Drag models, solids concentration and velocity distribution in a stirred tank

This paper aims on application of computational fluid dynamic (CFD) modelling on two-phase and multiphase flows in 75 mm conventional hydrocyclone, 350 mm dense medium cyclone (DMC) and 100 mm diameter laboratory column flotation. Along with classification experiments, a dual-planar high speed electrical resistance tomography (ERT) is used to measure the internal flow dynamics in situ in 75 mm hydrocyclone and column flotation at different operating conditions. Experiments are carried out in 75 mm hydrocyclone for different operational parameters and feed solids content varying in the range of 0–30 wt%. Results are presented in terms of the air core diameter and solids volume fraction contours using Maxwell’s conductivity equation. It is confirmed by ERT that the air core occupied area and wall solids conductivity levels decreases with increasing the feed solids concentration. Similarly, ERT is used to estimate the mean gas hold-up and radial distribution in order to understand the hydrodynamics of the column flotation. The effect of air superficial velocity and liquid flow rate on gas hold-up is discussed. Algebraic slip mixture model modified with lift, drag and rheology is used to predict the air core size, the solid concentration distribution and classification performance for the hydrocyclone. Validation of air core size and mean solid volume fractions by ERT measurements with the CFD simulations is attempted. The CFD predicted air core radius and medium segregation in the DMC is validated against literature based gamma ray tomography data. Further discrete phase model (DPM) is used to track and measure the residence times of different size and density coal particles. CFD predicted gas hold-up in the column flotation is also validated against in-house measured ERT and imaging data.

Measurements of solid concentration and particle velocity distributions near the wall of a cyclone

The software of CFD FLUENT was used to simulate the strengthening characteristics of three-bent-bladed turbine in solid-liquid suspension system. Diameter of stirred tank is T = 100mm. Four baffles are evenly distributed in the tank and two-phase material selection of glass ball-water system. Particle diameter is 250μm and solid volume fraction is 15%. The standard dual equation model is adopted in the liquid turbulence model. The Euler multiphase flow model is applied to simulate the suspension process. The strengthening effect of the impeller’s upturned angle is discussed on solid suspension, and the radial velocity and solid volume concentration distribution of solid particles are analyzed, respectively. The results showed that, compared with 30 degrees of upturned angle of three-bent-bladed turbine(30°UA-3BT), the axial velocity of solid particles did not increase significantly with 20 degrees of upturned angle of three-bent-bladed turbine(20°UA-3BT) in the stirred tank. But distribution of solid volume concentration was more uniform, which reduced the accumulation of solid particles at the bottom of tank and the clean area of the top of stirred tank. 20°UA-3BT is beneficial to the full mixing of solid and liquid. Therefore, the turbine has a good application prospect.

The scale‐up of a fluidized bed crystallizer was studied based on solid spatial concentration distribution in the crystallizer, which was obtained with the simulation of computational fluid dynamics (CFD). The variations of solid spatial concentration distributions in the crystallizers were investigated based on different specific energy inputs. A strategy for the scale‐up of the crystallizer was suggested based on the different states of solid suspension.

The vortex diode is a key candidate for the equipment of the passive safety system of the molten salt reactor. Experimental studies to determine the diodicity (ratio of reverse flow Euler number to the forward flow Euler number at the same Reynolds number) using high-temperature molten salt are strongly limited because of the huge technical effort and financial requirements for such studies; moreover, possible solutions that involve a scaling method that uses surrogate fluid to obtain the diodicity must be validated. To determine the diodicity and verify the scaling method, an experiment using one kind of heat transfer oil (Dowtherm-a) as the surrogate fluid was carried out. In addition, a computational fluid dynamics (CFD) simulation method was also adopted to study the flow characteristics in the vortex diode using three different fluids. The results show the following: it is feasible to study the diodicity of a vortex diode by a scaling experimental method using surrogate fluid, the CFD simulation method established in this paper can be applied to study the diodicity of the vortex diode, and the structure of the flow field and velocity distribution in the vortex chamber for reverse flow are independent of fluids and only related to the Reynolds number.

