Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

Prediction of the slug-to-churn flow transition in vertical two-phase flow

An assessment is made of the various viewpoints on the slug-to-churn flow transition in vertical upward flow in the light of recent experimental results obtained at Harwell Laboratory. It is found that the flooding model of McQuillan & Whalley and the bubble entrainment model of Barnea & Brauner give satisfactory results at low and high liquid flow rates, respectively. An improved model for flooding, which takes account of the effect of the falling film, has been proposed. It is shown that this new model is in good agreement with experimental results at both low and high liquid flow rates.     

Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow

New mechanistic bubble coalescence and break-up models considering turbulent suppression phenomena, which can possibly occur in the high liquid velocity condition of turbulent bubbly two-phase flow, are presented. The energy exchange mechanism between a turbulent eddy and interfacial structure was taken into account in the efficiency terms. Numerical simulations of turbulent bubbly flow were conducted in a CFD code to evaluate the newly developed models, in comparison with other advanced models coupled with a bubble-induced turbulent effect for one-group interfacial area transport equation. Local measurements of the bubble characteristics on the bubble size evolution along a vertical pipe flow were performed at KAERI-VAWL test facility using the five-sensor conductivity probe method to provide database for models validation. Results from the calculation clearly show the improvements of the newly developed models.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Flooding in vertical two-phase flow

The phenomenon of flooding limits the stability of a liquid film falling along the walls of a tube in which a gas is flowing upward. This paper describes a series of experiments to observe and photograph the flooding process. Flooding in a vertical perspex tube was observed by viewing axially along the tube from the top, and flooding on the walls of a stainless steel rod supported centrally within a perspex tube was observed by viewing normally through the tube walls. The resulting observations show that flooding occurs as a result of the formation and motion of a large disturbance wave on the surface of the liquid film. A simple theoretical treatment of flooding is presented, based on the observations of the flooding disturbance. The resulting equations enable the calculation of the gas velocity and the liquid wave height at flooding, and the predictions are in good agreement with experimental observations reported here and elsewhere.     

Liquid velocity distribution in two-phase bubble flow

An improved analytical treatment is developed which makes possible the satisfactory prediction of the liquid velocity distribution in two-phase bubble flow.In the analysis, the shear stress in the liquid phase is regarded as important. When the fluctuation of turbulent velocity can be subdivided into two components: one due to the inherent liquid turbulence independent of the existence of the bubble, (u′, υ′), and the other due to the additional liquid turbulence by the bubble agitation, (u″, υ″), it is possible to split the shear stress into two components, - ?$\text{u′υ′}$ and - ?$\text{u″υ″}$ corresponding to (u′, υ′) and (u″, υ″), respectively.A basic equation for the liquid velocity distribution is derived from further development of this treatment. The agreement between the measured velocity profiles and those calculated is quite close especially in the core region of a duct.     

Fundamental equations of turbulent two-phase flow

A new set of Reynolds equations for predicting turbulent two-phase flows has been developed by means of Reynolds averaging method on the unsteady laminar equations of two-phase flow. These equations involve average terms of products of turbulent fluctuations in some physical parameters in a large degree. The interaction forces between two phases, the pressures for dispersed phase, extra stresses except for pressure and the expressions for energy interchange between two phases have been discussed.     

Flow patterns in vertical two-phase flow

This paper is concerned with the flow patterns which occur in upwards gas-liquid two-phase flow in vertical tubes. The basic flow patterns are described and the use of flow pattern maps is discussed. The transition between plug flow and churn flow is modelled under the assumption that flooding of the falling liquid film limits the stability of plug flow. The resulting equation is combined with other flow pattern transition equations to produce theoretical flow pattern maps, which are then tested against experimental flow pattern data. Encouraging agreement is obtained.     

Void fraction,bubble velocity and bubble size in two-phase flow

Experiments were performed in atmosphereic vertical air-water flows, for void fractions between 0.25 and 0.75 (cross-sectional averages) and superficial liquid velocities of 1.3, 1.7 and 2.1 m/s. Local values of void fraction and bubble velocity as well as the bubble diameter were measured by means of a resistivity probe technique. Reliable values were obtained for the local void fraction over the entire range $\text{0 ≤ α ≤ 1}$. The void fraction profiles appeared to have a local maximum at the pipe center, local maxima close to the wall were obviously absent. The resistivity probes are shown to measure the velocity of the interface between the conducting and nonconducting phases, which equals the gas velocity only for low void fractions. The measured data for void fraction and bubble velocity were correlated by means of power law distribution functions, with exponents given by a function of the cross-sectionally averaged void fraction. The Sauter mean diameters for the bubble size spectra found, agree reasonably well with diameters predicted by a theoretical model based on the energy dissipation in the flow.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes

An experimental study on the interaction between Taylor bubbles rising through a co-current flowing liquid in a vertical tube with 32 mm of internal diameter is reported. The flow pattern in the bubble's wake was turbulent and the flow regime in the liquid slug was either turbulent or laminar. When the flow regime in the liquid slug is turbulent (i) the minimum distance between bubbles above which there is no interaction is 5D-6D; (ii) the bubble's rising velocity is in excellent agreement with the Nicklin relation; (iii) the experimental values of the bubble length compare well with theoretical predictions (Barnea 1990); (iv) the distance between consecutive bubbles varied from 13D to 16D and is insensitive to the liquid Reynolds number. When the flow regime in the liquid slug is laminar (i) the wake length is about 5D-6D; (ii) the minimum distance between bubbles above which there is no interaction is higher than 25D; (iii) the bubble's rising velocity is significantly smaller than theoretical predictions. These results were explained in the light of the findings of Pinto et al. (1998) on coalescence of two Taylor bubbles rising through a co-current liquid. Received: 2 February 2000 / Accepted: 15 March 2001     

