Stephen G. Beus

One-group interfacial area transport in vertical bubbly flow

Abstract In the two-fluid model, interfacial concentration is one of the important parameters. The objective of this study is to develop an interfacial area equation with the source and sink terms being properly modeled. For bubble coalescence, the random collisions between bubbles due to turbulence, and the wake entrainment process due to the relative motions of the bubbles, were included. For bubble breakup, the impact of turbulent eddies is considered. Compared with measured axial distributions of the interfacial area concentration under various flow conditions, the adjustable parameters in the source/sink terms were obtained for the simplified one-dimensional transport equation.

Experiments for entrainment rate of droplets in the annular regime

Abstract Two-fluid model predictions of film dryout in annular flow are limited by the uncertainties in the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate effects experimental data in the range of the operating conditions in industrial applications. Air–water and Freon-113 entrainment rate data have been obtained in 10 mm tubes using the double film extraction technique. These experiments have been scaled to approach high-pressure steam–water flow conditions. The effects of surface tension and density ratio, missing from most previous data sets, have been systematically tested. The entrainment rate mechanism is scaled by the Kelvin–Helmholtz instability at the film surface. Based on this analysis and the new data, a new correlation is proposed that is valid for low-viscosity fluids in small ducts in the ripple-annular regime.

Scaled entrainment measurements in ripple-annular flow in a small tube

High pressure steam–water annular flow was simulated with scaled air–water and Freon-113 experiments. A unique Freon-113 loop was built to obtain low surface tension and high vapor density data on entrainment fraction. The results were compared with two correlations available in the open literature. The Ishii and Mishima correlation was capable to collapse the data for air–water, Freon-113 and steam–water experiments satisfactorily. However the correlation needs to be adjusted for high Weber numbers of the gas phase. The data was limited to the ripple-annular regime because the film extraction technique is not reliable when the film becomes frothy.

Interfacial area transport and evaluation of source and sink terms for confined air–water bubbly flow

Abstract The interfacial area transport equation applicable to the bubbly flow is presented. The model is evaluated against data acquired by a state-of-the-art miniaturized double-sensor conductivity probe in an adiabatic air–water co-current vertical test loop under atmospheric pressure condition. In general, a good agreement, within the measurement error of ±10%, is observed for a wide range in the bubbly flow regime. The evaluation of the individual particle interaction mechanisms demonstrates the active interactions between the bubbles and highlights the mechanisms playing the dominant role in interfacial area transport. The analysis employing the drift flux model is also performed for the data acquired. Under the given flow conditions, the distribution parameter of 1.076 yields the best fit to the data.

Interfacial structures of confined air-water two-phase bubbly flow

The interfacial structure of the two-phase flows is of great importance in view of theoretical modeling and practical applications. In the present study, the focus is made on obtaining detailed local two-phase parameters in the air-water bubbly flow in a rectangular vertical duct using the double-sensor conductivity probe. The characteristic wall-peak is observed in the profiles of the interracial area concentration and the void fraction. The development of the interfacial area concentration along the axial direction of the flow is studied in view of the interfacial area transport and bubble interactions. The experimental data is compared with the drift flux model with C{sub 0} = 1.35.

Entrainment rate of droplets in the ripple-annular regime for small vertical ducts

Two-fluid model predictions of film dryout in annular flow are limited by the uncertainties in the constitutive relations for the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate effects experimental data in the range of the operating conditions in nuclear power reactors. Air/water and Freon-113 entrainment rate data have been obtained in 10 mm tubes using the film extraction technique. These experiments have been scaled to approach high pressure steam-water flow conditions. The effects of surface tension and density ratio, missing from most previous data sets, have been systematically tested. The entrainment rate mechanism is assumed to be a Kelvin-Helmholtz instability. Based on this analysis and two previous correlations, a new correlation is proposed that is valid for low viscosity fluids in small ducts in the ripple annular regime.

Dry Patch Stability of Shear Driven Liquid Films

The breakdown of the liquid film at the wall in annular gas-liquid flow may lead to the formation of a stable dry patch. For the case of heat transfer surfaces this causes a hot spot, The dry patch is a partial area on the solid surface that is non-wetted due to a local disturbance of the flow and is sustained by surface tension. Dry patch stability is dependent on a balance of body and surface forces. In the present study the interfacial shear force drives the film and the gravity force is negligible. A new computational fluid dynamics (CFD) solution of the flow field in the film around the dry patch has been obtained. The CFD results confirm Murgatroyds shear force model (1965), although the details are more complex. Furthermore, there is agreement between the CFD solution and the experimental value of the characteristic length scale, L, for the shear force. In addition new experimental data have been taken for adiabatic upward annular air-water and air-ethylene glycol flows at room temperature in a 9.5 mm diameter tube. They provide validation of Murgatroyds model over a wider range of the films Reynolds number than previous data.

Development of Interfacial Structure in a Confined Air-Water Cap-Turbulent and Churn-Turbulent Flow

The objective of the present work is to study and model the interfacial structure development of air-water two-phase flow in a confined test section. Experiments of a total of 9 flow conditions in a cap-turbulent and churn-turbulent flow regimes are carried out in a vertical air-water upward two-phase flow experimental loop with a test section of 20-cm in width and 1-cm in gap. The miniaturized four-sensor conductivity probes are used to measure local two-phase parameters at three different elevations for each flow condition. The bubbles captured by the probes are categorized into two groups in view of the two-group interfacial area transport equation, i.e., spherical/distorted bubbles as Group 1 and cap/churn-turbulent bubbles as Group 2. The acquired parameters are time-averaged local void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for both groups of bubbles. Also, the line-averaged and area-averaged data are presented and discussed. The comparisons of these parameters at different elevations demonstrate the development of interfacial structure along the flow direction due to bubble interactions.

Measurements of interfacial area concentration in two-phase flow with two-point conductivity probe. Brief communication

Kataoka, Ishii and Serizawa analyzed the measurements of the local time-averaged interfacial area concentration in two-phase flow with a two-point conductivity probe. They considered the influence of the bubble velocity fluctuation on the measurement and directly transferred the mathematics concept of the local time-averaged interfacial area concentration into the measurable parameters. In the end of the derivation, however, the expression of the interfacial area concentration was inappropriate due to the over-simplification to the integration limits of the probability distributions. Consequently, the resultant interfacial area concentration may be significantly lower than the actual value. Since the formula is very important for the interpretation of experimental data, we feel it is necessary to provide a correction to the original work.

Air-water experiment for annular flow pressure drop in a small pipe

New experimental data are obtained for pressure drop and entrainment for annular upflow in a vertical pipe. The 9.5-mm pipe has a hydraulic diameter similar to the subchannels in the fuel assemblies of water-cooled reactors. The test section has a length-to-diameter ratio of 440 to ensure fully developed annular flow. The pressure covers the range from 140 to 660 kPa. Therefore, the density ratio is varied by a factor of -4. This allows the investigation of the effect of pressure on the interfacial shear models. Gas superficial velocities between 25 and 126 m/s are tested, extending the range of previous data to higher gas velocities. The data are compared with well-known models for interfacial shear that represent the state of the art. Good results are obtained with the models by Wallis, and Henstock and Hanratty. When the model by Asali, Hanratty, and Andreussi is modified for the effect of pressure, the agreement is also good, and the data collapse with very little scatter. There is a close relationship between these models and mixing length theory such that the models may be viewed as correlations for the surface roughness. This points toward a more fundamental approach in terms of the interfacial structure.