Multi-fluid Approach Research Articles

Numerical modelling of a three-phase internal air-lift circulating photocatalytic reactor.

The photocatalytic degradation process has been recognized as a low-cost, environmentally friendly and sustainable technology for water and wastewater treatment. As a key carrier of the photocatalytic process, the semiconductor TiO2 has been used in many studies. Analysis and modelling of hydrodynamics in the three-phase flow system can provide useful information for process design, operation and optimization of the three-phase flow photocatalytic reactor, which requires research on the mixing and flow characteristics of the interphase regions in the reactor. In this study, we modelled the hydrodynamics in an internal air-lift circulating photocatalytic reactor using an Eulerian multi-fluid approach. Localized information on phase holdup, fluid flow patterns and mixing characteristics was obtained. The simulation results revealed that the distribution of solid particle concentration depends on the flow field in the internal air-lift circulating photocatalytic reactor. The distance between the draft tube and wall of the reactor and changes in the superficial gas velocity (Ug) were found to be influential factors in reactor performance. The computational model developed could support optimizing reactor design to improve the hydrodynamics and provide guidance for scale-up.

Numerical Simulation of Turbulent Flow and Mixing in Gas–Liquid–Liquid Stirred Tanks

The turbulent flow and macro-mixing processes in gas–liquid–liquid stirred vessels agitated by a Rushton turbine have been numerically simulated, based on the Eulerian multifluid approach. Both the isotropic k–e model and anisotropic Reynolds stress model are used for turbulence modeling. The numerical models are validated by comparing simulated flow field of agitated immiscible liquid–liquid dispersions to the corresponding experimental data from the literature. The predicted time traces of normalized concentration of inertial tracer and mixing time in gas–liquid–liquid stirred tanks are compared to the experimentally measured ones as well. Both turbulence models correspond reasonably well to the experimental data in liquid–liquid and gas–liquid–liquid stirred tanks, and the Reynolds stress model produces better results, in terms of flow field, homogenization curve, and mixing time, than the k–e model. The information reported in this work is useful for chemical/process engineers when undertaking relevan...

Modeling and simulation of gas-liquid-solid three-phase flow in under-balanced drilling operation

In this study, gas-liquid-solid three-phase flow in the annulus of a well with actual dimensions is simulated numerically considering under-balanced drilling (UBD) operations. The multi-fluid approach which is the most accurate and sophisticated method is used for the simulation. For this purpose, one-dimensional form of steady-state three-fluid model in the Eulerian frame of reference is used to simulate the three-phase flow in the UBD operation. The results have been validated with actual field data and also with the result of gas-liquid two-phase flow model. The comparisons show that three-phase numerical simulation gives better accuracy compared to two-phase numerical simulation and most of other models which are using mechanistic approach. Given the importance of the prediction and control of the bottom-hole pressure (BHP) during drilling operations, the effects of controlling parameters such as liquid and gas flow rate, drilling velocity, size of cuttings and choke pressure on the BHP are investigated. Also, due to the importance of the hole-cleaning during drilling operations, the effects of different controlling parameters on the solid volume fraction distribution during annulus are discussed. Results show that the increasing of the gas flow rate and decreasing of the cutting size can be used as a tool for improved hole-cleaning in the UBD operation.

CFD simulation of multiphase flows and erosion predictions under annular flow and low liquid loading conditions

For many industrial applications dealing with gas-liquid flow, transporting gas and liquid simultaneously causes many challenges. Prediction of erosion in multiphase flow is a complex problem due to lack of accurate models for calculating particle impact velocities in multiphase flow. Computational Fluid Dynamics (CFD) studies of annular flow are being conducted to investigate annular flow behavior and particle impact characteristics. Volume of Fluid (VOF) method was employed for air-water flow simulation with high gas velocities and low liquid rates. Simulation results are compared with results obtained with Eulerian-Eulerian with Multi-Fluid VOF approach with the same flow rates. CFD simulations of annular flow were also compared and validated with experimental data previously obtained with wire-mesh sensors. The liquid film thickness in bends can significantly affect erosion, therefore the simulation results of liquid film thickness trends are also investigated based on the gas and liquid flow rates.Particle tracking along with flow simulations have been solved simultaneously, and the maximum values of mass removal calculated with current erosion models were recorded in order to calculate the maximum erosion magnitudes. Particle impact characteristics including particle impact velocities, particle impact angles as well as particle impact number distribution along the bend were studied in several cases with different superficial gas and liquid velocities. Predicted erosion ratios are compared with available experimental data and show very good agreement.