Simulating the ultrafiltration of whey proteins isolate using a mixture model

The rheological behavior of the ore slurry plays a critical role in most of the mineral processing unit operations including filtration. This paper discusses the rheological tests conducted on a brecciated limestone ore slurry and the attempt to correlate the rheological behavior of the slurry with the filtration rate. Rheological experiments were carried out using a modular compact Rheometer. Solid concentration, temperature, particle size and particle size distribution (PSD) of the solids, shearing time, and surfactant dosages were found to have a significant impact on the slurry rheology. The Herschel–Bulkley model was used to describe the rheological behavior of the slurry. The variation of temperature was modeled using the Arrhenius type model equation, and the particle size distribution was incorporated using the Rosin–Rammler PSD model. It was found that the shear stress increased exponentially with an increase in solid concentration and a decrease in temperature. The maximum solid packing volume fraction was determined to be 0.647 and 0.569 at shear rates of 1400 and 503 s−1, respectively. The fluid flow activation energy was found to be 5.76 and 7.67 kJ/mol at 50% and 73% solids (w/w) respectively at a shear rate of 1120 s−1. Filtration rate was found to increase with an increase in temperature, particle size, and decrease in solid concentration. The addition of a surfactant, namely Guar gum to the slurry (up to 500 g/t), has not increased the shear stress (<23.4 Pa) or apparent viscosity (<0.0167 Pa·s) appreciably but increased the rate of filtration.

The main objective of the present work is to study the effect of an external store on a subsonic fighter aircraft. Generally most modern fighter aircrafts are designed with an external store installation. In this study, a subsonic fighter aircraft model has been manufactured using a computer numerical control machine for the purpose of studying the effect of the aerodynamic interference of the external store on the flow around the aircraft wing. A computational fluid dynamic (CFD) simulation was also carried out on the same configuration. Both the CFD and the wind tunnel testing were carried out at a Reynolds number 1.86×105 to ensure that the aerodynamic characteristic can certify that the aircraft will not be face any difficulties in its stability and controllability. Both the experiments and the simulation were carried out at the same Reynolds number in order to verify each other. In the CFD simulation, a commercial CFD code was used to simulate the interference and aerodynamic characteristics of the model. Subsequently, the model together with an external store was tested in a low speed wind tunnel with a test section sized 0.45 m×0.45 m. Measured and computed results for the two-dimensional pressure distribution were satisfactorily comparable. There is only a 19% deviation between pressure distribution measured in wind tunnel testing and the result predicted by the CFD. The result shows that the effect of the external storage is only significant on the lower surface of the wing and almost negligible on the upper surface of the wing. Aerodynamic interference due to the external store was most evident on the lower surface of the wing and almost negligible on the upper surface at a low angle of attack. In addition, the area of influence on the wing surface by the store interference increased as the airspeed increased.

Optimizing calculation of particle size distribution of feeding coal for circulating fluidized bed boiler

Two-phase (solid and gas) 2D fluidized bed reactor’s flow pattern was investigated. Computational fluid dynamics (CFD) simulation results were compared with those obtained experimentally. The CFD simulation is carried out using commercial software “Fluent”. Experiment is carried out in a fluidized bed containing spherical glass beads of diameter 300–350 μm. Initial volume fraction is fixed as 0.6. A multi-fluid Eulerian model incorporating the kinetic theory for solid particles was applied in order to simulate the gas–solid flow. Momentum exchange coefficients are calculated using Syamlal–O’Brien drag function. The kinetic energy lost during inter-particle collisions were characterized by specifying the restitution coefficient values from 0.9 to 0.99. The pressure drop and bed expansion ratio for various superficial velocities are compared with experimental results.

