Eulerian Multiphase Flow Model Research Articles

CFD simulation of gas mixing in anaerobic digesters

A computational fluid dynamics (CFD) model that characterizes gas mixing in anaerobic digesters was developed. The four gas mixing designs studied are: (1) unconfined mixing by two bottom diffusers, (2) confined mixing by one draft tube, (3) unconfined mixing by two cover mounted lances, and (4) confined mixing by two bubble guns. The flow fields for each design were obtained by solving an Eulerian multiphase flow model, assuming that the liquid phase is a non-Newtonian power-law fluid. The commercial CFD software, Fluent 14.5, was applied to simulate gas–liquid two-phase flow in the digester. A qualitative description of the fluid motion due to the generation of gas bubbles and quantitative identification of the flow fields of the liquid phase were made to compare the four mixing designs, in which the average velocity and a uniformity index for velocity were used to evaluate the mixing performance for each design. In addition, the velocity gradient for gas mixing along with its application to calculate the breakup number of a floc was investigated. Further, the mixing intensity that impacts the biological process and the justification of the simulation results were discussed.

Numerical predictions of flow boiling characteristics: Current status, model setup and CFD modeling for different non-uniform heating profiles

A detailed analysis of two-phase flow boiling characteristics inside high pressure systems is presented focusing on non-uniform axial heating profiles. For this purpose, a detailed numerical model has been developed after presenting the current status of the use of CFD techniques in flow boiling predictions. User defined functions written in C++ were compiled and hooked to the software in order to account for mass interaction between phases using the Eulerian multiphase flow model. The modeled domain is a 2 m long stainless steel pipe with inside and outside diameters of 15.4 mm, 25.4 mm, respectively. The base imposed uniform heat flux was 345.6 kW/m2, for mass flow rate of water of 0.161 kg/s and at a temperature of 200 °C. The model was validated against range of experimental data and the results are very promising for the use of CFD in flow boiling characterization. Effects of increasing uniform heat flux were considered for different increments of 30, 50 and 75% as reference to the basic applied heat flux. The influences of heat flux profile in the axial direction were investigated while maintaining the same total power. Different heat flux profiles of linearly increasing, linearly decreasing, sine, and cosine shapes were considered.

Influence of grain-size distribution on the dynamics of underexpanded volcanic jets

The dynamics of underexpanded volcanic jets is studied by means of a Eulerian multiphase flow model, accounting for kinetic and thermal non-equilibrium between gas and particles. Two-dimensional numerical simulations are analysed in terms of the scaling properties of the gas–solid flow based on the particle Stokes number St, defined as the ratio of the particle relaxation time τs and a typical flow time scale, here taken as the formation time of the jet Mach disk τM. For monodisperse mixtures, fine particles with St≪1 are tightly coupled to the gas during decompression and the typical flow patterns of supersonic free jets are reproduced. The multiphase flow model, in this case, gives results comparable to a dusty-gas model. However, for St≫1 we demonstrate that the effects of particle inertia and gas–particle drag are so relevant that the shock wave structure associated with gas decompression is obliterated, although the mixture velocity remains supersonic. We are therefore able to identify two different regimes of jet decompression (with/without Mach disk) that appear to be associated exclusively with the size of the ejected particles. For bidisperse mixtures, multiphase flow numerical simulations show that the features of underexpanded jet depend on the relative mass load of fine and coarse particles. A scaling analysis has been performed by means of a hybrid multiphase flow model, in which fine particles are mixed with the gas (in a dusty-gas approximation), while coarse particles are modelled as a disperse phase, with a modified Stokes number accounting for the mixture properties of the carrier pseudofluid. Both scaling analysis and numerical simulations with the hybrid model corroborate the analysis based on the Stokes number for bidisperse underexpanded jets, although particle–particle momentum exchange between particles of different size can affect the multiphase flow dynamics, especially in regimes with St~1. We finally extend our analysis to polydisperse mixtures, by defining a threshold between fine and coarse particles on the basis of their Stokes number. Numerical simulations and scaling analysis based on the hybrid model (in which all fine particles are mixed with the gas in the dusty-gas approximation and the coarsest particles are described by a single hydraulically equivalent disperse phase) demonstrate that the total particle size distribution can have a significant effect on the jet decompression dynamics, potentially affecting the stability and large-scale behaviour of the volcanic column.

