Affecting the phase split at a large diameter T-junction by using baffles

Current research has expanded on the existing database by conducting air–water experiments in a 0.125 m regular T-junction and a 0.125/0.076 m reduced T-junction. Inserts, cut to 30° and 45°, protruded from the side arm into the main pipe of the junction at different protrusion depths and their effect on the two-phase flow phase split at the junction measured. Depending on the approaching flow regime, inserts placed at the junction were seen to either enhance the partial phase separation occurring at the T-junction or promote a more equal flow split between the two downstream arms.     

Phase split of liquid–liquid two-phase flow at a horizontal T-junction

This paper provides data on the split of liquid/liquid two-phase flow at a horizontal T-junction. Phase maldistribution was measured for kerosene–water flow at the T-junction with equal pipe diameters of 67.4 mm. Data were taken with both stratified flow with a mixture at interface and dispersed flows approaching the junction. The degree of phase maldistribution was not very great but preferential emergence of either phase from the side-arm was observed depending on the flow rates of the two-phases. There are similarities with the limited split data from liquid/solid flows and the degree of separation is seen to depend on the dispersed/continuous phase density ratio. The data were compared to predictions from the correlation by Seeger et al. The Seeger equation gives but reasonable agreement.     

Evaluation of the Darcy's law performance for two-fluid flow hydrodynamics in a particle debris bed using a lattice-Boltzmann model

In the present paper, multiphase flow dynamics in a porous medium are analyzed by employing the lattice-Boltzmann modeling approach. A two-dimensional formulation of a lattice-Boltzmann model, using a D2Q9 scheme, is used. Results of the FlowLab code simulation for single phase flow in porous media and for two-phase flow in a channel are compared with analytical solutions. Excellent agreement is obtained. Additionally, fluid-fluid interaction and fluid-solid interaction (wettability) are modeled and examined. Calculations are performed to simulate two-fluid dynamics in porous media, in a wide range of physical parameters of porous media and flowing fluids. It is shown that the model is capable of determining the minimum body force needed for the nonwetting fluid to percolate through the porous medium. Dependence of the force on the pore size, and geometry, as well as on the saturation of the nonwetting fluid is predicted by the model. In these simulations, the results obtained for the relative permeability coefficients indicate the validity of the reciprocity for the two coupling terms in the modified Darcy's law equations. Implication of the simulation results on two-fluid flow hydrodynamics in a decay-heated particle debris bed is discussed. Received on 1 December 1999     

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed （CFB） designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process. Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-offbetween computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient. A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementa- tion is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed （solid flux） is implemented through additional mass source/sink terms in the continuity equations of the two phases, For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations, The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system, The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.     

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed (CFB) designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process.Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-off between computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient.A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementation is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed (solid flux) is implemented through additional mass source/sink terms in the continuity equations of the two phases.For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations. The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system.The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.     

Particle mixing rates using the two-fluid model

In this work, a new methodology is introduced to calculate the solids mixing rate in dense gas-fluidized beds using the two-fluid model. The implementation of this methodology into an existing two-fluid model code was carefully verified. The solids phase continuity equation was satisfied using our method, and the sensitivity of the computational results to the time step, computational cell size, and discretization scheme was investigated to determine the optimal simulation settings. Using these simulation settings, the degree of solids mixing was observed to rapidly (exponentially) increase with increasing operating pressure and linearly decrease with increasing bed diameter. Our novel methodology can be applied to analyze mixing processes in large lab-scale beds as an alternative to existing time-consuming simulation techniques such as computational fluid dynamics combined with the discrete element model.     

Axi-symmetric simulation of a two phase vertical thermosyphon using Eulerian two-fluid methodology

Numerical simulation of steady state operation of a vertical two phase closed thermosyphon is performed using the two-fluid methodology within Eulerian multiphase domain. A full scale axi-symmetric model is developed for computational fluid dynamics simulation of thermosyphon using ANSYS/FLUENT 13.0. The effects of evaporation, condensation and interfacial heat and mass transfer are taken into account within the whole domain. Cooling water jacket is also modelled along with the wall of thermosyphon to simulate the effect of conjugate heat transfer between the wall and fluid phase. The results obtained are presented and compared with available experimental investigations for a similar thermosyphon. It is established that two-fluid methodology can be used effectively for the purpose of simulation of two phase system like a typical thermosyphon.     