A numerical model has been developed to predict the velocity distribution and the concentration distribution for a nonuniform flocculated particle suspension for turbulent density stratified flow in secondary clarifiers. This model consists of a set of conservation equations for fluid mass and momentum and sediment concentration as well as a relationship for solids settling velocity. The turbulent stresses are calculated using the eddy-viscosity concept and the k-ε turbulence model. Since the strong local numerical instabilities near the reaction baffle lip, where the low-solids concentration surface return flow joins the high solids concentration bottom current, was successfully overcome in the iterative solution procedure, the calculation zone in this investigation can be extended to take into account the inlet zone of the clarifier. The model gave a satisfactory description of the influence of the density variations on the hydraulic regime and the solids concentration distribution in the clarifier. A good agreement was obtained between the experimental data and the numerical simulation. Key words: clarifier, numerical model, density stratification, turbulence.

A transient Eulerian-Eulerian simulation of bubbling regime hydrodynamics of coal ash particles in fluidized bed using different drag models

Simple reduced order models (ROMs) for the aerodynamic coefficients - lift, drag, and pitch moment - of a pitching NACA0012 airfoil are presented. The ROMs are designed for quick computation of the transient aerodynamic characteristics of the airfoil and are developed utilizing computational fluid dynamics (CFD) simulation results. The entire aerodynamic system is modeled as a single input, multi output system yielding three independent systems to be characterized. A systematic, two step process is employed to develop the ROMs for each aerodynamic system. First, a CFD simulation is conducted to determine the linearity of each system, and any nonlinear system is restructured as a nonlinear operator followed by a linear system to allow for the use of linear system identification techniques. A second CFD simulation is conducted to determine the frequency response of each linear system, and the coefficients of each ROM are extracted by fitting a second order model to each frequency response function. The ROMs are validated against an independent CFD simulation of a pitching airfoil and are shown to accurately model each aerodynamic coefficient.

While designing the power requirements of a ship, the most important factor to be considered is the ship resistance, or the sea drag forces acting on the ship. It is important to have an estimate of the ship resistance while designing the propulsion system since the power required to overcome the sea drag forces contribute to ‘losses’ in the propulsion system. There are three main methods to calculate ship resistance: Statistical methods like the Holtrop-Mennen (HM) method, numerical analysis or CFD (Computational Fluid Dynamics) simulations, and model testing, i.e. scaled model tests in towing tanks. At the start of the design stage, when only basic ship parameters are available, only statistical models like the HM method can be used. Numerical analysis/ CFD simulations and model tests can be performed only when the complete 3D design of the ship is completed. The present paper aims at predicting the calm water ship resistance using CFD simulations, using the Flow-3D software package. A case study of a roll-on/roll-off passenger (RoPax) ferry was investigated. Ship resistance was calculated at various ship speeds. Since the mesh affects the results in any CFD simulation, multiple meshes were used to check the mesh sensitivity. The results from the simulations were compared with the estimate from the HM method. The results from simulations agreed well with the HM method for low ship speeds. The difference in the results was considerably high compared to the HM method for higher ship speeds. The capability of Flow-3D to perform ship resistance analysis was demonstrated.

Pattern of fluid flow through open-cell foams is important because of its influence on the performance of processes such as filtration, adsorption and heterogeneous catalysis that make use of such foams. So far, however, the experimental verification of velocity profiles obtained by computational fluid dynamics (CFD) simulation was insufficient. Here, the effect of morphology of ceramic foams on local gas flow patterns is observed via the noninvasive magnetic resonance velocimetry (MRV) technique. In order to cross-validate the simulations with the experimental flow mapping results, micro-computed tomography (µCT) data of the entire foams were used for generating the computational network required for 3D CFD simulations of velocity fields within the pores. The results of CFD simulations and MRV measurements of gas flow showed a remarkable agreement with deviations mainly below 10 percent if the whole foam structure was utilized in CFD simulations. The qualitative and quantitative agreement between CFD and MRV results underlines the reliability of CFD simulations that are based on µCT data and underpins the capability of NMR-based measurements for in situ velocity measurements.Graphic abstract