‐Phase Flows with Distribution Functions

Numerical simulation of turbulent reacting or multiphase flows is gaining popularity as a tool for the analysis and optimization of many complex applications in process engineering. To make possible the accurate modeling of relevant reaction and transport processes, the respective distribution functions of mixture fraction or particle size must be considered in an adequate manner. In the present paper, novel approaches to make possible a more detailed yet efficient representation of distribution functions in turbulent, reacting multiphase flows are introduced. The application of the methods to the example of a system with mixing and reaction among three species is discussed.     

CFD modelling and scale-up of Confined Impinging Jet Reactors

Confined Impinging Jet Reactors (CIJRs) are appealing devices for precipitation of nanoparticles because of their high mixing efficiency. In fact, since precipitation processes are generally very fast, mixing plays a crucial role and it is of great importance to operate under very fast mixing conditions. In this work mixing and reaction in CIJRs are studied by means of Computational Fluid Dynamics (CFD). Mixing at the molecular level is modelled with a presumed Probability Density Function (PDF) approach: the Direct Quadrature Method of Moments coupled with the Interaction by Exchange with the Mean (DQMOM-IEM) model. The influence of operating conditions and reactor geometry on mixing is also evaluated and a scale-up criterion for CIJRs is developed, showing that scaling up by means of CFD is a practicable path, worth of further investigation.     

CFD Investigation of the Mixing of Yield‐Pseudoplastic Fluids with Anchor Impellers

The study was carried out to simulate the 3D flow domain in the mixing of pseudoplastic fluids possessing yield stress with anchor impellers, using a computational fluid dynamics (CFD) package. The multiple reference frames (MRF) technique was employed to model the rotation of the impellers. The rheology of the fluid was approximated using the Herschel–Bulkley model. To validate the model, the CFD results for the power consumption were compared to the experimental data. After the flow fields were calculated, the simulations for tracer homogenization were performed to simulate the mixing time. The effects of impeller speed, fluid rheology, and impeller geometry on power consumption, mixing time, and flow pattern were explored. The optimum values of c/D (impeller clearance to tank diameter) and w/D (impeller blade width to tank diameter) ratios were determined on the basis of minimum mixing time.     

CFD‐Simulation und LDA‐Messung der Strömungsvorgänge beim Fluidphasenresonanzmischen

The principle of fluid phase resonance mixing is to apply harmonic oscillating pressure via a gas cushion on a liquid phase in a vessel and thus to cause the liquid phase to start oscillating. This principle is simulated as an unsteady flow of two separate phases with open source CFD software OpenFOAM and the results are verified with measurements by Laser Doppler Anemometry.     

Estimation of kLa Values in Bench‐Scale Stirred Tank Reactors with Self‐Inducing Impeller by Multiphase CFD Simulations

A multiphase computational fluid dynamics (CFD) simulation methodology is developed and proposed for the estimation of the spatial distribution of k_La values in a bench‐scale reactor equipped with a self‐inducing impeller. The importance of estimating an apparent drag coefficient, which considers the effect of turbulence on the gas bubble rising velocity, is also tackled by applying different correlations available in literature, namely, Brucato, modified Brucato, and Pinelli correlations. The spatial distribution of k_La values in the agitated vessel is found from the CFD results using Danckwert's surface renewal model. An analysis of the gas volume fraction distribution obtained from the simulations is performed in order to choose the most suitable drag model. The modified Brucato correction correlation for the drag force exhibits the best agreement with experimental data.     

Multi‐Phase‐Multi‐Size‐Group Model for the Inclusion of Population Balances into the CFD Simulation of Gas‐Liquid Bubbly Flows

A CFD model for the simulation of gas‐liquid bubbly flow is developed. In the model, the multi‐phase flow is simulated by an Eulerian‐Eulerian approach using several phase definitions (from 3 to 10). The bubble size distribution is simulated by a solution of the discretized population balance equation with coalescence and break‐up of bubbles. The number of the discretized population balance equations in the model is larger than the number of the phases used in the flow field simulation. A desired accuracy in the simulation can be achieved by choosing a suitable number of phases as a compromise between accuracy and computational cost. With this model, more detailed flow hydrodynamics and bubble size distribution can be obtained. The model was tested with different operating conditions and for different numbers of dispersed phases in a bubble column, and was verified with a bubble size distribution obtained experimentally.     

Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels

Suspensions of solid particles into liquids within industrial stirred tanks are frequently carried out at an impeller speed lower than the minimum required for complete suspension conditions. This choice allows power savings which usually overcome the drawback of a smaller particle-liquid interfacial area. Despite this attractive economical perspective, only limited attention has been paid so far to the modelling of the partial suspension regime.     

