Fluid Dynamics in a Continuous Pump-Mixer
Abstract and Figures
The fluid dynamic (flow rates) and hydrodynamic behavior (local droplet size distributions and local holdup) of a continuous DN300 pump-mixer were investigated using water as the continuous phase and paraffin oil as the dispersed phase. The influence of the impeller speed (N = 375 to 425 rpm), the feed phase ratio (φF = 10 to 30 vol.-%), and the flow rate (V˙tot ≈ 0.5 to 2.3 L/min) were investigated by measuring the pumping height, local holdup of the disperse phase, and the droplet size distribution (DSD). The latter one was measured at three different vessel positions using an image-based telecentric shadowgraphic technique. The droplet diameters were extracted from the acquired images using a neural network. The Sauter mean diameters were calculated from the DSD and correlated with an extended model based on Doulah (1975), considering the impeller speed, the feed phase ratio, and additionally the flow rate. The new correlation can describe an extensive database containing 155 experiments of the fluid and hydrodynamic within a 15% error range.
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In this work, steady-state droplet size distributions in a DN300 stirred batch vessel with a Rushton turbine impeller are investigated using an insertion probe based on the telecentric transmitted light principle. High-resolution droplet size distributions are extracted from the images using a convolutional neural network for image-analysis in order to investigate the influence of impeller speed and phase fraction (up to 50 vol.-%). In addition, Sauter mean diameters were calculated and correlated with two semi-empirical approaches, while the standard approach only accomplished 5.7% accuracy, and the correlation of Laso et al. provided a relative mean error of 4.0%. In addition, the correlated exponent in the Weber number was fitted to the experimental data of this work yielding a slightly different value than the theoretical (−0.6), which allows a better representation of the low coalescence tendency of the system, which is usually neglected in standard procedures.
A novel shadowgraphic inline probe to measure crystal size distributions (CSD), based on acquired greyscale images, is evaluated in terms of elevated temperatures and fragile crystals, and compared to well-established, alternative online and offline measurement techniques, i.e., sieving analysis and online microscopy. Additionally, the operation limits, with respect to temperature, supersaturation, suspension, and optical density, are investigated. Two different substance systems, potassium dihydrogen phosphate (prisms) and thiamine hydrochloride (needles), are crystallized for this purpose at 25 L scale. Crystal phases of the well-known KH2PO4/H2O system are measured continuously by the inline probe and in a bypass by the online microscope during cooling crystallizations. Both measurement techniques show similar results with respect to the crystal size distribution, except for higher temperatures, where the bypass variant tends to fail due to blockage. Thiamine hydrochloride, a substance forming long and fragile needles in aqueous solutions, is solidified with an anti-solvent crystallization with ethanol. The novel inline probe could identify a new field of application for image-based crystal size distribution measurements, with respect to difficult particle shapes (needles) and elevated temperatures, which cannot be evaluated with common techniques.
The efficiency of many chemical engineering applications depends on the surface/volume ratio of the dispersed phase. Knowledge of this particle size distribution is a key factor for better process control. The challenge of measurements acquired by optical imaging techniques is the segmentation of overlapping particles, especially in high phase fraction flows. In this work, a convolutional neural network is trained to segment droplets in images acquired by a shadowgraphic approach. The network is trained on artificial images and implemented into a droplet size algorithm. The results are compared to an OpenSource segmentation approach. Knowledge of the particle size distribution is essential for understanding multiphase chemical engineering processes. Main problem in optical measurements is the segmentation of overlapping particles. A solution to this is a convolutional neural network trained with artificial images and used for particle segmentation at high holdups.
Liquid‐liquid two‐phase flow in a mixer of mixer‐settler has been studied via a computational fluid dynamics (CFD) simulation combined with the population balance model (PBM) and verified with particle image velocimetry (PIV) experiments. The simulation was performed using the multiple reference frame (MRF) approach, the Eulerian‐Eulerian two‐fluid model, and the standard k‐ϵ model. The effects of impeller speed, flow ratio, and impeller type on flow field, droplet diameter, and dispersed phase holdup were investigated. The results showed that CFD simulation combined with PBM could predict droplet size distribution (DSD). The smaller droplets were mainly in the bottom region of the mixer, larger ones were in the top part of the mixer, and the largest droplets appeared in the impeller centre region. The DSD and holdup were more sensitive to impeller speed than to the organic/aqueous flow ratio. A dual‐impeller mixer configuration was designed to enhance the mixing performance. Compared with single‐impeller, the installation of dual‐impellers could effectively avoid the dispersed phase dead zone above the lower impeller. When hc /T = 0.3, the best dispersing effect, such as uniform DSD and high mixing chamber space utilization, could be obtained. This article is protected by copyright. All rights reserved
Liquid-liquid disperse multiphase flow in a baffled tank stirred by a Rushton turbine is investigated by experiments and 3D simulations for different impeller speeds and volume fractions. Droplet size distributions are experimentally measured with an inline shadowgraphic probe and compared with fully transient coupled CFD-PBM simulations using the Eulerian multi-fluid framework, the inhomogeneous Multiple Size Group approach and a statistical turbulence model. The simulation model is assessed by a variation of size class and velocity group numbers, grid resolution and simulation domain extent. The model parameters for the breakup and coalescence kernels are fitted to match the measured droplet size distribution at a selected operation point. A subsequent application to different operation points shows that experimental droplet size trends are captured, albeit aside from the fitting point, deviations to data increase. The resulting droplet size distribution is analyzed by an assessment of the turbulent mixing, breakup and coalescence time scales.
