This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

Some characteristics of air-water two-phase flow in small diameter vertical tubes

This paper explores the recent research developments in high-heat-flux thermal management. Cooling schemes such as pool boiling, detachable heat sinks, channel flow boiling, microchannel and mini-channel heat sinks, jet-impingement, and sprays, are discussed and compared relative to heat dissipation potential, reliability, and packaging concerns. It is demonstrated that, while different cooling options can be tailored to the specific needs of individual applications, system considerations always play a paramount role in determining the most suitable cooling scheme. It is also shown that extensive fundamental electronic cooling knowledge has been amassed over the past two decades. Yet there is now a growing need for hardware innovations rather than perturbations to those fundamental studies. An example of these innovations is the cooling of military avionics, where research findings from the electronic cooling literature have made possible the development of a new generation of cooling hardware which promise order of magnitude increases in heat dissipation compared to today's cutting edge avionics cooling schemes.

Assessment of high-heat-flux thermal management schemes

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

Numerical flow simulation utilising a full multiphase model is impractical for a suspension possessing wide distributions in the particle size or density. Various approximations are usually made to simplify the computational task. In the simplest approach, the suspension is represented by a homogeneous single-phase system and the influence of the particles is taken into account in the values of the physical properties. This study concentrates on the derivation and closing of the model equations. The validity of the mixture model is also carefully analysed. Starting from the continuity and momentum equations written for each phase in a multiphase system, the field equations for the mixture are derived. The mixture equations largely resemble those for a single-phase flow but are represented in terms of the mixture density and velocity. The volume fraction for each dispersed phase is solved from a phase continuity equation. Various approaches applied in closing the mixture model equations are reviewed. An algebraic equation is derived for the velocity of a dispersed phase relative to the continuous phase. Simplifications made in calculating the relative velocity restrict the applicability of the mixture model to cases in which the particles reach the terminal velocity in a short time period compared to the characteristic time scale of the flow of the mixture. (75 refs.)

On the mixture model for multiphase flow

http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/178170/1/j.anucene.2013.06.014.pdf

Reactivity insertion transient analysis for KUR low-enriched uranium silicide fuel core

As the two-phase flow regime evolves from bubbly to slug flows along the flow direction in a vertical large diameter pipe, the void fraction increases first in the bubbly flow region, then decreases in the transitional region, and finally increases again in the slug flow region. The N-shaped profile of void fraction was numerically analyzed by using the one-dimensional two-fluid model. Its interfacial drag model was modified by including constitutive equations of C0 and Vgj developed by Shen et al. [2] for evolving two-phase flow from bubbly to slug flows in a large diameter pipe. The numerical calculation predicted well the N-shaped profile of the measured axial void fraction distribution from the present experiments. The predicted average gas and liquid velocities indicated that the average gas velocity increased significantly and the average liquid velocity decreased slightly when the void profile is N-shaped one. The phenomenon can be attributed to the formation and development of large bubbles of pipe size.

Interfacial Drag Model and Numerical Analysis for Gas-Liquid Two-Phase Flow in a Large Diameter Pipe

An approximate method for the quantification of a neutron radiography image was proposed for measuring the phase-distribution of multiphase materials with small neutrondashattenuation. Since it is not necessary for this method to put a standard calibration sample in a field of a view, this method has an advantage of measuring the phase-distribution of multiphase materials with unknown internal-structure and neutrondashattenuation in the object in an enlarged field of view. Although its application is limited to an object with small neutrondashattenuation, it was revealed from a numerical analysis that the approximate method can be applicable to heavy water, liquid sodium andliquid potassium, which are important materials in relation to research on the thermalhydraulics of the nuclear reactor. The validity of the approximate method was also confirmed experimentally by comparing the void fraction of air-water flows in round tubes measured by the approximate method with those by the other more-accurate method.

Approximate method for measurement of phase-distribution in multiphase materials with small neutrondashattenuation using a neutron beam as a probe

Dynamic behavior of a two-phase bubble, i.e. a steam bubble containing a droplet evaporating in the bubble, in the molten alloy was clearly visualized using high-frame-rate neutron radiography. In relation to some direct contact heat exchanger design with molten lead–bismuth (Pb–Bi), experiments have been done at JRR-3M of JAEA (Japan Atomic Energy Agency) with water droplets evaporating in a stable thermally stratified Newton's alloy pool. The instantaneous shape and size of the bubble has been iteratively estimated from the void fraction distributions and total void volume by assuming a symmetrical bubble shape.

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Shape measurement of bubble in a liquid metal

In an actual boiling channel, e.g., a boiler water-tube, the circumferential heat flux is not uniform. Thus, the critical heat flux (CHF) of a non-uniformly heated tube becomes an important design factor for conventional boilers, especially for a compact water-tube boiler with a tube-nested combustor. A small compact boiler is operated under low-pressure and low-mass-flux conditions compared with a large-scale boiler, thus the redistribution of liquid film strongly affects the characteristics of CHF. In this investigation, non-uniform heat flux distribution along the circumferential direction was generated by using the Joule heating of SUS304 tubes with the wall thickness distribution. The heated length of test-section was 900 mm with an inner diameter of 20 mm and an outer diameter of 24 mm. The center of the inner tube surface was shifted by e=0, 0.5, 1.0, 1.5 mm from the center of the outer tube surface. The heat flux ratio between maximum and minimum heat flux of these tubes corresponded to 1.0, 1.7, 3.0, and 7.0, respectively. The experimental conditions were as follows: system pressure at 0.3 and 0.4 MPa, mass flux of 10–100kg/(m2s), inlet temperatures at 30° and 80°. The experimental results showed an increase in the critical heat flux substantiated by the existence of the redistribution of the flow. These characteristics are explained by using a concept similar to that of Butterworth's spreading model. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(1): 47–60, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20095

Kaichiro Mishima

Papers

Reactivity insertion transient analysis for KUR low-enriched uranium silicide fuel core

Interfacial Drag Model and Numerical Analysis for Gas-Liquid Two-Phase Flow in a Large Diameter Pipe

Approximate method for measurement of phase-distribution in multiphase materials with small neutrondashattenuation using a neutron beam as a probe

Shape measurement of bubble in a liquid metal

Critical heat flux in non-uniformly heated tube under low-pressure and low-mass-flux condition