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.     

Effect of heat transfer augmentation on two-phase flow instabilities in a vertical boiling channel

The effect of different heater surface configurations on two-phase flow instabilities has been investigated in a single channel, forced convection, open loop, up-flow system. Freon-11 is used as the test fluid, and six different heater tubes with various inside surface configurations have been tested at five different heat inputs. In addition to temperature and pressure recordings, high speed motion pictures of the two-phase flow were taken for some of the experiments to study the two-phase flow behavior at different operating points. Experimental results are shown on system pressure drop versus mass flow rate curves, and stability boundaries are also indicated on these curves. Comparison of different heater tubes is made by the use of the stability boundary maps and the plots of inlet throttling necessary to stabilize the system versus mass flow rate. Tubes with internal springs were found to be more stable than the other tubes.     

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.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

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.     

Enhancement of heat transfer due to bubbles passing through a narrow vertical rectangular channel (Change in heat transfer along flow)

The objective of this paper is to make clear how heat transfer coefficient changes along the flow with the passing bubbles through a narrow vertical rectangular channel (20 mm wide, 2 mm deep and 450 mm long). The experiments were done using subcooled water of 80, 60, and 40 K at atmospheric pressure in which the air bubbles were injected into the channel at a designated period from 0.125 to 1.0 s and their length was controlled to be equal to 0.03, 0.02, and 0.01 m. The experiment shows that the heat transfer coefficients decrease along the flow and then reach a constant value beyond a certain distance from the leading edge of the heated surface where the flow becomes fully developed in both the velocity and the thermal conditions. Under the fully developed conditions, the heat transfer coefficients are predicted well by the existing theoretical analysis in which both the convective term and evaporation on the interface are ignored.     

A modified heat transfer correlation for two-phase flow

Experimental investigations for two-phase flow under constant heat flux condition are carried out by varying the mass flow rate of gas and liquid phases. A modified correlation for Nusselt number is developed based on the experimental measurements involving superficial gas and liquid Reynolds number, fluid properties and Lockhart-Martinelli parameter. The accuracy of this correlation for all two-phase flow regimes is validated with the recent correlation proposed by Kim and Ghajar.     

Magnetohydrodynamic heat transfer in two-phase flow between parallel plates

This study dealt with two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel. Both phases were incompressible and the flow was assumed to be steady, one-dimensional and fully developed. The present study was expected to be useful in the understanding of the effect of the presence of slag layers on the heat transfer characteristics of a coal-fired MHD generator.The problem was investigated, in which one of the two fluids was assumed to be electrically non-conducting. The transport properties of the two fluids were taken to be constant, and the plates were assumed to be maintained at constant and equal temperatures. In this case, the governing differential equations were linear, and an exact solution was obtained. Results were presented for various height and viscosity ratios for the two fluids and for two values of the electric field loading parameter. The governing equations were also solved numerically in order to verify the exact solution.     

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.     

Flow characteristics of two-phase dispersed annular streams in heated tubes

Patterns and characteristics of flow through heated tubes are investigated on the basis of concepts of two-phase dispersed annular flow patterns [1] within the framework of the three-velocity and single-temperature equilibrium model, with flowrates of the mixture not too close to critical. Conditions for onset of burnout of the second kind, i.e., deterioration in the transfer of heat leading to an abrupt rise in the temperature of the heating surface, and, as such, associated with desiccation of the thin film of liquid on the wall [2, 3], are investigated. Hydraulic drag, the flowrate of liquid in the film, and the true steam content by volume are among the factors discussed. Two-phase flow patterns in dispersed annular flow are characterized by the combined motion of the three components of the mixture: vapor, the liquid wall film, and droplets. The assumption entertained is that each component of the mixture acquires its own velocity, and that the temperature of the mixture is equal, in each cross section through the channel, to the saturation temperature at the pressure prevailing in the particular cross section.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 78–88, July–August, 1973.     

Two-phase annular flow and evaporative heat transfer in a microchannel

A physical and mathematical model has been developed to predict the two-phase flow and heat transfer in a microchannel with evaporative heat transfer. Sample solutions to the model were obtained for both constant wall temperature and constant wall heat flux conditions. Results are provided for evaporation rate, liquid film thickness, liquid and vapor phase pressure and temperature distributions. In addition to the sample calculations that were used to illustrate the transport characteristics, computations based on the current model were performed to generate results for comparisons with the experimental results of Qu and Mudawar (2004) where two different mass flow rates of the working fluid were used in the experiment. The comparisons of total pressure drops with the experimental data of Qu and Mudawar (2004) cover the wall heat flux range of 142.71-240 W/cm² with a total channel mass flux of 400.1 kg/m² s and also the wall heat flu range of 99.54-204.39 W/cm² with total channel mass flux of 401.9 kg/m² s. The calculated results from the current model match closely with those of Qu and Mudawar (2004).     

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