R.T. Lahey

ANALYSIS OF PHASE DISTRIBUTION IN FULLY DEVELOPED LAMINAR BUBBLY TWO-PHASE FLOW

Abstract A two-fluid model of multidimensional laminar bubbly two-phase flow is developed and used to analyze vertical pipe flows. A Galerkin finite element method is utilized to perform the numerical evaluations. Good agreement is found with the available data when adequate models for the lateral lift force and wall force on the dispersed phase (i.e. the bubbles) are used.

3-D turbulence structure and phase distribution measurements in bubbly two-phase flows

Turbulent bubbly air/water two-phase up and down flows in a circular test section were investigated. Important flow quantities such as local void fraction, liquid velocity and the Reynolds stresses were measured using both single-sensor and three-sensor hot-film anemometer probes. For up flows, it was found that the bubbles tended to migrate toward the wall and thus the void fraction profile showed a distinct peak near the wall. In contrast, for down flows, it was found that the bubbles tended to migrate toward the center of the pipe causing void “coring”. It was also found that the observed wall peaking and coring phenomena, and thus the radial void distribution in up and down flows, could be predicted by considering the turbulence structure of the continuous phase and lateral lift force acting on the dispersed phase (i.e. the bubbles). All Reynolds stress components were measured using a special 3-D conical probe. In two-phase flows, the normal Reynolds stress components (i.e. u2, v2and w2) showed nearly flat profiles in the core region (r/R < 0.8) and, except near the wall, the turbulence structure was more anisotropic compared to single-phase flows. Normally, the presence of the bubbles increased the level of turbulence in the flow. However, because the bubbles in turbulent two-phase flow enhance dissipation as well as promoting the production of turbulence kinetic energy, it was found that for higher flow rates the presence of bubbles suppressed the level of turbulence.

THE ANALYSIS OF VIRTUAL MASS EFFECTS IN TWO-PHASE FLOW

Abstract One of the primary difficulties in the mathematical modelling of two-phase flows is the complexity of the interfacial transfer phenomena. The present study is concerned with the so-called virtual mass force during the acceleration of a two-phase mixture. It is shown that this interfacial force must be objective, and thus invariant under a change of reference frame. The most general form of an objective virtual mass acceleration is derived and appropriate experiments are suggested for verification and parameter determination.

Application of general constitutive principles to the derivation of multidimensional two-phase flow equations

Abstract The process of determining appropriate constitutive equations for multidimensional time averaged two-phase flow equations is studied from the point of view of starting from general principles, and proceeding to specific constitutive equations which contain known physical effects. Energetic effects and phase change are not considered. Models are given for the interfacial momentum transfer, the laminar and turbulent (Reynolds) stresses, and the pressure differences between the phases, and between a given phase pressure and the interfacial average pressure.

Phase distribution in bubbly two-phase flow in vertical ducts

Abstract The lateral phase distribution in bubbly flows in vertical ducts was analyzed using a three-dimensional two-fluid model. The constitutive relations of the model are based on analytic and experimental information on the behavior of a single bubble, and on the assumption of linear superposition of shear-induced and bubble-induced turbulence. The experiments chosen to test the model include available data for pipes and new data obtained in an isosceles triangular duct. While most of the data could be reproduced satisfactorily by the model, some could not. This is attributed to certain physical mechanisms that are still not well understood and therefore were not included in the constitutive relations.

Development of a k-ε Model for Bubbly Two-Phase Flow

An extension of the k-[epsilon] model for bubbly two-phase flow is proposed and tested against experimental data. The basic assumption made is that the shear-induced turbulence and bubble-induced turbulence may be linearly superposed. This assumption results in a model with two time constants that matches both homogeneous two-phase turbulence data (Lance and Bataille, 1991) and pipe data (Serizawa, 1986). The coefficients of the single-phase k-[epsilon] model have not been modified and only one additional coefficient is required: the virtual volume coefficient of the bubbles, which may be determined from first principles. This model not only agrees with the data trends, but it also predicts the turbulence suppression which has been measured for high Reynolds number bubbly air/water flows in pipes.