Multi-fluid Approach to High-frequency Waves in Plasmas. II. Small-amplitude Regime in Partially Ionized Media

Abstract The presence of neutral species in a plasma has been shown to greatly affect the properties of magnetohydrodynamic waves. For instance, the interaction between ions and neutrals through momentum transfer collisions causes the damping of Alfvén waves and alters their oscillation frequency and phase speed. When the collision frequencies are larger than the frequency of the waves, single-fluid magnetohydrodynamic approximations can accurately describe the effects of partial ionization, since there is a strong coupling between the various species. However, at higher frequencies, the single-fluid models are not applicable and more complex approaches are required. Here, we use a five-fluid model with three ionized and two neutral components, which takes into consideration Hall’s current and Ohm’s diffusion in addition to the friction due to collisions between different species. We apply our model to plasmas composed of hydrogen and helium, and allow the ionization degree to be arbitrary. By analyzing the corresponding dispersion relation and numerical simulations, we study the properties of small-amplitude perturbations. We discuss the effect of momentum transfer collisions on the ion-cyclotron resonances and compare the importance of magnetic resistivity, and ion–neutral and ion–ion collisions on the wave damping at various frequency ranges. Applications to partially ionized plasmas of the solar atmosphere are performed.

MULTI-FLUID APPROACH TO HIGH-FREQUENCY WAVES IN PLASMAS. I. SMALL-AMPLITUDE REGIME IN FULLY IONIZED MEDIUM

Ideal MHD provides an accurate description of low-frequency Alfv\'en waves in fully ionized plasmas. However, higher frequency waves in many plasmas of the solar atmosphere cannot be correctly described by ideal MHD and a more accurate model is required. Here, we study the properties of small-amplitude incompressible perturbations in both the low and the high frequency ranges in plasmas composed of several ionized species. We use a multi-fluid approach and take into account the effects of collisions between ions and the inclusion of Hall's term in the induction equation. Through the analysis of the corresponding dispersion relations and numerical simulations we check that at high frequencies ions of different species are not as strongly coupled as in the low frequency limit. Hence, they cannot be treated as a single fluid. In addition, elastic collisions between the distinct ionized species are not negligible for high frequency waves since an appreciable damping is obtained. Furthermore, Coulomb collisions between ions remove the cyclotron resonances and the strict cut-off regions that are present when collisions are not taken into account. The implications of these results for the modelling of high-frequency waves in solar plasmas are discussed.

Two-Temperature Nonequilibrium Model of a Marine Boundary Layer Laden with Evaporating Ocean Spray under High-Wind Conditions

AbstractA nonequilibrium two-temperature multiphase model of the atmospheric boundary layer above wave crests that is laden with evaporating ocean spray in high-wind condition is presented. The governing equations are derived from basic physical principles of conservation of momentum, mass, and thermal energy in multiphase flows. The model derivation uses an Eulerian multifluid approach that considers spray as a continuous medium interacting with the gas phase. The E − ε turbulence closure is used. The developed theoretical framework accounts for the nonuniform ocean spray distribution and the thermal energy exchange between air and spray droplets that, in general, have different temperatures above the wave crest level. Such thermodynamic nonequilibrium conditions are shown to exist when the spray concentration is relatively low and the air humidity is far from saturation. The mechanical and thermodynamic effects of the evaporating spray on airflow and heat transport characteristics are obtained and shown to depend sensitively on the spray concentration.

Strain distribution on material surfaces during combustion regime transitions

A multi-fluid state approach is used to analyse the underlying conditions for burning mode transitions from close to the corrugated flamelet regime to distributed reactions. Turbulent (Ret ≃ 380) premixed DME/air flames were aerodynamically stabilised in a back-to-burnt opposed jet configuration with the Damköhler number varied through the mixture stoichiometry. Simultaneous Mie scattering, OH-PLIF and PIV allowed the delineation of five separate fluid states (reactants, combustion products, mixing fluid, mildly and strongly reacting fluids) with associated material surfaces. The analysis shows self-sustained flames in low strain regions with a collocated flow acceleration for higher Damköhler numbers. By contrast, in highly strained regions (e.g. beyond the twin flame extinction point) the burning mode is governed by the counter-flowing hot combustion products resulting in increased levels of vorticity and an absence of a preferential dilatation direction. The current analysis provides novel insights into combustion regime transitions by means of (i) strain rate statistics conditioned upon material surfaces and (ii) the evolution of fluid state interface probabilities as a function of the Damköhler number. The work further shows (iii) that the combustion mode influences scalar transport and that increased levels of turbulence retards the transition to non-gradient transport.