Model-based analysis of the impact of the distributor on the hydrodynamic performance of industrial polydisperse gas phase fluidized bed polymerization reactors

A two dimensionally Eulerian–Eulerian multiphase flow model coupled with a population balance modeling (CFD–PBM) simulation was implemented to investigate the fluidization structure in an industrial scale gas phase polymerization reactor (FBR). Direct quadrature method of moments (DQMOM) was employed in this model to solve the PBM. Two cases including perforated distributor and complete sparger have been applied to examine the flow structure through the bed. A simulation of the reactor with perforated distributor was performed first to validate and evaluate the impact of distributor's characteristics on the fluidization behaviors. The predicted results were in good agreement with the industrial data in terms of pressure drop and bed height. The results showed that different heterogeneous flow patterns were created in a perforated distributor, due to more kinetic energy and jet formation above the distributor. A dead zone is expected to be formed near the corners of the perforated distributor. In addition, the cluster formation is expected to be decreased in comparison with the complete sparger plate distributor. Furthermore, the results predicted bigger bubble diameter in the case of the perforated distributor by using an image processing technique. The information obtained from this study could be important to assure efficient industrial operations of FBRs.

On the Computational Modeling of Unfluidized and Fluidized Bed Dynamics

Two factors of great importance when considering gas–solid fluidized bed dynamics are pressure drop and void fraction, which is the volume fraction of the gas phase. It is, of course, possible to obtain pressure drop and void fraction data through experiments, but this tends to be costly and time consuming. It is much preferable to be able to efficiently computationally model fluidized bed dynamics. In the present work, ANSYS Fluent® is used to simulate fluidized bed dynamics using an Eulerian–Eulerian multiphase flow model. By comparing the simulations using Fluent to experimental data as well as to data from other fluidized bed codes such as Multiphase Flow with Interphase eXchanges (MFIX), it is possible to show the strengths and limitations with respect to multiphase flow modeling. The simulations described herein will present modeling beds in the unfluidized regime, where the inlet gas velocity is less than the minimum fluidization velocity, and will deem to shed some light on the discrepancies between experimental data and simulations. In addition, this paper will also include comparisons between experiments and simulations in the fluidized regime using void fraction.

Integration of a new shape-dependent particle–fluid drag coefficient law in the multiphase Eulerian–Lagrangian code MFIX-DEM

A new shape-dependent fluid–particle drag law has been added into the open source fluid dynamic software MFIX-DEM (MFIX-Discrete Element Method), which is the Eulerian–Lagrangian version of the classic MFIX Eulerian–Eulerian multiphase flow model. The drag law had been obtained by previous settling experiments of volcanic pumices in a motionless Newtonian liquid (water or alcohol). Pumices are characterized by a highly irregular shape, which is much different from a sphere and drastically influences fluid drag. The new drag law defines the particle–fluid drag coefficient as a function of both the fluid regime and particle characteristics, of which the shape factor is a compact descriptor that quantifies how the particle shape differs from a simple sphere. As a validation of the integration of the new drag law in the simulation software MFIX-DEM, the code has been used to replicate the experiment results. The comparison with simulations performed with other formulas demonstrates that, by means of the new drag law, a significant improvement in the capability of the MFIX-DEM code to predict the terminal velocities of irregularly shaped particles is obtained. Thanks to this implementation, MFIX-DEM should be used, from now on, for simulating fluid–particle flows in which the particles are significantly different from simple spheres, as is usually the case of environmental flows like explosive eruptions or ash and pollutant dispersal. Based on the results of this research, in the future an improved version of MFIX-DEM will be also presented, with a drag law useful also in the case of mixtures to be treated with a Eulerian–Eulerian multiphase model.

Dynamic compaction of granular materials

An Eulerian hyperbolic multiphase flow model for dynamic and irreversible compaction of granular materials is constructed. The reversible model is first constructed on the basis of the classical Hertz theory. The irreversible model is then derived in accordance with the following two basic principles. First, the entropy inequality is satisfied by the model. Second, the corresponding 'intergranular stress' coming from elastic energy owing to contact between grains decreases in time (the granular media behave as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to von Mises-type yield limit. The yield limit depends on the volume fraction of the solid. The sound velocity at the yield surface is smaller than that in the reversible model. The last one is smaller than the sound velocity in the irreversible model. Such an embedded model structure assures a thermodynamically correct formulation of the model of granular materials. The model is validated on quasi-static experiments on loading-unloading cycles. The experimentally observed hysteresis phenomena were numerically confirmed with a good accuracy by the proposed model.