On the development of an objective flow regime indicator

Abstract A high intensity dual beam X-ray system was designed and constructed to make chordal-average void fraction measurements. This X-ray system employed a DC excited tube filament, full wave rectification and high voltage filtering to produce a stable photon source. The large photon flux produced by the X-ray system allowed analog linearization of the signal. A series of chordal-average void fraction measurements were made and used to generate probability density functions (PDF) and power spectral density (PSD) functions. The first four moments associated with these distributions were studied as possible flow regime indicators. The moments of the PDF indicated the various flow regime transitions. The moments of the PSD also show some flow regime transition information, but were sensitive to liquid phase velocity. The PDF variance, or second moment about the mean, was found to be the best indicator of flow regime. A variance of 0.04 appear to adequately discriminate between the bubbly, slug and annular flow regimes for low pressure air/water flow in a 2.54 cm I.D. vertical tube.

Phase distribution in complex geometry conduits

Abstract Bubbly air/water two-phase flow data have been taken as an isosceles triangle using hot film probes. It was found that a 3-D two-fluid model was able to predict these data and those taken previously in circular conduits. It appears that mechanically-based CFD predictions of bubbly two-phase flows is possible for many cases of practical concern.

The analysis of two-phase flow and heat transfer using a multidimensional, four field, two-fluid model

Abstract This paper reviews the state-of-the-art in the prediction of multidimensional multiphase flow and heat transfer phenomena using a four field, two-fluid model. It is shown that accurate mechanistic computational fluid dynamic (CFD) predictions are possible for a wide variety of adiabatic and diabatic flows using this computational model. In particular, the model is able to predict the bubbly air/water upflow data of Serizawa (Serizawa, A., 1974. Fluid dynamic characteristics of two-phase flow. Ph.D. thesis, (Nuclear Engineering), Kyoto University, Japan), the downflow data of Wang et al. (Wang, S.K., Lee, S.J., Lahey Jr., R.T., Jones, O.C., 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13 (3), 327–343), the isosceles triangle upflow data of Lopez de Bertodano et al. (Lopez de Bertodano, M., Lahey Jr., R.T., Jones, O.C., 1994b. Phase distribution in bubbly two-phase flow in vertical ducts. Int. J. Multiphase Flow 20 (5), 805–818), the heated annular R-113 subcooled boiling data of Velidandala, et al. (Velidandla, V., Pulta, S., Roy, P., Kaira, S.P., 1995. Velocity field in turbulent subcooled boiling flow. ASME Preprint HTD-314, 107–123) and the R-113 CHF data of Hino and Ueda (Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled boiling-part 2, flow characteristics. Int. J. Multiphase Flow 11, 283–297). It can also predict external two-phase flows, such as those for spreading two-phase jets (Bonetto, F., Lahey Jr., R.T., 1993. An experimental study on air carryunder due to a plunging liquid jet. Int. J. Multiphase Flow 19 (2), 281–294) and multiphase flows around the hull of naval surface ships (Carrica, P.M., Bonetto, F., Drew, D.A., Lahey, R.T., 1999. A polydispersed model for bubbly two-phase flow around a surface ship. Int. J. Multiphase Flow 25 (2), 257–305).

A polydisperse model for bubbly two-phase flow around a surface ship

Abstract A three dimensional polydisperse model for bubbly two-phase flow around a surface ship is presented. The Boltzmann equation for the bubble mass probability density function is evaluated using a multigroup approach with groups of constant bubble mass. The intergroup transfer mechanisms are bubble breakup, coalescence and the dissolution of air into the ocean, and their effects on the two-phase flow field are analyzed. A three dimensional two-fluid model is used for each bubble mass group to calculate the group’s average gas velocity, resulting in four scalar equations per group. The air entrainment process is modeled using simulated breaking bow waves and the steady-state evolution of the gas bubbles for zero Froude number is obtained. It was found that intergroup transfer is very important in these flows. Some of the research areas that need further improvement for the numerical prediction of polydisperse two-phase flow around a ship have been identified and are discussed.