A differential velocities-based study of diffusion effects in shear banding micellar solutions

By using the generalized bracket approach of non-equilibrium thermodynamics, we recently developed a multi-fluid approach to account for the Fickian diffusion and stress-induced migration in wormlike micellar solutions. In this work, we propose a modification to this framework where differential velocities are not treated as intermediate variables anymore. As the differential velocities are now used as state variables, additional boundary conditions arising from the presence of the diffusive derivative terms can be directly imposed with respect to these variables. The advantage of this modification is that no microstructural information is required for the specification of the boundary conditions. Sample calculations on this new model performed for transient cylindrical Couette flow revealed that the diffusional processes greatly affect the temporal evolution of the rheology and microstructure of the wormlike micelles. In the nonlinear viscoelastic regime, the stress-induced migration dominates over the Fickian diffusion. The smaller the diffusivity constant, the more time is required to reach steady state. Furthermore, the steady-state solution was found to be independent of the (nonzero) value of the diffusivity constant. To smooth the kink between the shear bands and to obtain a unique solution, we believe that nonlocal and surface effects would have to be accounted for. The proposed multi-fluid description of diffusion is general and could be applied to other complex fluids such as polymer solutions.

A strategy for the qualification of multi-fluid approaches for nuclear reactor safety

CFD-simulations for two-phase flows applying the multi-fluid approach are not yet qualified to provide reliable predictions for unknown flows. Among others, one important reason is the missing agreement within the community on closure models to be used. Considering specific phenomena or not, using different models and adjustable constants, most papers presenting a model validation end up with a good agreement with experimental data. However a case by case selection of models and constants does not help to improve the predictive capabilities of such models. For this reason the definition of baseline models considering all known phenomena that could be important is proposed. In such baseline models all parameter have to be defined, i.e., there are no tuning parameters by definition. Therefore these baseline models have to be applied to many experiments with different complexity. Shortcomings of the models and our physical understanding of the complex flow phenomena have to be identified by detailed analyses on the deviations between experimental data and simulation results. A modification of the baseline model will only be done if it bases on physical considerations and improves the overall performance of the model. This requires a huge effort, but seems to be the only way to improve the situation. In particular more complete experimental data are required. Joint activities on the development of such baseline models are desirable. The paper illustrates this strategy by a baseline model for polydisperse bubbly flows which is presently developed at HZDR.

THE IMPACT OF DUST EVOLUTION AND PHOTOEVAPORATION ON DISK DISPERSAL

Protoplanetary disks are dispersed by viscous evolution and photoevaporation in a few million years; in the interim small, sub-micron sized dust grains must grow and form planets. The time-varying abundance of small grains in an evolving disk directly affects gas heating by far-ultraviolet photons, while dust evolution affects photoevaporation by changing the disk opacity and resulting penetration of FUV photons in the disk. Photoevaporative flows, in turn, selectively carry small dust grains leaving the larger particles---which decouple from the gas---behind in the disk. We study these effects by investigating the evolution of a disk subject to viscosity, photoevaporation by EUV, FUV and X-rays, dust evolution, and radial drift using a 1-D multi-fluid approach (gas + different dust grain sizes) to solve for the evolving surface density distributions. The 1-D evolution is augmented by 1+1D models constructed at each epoch to obtain the instantaneous disk structure and determine photoevaporation rates. The implementation of a dust coagulation/fragmentation model results in a marginal decrease in disk lifetimes when compared to models with no dust evolution; the disk lifetime is thus found to be relatively insensitive to the evolving dust opacity. We find that photoevaporation can cause significant reductions in the gas/dust mass ratio in the planet-forming regions of the disk as it evolves, and may result in a corresponding increase in heavy element abundances relative to hydrogen. We discuss implications for theories of planetesimal formation and giant planet formation, including the formation of gas-poor giants. After gas disk dispersal, $\sim 3\times 10^{-4}$ \ms\ of mass in solids typically remain, comparable to the solids inventory of our solar system.