Study on Cuttings Transport Efficiency Affected by Stabilizer's Blade Shape in Vertical Wells

Effective cuttings transport means a better hole cleaning in drilling operations, which can increase the rate of penetration (ROP), and avoids pipe sticking, higher drag and torque problems. This paper aimed to analyze cuttings transport efficiency affected by different blade shapes of stabilizers, which is often overlooked in drilling. For this purpose, Eulerian multiphase flow model was used to simulate the influence of different blade types of stabilizers on cuttings transport efficiency under rotating coordinates. Numerical simulations indicate that straight blade stabilizer is obviously superior to helical blade for cuttings transport efficiency in vertical wells using the same hydraulic parameter and rotating speed. Field tests were conducted in some medium-deep wells of Daqing Oil Field, and the results showed that repeated fragmentation of cuttings, bit balling and pipe sticking problems were improved, and ROP was obviously raised.

Free‐surface turbulent flow induced by a Rushton turbine in an unbaffled dish‐bottom stirred tank reactor: LDV measurements and CFD simulations

AbstractLaser Doppler velocimetry measurements and computational fluid dynamic (CFD) simulations of turbulent flows with free‐surface vortex in an unbaffled dish‐bottom stirred tank reactor agitated by a Rushton turbine are presented. Measurements of the three mean and fluctuating components of the velocity vector are made in order to characterise the flow field and to provide data for CFD model validation. An Eulerian–Eulerian multiphase flow model coupled with a volume‐of‐fluid method for capturing the gas–liquid interface is applied to determine the vortex shape and to compute the flow field. Turbulence is modelled using the standard k−ε, shear‐stress transport and the differential Reynolds‐stress model with two variants of the pressure‐strain correlation. The predicted mean flow field obtained using all four turbulence models are on the whole similar and generally in good agreement with measurements. However, the Reynolds‐stress models provide somewhat better predictions of the mean axial velocity. The turbulent kinetic energy is well predicted in the flow below the impeller, near the bottom of the tank; whereas it is underpredicted in the region close to the impeller and near the wall by all turbulence models.

CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters

This paper presents an Eulerian multiphase flow model that characterizes gas mixing in anaerobic digesters. In the model development, liquid manure is assumed to be water or a non-Newtonian fluid that is dependent on total solids (TS) concentration. To establish the appropriate models for different TS levels, twelve turbulence models are evaluated by comparing the frictional pressure drops of gas and non-Newtonian fluid two-phase flow in a horizontal pipe obtained from computational fluid dynamics (CFD) with those from a correlation analysis. The commercial CFD software, Fluent12.0, is employed to simulate the multiphase flow in the digesters. The simulation results in a small-sized digester are validated against the experimental data from literature. Comparison of two gas mixing designs in a medium-sized digester demonstrates that mixing intensity is insensitive to the TS in confined gas mixing, whereas there are significant decreases with increases of TS in unconfined gas mixing. Moreover, comparison of three mixing methods indicates that gas mixing is more efficient than mixing by pumped circulation while it is less efficient than mechanical mixing.

Measurements and modelling of free-surface turbulent flows induced by a magnetic stirrer in an unbaffled stirred tank reactor

Abstract Measurements and numerical simulations of turbulent flows with free-surface vortex in an unbaffled reactor agitated by a cylindrical magnetic stirrer are presented. Measurements of the three mean and fluctuating components of the velocity vector are made using a laser Doppler velocimetry in order to characterise the flow field at different speeds of the stirrer. A homogeneous Eulerian–Eulerian multiphase flow model coupled with a volume-of-fluid method for interface capturing is applied to determine the vortex shape and to compute the turbulent flow field in the reactor. Turbulence is modelled using a second-moment differential Reynolds-stress transport (RST) model, but for some cases the k – e / k – ω based shear-stress transport (SST) model is also used. The predictions obtained using the ANSYS CFX-5.7 computational fluid dynamics code are compared with the images of the vortex and the measured distributions of mean axial, radial and tangential velocities and turbulent kinetic energy. The predicted general shape of the liquid free-surface is in good agreement with measurements, but the vortex depth is underpredicted. The overall agreement between the measured and the predicted axial and tangential velocities obtained with the RST model is good. However, the radial velocity is significantly underpredicted. Predictions of the turbulent kinetic energy yield reasonably good agreement with measurements in the bulk flow region, but discrepancy exists near the reactor wall where this quantity is underpredicted. The SST model predictions are generally of the same quality as those of the RST model, with the latter model providing better predictions of the tangential velocity distribution.