竖置管流中液固两相脉动特性和颗粒浓度分布

利用激光多普勒分相测量技术,考察了液固两相自下而上通过竖置矩形管时,固、液两相的时均速度、流向及横向的脉动强度和颗粒相的相对浓度分布,证实了颗粒浓度的横向分布主要取决于颗粒的横向脉动强度分布（即npvp′2^-=常数）的分析结果。     

A two-phase, two-component model for vertical upward gas-liquid annular flow

In this paper, a new two-fluid two-component computational fluid dynamics (CFD) model is developed to simulate vertical upward two-phase annular flow. The two-phase VOF scheme is utilized to model the roll wave flow, and the gas core is described by a two-component phase consisting of liquid droplets and gas phase. The entrainment and deposition processes are taken into account by source terms of the governing equations. Unlike the previous models, the newly developed model includes the effect of liquid roll waves directly determined from the CFD code, which is able to provide more detailed and, the most important, more self-standing information for both the gas core flow and the film flow as well as their interactions. Predicted results are compared with experimental data, and a good agreement is achieved.     

One-dimensional two-fluid equations for horizontal stratified two-phase flow

Advanced computer codes for water reactor loss-of-coolant analysis are based on the use of the two-fluid model of two-phase flow, in which conservation equations are solved for the gas and liquid phases separately. The standard two-fluid equations, however, sometimes predict the growth of instabilities in the flow, and occasionally become improperly posed. These difficulties have in the past led to the proposal of several different forms for the conservations equations.To help resolve these uncertainties a widely accepted form of the one-dimensional two-fluid equations is used to calculate wave propagation speeds, and stability limits, for the illustrative case of a frictionless horizontal stratified gas-liquid flow. Calculated propagation velocities are shown to agree with the appropriate limit of an exact solution, and the predicted stability limits are found consistent with available observations on the stability of the stratified flow regime.These comparisons help improve confidence in the ability of the two-fluid equations to analyse more complex problems in transient two-phase flow.     

Fluid dynamics of horizontal air–water slug flows through a dividing T-junction

Experimental data from horizontal air–water slug flows were obtained in a test facility which was a 34 mm internal diameter, 10 m long Plexiglas pipe connected to the 90° branch arms from a T-junction. The test points were located on the flow pattern map in the proximity of the transition lines which separates different flow patterns. Capacitive probes with helical and concave plate sensors were used to quantify the dynamic liquid holdup in each branch. They were combined with Venturi nozzles + differential pressure transmitters in each outlet branch for measuring the two-phase mass flow rates. The dynamic characteristics of the slug flow splitting in a T-junction were studied from the acquired signals. Diaphragm straight-through type valves were used in the run and in the lateral branch arms to imitate equipments consuming the two-phase flow after the T-junction. This assembly can also be used as a gas–liquid separation system. The results showed different mechanisms acting on the slug flow division phenomenon. Liquid accumulation into the run branch, between the TJ and the control valve, caused more gas to come to the lateral branch.     

The effect of fine evaporating droplets on the adiabatic-wall temperature in a compressible two-phase boundary layer

A steady-state supersonic flow of a viscous heat-conducting gas with an admixture of small droplets over a flat plate is considered. The plate surface is assumed to be thermally insulated, and its equilibrium temperature is greater than the evaporation point of the droplets. In contrast to previous publications, the case of low-inertia droplets, which do not deposit onto the wall and have time to evaporate in the boundary layer, is considered. Within the two-fluid approximation for the laminar gasdroplet boundary layer with a compressible carrier phase, a parametric numerical study of the effect of evaporating droplets on the boundary layer structure and the temperature of the adiabatic wall is performed. The similarity parameters are found and the range of these parameters is determined, in which the adiabatic-wall temperature is reduced substantially due to the droplet evaporation even for very low initial concentrations of the liquid phase. This makes promising the use of the condensed phase in the schemes of gasdynamic energy separation based on heat transfer between the flows in subsonic and supersonic boundary layers.     

Smoothed particle hydrodynamics for coarse-grained modeling of rapid granular flow

We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics(SPH) solutions of a set of continuum equations.This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization.We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow,thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization.Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.     

An unstructured grid Reynolds stress model for separated turbulent flow simulations

Most of the turbulence models in the literature contain simplified assumptions which make them computationally inexpensive but of limited accuracy for the solution of separated turbulent flows. Dramatic improvements in computer processing speed and parallel processing make it possible to use more complete models, such as Reynolds Stress Models, for separated turbulent flow simulations, which is the focus of this work. The Reynolds Stress Model consists of coupling the Reynolds transport equations with the Favre–Reynolds averaged Navier–Stokes equations, which results in a system of 12 coupled non-linear partial differential equations. The solutions are obtained by running the PUMA_RSM computational fluid dynamics code on unstructured meshes. The equations are solved all the way to the wall without using any wall functions. Results for high Reynolds number flow around a 6:1 prolate spheroid and a Bell 214ST fuselage are presented. For the prolate spheroid basic flow features such as cross-flow separation are simulated. Predictions of circumferential locations of cross flow separation points are in good agreement with the experiment. A grid refinement study is performed to improve the computations. The fine mesh solution predicted locations of primary and secondary separation points with errors of roughly 2° and 0°, respectively. Flow simulations around an isolated Bell 214ST helicopter fuselage were also performed. Predicted pressure and drag force correlate well with the wind tunnel data, with a less than 10% deviation from the experiment. Drag predictions also show relative speed of Reynolds Stress Model compared to Large Eddy Simulation to compute time averaged quantities. For numerical solutions parallel processing is applied with the MPI communication standard. The code used in this study is run on Beowulf clusters. The parallel performance of the code PUMA_RSM is analysed and presented.     