Modeling and simulation of mixing in water-in-oil emulsion flow through a valve-like element using a population balance model

Emulsion flows are very common in natural processes as well as in several engineering areas, such as in the process of desalting crude oil that occurs in refineries. This kind of flow is described as a polydispersed multiphase flow. In this work, we evaluated the behavior of water-in-oil emulsion flowing through a duct with an element used to mimic the effect of a globe valve. An Eulerian multi-fluid approach was employed by solving the population balance equation coupled with computational fluid dynamics. Coalescence and breakage models recently developed were extended to this inhomogeneous model. A bivariate population balance problem was also solved to demonstrate the mixing caused by the valve-like element. The simulated results showed good agreement with the available experimental data for the Sauter and DeBroukere mean diameters.

Heat transfer partitioning model of film boiling of particle cluster in a liquid pool: implementation in a CFD code

In the present work an effective heat transfer partitioning model of three phase (particles, liquid and vapour) flow and thermal interaction have been developed by a multi-fluid approach under film boiling condition. The in-house multiphase flow code is based on finite volume method of discretization and SIMPLE-based pressure correction algorithm. From consideration of mass, momentum and energy balance across the liquid–vapour interface, the vapour bubble generated from the vapour film have been modeled and incorporated in the code. Different interaction terms between each phase are incorporated depending upon the flow regime. The code is validated with in-house and available experimental results. Finally the effect of relevant parameters on void generation under film boiling condition of particles is estimated.

Numerical Modelling of Debris Bed Water Quenching

Debris beds may be formed during a nuclear reactor severe accident and coolability of these beds is important to avoid release of radioactive materials into the environment. However, debris bed water quenching is challenging to understand, and model, because of the complex multi-phase flow and heat transfer physics involved which may include boiling. This paper develops a modelling method for boiling and demonstrates its abilities with some applications. The model is based on a multi-fluid approach, in which one phase represents the liquid, the second phase the gas phase the third phase represents the solid debris bed. In each fluid phase a set of conservation equations for mass, energy and momentum are solved with appropriate inter-phase exchange terms coupling the fluid phases.

A multi-fluid modelling approach for the air entrainment and internal bubbly flow region in hydraulic jumps

This paper proposed a numerical modelling framework aiming to couple both Volume-Of-Fluid (VOF) model and MUltiple-SIze-Group (MUSIG) model to handle the formation of large-scale free surface, bubble entrainment and bubble dispersion in hydraulic oscillating jumps. To consider all essential physics, the modelling framework resolves and couples the flow structure of three different fluids (i.e. continuous air and water and dispersed air bubbles) using the Eulerian–Eulerian multi-fluid approach. To model the air entrainment at the jump toe, a sub-grid scale air entrainment model was also implemented within the framework. To evaluate the capability of the proposed model, model predictions were validated against experimental data of (Chachereau and Chanson, 2010). Comparisons between predicted and measured results are in satisfactory agreement demonstrating the potential of the proposed methodology. Discussions on the drawbacks and deficiencies of the current model are also included.

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

In this paper, discussions of a recently improved Computational Fluid Dynamics (CFD) methodology for virtual experimental investigation of the heat treatment for cast aluminium parts are presented. The immersion quenching process of the heated work piece in a sub-cooled liquid pool is handled by employing the Eulerian multi-fluid modelling approach, which is implemented within the commercial CFD code AVL FIRE®. The applied heat and mass transfer rates are modelled based on the different boiling regime, which is controlled by the Leidenfrost temperature. The objective of the present research is to present an updated quenching model where variable Leidenfrost temperature is applied. Furthermore, simulation results are compared with available measurements for a wide variety of quenching scenarios involving immersion cooling of the step plate and real cylinder head with different solid parts orientations. The temperature histories predicted by the presented model fit very well with the available experimental data at different monitoring locations ©2014 Journal of Mechanical Engineering. All rights reserved.

Predictions of coal combustion and desulfurization in a CFB riser reactor by kinetic theory of granular mixture with unequal granular temperature

A multi-fluid Eulerian modeling approach is employed to simulate coal combustion and desulfurization in a CFB riser reactor. The unsteady processes of gas–solid two phase flow, heat and mass transfer incorporating the devolatilization, heterogeneous and homogeneous reactions, and sorbent model are considered in the simulation. The dispersed solid phase within the CFB riser reactor is modeled as two continuous phases with different diameters and densities. The constitutive properties of the dispersed solid phases are predicted by the kinetic theory of granular mixture (KTGM) with unequal granular temperature. By numerical simulations, the distributions of volume fraction, velocity, temperature and concentrations of gas species are studied. Two-dimensional simulation results for a CFB riser reactor are compared with experimental data for gas species concentration and temperature. The impact of the inlet region on coal combustion and limestone calcination is observed. This model has demonstrated its capability to predict the main fluid mechanic/fluidization and chemical reactions during coal combustion and desulfurization in CFB riser reactors.