The approach coupling computational fluid dynamics and a population balance model (PBM) was adopted to simulate the hydraulic performance of liquid-liquid dispersions in a pump-mixer. Behaviors of the drop breakage and coalescence were considered in the PBM. To validate simulation methods and strategies, simulated drop size distributions were compared with experimental data and a good agreement was obtained. Flow structures in the pump-mixer were analyzed and two recirculation loops were observed. Holdup profiles reveal that the dispersed phase is unevenly distributed in space, which is more obvious at lower rotating speeds. Simulation results show that breakup regions are mainly located near the impeller where high energy dissipation rates exist, while coalescence regions were observed in the whole mixer. Distributions of the drop mean diameter were displayed. It indicated that the drop size is uniformly distributed in space at higher rotating speeds.
Flow simulations are performed on single-phase flow in a baffled tank stirred by a Rushton turbine at a Reynolds number of 40000. The flow physics are discussed, and the benefits of a scale-adaptive simulation (SAS) compared with classical unsteady Reynolds-averaged Navier-Stokes (URANS) models are highlighted. The effect of geometry simplifications, i.e., infinitely thin blades, is illustrated. Furthermore, due to the existence of low-frequency flow instabilities, the necessity of utilizing a full 360° computational domain and the consideration of up to 150 impeller revolutions in the simulation is demonstrated. By a zonal grid refinement within the blade and wake region, the successively resolved portion of the turbulent spectrum is investigated. Even on computational grids typically employed for URANS simulations, the SAS shows a considerably improved prediction of mean velocity and turbulence statistics, compared with conventional URANS models, and should thus be preferred, e.g., to an under-resolved large eddy simulation (LES).
The influence of dispersed-phase viscosity on droplet breakup in a pump-mixer was determined using a direct measurement approach, which was performed using a high-speed online camera. The experimental results show that the interfacial stress and internal viscous stress can be applied to characterize the influence of the interfacial tension and dispersed-phase viscosity on drop breakup respectively. The daughter droplet size presents a bell-shaped distribution, and is slightly dependent on the drop restoring stress. An empirical correlation of the drop breakup frequency function is established to include the influence of the dispersed phase viscosity. Moreover, the new correlation reveals a clear physical relationship between the variables of physical properties and hydraulic parameters, which strengthens its extensibility when applied to other systems or equipment.
Drop size distribution (DSD) or mean droplet size (d32) and liquid holdup are two key parameters in a liquid–liquid extraction process. Understanding and accurately predicting those parameters are of great importance in the optimal design of extraction columns as well as mixer–settlers. In this paper, the method of built-in endoscopic probe combined with pulse laser was adopted to measure the droplet size in liquid–liquid dispersions with a pump-impeller in a rectangular mixer. The dispersion law of droplets with holdup range 1% to 24% in batch process and larger flow ratio range 1/5 to 5/1 in continuous process was studied. Under the batch operation condition, the DSD abided by log-normal distribution. With the increase of impeller speed or decrease of dispersed phase holdup, the d32 decreased. In addition, a prediction model of d32 of kerosene/deionized system was established as d32/D = 0.13(1 + 5.9φ)We−0.6. Under the continuous operation condition, the general model for droplet size prediction of kerosene/water system was presented as d32/D = C3(1 + C4φ)We−0.6. For the surfactant system and extraction system, the prediction models met a general model as d32/D = bφⁿWe−0.6.
The direct experimental data for droplet breakage frequency and daughter droplet size distribution is urgently required for the application of the population balance model. To meet this requirement, a method to directly measure the droplet breakage in the pump-mixer was developed using a high speed online camera. Two typical breakup patterns, tensile breakup and revolving breakup were observed and the number of the breakup fragments was determined. The multiple breakage was treated as a series of binary breakups. In order to precisely describe the daughter size distribution, these binary breakups were divided into three different types, i.e. the original tensile breakup, intermediate tensile breakup, and revolving breakup. The influences of the rotating speed and interfacial tension on the droplet breakup frequency and daughter droplet size distribution were then quantitatively investigated. Empirical correlations were proposed and good agreement was found between the prediction results and the experimental data.