Polydispersed Flow Research Articles

An Euler–Lagrange strategy for simulating particle-laden flows

In this work, a strategy capable of simulating polydisperse flows in complex geometries is employed where the fluid transport equations are solved in an Eulerian framework and the dispersed phase is represented as Lagrangian particles. Volume filtered equations for the carrier phase are derived in detail for variable density flows, and all unclosed terms are discussed. Special care is given to the interphase coupling terms that arise, in order to ensure that they are implemented consistently and that they converge under mesh refinement. This provides the flexibility of using cell sizes that are smaller than the particle diameter if necessary. Particle collisions are handled using a soft-sphere model that has been modified for parallel efficiency. Simulations are carried out for a number of laboratory-scale configurations, showing excellent agreement with experiments.

Size-velocity correlations in hybrid high order moment/multi-fluid methods for polydisperse evaporating sprays: Modeling and numerical issues

Kah et al. (2010) [30,33] recently developed the Eulerian multi-size moment model (EMSM) which tackles the modeling and numerical simulation of polydisperse multiphase flows. Using a high order moment method in a compact interval, they suggested to reconstruct the number density function (NDF) by entropy maximization, which leads to a unique and realizable NDF, potentially in several size intervals, thus leading to an hybrid method between Multifluid and high order. This reconstruction is used to simulate the evaporation process, by an evaluation of the flux of droplet disappearance at zero size, the fluxes of droplets between size intervals, and an accurate description of the size shift induced by evaporation Massot et al. (2010) [15]. Although this method demonstrated its potential for evaporating polydisperse flows, two issues remain to be addressed. First, the EMSM only considers one velocity for all droplets, thus decoupling size from velocity, which is too restrictive for distributions with a large size spectrum. In most applications size-conditioned dynamics have to be accounted for. Second, the possibility to have separated dynamics for each size can lead to quasi-monodisperse distributions, which corresponds to a hard limiting case for the EM algorithm. So the behavior of the algorithm needs to be investigated, in order to reproduce the entire moment space with a reasonable accuracy. The aim of this paper is thus twofold. The EM and its related algorithm are enhanced by using a more accurate integration method in order to handle NDF close to the frontier of the moment space associated with an adaptive number of parameters to reconstruct the NDF accurately and efficiently, as well as tabulated initial guess to optimize the computational time. Then, a new model called CSVM (coupled size-velocity moments model) is introduced. Size-velocity correlations are addressed either in the evaporation and drag processes, or in the convective transport. To reach this goal, a velocity reconstruction for each size is suggested, using only one additional moment per dimension, and which can be directly applied to several size intervals. Thus, this method is a direct generalization of EMSM. To handle the convective transport, a flux splitting scheme is proposed, based on the underlying kinetic description of the disperse phase. Comparing to existing approaches, a main novelty of the CSVM is that our kinetic approach ensures built-in realizability conditions, no additional corrections of the moments being needed at each time step. The full strategy is first evaluated in 0D and 1D cases, which either demonstrates the ability to reproduce both evaporation, drag force and convection with size-velocity correlations, or the possible extension to several size intervals. Finally, the method is applied on 2D cases with only one section, showing the ability of the CSVM and its related algorithms to capture the main physics of polydisperse evaporating sprays with a minimal number of moments.

Development of a diffusion-inertia model for calculating bubble turbulent flows: Isothermal polydispersed flow in a vertical pipe

Development of a diffusion-inertia model for calculating bubble turbulent flows: Isothermal polydispersed flow in a vertical pipe

The FDF or LES/PDF method for turbulent two-phase flows

In this paper, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalislm is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF.

On the role of the lateral lift force in poly-dispersed bubbly flows

An extensive experimental database comprising air–water as well as steam-water upwards vertical pipe flows for a pressure up to 6.5 MPa was used to investigate the effect of the lateral lift force on turbulent poly-dispersed flows with medium or high gas volume fraction. It was clearly shown that the lift force plays an important role also in such flows. Several effects such as bubble coalescence and breakup as well as fast rising large bubbles which push small bubbles towards the pipe wall superpose the effect of the lift force but can be separated from this effect. The critical bubble diameter, at which the lift force changes its sign, predicted by using Tomiyama’s correlation agrees well with experimental data obtained for turbulent air–water and steam-water flows with medium and high void fraction and a broad spectrum of bubbles sizes. The values for this critical bubble diameter are confirmed by the experimental data within the frame of the uncertainty of the data. Consequences of the action of the lateral lift force on flow structures in different flow situations are discussed. From the investigations it can be concluded that the lift force including the bubble size dependent change of its sign should be considered in a proper numerical 2D or 3D-simulation on flows in which bubbles in the range of several millimeters are present.