Particle drag in a dilute turbulent two-phase suspension flow

The drag between phases plays an important role in the study of a turbulent two-phase suspension flow and its physical understanding will greatly promote progress in theoretical treatments of a whole range of important industrial and technical problems involving such a flow. The conventional practice of using the results of measurements based on a single particle in a laminar stream for the case of a turbulent flow of a dilute suspension is questioned. An analysis of the results of local measurements of upward turbulent flows of a solid particle-air two-phase suspension leads to the determination of the realistic particle drag coefficient over a wide range of flow conditions. It is established that the particle drag can be described by the simple Stokes law, based on an apparent turbulent viscosity of the fluid for the particles in the suspension flow. A correlation is provided for this apparent turbulent viscosity in terms of the particle size and concentration in the suspension, the local flow turbulence Reynolds number and the particle-to-fluid density ratio.     

A laser-fluorescence technique for turbulent two-phase flow measurements

A non-intrusive measurement technique has been developed for accurate determination of gas and particle velocities in a turbulent two-phase flow field. The principle of the technique is based on the discrimination between the scattered light from particles and the fluorescence emission from particles coated with a fluorescent dye. A high-powered, argon-ion based, single-channel, on-axis backscatter laser-Doppler velocimetry system was used. The fluorescent dye was Rhodamine 6G. A study of the gas-solid two-phase flow behaviour in the freeboard of a cold gas-fluidized bed was undertaken. The solid phase contained two particle groups: bed material (sand) and fuel particles (wood). Measurements of the axial velocity and turbulence intensity distributions of the gas phase and both particle groups within the solid phase were made along the column centre and across the freeboard. Excellent discrimination of velocities from the two phases and from the two particle groups within the solid phase was achieved.     

Modelling of annular dispersed two-phase flow in vertical pipes

An investigation is made into the reliability with which pressure loss, film thickness and liquid entrainment can be predicted by an annular flow model that is based on the well-known two-fluid (separated flow) concept. For this purpose a two-fluid model is presented which accounts for the interrelation between these variables. In this connection the existence of multiple liquid hold-up solutions is mentioned. New correlations for interfacial friction and liquid fraction entrained are proposed using data compiled previously at AERE Harwell. Our new model is compared with previous models. Differences between predictions are illustrated by reference to the Harwell data bank, recent large-diameter tests and hypothetical gas-well cases relevant to the oil industry. Application of the annular flow models, in particular their entrainment correlations, appears to give rise to widely varying results, restricting the predictive value of the models when extrapolated to large-diameter and/or high pressure systems.     

Modeling analysis of bubble flow regime in a closed two-phase thermosyphon

Predictions of the operating liquid level in the evaporator of a closed two-phase thermosyphon (gravity heat pipe) are given throughout a simplified analysis which takes the influence of the dimension and condensation heat transfer in the condenser of the heat pipe into account. In order to verify the accuracy of our model comparison of the present study with some published results is made by means of computational examples.     

Dynamics of disk-like particles in turbulent vertical channel flow

The dynamical behavior of inertial disk-like particles in turbulent vertical channel flow is investigated by an Eulerian–Lagrangian point-particle approach. Gravity effects on distribution, translation, rotation and orientation statistics of non-spherical particles modeled as oblate spheroids have been studied both in an upward and a downward flow and compared with results obtained in the absence of gravity. Altogether 12 different particle classes have been studied, with inertia and shape parameterized by means of Stokes number St and aspect ratio λ ≤ 1. The St = 5 disk-like particles distribute more evenly across the channel in upward than in downward flow. The gravity effect on the particle concentration diminishes with large inertia and the spheroid shape has only a modest influence. Although the gravity significantly affects the streamwise and wall-normal mean slip velocities with increasing inertia, the particle shape rarely has any impact on the translational motion, except for the mean wall-normal velocity. The fluctuations of the velocity of disk-like particles are mainly ascribed to inertia, whereas the gravity and shape only have marginal effects. The presence of gravity is moreover found to have a negligible effect on the particles’ orientation and rotation, in spite of the striking effect of λ on the orientation and rotation seen in the near-wall region. The tendency of the disks to align their symmetry axis orthogonal to the fluid vorticity in the channel center is stronger for particles with modest inertia. In the near-wall region, however, oblate spheroids preferentially align with the fluid vorticity for St >> 1. The observed behavior is believed to be caused by the influence of the gravity force on the turbophoresis; i.e. that inertial particles move towards low-turbulence regions.     

Wave coalescence and entrainment in vertical annular two-phase flow

A rigorous model for wave coalescence has been derived. The wave coalescence process has also been modelled by a Monte-Carlo technique. The results of the theories are in general in good agreement with the available experimental data. It had been noted that coalescence of two waves was accompanied by a large burst of entrainment. The above coalescence theory has been used to calculate that component of entrainment that is due to coalescence. Comparison of this and experimental data shows that the entrainment due to coalescence can be a significant portion of the total entrainment.