**4.1.2 Evaluation of existing correlations**

Example of the calculated behaviors in the test channel and detail of slug behavior of are shown in Fig.23. As shown in Fig.23, the fluid mixing between Ch.1 and Ch.2 was observed at a gap between the subchannels. Though inlet quality of both subchannels were equivalent in this case (inlet quality ratio (*X*2/*X*1) was equal to 1.0), fluid mixing occurred between 2 subchannels.

The existing two-phase flow correlation for fluid mixing (fluctuating pressure model (Takemoto, 1997) was evaluated using detailed numerical simulation data. The fluctuating pressure model is expressed as follows:

$$|w\_r| = \sqrt{\frac{2\rho\_l \left|\Delta p\_r\right|}{K\left(1-x\right)^2 \left[1+Bx\left(\frac{\rho\_l}{\rho\_s}-1\right)\right]}} = f(x)\sqrt{|\Delta p\_r|}\tag{21}$$

Development of Two-Phase Flow Correlation

012345

X2/X1

0.00 0.05 0.10 0.15 0.20 0.25 X2(-)

showed underestimation and overestimation respectively.

Predicted

g,T g,S

Fig. 24. Evaluation of the fluctuating pressure model for BWR cases (Case B1~B8).

(a) Gas (b) Liquid

Mass Flow Rate between

(a) 1.3mm gap spacing (Case F1~F4) (b) 1.0mm gap spacing (Case F5~F8)

Evaluated mixing coefficients by fluctuating pressure model and conventional fluid mixing model (Kelly and Kazimi, 1980) for FLWR cases are shown in Fig.25. Predicted mixing coefficients by the TPFIT are also shown in figures. The evaluated mixing coefficients by fluctuating pressure model for relatively low inlet quality cases were in reasonable agreement with the predicted results for both 1.3 mm and 1.0 mm gap spacing. However, evaluated mixing coefficients by conventional fluid mixing model were different from predicted mixing coefficients by the TPFIT code both qualitatively and quantitatively. Evaluated mixing coefficients for relatively high inlet quality cases (inlet quality ratio (*X*2/*X*1) is large) by fluctuating pressure model and conventional fluid mixing model

Fig. 25. Evaluation of the existing correlations for FLWR cases (Case F1~F8).

Subchannels (kg/s)

−0.1


l (

−)

0

0.1

0.2

012345

X2/X1

Fluctuating Pressure Model Cross Flow Model

TPFIT

Gap Width:1.0mm

Predicted

l,T l,S

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 X2(-)

subchannels.

−0.1

TPFIT

Gap Width:1.3mm

Fluctuating Pressure Model Cross Flow Model


Mass Flow Rate between

Subchannels (kg/s)

0

g (

−)

0.1

0.2

for Fluid Mixing Phenomena in Boiling Water Reactor 309

evaluated mixing coefficients, *m,T* were in reasonable agreement with the predicted results. Evaluated mixing coefficients by use of time averaged pressure difference, *m,S* overestimated the predicted results in almost all cases, and it is understood that the fluctuating component of pressure difference restrains the fluid mixing between

where,

*wT*: evaluated moved mass flow rate by the fluctuating pressure model [kg/s]


*B*:time averaged two-phase flow pressure loss coefficient [-]

Fig. 23. Calculated slug behavior of case F5 in mixing section.

By the fluctuating pressure difference model, mixing coefficients for both phases are evaluated by following equations.

$$
\Gamma\_{w,T} = \frac{w\_{w,T}}{\mathcal{W}\_{w1} + \mathcal{W}\_{w2}} \tag{22}
$$

where,

$$w\_{l,T} = -\left(1 - \mathbf{x}\right) f\left(\mathbf{x}\right) \frac{\Delta p\_{\tau}}{\sqrt{|\Delta p\_{\tau}|}} , \; w\_{g,T} = -\mathbf{x} f\left(\mathbf{x}\right) \frac{\Delta p\_{\tau}}{\sqrt{|\Delta p\_{\tau}|}}\tag{23}$$

In above equations, instantaneous pressure difference values and time averaged values (pressure loss coefficient, quality and two-phase flow pressure loss coefficient) are evaluated by numerical results.

