**1. Introduction**

286 Computational Simulations and Applications

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Combustion in SI Engines: Comparisons of Predictions of a Fractal Burning Model

Turbulent Flame Propagation in a Spark Ignition Engine by Using Fractal Burning

The two-phase fluid mixing phenomena in fuel bundles of BWR plays an important role in the thermal-hydraulic performance of the fuel rod bundle, because it has strong effects on spatial distributions of the void fraction, quality and mass flow rate within it. The subchannel analysis method has been used for the prediction of the macroscopic thermalhydraulic characteristics, such as critical power and pressure loss, of a wide variety of fuel rod bundle designs. This method evaluates the fluid mixing effects using a unique model, known as a "cross flow model". The first successful cross flow model for gas-liquid twophase flow was devised by Lahey and Moody (1993). In their model, cross flow phenomena were decomposed into three components, namely flow diversions caused by transverse pressure gradients, turbulent mixing caused by stochastic pressure and flow fluctuations and a void drift that is unique to gas-liquid two-phase flow.

Recently, there were studies of cross flow model improvements. Kawahara et al. (1999) presented an improved turbulent mixing model based on RMS (Root Mean Square) values of subchannel-to-subchannel differential pressure fluctuations. One of the advantages of this model was its ability to consider channel gap geometries and scales. Sumida et al.(1995) and Takemoto et al.(1997) supposed that the turbulent mixing and void drift phenomena were only transient components of the diversion cross flow caused by differential pressure fluctuations between the subchannels, and formulated the model known as the "fluctuating pressure model". Although both models appear promising for predicting the fluid mixing phenomena however, their applicability under actual plant operation conditions is presently unclear because it is impossible to simulate differential pressure fluctuations under steamwater high-pressure conditions without relying on experimental data. Although the cross flow model remains the most popular approach today, the mechanics of the third component, the void drift, are still unclear and there is no widely accepted understanding of it yet.

In the cross flow model and subchannel analysis, two-phase flow correlations are used to evaluate effects of flow conditions on two-phase flow characteristic easily. To create, modify or confirm these correlations, "actual scale tests" those simulate flow conditions and flow channel of actual fuel bundles are required. In actual BWR, pressure and temperature equals to about 7.2MPa and 560K respectively. Then the actual scale tests take a long time and

Development of Two-Phase Flow Correlation

of volume fraction of liquid.

Two-phase fluid density

*k*

and gas phases in two phase flow are defined as following equation.

Energy:

for Fluid Mixing Phenomena in Boiling Water Reactor 289

1 *<sup>k</sup>*

(4)

(5)

*g l f =1- f* (6)

*f f* (7)

in

*e e p u T u q t x x xx*

where *u*, *p*, *e*, *T* are velocity, static pressure, internal energy and temperature, and *g* and

the momentum equation are gravity and surface tension force, respectively. In above equations, subscripts *g* and *l* are used to represent gas and liquid phases. The mass of liquid

 

 

pressure and temperature fields based on the fluid property routine.

Fig.2 for 3-dimensional case). The function *F*(**x**) is expressed as follows:

1

*i i i*

**2.2 Outline of advanced interface tracking method** 

*k k kk*

*l l l g g g*

 

is calculated as sum of mass of both phases:

*l g*

Eqs. (1) and (2) are solved in the advanced interface tracking method described in sec.2.2. The momentum equation (Eq. (3)) is solved by the CIP (Cubic Interpolated Pseudo-particle) method (Yabe and Aoki, 1991). The energy equation (Eq. (4)) is used to obtain the Poison equation for static pressure. Temperature is estimated by means of a fluid property routine based on the static pressure and local density of both phases. The ILUCGS method is used to solve the Poison equation for static pressure. In the TPFIT code, a Cartesian coordinate system and staggered grid are used. The surface tension force in the momentum equation is estimated using the CSF model (Blackbill et al., 1992). In the CSF model, volume fraction of liquid *fl* is required and evaluated in the advanced interface tracking method, too. The local viscosities and thermal conductivities of liquid and gas were evaluated using solved static

The fundamental concept of the advanced interface tracking method is quite simple. That is, a transported volume of liquid and gas between neighboring calculation control volumes during each time step is calculated through the movement of approximated gas-liquid interfaces, as estimated in the Lagrangian system. Schematic drawings of the major three operational steps within each time step in the two-dimensional case are shown in Figure 1. In the first step (reconstruction step), as shown in Figure 1 (a), a gas-liquid interface in each control area for calculations is reconstructed, taking account of the liquid fraction represented by it and its surroundings. In the reconstruction step, the gas-liquid interface is approximated by a linear function: *F*(**x**) as same as PLIC (Gueyffier, et al., 1999) method (see

*F ax b xxx*

<sup>123</sup> , ,, *mn*

**<sup>x</sup> x** (8)

 

*f f f f*

In Eq. (5), *f* is volume fraction of fluid, and Volume fraction of gas phase is evaluated by use

 

entail great cost, development of a method that enables the thermal-hydraulic design of BWRs without these actual size tests is desired.

It is expected that large scale numerical simulations (numerical simulations by large scale computer) would replace certain large-scale tests and thermal-hydraulic information, some of which is currently difficult or impossible to measure experimentally, would be obtained. And new design method will be developed based on these numerical simulations.

For this reason we developed an advanced thermal-hydraulic design method for BWRs using innovative two-phase flow simulation technology. For this, the following are required: (1) an advanced simulation method with high accuracy prediction, (2) verification of simulation method; and, (3) analytical method to confirm or modify the correlations by detailed numerical simulation data. In this study, we are developing the method to create or modify the two-phase flow correlations for the fluid mixing phenomena in BWR based on advanced numerical simulation technic.