Extension of the inhomogeneous MUSIG model for bubble condensation

Bubble condensation plays an important role, e.g. in sub-cooled boiling or steam injection into pools. Since the condensation rate is proportional to the interfacial area density, bubble size distributions have to be considered in an adequate modeling of the condensation process. The effect of bubble sizes was clearly shown in experimental investigations done previously at the TOPFLOW facility of FZD. Steam bubbles were injected into a sub-cooled upward pipe flow via orifices in the pipe wall located at different distances from measuring plane. 1 mm and 4 mm injection orifices were used to vary the initial bubble size distribution. Measurements were done using a wire-mesh sensor. Condensation is clearly faster in case of the injection via the smaller orifices, i.e. in case of smaller bubble sizes. Recently the Inhomogeneous MUSIG model was implemented into the CFD code CFX from ANSYS enabling the simulation of poly-dispersed flows including the effects of separation of small and large bubbles due to bubble size dependent lift force inversion. It allows to divide the dispersed phase into size classes regarding the mass as well as regarding the momentum balance. Up to now transfers between the classes in the mass balance can be considered only by bubble coalescence and breakup (population balance). Here an extension of the model is proposed to include the effects due to phase transfer. The paper focuses on the derivation of equations for the extension of the Inhomogeneous MUSIG model and presents some first results for verification and validation.

Development and implementation of a polydispersed multiphase flow model in OpenFOAM

Abstract The two-phase flow solver implemented in the open-source OpenFOAM code was extended to a multiphase flow formulation ( n dispersed and one continuous phases) and then coupled to the population balance equation (PBE) solution by the Direct Quadrature Method of Moments (DQMOM), originating a polydispersed multiphase flow solver. Although each dispersed phase has its own velocity field, the present implementation considers only the interfacial momentum exchange between the continuous and the dispersed phases. The multiphase flow formulation was described and the details of the PBE–CFD coupling algorithms in OpenFOAM were provided. The implementation of the multiphase flow code was verified and evaluated against the original OpenFOAM two-phase flow solver for flow through a 2D backward facing step, using simplified breakage and aggregation kernels. The computational cost of both codes were compared for serial and parallel simulations.

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of Alves et al. (2002a, b, 2004). The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.

MATHEMATICAL MODEL OF TWO-PHASE FLOWS LOADED WITH LIGHT AND HEAVY PARTICLES TO ANALYZE CFB PROCESSES

Mathematical modeling of polydispersed (gas-solid particles) flow with light (ash) and heavy (corundum) particles is presented to analyze manifold process occurring in circulating fluidized beds (CFB). This study covers the process of turbulent mixing of particle and particle-particle collision, particle-surface collision and pertains the gravitation and viscous drag and lift forces. The 2D RANS (Reynolds Averaged Navier-Stokes) equations are used for numerical modeling of uprising polydispersed turbulent flow with implemented k-Lh model of closure. The flow domain is a round pipe with diameter of 30 mm and height of 100 calibers (pipe diameters). The flow (mean velocity up to 10 m/s) carries two fractions of ash particles (material density of 1020 kg/m 3 and sizes of 0.25 and 0.4 mm) and corundum particles (material density of 4000 kg/m 3 and size 0.4 mm). Two mass loadings – 5 and 10 kg/kg – were considered. The results are presented in the form of distribution of axial and radial velocity components of gaseous and solid phases, particle mass concentration and kinetic turbulent energy along the flow height at steady-state flow cross-sections.

A note on the consistency of hybrid Eulerian/Lagrangian approach to multiphase flows

The aim of the present paper is to introduce and to discuss inconsistency errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hybrid models, two turbulence models are implicitly used at the same time and it is important to check that they are consistent, in spite of their apparent different formulations. This issue is best revealed in the case of very small particles, or tracer-limit particles, where it is assessed that coupling inconsistent turbulence models (Eulerian and Lagrangian) can result in non-physical results, notably for second-order fluid velocity moments. Computations for fluid particles in a turbulent channel flow using several coupling strategies are presented to illustrate this question.