To estimate effects of fluctuating pressure on the mixing coefficients, the mixing coefficients using time averaged pressure difference were also evaluated for BWR cases:

$$
\Gamma\_{w,S} = \frac{w\_{w,S}}{W\_{w1} + W\_{w2}} \tag{24}
$$

where,

$$\Delta w\_{l,s} = -\left(1 - \mathbf{x}\right) f(\mathbf{x}) \frac{\Delta p\_s}{\sqrt{|\Delta p\_s|}},\\ w\_{g,s} = -\mathbf{x} f(\mathbf{x}) \frac{\Delta p\_s}{\sqrt{|\Delta p\_s|}}\tag{25}$$

Evaluated mixing coefficients by fluctuating pressure model, *m,T* are shown in Fig.24. Predicted mixing coefficients by TPFIT code and *m,S* are also shown in figures. The

By the fluctuating pressure difference model, mixing coefficients for both phases are

,

*m T*

*l T g T*

using time averaged pressure difference were also evaluated for BWR cases:

,

*m S*

*l S g S*

,

*w W W*

, , 1 () , ( ) *T T*

In above equations, instantaneous pressure difference values and time averaged values (pressure loss coefficient, quality and two-phase flow pressure loss coefficient) are evaluated

To estimate effects of fluctuating pressure on the mixing coefficients, the mixing coefficients

, , 1 () , ( ) *S S*

Evaluated mixing coefficients by fluctuating pressure model, *m,T* are shown in Fig.24. Predicted mixing coefficients by TPFIT code and *m,S* are also shown in figures. The

*p p w x f x w xf x*

,

*w W W*

1 2 *m S*

*m m*

*<sup>p</sup> <sup>p</sup> w x f x w xf x*

1 2 *m T*

*T T*

*S S*

*p p*

*p p*

(22)

(24)

(23)

(25)

*m m*

*wT*: evaluated moved mass flow rate by the fluctuating pressure model [kg/s]

*K*:time averaged pressure loss coefficient [-]

*B*:time averaged two-phase flow pressure loss coefficient [-]

Fig. 23. Calculated slug behavior of case F5 in mixing section.

*x*:time averaged quality [-]

evaluated by following equations.

where,

where,

where,

by numerical results.

evaluated mixing coefficients, *m,T* were in reasonable agreement with the predicted results. Evaluated mixing coefficients by use of time averaged pressure difference, *m,S* overestimated the predicted results in almost all cases, and it is understood that the fluctuating component of pressure difference restrains the fluid mixing between subchannels.

Fig. 24. Evaluation of the fluctuating pressure model for BWR cases (Case B1~B8).

Fig. 25. Evaluation of the existing correlations for FLWR cases (Case F1~F8).

Evaluated mixing coefficients by fluctuating pressure model and conventional fluid mixing model (Kelly and Kazimi, 1980) for FLWR cases are shown in Fig.25. Predicted mixing coefficients by the TPFIT are also shown in figures. The evaluated mixing coefficients by fluctuating pressure model for relatively low inlet quality cases were in reasonable agreement with the predicted results for both 1.3 mm and 1.0 mm gap spacing. However, evaluated mixing coefficients by conventional fluid mixing model were different from predicted mixing coefficients by the TPFIT code both qualitatively and quantitatively. Evaluated mixing coefficients for relatively high inlet quality cases (inlet quality ratio (*X*2/*X*1) is large) by fluctuating pressure model and conventional fluid mixing model showed underestimation and overestimation respectively.

Development of Two-Phase Flow Correlation

Fig. 28. Examples of simulation results.

Fig. 29. Axial cross-sectional averaged pressure and void fraction distribution.

for Fluid Mixing Phenomena in Boiling Water Reactor 311

bottom. Gas and liquid flows pass through three sections along the axial direction, i.e. developing, mixing and outlet sections. Grid numbers are 120×260×1600 (49,920,000). Saturated water and steam at 7.2MPa are used as working fluids. Steam and liquid are injected at constant velocities with values tabulated. The total mass flux is set to 400kg/m2s.