Simulation of refrigerant flow boiling in serpentine tubes

Numerical simulations were conducted to investigate the refrigerant flow boiling in a horizontal serpentine round tube with the Eulerian multiphase flow model and a phase-change model for the mass transfer. Correspondingly, an experimental investigation was conducted to provide validation and data for the simulations. The liquid/vapor phase distributions show stratification in horizontal tubes, indicating the buoyancy force caused by gravity acceleration is dominant, especially when the vapor void fraction is sufficiently high. The adiabatic bend sections served to redistribute the vapor phase, which was induced by the centrifugal force and re-condensation of the vapor (due to thermal non-equilibrium of two phases). The phase distributions in the bend sections showed the competitive influence of buoyancy force and centrifugal force at different operating conditions. In all cases, the numerical simulations appear reasonably consistent with the experimental observations. In particular, the simulation very well explains the bend effects on flow reconstruction and thermal non-equilibrium release observed in the experiments.

Simulation of Fiber Suspensions—A Multiscale Approach

Abstract The present effort is the development of a multiscale modeling, simulation methodology for investigating complex phenomena arising from flowing fiber suspensions. The present approach is capable of coupling behaviors from the Kolmogorov turbulence scale through the full-scale system in which a fiber suspension is flowing. Here the key aspect is adaptive hierarchical modeling. Numerical results are presented for which focus is on fiber floc formation and destruction by hydrodynamic forces in turbulent flows. Specific consideration was given to dynamic simulations of viscoelastic fibers in which the fluid flow is predicted by a method that is a hybrid between direct numerical simulations and large eddy simulation techniques and fluid fibrous structure interactions will be taken into account. Dynamics of simple fiber networks in a shearing flow of water in a channel flow illustrate that the shear-induced bending of the fiber network is enhanced near the walls. Fiber-fiber interaction in straight ducts is also investigated and results show that deformations would be expected during the collision when the surfaces of flocs will be at contact. Smaller velocity magnitudes of the separated fibers compare to the velocity before collision implies the occurrence of an inelastic collision. In addition because of separation of vortices, interference flows around two flocs become very complicated. The results obtained may elucidate the physics behind the breakup of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow at the continuum level where an Eulerian multiphase flow model can be developed for industrial use.

Multiscale modeling of fluid turbulence and flocculation in fiber suspensions

A mathematically rigorous, multiscale modeling methodology capable of coupling behaviors from the Kolmogorov turbulence scale through the full scale system in which a fiber suspension is flowing is presented. Here the key aspect is adaptive hierarchical modeling. Numerical results are presented focus of which are on fiber floc formation and destruction by hydrodynamic forces in turbulent flows. Specific consideration was given to molecular-dynamics simulations of viscoelastic fibers in which the fluid flow is predicted by a method which is a hybrid between direct numerical simulations and large eddy simulation techniques, and fluid fibrous structure interactions were taken into account. The present results may elucidate the physics behind the breakup of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow at the continuum level where an Eulerian multiphase flow model can be developed for industrial use.

Computer simulation of flocs interactions: Application in fiber suspension

The present effort is the development of a multiscale modeling, simulation methodology for investigating complex phenomena arising from flowing fiber suspensions. Specific consideration was given to dynamic simulations of viscoelastic fibers in which the fluid flow is predicted by a method that is a hybrid between Direct Numerical Simulations (DNS) and Large Eddy Simulation techniques (LES), and fluid fibrous structure interactions (FSI) will be taken into account. Numerical results are presented for which focus is on fiber floc deformation by hydrodynamic forces in turbulent flows. Dynamics of simple fiber networks in a shearing flow of water in a channel flow illustrate that the shear-induced bending of the fiber network is enhanced near the walls. Fiber–fiber interaction in straight ducts is also investigated and results show that deformations would be expected during the collision when the surfaces of flocs will be at contact. Smaller velocity magnitudes of the separated fibers compare to the velocity before collision implies the occurrence of an inelastic collision. In addition because of separation of vortices interference flows around two flocs become very complicated. The results opening the possibility for developing a meaningful numerical model of the fiber flow at the continuum level where an Eulerian multi-phase flow model can be developed for industrial use.

Numerical simulation of 2d fluid flow in an partially filled simplified extruder model

AbstractA simplified partly filled two‐dimensional model of a single‐screw extruder was analyzed with a full and a limited Eulerian multiphase flow model. The numerical calculations have been validated with experimental data and a good agreement was found.