INFLUENCE OF THE BACKREACTION OF STREAMING COSMIC RAYS ON MAGNETIC FIELD GENERATION AND THERMAL INSTABILITY

Using a multi-fluid approach, we investigate streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays propagating perpendicular to the background magnetic field. Perturbations are considered to be also across the magnetic field. The back-reaction of cosmic rays resulting in strong streaming instabilities is taken into account. It is shown that for sufficiently short wavelength perturbations, the growth rates can exceed the growth rate of cosmic-ray streaming instability along the magnetic field found by Nekrasov & Shadmehri (2012), which is in its turn considerably larger than the growth rate of the Bell instability (2004). The thermal instability is shown not to be subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability has been derived which includes sound velocities of plasma and cosmic rays, Alfv\'{e}n and cosmic-ray streaming velocities. The relation between these parameters determines the kind of thermal instability ranging from the Parker (1953) to the Field (1965) instabilities. The results obtained can be useful for a more detailed investigation of electron-ion astrophysical objects such as supernova remnant shocks, galaxy clusters and others including the dynamics of streaming cosmic rays.

Numerical simulation of immersion quenching process for cast aluminium part at different pool temperatures

The present paper outlines the recently improved Computational Fluid Dynamics (CFD) model to simulate the immersion quench cooling process. The main application area of the presented method is heat treatment of cast aluminium parts, mostly cylinder heads in automotive internal combustion engines, where an accurate heat treatment prediction plays an important role in conceptual and thermal analysis. In order to achieve low residual stress levels resulting from even temperature distribution during the cooling process, and thereby to prevent component failure during operation, the numerical model of the quenching process, as developed within the commercial CFD code AVL FIRE®, was improved by allowing for variable Leidenfrost temperature. Preliminary results of variable Leidenfrost temperature model together with the implementation of additional interfacial forces, such as lift and wall lubrication forces are presented. Only the enthalpy equation is solved in the solid domain to predict the thermal field, whereas the Euler-Eulerian multi-fluid modelling approach is used to handle the boiling two-phase flow and the heat transfer between the heated structure and the sub-cooled liquid. The results of the improved quenching model are compared with available measurement data for various water temperatures ranging from 303 K to 353 K. Using the step plate with variable thickness sections along its height as the model test case, different solid part orientations were investigated and obtained temperature profiles were analysed. The temperature histories predicted by the presented model correlate very well with the provided measurement data at different monitoring positions. The temperature distribution within the solid part, obtained from the CFD simulation, can therefore serve as a realistic input for subsequent Finite Element Analysis (FEA) of thermal stresses within the quenched solid part.

Numerical Simulation of a Spouted Bed Using Computational Fluid Dynamics (CFD)

In this article, computational fluid dynamics (CFD) technology is used to model a spouted bed(SB). The multifluid Eulerian-Eulerian approach based on kinetic theory of granular flows and Gidaspow's drag model for the interaction between gas and particles are applied in the modeling. The effects of the SB properties—that is, cone angle, particle size, cylinder diameter, and static bed height of particles—on its dynamics performance are investigated. The simulated results—that is, flow pattern of particles, fountain height, voidage, and particle velocity of the spout zone—are presented. It is shown that periodic fluctuation of spouting appears in an SB with conical angle of 30° and inlet velocity at 16.6 m/s. When the SB cylinder diameter becomes 0.52 m, periodic fluctuation appears, too. The stable spouting of the SB with a 90° cone angle could be obtained at an inlet air velocity of 24.3 m/s. The fountain height of particles decreased with an increase in particle size and the static bed height of particles. It is kept at about 0.19 m when different SB cylinder diameters in the range of 0.36 to 0.48 m are used. In the spouting region, the voidage decreased with static particle height in bed, but the particle velocity increased. For a certain particle size, the voidage decreased with an increase in particle height, but the velocity of the particles increased. It was also found that the cylinder diameter did not affect the volume fraction of particles except for the cylinder diameter 0.52 m and the change in particle velocity was minimal in the spout zone. With the different static bed height of particles used, the voidage and particle velocity did not change much at the same level of spout zone.