#### **4.2 Development of correlation base on detailed numerical simulation results**

In section 4.1, existing correlations for the two-phase flow fluid mixing phenomena were examined. However, enough results were not obtained. Then, we try to develop new correlation for fluid mixing phenomena in tight lattice rod bundle based on numerical results.

Fig. 26. Simulated region in rod bundle.

Fig. 27. Modeled two sub-channels.

The simulated region in a tight-lattice rod bundle is schematically shown in Fig.26. The diameter of fuel rods is 13.0mm. The smallest gap spacing between two adjacent fuel rods is 1.3mm. Numerical domain used in this simulation is shown in Fig.27. The length and width of the simulated region are 13.0mm and 6.0mm respectively. The two subchannels are separated by a partition plate with the thickness of 0.2mm, in the upper part of which there is a slit with the height of 40mm. Water and steam flow into the subchannels through the

In section 4.1, existing correlations for the two-phase flow fluid mixing phenomena were examined. However, enough results were not obtained. Then, we try to develop new correlation for fluid mixing phenomena in tight lattice rod bundle based on numerical

6

**4.2 Development of correlation base on detailed numerical simulation results** 

Fuel rod

13

The simulated region in a tight-lattice rod bundle is schematically shown in Fig.26. The diameter of fuel rods is 13.0mm. The smallest gap spacing between two adjacent fuel rods is 1.3mm. Numerical domain used in this simulation is shown in Fig.27. The length and width of the simulated region are 13.0mm and 6.0mm respectively. The two subchannels are separated by a partition plate with the thickness of 0.2mm, in the upper part of which there is a slit with the height of 40mm. Water and steam flow into the subchannels through the

Partition plate

unit:mm

Steam inflow section

Water

6

Developing section

Mixing section

Outlet section

Ø13

1.30

Fig. 26. Simulated region in rod bundle.

Ch.2

A

*x*= *y*=0.05

*y*

*z*

Ch.1

Fig. 27. Modeled two sub-channels.

A'

*x*

results.

bottom. Gas and liquid flows pass through three sections along the axial direction, i.e. developing, mixing and outlet sections. Grid numbers are 120×260×1600 (49,920,000). Saturated water and steam at 7.2MPa are used as working fluids. Steam and liquid are injected at constant velocities with values tabulated. The total mass flux is set to 400kg/m2s.

Fig. 28. Examples of simulation results.

Fig. 29. Axial cross-sectional averaged pressure and void fraction distribution.

Development of Two-Phase Flow Correlation

from the following equation:

void fraction of the bubble zone,

the slug, given by Taitel and Barnea (1990)

where 

where

Here 

the slug, *Vs*, is given as

to evaluate the acceleration pressure drop for vertical flow:

for Fluid Mixing Phenomena in Boiling Water Reactor 313

In the slug front region, flow after the bubble is highly disturbed and vortexes may occur there. Then additional pressure loss must be considered. A slug that has stabilized in length can be considered as a body receiving and losing mass at equal rates. The velocity of the liquid in the film just before pickup is lower than that in the slug and a force is therefore necessary to accelerate this liquid to slug velocity. This force manifests itself as a pressure drop. If the pressure along the liquid film in the bubble zone can be assumed to be essentially constant, this force can be evaluated by the sum of gravity and wall shear stress in the liquid film zone (Taitel and Barnea, 1990). Here the following equations are employed

> *le a s le W P VV A*

*le*, *Vle* are the void fraction and mean velocity of liquid film at font of liquid slug. *Vt*

where *Wle* is the rate at which mass is picked up by the liquid slug, which can be obtained

· ·1 · *W A VV le l* 

is the propagation velocity of the slug unit or average translational velocity of the nose of

Here, *Db* is the bubble diameter, which may be approximately estimated from the average

· *D A b b* 

0 1 *<sup>b</sup> <sup>L</sup> b l b*

1 *<sup>g</sup> <sup>l</sup>*

*W W*

 

 

*<sup>l</sup>* is the local void fraction in the bubble zone. In Eq.(28), the mean velocity of fluid in

*l g*

 

<sup>2</sup>

*V V*

2 0. · *l s ls*

*L*

*s*

*sf*

*L*

*A* 

3

The pressure drop due to acceleration takes place in the slug front which penetrates a distances into the body of the slug. The depth of penetration of the liquid film into the slug appears to depend on the relative velocity between slug and film, and may be obtained from

*V*

the following equation (Dukler and Hubbard, 1975).