Prediction of the Induced Gas Flow Rate from a Self‐Inducing Impeller with CFD

The complex task of describing computationally two‐phase turbulent flows in aerated stirred‐tank reactors was overcome by proposing that the gas flow rate in the hollow impeller can be estimated from single‐phase flow simulations of the liquid phase in the reactor: the pressure at the impeller surface obtained from liquid phase simulations can be related to the gas induction rate. A commercial lab‐scale reactor with a radial six‐bladed hollow impeller was chosen for the study. To validate the presented methodology, the induced gas flow rate was measured experimentally from the tracking of the position of bubbles in a dynamic sequence of flow images. Notwithstanding the simplifications assumed in the presented CFD methodology, good agreement has been obtained between numerical results and experiments.     

Development and validation of a two phase CFD model for tubular biodiesel reactors

The use of biodiesel as an alternative to diesel has gained increasing momentum over the past 15 years. To meet this growing demand there is a need to optimise the transesterification reactor at the heart of the biodiesel production system. Assessing the performance of innovative reactors is difficult due to the liquid–liquid reaction mixture that is affected by mass transfer, reaction kinetics and component solubility. This paper presents a Computational Fluid Dynamic model of a tubular reactor developed in ANSYS CFX that can be used to predict the onset of mixing via turbulent flow. In developing the model an analysis of the reaction mixture is provided before the presentation of experimental data, which includes flow visualisation results and temperature dependant viscosity and density data for each phase. The detailed data and model development procedure represents an advancement in the modelling of the two phase transesterification reaction used in biodiesel production.     

Numerical Simulation of Dispersed Gas/Liquid Flows in Bubble Columns at High Phase Fractions using OpenFOAM®. Part II – Numerical Simulations and Results

The design of industrial gas/liquid reactors such as bubble columns requires detailed information with respect to the flow structure and characteristics of two‐ or multiphase systems in the reactor. The contribution is focused on the evaluation of the simulation results obtained by model selection. The results are further compared with those reported in literature. The simulation has been performed with the CFD software OpenFOAM®. The main focus of the numerical simulation was set on capturing the characteristic process and design parameters of bubble columns.     

CFD modeling of gas dispersion and bubble size in a double turbine stirred tank

In the present paper, gas dispersion in a double turbine baffled stirred tank is modeled using a commercial computational fluid dynamics (CFD) code FLUENT 6.1 (Fluent Inc., USA). A bubble number density equation is implemented in order to account for the combined effect of bubble break-up and coalescence in the tank. In the proposed work, the impellers are explicitly described in three dimensions using multiple reference frame model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-ε turbulent model and modified standard drag coefficient for the momentum exchange. The model predicts spatial distribution of gas holdup, average local bubble size and flow structure. The results are compared with experimental and numerical finding reported in the literature and good agreement between the present model and measurements of Alves et al. [Gas liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering Science, 2002, 57, 487-496] is achieved.     

Numerical and Experimental Study of Catalyst Loading and Body Effects on a Gas‐Liquid Trickle‐Flow Bed

The influence of tortuosity and fluid volume fractions on trickle‐flow bed performance was analyzed. Hydrodynamics of the gas‐liquid downward flow through trickle beds, filled with industrial trilobe catalysts, were investigated experimentally and numerically. The pressure drop and liquid holdup were measured at different gas and liquid velocities and in two different loading methods, namely, sock and dense catalyst loading. The effect of sharp corners on hydrodynamic parameters was considered in a bed with rectangular cross section. The reactor was simulated, considering a three‐phase model, appropriate porosity function, and interfacial forces based on the Eulerian‐Eulerian approach. Computational fluid dynamics (CFD) simulation results for pressure drop and liquid holdup agreed well with experimental data. Finally, the velocity distribution in two types of loading and the effect of bed geometry in CFD results demonstrated that pressure drop and liquid holdup were reduced compared to a cylindrical one due to high voidage at sharp corners.     

Effect of a Draft Tube on the Fluid Dynamics of a Spouted Bed: Experimental and CFD Studies

Knowledge about the gas and particle dynamics in spouted beds is important in the evaluation of particle circulation rates and the efficiency of gas-solid contacts. In this work, the mechanism of transition from a static bed to a spouted bed was numerically simulated using a Eulerian multiphase model. This model was applied to two distinct spouted bed geometries: a conventional device and a spouted bed with draft tube. The radial voidage and particle velocity profiles along the longitudinal position in the annular and spout regions were simulated for the geometries under study. The characteristic simulated curves were congruous with the experimental data.     

