Rate of deposition of droplets in annular two-phase flow

Droplets in a turbulent flow will deposit on surrounding surfaces. This paper critically examines measurements of the deposition rate with the goal of outlining our present ability to predict this quantity for annular two-phase flows.     

Droplet deposition in an annular geometry

An analytical approach to the problem of droplet deposition in annular flow through an annulus is presented. The underlying theory, due to Hutchinson et al. (1971), allows the droplet deposition to be treated as a diffusion process and the results obtained enable some properties of mass transfer coefficients in non-circular geometries to be explained.     

Drops in annular two-phase flow

Drops, one of the forms in which liquid is present in annular gas—liquid flow, are formed from the wall film, carried by the gas or vapour and redeposited. During this time they exert a strong influence on many important parameters of both flow and heat transfer. The available information on the creation, size and velocity, and removal of drops is identified and reviewed.

This review shows that there is an extensive literature on drops and the associated topic of waves in annular gas—liquid flows. In spite of the large number of papers that have been published, there are still some fundamental questions which remain unanswered and there are large gaps in the parameter ranges to be considered.     

Transient flow redistribution in annular two-phase flow

A model is described for the prediction of transient flow redistribution in vertical annular two-phase flow. The model is based on an analysis of the local parameters controlling the flow and takes account of the diffusive motion of entrained droplets and the delay time for change in the wave structure on the film. Comparisons are made with experimental results on inlet effects and it is shown that the wall injection experimental results can be described by the model. The jet injection results are not fitted by the model and it is shown that some additional deposition mechanism must be present.     

Drop sizes in annular two-phase flow

Drop sizes in annular flow have been measured using a diffraction technique. Several series of experiments were carried out to determine the effect of gas velocity, drop concentration, film flow rate and tube diameter on drop size. Film flow rate and tube diameter have been found to have very little influence on the sizes of drops produced. An empirical equation which describes the drop sizes is presented.     

Vapor core turbulence in annular two-phase flow

 This paper reports a new technique to measure vapor turbulence in two-phase flows using hot-film anemometry. Continuous vapor turbulence measurements along with local void fraction, droplet frequency, droplet velocity and droplet diameter were measured in a thin, vertical duct. By first eliminating the portion of the output voltage signal resulting from the interaction of dispersed liquid droplets with the HFA sensor, the discrete voltage samples associated with the vapor phase were separately analyzed. The data revealed that, over the range of liquid droplet sizes and concentrations encountered, the presence of the droplet field acts to enhance vapor turbulence. In addition, there is evidence that vapor turbulence is significantly influenced by the wall-bounded liquid film. The present results are qualitatively consistent with the limited data available in the open literature. Received: 17 August 1998/Accepted: 12 April 1999     

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.     

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03-14.4 mm diameter and pressures of 0.1-7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.     

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.     

Liquid film circumferential asymmetry prediction in horizontal annular two-phase flow

This study considers the prediction of the degree of asymmetry in the circumferential distribution of the liquid film in the tube cross section of horizontal annular gas–liquid two-phase flow, endemic of the lower region of this flow regime near the stratified-wavy flow transition boundary. Focusing on disturbance waves as the predominant mechanism for transporting the liquid in the annular film from the bottom to the top of the tube to counterbalance the draining effect of gravity, a new prediction method for the degree of asymmetry in the annular liquid film is proposed that outperforms existing correlations. Flow pattern maps for horizontal gas–liquid two-phase flow of frequent use in the design of evaporators and condensers can thus be explicitly updated to account for both symmetric and asymmetric annular flows. The underlying experimental database contains 184 measured liquid film circumferential profiles, corresponding to 1276 local liquid film thickness measurements collected from 15 different literature studies for tube diameters from 8.15 mm to 95.3 mm.     

Pressure drop prediction in annular two-phase flow in macroscale tubes and channels

A new prediction method for the frictional pressure drop in annular two-phase flow is presented. This new prediction method focuses on the aerodynamic interaction between the liquid film and the gas core in annular flows, and explicitly takes into account the asymmetric liquid film distribution in the tube cross section induced by the action of gravity in horizontal tubes operated at low mass fluxes. The underlying experimental database contains 6291 data points from the literature with 13 fluid combinations (both single-component saturated fluids such as water, carbon dioxide and refrigerants R12, R22, R134a, R245fa, R410a, R1234ze, and two-component fluids such as water-argon, water-nitrogen, alcohol-argon, water plus alcohol-argon and water-air), vertical and horizontal tubes and annuli with diameters from 3 mm to 25 mm, and both adiabatic and evaporating flow conditions. The new prediction method is very simple to implement and use, is physically based and outperforms existing pressure drop correlations (mean absolute error of 12.9%, and 7 points out of 10 captured to within ±15%).     

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.     

Effect of secondary flow on droplet distribution and deposition in horizontal annular pipe flow

In horizontal annular dispersed pipe flow the liquid film at the bottom is thicker and rougher than at the top of the pipe. A turbulent pipe flow experiencing a variation of roughness along the pipe wall will show a secondary flow. Such secondary flow, consisting of two counter-rotating cells in the cross-section of the tube, can change the distribution of the droplets inside the pipe and their deposition at the wall. Here, we compare the behaviour of the droplets (dispersed phase) with and without secondary flow, using large-eddy simulations. It is shown that the presence of secondary flow increases the droplet concentration in the core of the pipe and the droplet deposition-rate at the top of the pipe.     

The effect of swirl on critical heat flux in annular two-phase flow

The adaptation of a calculation method for critical heat flux using an annular flow model is described. If the swirl is assumed to deposit all the entrained drops onto the liquid film and to persist for a certain distance after the swirl device, good comparisons with experiment are obtained. A simple method for calculating the length over which the swirl persists is given.     

The effect of orifices on the liquid distribution in annular two-phase flow

The effect of using orifices to disrupt the water film in air-water annular two-phase flow has been studied experimentally in a vertical tube by measuring the wall film flowrate at various distances upstream and downstream of several different sizes of orifice. The orifices cause a temporary reduction in the downstream water film flowrate, which returns to its equilibrium value further downstream. The experimental results have been used, together with those of other investigators, to compare the effects of orifices to those of swirl tapes, and further to compare the processes of entrainment and deposition within annular two-phase flow.     

Research on heat transfer of two-phase dispersed flow in narrow annular channel

Narrow channel heat transfer technique is a new developing heat transfer technique in recent years. As the temperature of droplet, steam and wall are decided by forced convection heat transfer between the steam and the wall, between the droplet and the wall, between the steam and the droplet and radiation heat transfer, which makes heat transfer mechanism of dispersed flow be difficultly interpretative. Dispersed flow in narrow annular channel is analyzed in the paper, investigating the influence of all kinds of heat transfer processes on dispersed flow, building annular channel dispersed flow model using thermodynamic non-equilibrium model. Calculation results show heat transfer is mainly controlled by heat transfer process between steam and wall. When temperature is low, radiation can be ignored on heat transfer coefficient calculation. The calculation of model can provide a reference for engineering application of steam generator, refrigeration system and so on.