And the acceleration gradient in the slug front is given by,

*dx*

*b*. , (28)

*le l le* (29)

1.2 0.35 *V V ls b gD* (30)

(31)

(33)

(32)

(34)

Figure 28 shows the time change of void fraction distribution observed from the section A-A', as indicated in Fig.27. The red color denotes the fuel rod. It can be seen that the gas phases cross the slit mutually. Figure 29 shows the axial cross-sectional pressure and void distributions around a slug bubble. It illustrates that most of pressure gradient takes place in liquid slug zone and the pressure almost keeps constant in large bubble zone. Below the bubble, there exists large pressure gradient. This is reasonable because flow after the bubble is highly disturbed and vortexes may occur there.

In simulation results, strong correlation for liquid phase means that liquid fluid mixing occurs due to local inter-subchannel differential pressure. Then we decided to develop an approximate model for prediction of differential pressure between subchannels. Pressure difference between subchannels is induced by difference of axial pressure distribution in each subchannel. Therefore, to evaluate mixing flow rate between subchannels by fluid mixing phenomena, axial pressure distribution in subchannels must be required. In following section, axial pressure distribution (axial pressure loss) model is developed.

Fig. 30. Physical model for slug flow.

Based on the above-mentioned results of the numerical simulation, we considered pressure distributions in bubble zone, slug front and slug core (see Fig.30). In the bubble zone, the pressure almost keeps constant in this zone. Therefore, pressure drop across a bubble zone is assumed to be zero as follows:

$$\frac{dP\_b}{dz} = 0\tag{26}$$

In slug front and slug core, there are three contributions to the pressure drop across a slug. The first, *dPa,s*, is the pressure drop that results from the acceleration of the slow moving liquid film to slug velocity in the slug front zone. The second, *dPf,s*, is the pressure drop required to overcome wall shear. The third, *dPg,s*, is the static head pressure drop. The total pressure gradient across a liquid slug is thus given by

$$\frac{dP\_s}{dz} = \frac{dP\_{a,s}}{dz} + \frac{dP\_{f,s}}{dz} + \frac{dP\_{g,s}}{dz} \,. \tag{27}$$

In the slug front region, flow after the bubble is highly disturbed and vortexes may occur there. Then additional pressure loss must be considered. A slug that has stabilized in length can be considered as a body receiving and losing mass at equal rates. The velocity of the liquid in the film just before pickup is lower than that in the slug and a force is therefore necessary to accelerate this liquid to slug velocity. This force manifests itself as a pressure drop. If the pressure along the liquid film in the bubble zone can be assumed to be essentially constant, this force can be evaluated by the sum of gravity and wall shear stress in the liquid film zone (Taitel and Barnea, 1990). Here the following equations are employed to evaluate the acceleration pressure drop for vertical flow:

$$
\Delta P\_s = \frac{\mathcal{W}\_{\rm le}}{A} \left( V\_s - V\_{\rm le} \right),
\tag{28}
$$

where *Wle* is the rate at which mass is picked up by the liquid slug, which can be obtained from the following equation:

$$\mathcal{W}\_{\mathbb{k}} = \rho\_{\mathbb{l}} \colon A \cdot \left(\mathbb{1} - \alpha\_{\mathbb{k}}\right) \cdot \left(V\_{\mathbb{l}} - V\_{\mathbb{k}}\right) \tag{29}$$

where *le*, *Vle* are the void fraction and mean velocity of liquid film at font of liquid slug. *Vt* is the propagation velocity of the slug unit or average translational velocity of the nose of the slug, given by Taitel and Barnea (1990)

$$V\_{\parallel} = 1.2V\_{\ast} + 0.35\sqrt{gD\_{\ast}} \tag{30}$$

Here, *Db* is the bubble diameter, which may be approximately estimated from the average void fraction of the bubble zone, *b*.

