Modeling two-phase flow

Interfacial area measurement. Knowledge of the interfacial area is indispensable in modeling two-phase flow (Dejesus and Kawaji, 1990), which determines the interphase transfer of mass, momentum, and energy in steady and transient flow. Ultrasonic techniques are used for such measurements. Since there is no direct relationship between the measurement of ultrasonic transmission and the volumetric interfacial area in bubbly flow, some estimate of the average bubble size is necessary to permit access to the volumetric interfacial area (Delhaye, 1986). In bubbly flows with bubbles several millimeters in diameter and with high void fractions, Stravs and von Stocker (1985) were apparently the first, in 1981, to propose the use of pulsed, 1- to 10-MHz ultrasound for measuring interfacial area. Independently, Amblard et al. (1983) used the same technique but at frequencies lower than 1 MHz. The volumetric interfacial area, T, is defined by (Delhaye, 1986)... 

Dukler, A. E., 1978, Modelling Two-Phase Flow and Heat Transfer, Keynote Paper KS-11, Proc. 6th Int. Heat Transfer Conf., Toronto, Canada. (3)... 

A field-scale simulator based on this approach would probably require simpler equations that captured the relevant phenomena without explicitly addressing many of them. Chapter 15, by Prieditis and Flumerfelt, models two-phase flow in a network of interconnected channels that consist of constricted tube segments. Work on the creation of a model that contains capillary snap-off in a network similar to that of Figure 6 has very recently been started at the University of Texas (R. Schechter, personal communication, October 26, 1987). 

The main impact for modeling two-phase flow in porous media came from petroleum reservoir simulation [4, 5] and from hydrology [6]. Most available models are based on the concept of capillary pressure and on some upscaling of capillary information from the micro to the macro scale. We will restrict ourselves to that case. 

The basic problem in modelling two-phase flow is the question to what extent equilibrium exists between the phases. In general, there is no equilibrium. Yet, as a rule equilibrium is assumed, since this simplifies the analytical treatment of the problem. Fundamental considerations on two-phase flow can, for example, be encountered in [6]. In what follows the model of Leung [7, 8] is described. The presentation draws upon [8]. 

A basic problem for modelling two-phase flow is whether equilibrium exists between the two phases. This is generally not the case. However, equilibrium is usually assumed because it facilitates the analytical treatment of the problem. 

Modeling two-phase flow in the PEFC channel is numerically very challenging. Wang et al. [57] envisaged the mini-channels as structured and ordered porous media. A two-phase channel flooding model was developed based on the two-phase mixture description. They also developed a one-dimensional analysis and obtained an analytical solution for the Hquid water profile (in terms of liquid saturation) along flow channels ... 

Modeling two-phase flow in PEM fuel cell channels. J. Power Sources, 179, 603-617. 

Chapter 1 provides a general overview and introduction of the principles and techniques of physical and mathematical modeling discussed in the book. It provides the rationale for modeling two-phase flow in gas-agitated reactors of materials processes. Chapter 2 presents the turbulence structure of two-phase jets and the impact on the mixing and chemical reaction rates in materials reactors agitated by... 

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

For two-phase flow through pipes, an overall dimensionless dis-eharge eoeffieient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality ehoked flow. Leung [28] indieated that Equation 12-11 be multiplied by a faetor of 0.9 to bring the value in line with the elassie homogeneous equilibrium model (HEM). Equation 12-11 then beeomes... 

The quasi-one-dimensional model of two-phase flow in a heated capillary slot, driven by liquid vaporization from the interface, is described in Chap. 8. It takes... 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

Part 1. Presentation of the model. Int J Heat Mass Transfer 47 3375-3385 Tiselj I, Hetsroni G, Mavko B, Mosyak A, Pogrebnyak E, Segal Z (2004) Effect of axial conduction on the heat transfer in micro-channels Int J Heat Mass Transfer 47 2551-2565 Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski DL (1999) Gas-liquid two-phase flow in microchannels. Part I. Two-phase flow patterns. Int J Multiphase Flow 25 377-394 Tsai J-H, Lin L (2002) Transient thermal bubble formation on polysihcon micro-resisters. J Heat Transfer 124 375-382... 

Zhao and Rezkallah (1993), Rezkallah (1996), and more recently Lowe and Rezkallah (1999) developed two-phase flow transition models for micro-gravity channel flows based on liquid and gas Weber numbers. Zhao and Rezkallah (1993) suggested Wees 1 as the upper boundary for the surface tension-dominated zone, and Wees 20 as the lower boundary for the inertia-dominated zone. 

Ishii (1977) One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase regimes. AML Report ANL-77-47 Ide H, Matsumura H, Tanaka Y, Fukano T (1997) Flow patterns and frictional pressure drop in gas-liquid two-phase flow in vertical capUlary channels with rectangular cross section, Trans JSME Ser B 63 452-160... 

A physical model of ONB for the explosive boiling and dryout, was suggested. In order to understand why dryout occurred even at a low value of vapor quality x, it is important to keep in mind that the liquid film does not cover the entire heated surface of the micro-channel, and two-phase flow is characterized by an unsteady cyclic behavior. The following assumptions are made in the development of the model ... 

Landau LD, Lifshitz EM (1959) Fluid mechanics, 2nd edn. Pergamon, London Landerman CS (1994) Micro-channel flow boiling mechanisms leading to Burnout. J Heat Transfer Electron Syst ASME HTD-292 124-136 Levich VG (1962) Physicochemical hydrodynamics. Prentice HaU, London Morijama K, Inoue A (1992) The thermohydraulic characteristics of two-phase flow in extremely narrow channels (the frictional pressure drop and heat transfer of boiling two-phase flow, analytical model). Heat Transfer Jpn Res 21 838-856... 

Chapter 9 consists of the following in Sect. 9.2 the physical model of two-phase flow with evaporating meniscus is described. The calculation of the parameters distribution along the micro-channel is presented in Sect. 9.3. The stationary flow regimes are considered in Sect. 9.4. The data from the experimental facility and results related to two-phase flow in a heated capillary are described in Sect. 9.5. 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

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