Linear dynamic model for porous media saturated by two immiscible fluids

A linear isothermal dynamic model for a porous medium saturated by two immiscible fluids is developed in the paper. In contrast to the mixture theory, phase separation is avoided by introducing one energy for the porous medium. It is an important advantage of the model based on one energy approach that it can account for the couplings between the phases. The volume fraction of each phase is characterized by the porosity of the porous medium and the saturation of the wetting phase. The mass and momentum balance equations are constructed according to the generalized mixture theory. Constitutive relations for the stress, pore pressure are derived from the free energy function. A capillary pressure relaxation model characterizing one attenuation mechanism of the two-fluid saturated porous medium is introduced under the constraint of the entropy inequality. In order to describe the momentum interaction between the fluids and the solid, a frequency independent drag force model is introduced. The details of parameter estimation are discussed in the paper. It is demonstrated that all the material parameters in our model can be calculated by the phenomenological parameters, which are measurable. The equations of motion in the frequency domain are obtained in terms of the Fourier transformation. In terms of the equations of motion in the frequency domain, the wave velocities and the attenuations for three P waves and one S wave are calculated. The influences of the capillary pressure relaxation coefficient and the saturation of the wetting phase on the velocities and attenuation coefficients for the four wave modes are discussed in the numerical examples.     

Impulsive motion of a suspension: Effect of antisymmetric stresses and particle rotation

A two-phase continuum theory (two-fluid model) for a suspension of rigid spherical particles in a Newtonian fluid is applied to investigate theoretically the flow induced by impulsive motion of an infinite flat plate. Consideration of rotational intertia of the particles gives rise to an antisymmetric part of the volume averaged stress tensor of the continuous phase. The influence of particle rotation and of antisymmetric stresses of the continuous phase, which depend on the relative rotational motion between the particles and the ambient fluid, on the motion of each phase and on the skin friction is examined.Approximate solutions to the equations, corresponding to the physical situation of large and small particle slip, are obtained by power series expansions for small and large times.     

Stability analysis of annular flow structure, using a discrete form of the “two-fluid model”

The differential form of the “two-fluid model” for annular flow, neglecting surface tension, is ill-posed, and it is not suited for examining the stability of the steady-state solutions with respect to the average film thickness. It is shown here that a discrete (difference) representation of the two-fluid model may lead to an appropriate criterion for the stability of the steady-state solutions. Exactly the same criterion is obtained from the requirement that the kinematic waves will propagate in the downstream direction. The suggested discrete form of the “two-fluid model” is used to perform transient simulation and for examining the system response to finite disturbances.     

A study on the numerical stability of the two-fluid model near ill-posedness

The two-fluid model is widely used in studying gas–liquid flow inside pipelines because it can qualitatively predict the flow field at low computational cost. However, the two-fluid model becomes ill-posed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the Euler implicit method for the time derivatives in conjunction with the two-fluid model is analyzed. A pressure correction algorithm for the two-fluid model is carefully implemented to minimize its effect on numerical stability. von Neumann stability analysis shows that the central difference scheme is more accurate and more stable than the 1st-order upwind, 2nd-order upwind, and QUICK schemes. The 2nd-order upwind scheme is much more susceptible to instability than the 1st-order upwind scheme and is inaccurate for short waves. Excellent agreement is obtained between the predicted and computed growth rates of harmonic disturbances. The instability associated with the two-fluid model discretized system of equations is related to but quantitatively different from the instability associated with ill-posedness of the two-fluid model. When the computation becomes unstable due to the ill-posedness, the machine roundoff errors from a selected range of short wavelengths, which scale with the grid size, are amplified rapidly to render the computation of any targeted long wavelength variation useless. For the viscous two-fluid model with wall friction and interfacial drag, a small-amplitude long wavelength disturbance grows due to viscous Kelvin–Helmholtz instability without triggering the grid scale short waves when the system remains well posed. Under such a condition, central difference is found to be the most accurate discretization scheme among those investigated.