Computational fluid dynamics modeling of gas dispersion in multi impeller bioreactor

In the present study, experiments have been carried out to identify various flow regimes in a dual Rushton turbines stirred bioreactor for different gas flow rates and impeller speeds. The hydrodynamic parameters like fractional gas hold-up, power consumption and mixing time have been measured. A two fluid model along with MUSIG model to handle polydispersed gas flow has been implemented to predict the various flow regimes and hydrodynamic parameters in the dual turbines stirred bioreactor. The computational model has been mapped on commercial solver ANSYS CFX. The flow regimes predicted by numerical simulations are validated with the experimental results. The present model has successfully captured the flow regimes as observed during experiments. The measured gross flow characteristics like fractional gas hold-up, and mixing time have been compared with numerical simulations. Also the effect of gas flow rate and impeller speed on gas hold-up and power consumption have been investigated.

Effects of Polydispersity in Bubbly Flows

This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows. First, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness. Next, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics. Finally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.v

Benchmark database on the evolution of two-phase flows in a vertical pipe

Based on many years of experience, a new extensive and high-quality database was obtained for steady-state upward air–water flows in a vertical pipe with an inner diameter of 195.3 mm using the wire-mesh sensor technology. During the experiments, the sensor was always mounted on the top of the test section while the distance between gas injection and measuring plane was varied up to 18 different L/D by using gas injection chambers at different vertical positions. The gas was injected via holes in the pipe wall. In this new test series the pressure was kept at 0.25 MPa (absolute) at the location of the active gas injection while the temperature was constant at 30 °C ± 1 K. The experiments were done for 48 combinations of air and water superficial velocities varying from 0.04 m/s to 1.6 m/s for water and 0.0025 m/s to 3.2 m/s for air. From the raw data time-averaged data as: radial gas volume fraction profiles, bubble size distributions, radial volume fraction profiles decomposed according to the bubble size and the radial profiles of the gas velocity were calculated. The consistency of this data was thoroughly checked. They are characterized by a high resolution in space, which makes them suitable for the development and validation of CFD-grade closure models, e.g. for bubble forces and coalescence and break-up. It is also an ideal base to validate CFD approaches for poly-dispersed flow. For this reason it is proposed to use the database as a benchmark for modelling poly-dispersed flows.

Modeling of ascending polydisperse flow with allowance for heterogeneous combustion, particle rotation, and turbulent and pseudoturbulent effects

A closed system of equations that describes motion and physicochemical processes in ascending polydisperse flow with allowance for the rotation of the dispersed phase, the aerodynamic-drag, gravity, and Magnus forces, and the interaction of particles with each other and with the reactor wall is constructed. The equations of motion and heat transfer of the solid phase are closed at the level of equations for the second moments of pulsations of the linear and angular velocities of particles and their temperature. The pulsation characteristics of the carrying medium are computed using the equation for the turbulent gas energy.

CFD modelling of polydispersed bubbly two-phase flow around an obstacle

A population balance model (the Inhomogeneous MUSIG model) has recently been developed in close cooperation between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD-Code CFX [Krepper, E., Lucas, D., Prasser, H.-M, 2005. On the modelling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611; Frank, T., Zwart, P.J., Shi, J.-M., Krepper, E., Rohde, U., 2005. Inhomogeneous MUSIG Model—a population balance approach for polydispersed bubbly flows, International Conference “Nuclear Energy for New Europe 2005”, Bled, Slovenia, September 5–8, 2005; Krepper, E., Beyer, M., Frank, Th., Lucas, D., Prasser, H.-M., 2007. Application of a population balance approach for polydispersed bubbly flows, 6th Int. Conf. on Multiphase Flow Leipzig 2007, (paper 378)]. The current paper presents a brief description of the model principles. The capabilities of this model are discussed via the example of a bubbly flow around a half-moon shaped obstacle arranged in a 200 mm pipe. In applying the Inhomogeneous MUSIG approach, a deeper understanding of the flow structures is possible and the model allows effects of polydispersion to be investigated. For the complex flow around the obstacle, the general structure of the flow was well reproduced in the simulations. This test case demonstrates the complicated interplay between size dependent bubble migration and the effects of bubble coalescence and breakup on real flows. The closure models that characterize the bubble forces responsible for the simulation of bubble migration show agreement with the experimental observations. However, clear deviations occur for bubble coalescence and fragmentation. The models applied here, which describe bubble fragmentation and coalescence could be proved as a weakness in the validity of numerous CFD analyses of vertical upward two-phase pipe flow. Further work on this topic is under way.

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– ɛ turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– ɛ equations. An implementation into CFX is planned.