$$D\_{\flat} = \sqrt{A \cdot \alpha\_{\flat}} \tag{31}$$

where

312 Computational Simulations and Applications

Figure 28 shows the time change of void fraction distribution observed from the section A-A', as indicated in Fig.27. The red color denotes the fuel rod. It can be seen that the gas phases cross the slit mutually. Figure 29 shows the axial cross-sectional pressure and void distributions around a slug bubble. It illustrates that most of pressure gradient takes place in liquid slug zone and the pressure almost keeps constant in large bubble zone. Below the bubble, there exists large pressure gradient. This is reasonable because flow after the bubble

In simulation results, strong correlation for liquid phase means that liquid fluid mixing occurs due to local inter-subchannel differential pressure. Then we decided to develop an approximate model for prediction of differential pressure between subchannels. Pressure difference between subchannels is induced by difference of axial pressure distribution in each subchannel. Therefore, to evaluate mixing flow rate between subchannels by fluid mixing phenomena, axial pressure distribution in subchannels must be required. In following section, axial pressure distribution (axial pressure loss) model is developed.

Based on the above-mentioned results of the numerical simulation, we considered pressure distributions in bubble zone, slug front and slug core (see Fig.30). In the bubble zone, the pressure almost keeps constant in this zone. Therefore, pressure drop across a bubble zone

<sup>0</sup> *<sup>b</sup> dP*

In slug front and slug core, there are three contributions to the pressure drop across a slug. The first, *dPa,s*, is the pressure drop that results from the acceleration of the slow moving liquid film to slug velocity in the slug front zone. The second, *dPf,s*, is the pressure drop required to overcome wall shear. The third, *dPg,s*, is the static head pressure drop. The total

> , , , *a s <sup>f</sup> <sup>s</sup> <sup>g</sup> <sup>s</sup> <sup>s</sup> dP dP dP dP dz dz dz dz*

*dz* (26)

. (27)

is highly disturbed and vortexes may occur there.

Fig. 30. Physical model for slug flow.

is assumed to be zero as follows:

pressure gradient across a liquid slug is thus given by

$$\alpha\_{\flat} = \frac{1}{L\_{\flat}} \int\_{0}^{L\_{\flat}} \alpha\_{\flat} d\mathbf{x} \tag{32}$$

Here *<sup>l</sup>* is the local void fraction in the bubble zone. In Eq.(28), the mean velocity of fluid in the slug, *Vs*, is given as

$$V\_{\circ} = \frac{1}{A} \left( \frac{\mathcal{W}\_{l}}{\rho\_{l}} + \frac{\mathcal{W}\_{\circ}}{\rho\_{\circ}} \right) \tag{33}$$

The pressure drop due to acceleration takes place in the slug front which penetrates a distances into the body of the slug. The depth of penetration of the liquid film into the slug appears to depend on the relative velocity between slug and film, and may be obtained from the following equation (Dukler and Hubbard, 1975).

$$L\_{\prec} = 0.3 \frac{\rho\_{\succ} \left(V\_{\succ} - V\_{\succ}\right)^{\ast}}{2} \tag{34}$$

And the acceleration gradient in the slug front is given by,

Development of Two-Phase Flow Correlation

Fig. 31. Instantaneous axial pressure distribution.

weights in the total pressure drop.

for Fluid Mixing Phenomena in Boiling Water Reactor 315

Here, the model is evaluated with the axial pressure profile obtained from the numerical simulation for a subchannel with cross flow. Figure 31 shows the evaluation results at an instant with time of 0.8600 s. From the figure, it can be seen that the prediction of the model is generally in agreement with the simulation results, especially for mixing section (abscissa from 20 mm to 60 mm). This means the model may be applicable to subchannels. And furthermore, we can see that the three contributions to pressure drop have almost similar

(Distance from Outlet=32.5mm)

*z*=127.5mm

Fig. 32. Fluctuation of differential pressure between two subchannels.

