Isao Kataoka

Turbulence structure of air-water bubbly flow—II. local properties

Abstract Microstructure was studied experimentally in air-water two-phase bubbly flow flowing upward in a vertical pipe of 60 mm diameter under atmospheric pressure. The results indicate that over a large portion of fully-developed bubbly flow the phases, the velocities of bubbles and water, and the ratio between the velocities of the phases have fairly flat radial profiles. In the wall region a maximum void fraction was observed. Spectra of the velocities of bubbles and water showed a Poisson distribution and a normal distribution function, respectively. The experimental evidence indicated a trend for the turbulent intensity to decrease first with increasing gas flow rate for constant water velocity and to increase again with a further increase in the gas flow rate. This phenomenon was more significant for a higher water velocity.

Turbulence structure of air-water bubbly flow—I. measuring techniques

This paper, the first in a series describing our work on the turbulence structure of air-water bubbly flow, describes the principles of measurement and specially developed electronic instrumentation for determining various important local parameters, and the rates of turbulent transport of heat and bubbles in air-water two-phase bubbly flow. These instruments indicate the phase distribution, the bubble velocity and its spectrum, the water velocity and the turbulent intensity, and the turbulent dispersion coefficient of bubbles. Brief discussions are also presented on the accuracy of these techniques.

Local formulation and measurements of interfacial area concentration in two-phase flow

Abstract The interfacial area concentration is one of the most important parameters in analyzing two-phase flow based on the two-fluid model. The local instantaneous formulation of the interfacial area concentration is introduced here. Based on this formulation, time and spatial averaged interfacial area concentrations are derived, and the local ergodic theorem (the equivalency of the time and spatial averaged values) is obtained for stationary developed two-phase flow. On the other hand, the global ergodic theorem is derived for general two-phase flow. Measurement methods are discussed in detail in relation to the present analysis. The three-probe method, with which local interfacial area concentration can be measured accurately, has been proposed. The one-probe method under some statistical assumptions has also been proposed. In collaboration with the experimental data for the interfacial velocity, radial profiles of the local interfacial area concentration are obtained based on the one-probe method. The result indicates that the local interfacial area concentration has a peak value near the tube wall in bubbly flow. This is consistent with the near wall peak of local void fraction separately observed. In slug flow it shows a higher value in the central region of the tube for that particular set of data.

Local instant formulation of two-phase flow

Abstract The local instant formulation of mass, momentum and energy conservations of two-phase flow has been developed. Distribution, an extended notion of a function, has been introduced for this purpose because physical parameters of two-phase flow media change discontinuously at the interface and the Lebesgue measure of an interface is zero. Using a characteristic function of each phase, the physical parameters of two-phase flow have been defined as field quantities. In addition to this, the source terms at the interface are defined in terms of the local instant interfacial area concentration. Based on these field quantities, the local instant field equations of mass, momentum and total energy conservations of two-phase flow have been derived. Modification of these field equations gives the single field representation of the local instant field equations of two-phase flow. Neglecting the interfacial force and energy, this formulation coincides with the field equations of single-phase flow, except in the definition of differentiation. The local instant two-fluid formulation of two-phase flow has also been derived. This formulation consists of six local instant field equations of mass, momentum and total energy conservations of both phases. Interfacial mass, momentum and energy transfer terms appear in these equations, which are expressed in terms of the local instant interfacial area concentration.

Basic equations of turbulence in gas-liquid two-phase flow

Abstract Basic equations of turbulence in gas-liquid two-phase flow were derived. Based on the local instant formulation of two-phase flow and its averaging, the conservation equations of mass and momentum were obtained for the fluctuating part of the velocity. From these equations, the conservation equations of turbulent energy and turbulent dissipation were derived. In the equation of turbulent energy, interfacial terms were composed of turbulence production due to the relative velocity between the two phases and the exchange between turbulent and surface energy. In the equation of turbulent dissipation, many interfacial terms appear. Some discussions on these interfacial terms and their physical aspects are presented.

Scaling laws for thermal-hydraulic system under single phase and two-phase natural circulation

Abstract Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.

Turbulence structure of air-water bubbly flow—III. transport properties

An experimental study of heat and bubble transport in turbulent air-water bubbly flow was carried out by means of tracer techniques. Helium tracer gas concentration data and temperature distributions were used to extract bubble and heat diffusivity information. The results indicated that the turbulent velocity components of the liquid phase play a predominant role in the turbulent transport process. A systematic increase of diffusivity of heat, ϵH, with quality and water velocity was observed. An empirical correlation for the diffusivity ratio ϵH,TP/ϵH,SP is presented. The Peclet number, u′covbar|dφ, for bubble dispersion can be approximated by 2.0, independent of the flow variables. The bubble-to-heat diffusivity ratio, φ/ϵH, approaches unity with increasing quality and water velocity. Momentum transport is also discussed, based on a mixing length theory.

Turbulence suppression in bubbly two-phase flow

Abstract A particular phenomenon of turbulence reduction in bubbly two-phase flow is discussed based on the experimental observations and theoretical derivation of turbulence energy balance equations. The importance of the mechanisms involved in this phenomenon has been stressed for a better understanding of the complex nature of bubbly two-phase flow. It has been concluded that the local turbulence energy of the liquid phase can be changeable to an energy required to maintain the surface structure and vice versa, which in turn relates to turbulence energy dissipation through the fragmentation process of turbulence eddies. It is also suggested that the phase distribution mechanism is interrelated to the above mentioned energy exchange mechanism.

Interfacial area concentration in bubbly flow

Abstract Interfacial area concentration is one of the most important parameters in two-phase flow. It is related to mass, momentum and energy transfer at the interface. In bubbly flow, it has close relation to bubble diameter. Interfacial area concentration was measured with particular attention to bubble diameter at inlet. The relationship between bubble diameter and interfacial area was theoretically considered. The possibilities of measurement methods of interfacial area concentration with multiprobes were discussed and a preliminary experiment for one of these methods was carried out.

BASIC EQUATION OF TURBULENCE AND MODELING OF INTERFACIAL TRANSFER TERMS IN GAS-LIQUID TWO-PHASE FLOW

Abstract Turbulence is one of the most important phenomena in analyzing thermohydrodynamic characteristics of gas-liquid two-phase flow. For the purpose of accurate prediction of the turbulence phenomena, a basic conservation equation of Reynolds stress was derived based on the local instant formulation of mass and momentum conservations of two-phase flow. In this equation, interfacial transfer terms of turbulence appear as source terms. Detailed considerations on these transport terms were carried out. It was shown that they consist of a viscous damping term due to small scale interfacial structures, a drag induced turbulence generation term due to large scale interfacial structures and a term representing the exchange between surface energy and turbulence. Based on the mechanistic modeling and turbulence modulations, carried out were physical interpretations of interfacial area concentrations of small and large scale interfacial structures, a viscous damping term due to small scale interface and turbule...