多流体モデルによる気泡塔内多分散気泡流の数値計算(流体工学,流体機械)

Bubble coalescence and breakup models are implemented into the (N+2)-field model, which is a hybrid combination of a multi-fluid model and an interface tracking method to examine the applicability of available bubble coalescence and breakup models to poly-dispersed bubbly flows in bubble columns. The implemented models are a breakup model proposed by Luo & Svendsen and coalescence models proposed by Prince & Blanch and Wang et al. The validation of these models is carried out using experimental data for a coalescence-dominating flow, a breakup-dominating flow, a flow in-between, and a flow with low coalescence-breakup frequencies. Good predictions of void and bubble size distributions for the four kinds of poly-dispersed bubbly flows in bubble columns are obtained. It is also demonstrated that all the possible bubble coalescence mechanisms, i.e. bubble coalescence caused by bubble collisions due to turbulent eddies, the difference in bubble velocities and shear slip, and bubble coalescence due to wake entrainment, should be taken into account for obtaining good predictions.

Numerical simulation of the influence of stationary louver and coal particle size on distribution of pulverized coal to the feed ducts of a power plant burner

One of the key requirements related to successful utilization of plasma technology as an oil-free backup system for coal ignition and combustion stabilization in power plant boilers is provision of properly regulated pulverized coal distribution to the feed ducts leading the fuel mixture to a burner. Proper regulation of coal distribution is deemed essential for achieving an adequate pulverized coal concentration in the zone where thermal plasma is being introduced. The said can be efficiently achieved by installation of stationary louver in the coal-air mixing duct ahead of the feed ducts of a burner. The paper addresses numerical simulation of a two-phase flow of air-pulverized coal mixture in the mixing ducts, analyzing the effects of particle size distribution on pulverized coal distribution to the burner feed ducts. Numerical simulation was performed using the FLUENT 6.3 commercial code and related poly-dispersed flow module, based on the PSI-CELL approach. Numerical experiments have been performed assuming a mono-dispersed solid phase with particle diameter ranging from 45 mm to 1200 mm. Distance between the louver blades and the resulting effect on the flow profile was analyzed as well. Results obtained indicate that the size of coal particles considerably influence the overall solid phase distribution. While fine particles, with diameters at the lower end of the above specified range, almost fully follow the streamlines of the continuous phase, coarser particles, which hit the louver blades, deflect towards the thermal plasma zone. In this manner, a desired phase concentration in the considered zone can be reached. For the said reason, installation of stationary louver have been deemed a very efficient way to induce phase separation, primarily due to more pronounced impact of the installed louver on discrete phase flow then the impact on the flow of the continuous phase.

Evaluation of numerical strategies for large eddy simulation of particulate two-phase recirculating flows

Predicting particle dispersion in recirculating two-phase flows is a key issue for reacting flows and a potential application of large eddy simulation (LES) methods. In this study, Euler/Euler and Euler/Lagrange LES approaches are compared in the bluff body configuration from Borée et al. [J. Borée, T. Ishima, I. Flour, The effect of mass loading and inter-particle collisions on the development of the polydispersed two-phase flow downstream of a confined bluff body, J. Fluid Mech. 443 (2001) 129–165] where glass beads are injected into a complex recirculating flow. These tests are performed for non-reacting, non-evaporating sprays but are mandatory validations before computing realistic combustion chambers. Two different codes (one explicit and compressible and the other implicit and incompressible) are also tested on the same configuration. Results show that the gas flow is well predicted by both codes. The dispersed phase is also well predicted by both codes but the Lagrangian approach predicts root-mean-square values more accurately than the Eulerian approach. The effects of mesh, solvers and numerical schemes are discussed for each method.

Implementation and analysis of numerical solution of the population balance equation in CFD packages

Simulation of polydisperse flows must include the effects of particle–particle interaction, as breakage and aggregation, coupling the population balance equation (PBE) with the multiphase modelling. In fact, the implementation of efficient and accurate new numerical techniques to solve the PBE is necessary. The direct quadrature method of moments, known as DQMOM, is a moment-based method that uses an optimal adaptive quadrature closure and came into view as a promising choice for this implementation. In the present work, DQMOM was implemented in two CFD packages: the commercial ANSYS CFX, through FORTRAN subroutines, and the open-source OpenFOAM, by directly coding the PBE solution. Transient zero-dimensional and steady one-dimensional simulations were performed in order to explore the PBE solution accuracy using several interpolation schemes. Simulation cases with dominant breakage, dominant aggregation and invariant solution (equivalent breakage and aggregation) were simulated and validated against an analytical solution. The solution of the population balance equation was then coupled to the two-fluid model, considering that all particles classes share the same velocity field. Momentum exchange terms were evaluated using the local instantaneous Sauter mean diameter of the size distribution function. The two-dimensional tests were performed in a backward facing step geometry where the vortex zones traps the particles and provides high rates of breakage and aggregation.