$$\frac{dP\_{a,s}}{dz} = \frac{\Delta P\_s}{L\_{sf}} \cdot \tag{35}$$

In the slug front and slug core region, frictional and gravity pressure drop are acting in subchannels. Frictional pressure drop takes place when liquid slug moves along the channel wall. For the calculation of this term, the similarity analysis for two-phase frictional pressure drop (Dukler et al., 1975) is applied. Within the liquid slug the bubble size is usually small and thus the flow can be deemed as the homogeneous one with negligible two-phase slip. Under this condition, the frictional pressure drop can be calculated as follows:

$$\frac{dP\_{f,s}}{dz} = \frac{2f\_s}{D\_h} \left[ \rho\_\uparrow \left( 1 - a\_\downarrow \right) + \rho\_\downarrow a\_\downarrow \right] V\_\downarrow^2 \tag{36}$$

For "non-slip" conditions *fs* could be correlated as a unique function of *Res*

$$f\_\* = 0.079 \cdot \text{Re}\_\*^{-0.025} \tag{37}$$

Here the Reynolds number *Res* is defined in the following manner:

$$Re\_s = D\_h V\_s \frac{\rho\_l \left(1 - \alpha\_\*\right) + \rho\_g \alpha\_\*}{\mu\_l \left(1 - \alpha\_\*\right) + \mu\_g \alpha\_\*} \tag{38}$$

The static head term for the slug front and slug core can be obtained from the following simple equation:

$$\frac{dP\_{\rm x,s}}{dz} = \left[\rho\_{\uparrow}\left(1 - a\_{\ast}\right) + \rho\_{\downarrow}a\_{\ast}\right]g\tag{39}$$

The axial relative pressure in question could be obtained through the integration of differential pressure as follows

$$\begin{aligned} P &= \int\_{0}^{z} \frac{dP}{dz} dz\\ \frac{dP}{dz} &\int\_{z}^{D\_{s}^{p}} \frac{dP\_{s}}{dz} \text{ in slug zone} \\ \frac{dP\_{b}}{dz} &\text{in bubble zone} \end{aligned} \tag{40}$$

The above equations are incomplete and some parameters are still unknown, such as local void fraction in the bubble zone *<sup>l</sup>*, the mean velocity of liquid film at front of liquid slug, the bubble length *Lb* as well as that of slug unit *Lu*, and instantaneous bubble distribution. These parameters may be predicted by assuming the idealized bubble shape and setting the initial bubble distribution along the channel. We leave them for future study. In this study we aim at exploring the mechanism of differential pressure fluctuation inducing cross flow as a first step, therefore numerical simulation results are used to evaluate these unknown parameters for simplicity. In addition, a criterion to reduce the detailed three-dimensional simulation results is introduced to determine locations and lengths of bubble zones (or slug zones). The regions, where the cross-sectional averaged void fraction is larger than 0.3, are deemed as bubble zones. Other regions are regarded as slug zones.

*a s*, *a*

In the slug front and slug core region, frictional and gravity pressure drop are acting in subchannels. Frictional pressure drop takes place when liquid slug moves along the channel wall. For the calculation of this term, the similarity analysis for two-phase frictional pressure drop (Dukler et al., 1975) is applied. Within the liquid slug the bubble size is usually small and thus the flow can be deemed as the homogeneous one with negligible two-phase slip.

, <sup>2</sup> <sup>2</sup> 1 · *f s <sup>s</sup>*

 

 1 1

*l s gs*

 

 

*l s gs*

 

in slug zone

in bubble zone

The above equations are incomplete and some parameters are still unknown, such as local

the bubble length *Lb* as well as that of slug unit *Lu*, and instantaneous bubble distribution. These parameters may be predicted by assuming the idealized bubble shape and setting the initial bubble distribution along the channel. We leave them for future study. In this study we aim at exploring the mechanism of differential pressure fluctuation inducing cross flow as a first step, therefore numerical simulation results are used to evaluate these unknown parameters for simplicity. In addition, a criterion to reduce the detailed three-dimensional simulation results is introduced to determine locations and lengths of bubble zones (or slug zones). The regions, where the cross-sectional averaged void fraction is larger than 0.3, are

 

The static head term for the slug front and slug core can be obtained from the following

 , 1 · *g s l s gs g*

0

 

deemed as bubble zones. Other regions are regarded as slug zones.

