Donald A. Drew

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.

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.

The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a Reynolds Stress Model

The void fraction distribution for turbulent bubbly air/water upflows and downflows in a pipe was analyzed using a three-dimensional two-fluid model. A τ-e turbulence model was used for the continuous (liquid) phase. The τ-e transport equations yield all components of the Reynolds stress tensor for the liquid phase momentum equations

The analysis of nonlinear density-wave oscillations in boiling channels

Thermally induced flow instabilities in uniformly heated boiling channels have been studied analytically. The classical homogeneous equilibrium model was used. This distributed model was transformed into an integrodifferential equation for inlet velocity. A linear analysis showed interesting features (i.e. islands of instability) of the marginal stability boundary which appear when the effects of gravity and friction were systematically considered. A quasilinear Hopf-bifurcation analysis, valid near the marginal-stability boundaries, gives the amplitude and frequency of limit-cycle oscillations that can appear on the unstable side of the boundary. The analysis also shows cases where a finite-amplitude perturbation can cause a divergent instability on the stable side of the linear-stability boundary.

Lateral inertial migration of a small sphere in fast laminar flow through a membrane duct

Abstract The hydrodynamic response of a small suspended sphere to laminar flow is studied for relatively fast flow rates in a duct with porous walls. There is a lift effect on the sphere which competes with a wall suction effect. The details of this balance determine whether the sphere will reach the membrane. An expression is developed, from first principles, to predict conditions under which a sufficiently long cross-flow plate and frame membrane module exposed to dilute suspensions of essentially spherical particles will not foul, assuming nonhydrodynamic attractions between a particle and the membrane are negligible. This is the first expression which might be properly tested experimentally to determine if the elevated permeation rates observed with colloidal suspensions (Porter, 1972) are due to particle lift or to some other phenomena such as a flowing cake. The strongest particle lift effect occurs when the sphere is much closer to one wall than the other and is due to convective interaction of the disturbance caused by the sphere and the undisturbed flow, in the presence of the nearby wall. The lift velocity has the same dependence on parameters as the previous results derived for slow laminar flow (Cox and Brenner, 1968; Ho and Leal, 1974). However, the maximum lift velocity is smaller than that found by Vasseur and Cox (1976) by roughly a factor of 2.6. These results agree with those of Schonberg and Hinch (1989) in the following features: the equilibrium position moves with increasing Reynolds number towards the wall, the magnitude of the velocity near the wall is in good agreement, and our results extend to higher Reynolds number. Also, the results are compared with the experiments of Segre and Silberberg (1962a, b).

Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe

The radial distribution of the volumetric vapour (or void) fraction in steady, fully developed turbulent two-phase flow is described for vertical low-quality bubbly flows in a circular pipe. The analysis is based on the phasic equations of conservation of momentum in the axial and radial directions. Mixing-length theory is used to model the turbulent stresses in the continuous phase. The predicted flow structure shows three distinct regions. The ‘outer’ region, that is, the region away from the wall and the centre-line, has a uniform void distribution. For upflow, a bubble layer is predicted near the wall, while for downflow, vapour coring is predicted, with a peak in void fraction at the centre-line. These predictions are in agreement with observed void profiles.

Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows

Constitutive relations for the lift force on the particulate phase and the effect of Brownian motion are presented. These constitutive relations are derived subject to three new principles of constitutive equations. The effects of lift and Brownian motion in basic parallel flows are considered in order to determine the importance and the consequences of these effects. The relation of the Brownian motion model involving momentum balance to the diffusive model of particle motions is studied. Dimensional and scaling arguments are given.

The effect of virtual mass on the numerical stability of accelerating two-phase flows

Abstract The effect of the virtual mass in accelerating two-phase flow was studied for various nozzle/diffuser flows. It was found that the final results were insensitive to virtual mass effects, but the numerical stability and efficiency was greatly improved. An analysis of the eigenvalues of the mathematical systems shows that virtual mass models improve numerical stability and efficiency by changing the nature of the eigenvalues.