Effect of operating parameters inside circulating fluidized bed reactor riser with ring baffles using CFD simulation and experimental design analysis

The effect of the operating parameters on the system hydrodynamics and mixing inside two circulating fluidized bed reactor (CFBR) risers with different ring baffle configurations were investigated using computational fluid dynamics simulations and a 2⁴ factorial experimental design analysis. The operating parameters varied were the gas inlet velocity, and the mass flux, diameter and density of the solid particles, while the response variables were the standard deviation of the solid volume fraction (SVF) in the radial direction (SDSVF-RD) and the average SVF (ASVF). The results from the two CFBR risers with different ring baffle configurations showed a similar trend. The operating parameters that significantly affected the ASVF in both modified CFBR risers were the inlet gas velocity and solid particle mass flux, while those that significantly affected the SDSVF-RD were the inlet gas velocity and the inlet gas velocity–solid particle diameter–solid particle density interaction. For these systems, the lowest and highest ASVF was approximately 0.07 and 0.20, respectively, while the lowest and highest SDSVF-RD was 0.01 and 0.04, respectively. The low variability of the solid particle distribution and the high solid particle concentration will be suitable for chemical reactions. All the obtained results could be explained in terms of the system hydrodynamics. Finally, regression models to predict the mean solid particle concentration and variability of solid particle distribution in the system were obtained.     

Development of a 3D Hybrid Intelligent‐Mechanistic Model for Simulation of Multiphase Chemical Reactors

A novel intelligent‐mechanistic model was developed to understand the behavior of multiphase chemical reactors. Computational fluid dynamics (CFD) and an intelligent algorithm were combined to predict different levels of 3D cylindrical bubble‐column reactors. An adaptive neuro‐fuzzy inference system (ANFIS) was used as the intelligence algorithm, and different ANFIS parameters were evaluated. With about one third of the training data the method can predict the overall behavior of the gas fraction in the reactor. A number of rules significantly influence the accuracy of the ANFIS method. After finding appropriate parameters, the method is applied for prediction of points which are not simulated with CFD, representing ANFIS mesh refinement. Also, bubble‐column reactors without training of exact values of measured data or numerical results can be predicted. Main advantages are time savings and reduction of computational expenses.     

Enhanced removal of nitrate and phosphate from wastewater by Chlorella vulgaris: Multi-objective optimization and CFD simulation

To enhance the efficiency of wastewater biotreatment with microalgae, the effects of physical parameters need to be investigated and optimized. In this regard, the individual and interactive effects of temperature, p H and aeration rate on the performance of biological removal of nitrate and phosphate by Chlorella vulgaris were studied by response surface methodology(RSM). Furthermore, a multi-objective optimization technique was applied to the response equations to simultaneously find optimal combinations of input parameters capable of removing the highest possible amount of nitrate and phosphate. The optimal calculated values were temperature of 26.3 °C, pH of 8 and aeration rate of 4.7 L·min~(-1). Interestingly, under the optimum condition, approximately 85% of total nitrate and 77% of whole phosphate were removed after 48 h and 24 h, respectively, which were in excellent agreement with the predicted values. Finally, the effect of baffle on mixing performance and, as a result, on bioremoval efficiency was investigated in Stirred Tank Photobioreactor(STP) by means of Computational Fluid Dynamics(CFD). Flow behavior indicated substantial enhancement in mixing performance when the baffle was inserted into the tank. Obtained simulation results were validated experimentally. Under the optimum condition, due to proper mixing in baffled STP, nitrate and phosphate removal increased up to 93% and 86%,respectively, compared to unbaffled one.     

Simulation of Barium Sulfate Precipitation using CFD and FM‐PDF Modeling in a Continuous Stirred Tank

A mixing‐precipitation model combining computational fluid dynamics (CFD), finite‐mode PDF (probability density function) model, population balance and kinetic modeling has been proposed to simulate the barium sulfate precipitation process in a continuous stirred tank agitated by a Rushton turbine. The effect of various operating conditions such as impeller speed, feed concentration, feed position and mean residence time on the barium sulfate precipitation process is clearly demonstrated. It is shown that the mean crystal size increases by increasing the impeller speed and mean residence time. However, when the feed concentration is increased, the mean crystal size decreases. The predictions are in reasonable agreement with the experimental data in the literature.     

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

The mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.     

Measurement of Local Phase Holdups in a Two‐ and Three‐Phase Bubble Column

A new invasive sensing probe for the measurement of local phase holdups in two‐ and three‐phase reactors is described. The local gas and solids holdups in a bubble column with a volume of V = 2 m³ at varying operating conditions (gas velocity, sparger design, solids content and density) are measured by means of differential pressure measurement in combination with either time domain reflectometry or electrical conductivity measurement. The phase distribution profiles at two‐ and three‐phase operating conditions are described. The influence of the sparger design on the shape of these profiles, the influence of the solid phase on the gas distribution, the solids distribution and the gas‐stow effect above the sparger because of a dense particle layer are capable of experimental proof for the first time.