*s*

*b*

*z*

*dP P dz dz dP dP dz dz dP dz*

 

 

The axial relative pressure in question could be obtained through the integration of

*l s s gs*

  *V*

(36)

0.025 0.07 ·9 *<sup>s</sup> R <sup>s</sup> f e* (37)

(39)

*<sup>l</sup>*, the mean velocity of liquid film at front of liquid slug,

(38)

(40)

Under this condition, the frictional pressure drop can be calculated as follows:

*dP f*

*z D*

For "non-slip" conditions *fs* could be correlated as a unique function of *Res*

*d*

Here the Reynolds number *Res* is defined in the following manner:

*dP dz*

simple equation:

differential pressure as follows

void fraction in the bubble zone

*h*

*s hs*

*Re D V*

*dP P dz L*

*sf*

. (35)

Fig. 31. Instantaneous axial pressure distribution.

Here, the model is evaluated with the axial pressure profile obtained from the numerical simulation for a subchannel with cross flow. Figure 31 shows the evaluation results at an instant with time of 0.8600 s. From the figure, it can be seen that the prediction of the model is generally in agreement with the simulation results, especially for mixing section (abscissa from 20 mm to 60 mm). This means the model may be applicable to subchannels. And furthermore, we can see that the three contributions to pressure drop have almost similar weights in the total pressure drop.

Fig. 32. Fluctuation of differential pressure between two subchannels.

Development of Two-Phase Flow Correlation

*Trans. JSME*, *Ser. B*, 66, pp. 1191-1197

**6. Acknowledgment** 

Japanese).

219-232.

97.

541.

10532.

284.

132

3107-3113 (in Japanese).

**7. References** 

for Fluid Mixing Phenomena in Boiling Water Reactor 317

This research was conducted using a supercomputer of the Japan Atomic Energy Agency.

Lahey, Jr, R. T. & Moody, F. J., (1993), *The Thermal-Hydraulics of a Boiling Water Nuclear* 

Kawahara, A., Sadatomi, M. & Tomino, T., (2000), Prediction of Gas and Liquid Turbulent

Sumida, I,, Yamakita, T., Sakai, S., Iwai, K., & Kondo, T., (1995), Investigation of Two-Phase

Takemoto, S., Kondo, T., Inatomi, T., Sakai, S., Wakai, K., & Sumida, I., (1997), Investigation

Yabe, T., & Aoki, T., (1991), A Universal Solver for Hyperbolic Equations by Cubic-

Brackbill, J. U., Kothe, D. B., & Zemach, C., (1992), A Continuum Method for Modeling

Gueyffier, D., Nadim, J. Li, A., Scardovelli, R., & Zaleski, S., (1999), Volume-of-Fluid

Rayleigh, L., (1879), On the Capillary Phenomena of Jets, *Proc. R. Soc. London*, 29, p. 71-

Moran, K., Inumaru, J., & Kawaji, M., (2002), Instantaneous hydrodynamics of a laminar

Nusselt, W., (1916), Die oberflachenkondensation des wasserdamphes, *VDI-Zs 60*,

Yoshida, H., Nagayoshi, T., Takase, K., & Akimoto, H., (2007), Development of Design

Uchikawa, S., Okubo, T., Kugo, T., Akie, H., Takeda, R., Nakano, Y., Ohnuki, A., &

Taitel, Y., & Barnea, D., (1990), Two-Phase Slug Flow, *Advances in Heat Transfer*, 20, pp. 83-

Technology on Thermal-Hydraulic Performance in Tight-Lattice Rod Bundles: IV - Numerical Evaluation of Fluid Mixing Phenomena using Advanced Interface-Tracking Method –, *Proc. of ICONE15 (CD-ROM)*, Nagoya, Japan, September 22-26,

Iwamura, T., (2007), Conceptual Design of Innovative Water Reactor for Flexible Fuel Cycle (FLWR) and its Recycle Characteristics, *J. Nucl. Sci. Tech.*, 44, 3, pp.277-

Surface Tension, *J.* Comput*. Phys*., 100, pp. 335-354.

wavy liquid film, *Int. J of Multiphase Flow*, 28 pp.731-755.

Flows, *J. Comput. Phys*., 152, pp. 423-456.

Mixing Rates between Rod Bundle Subchannels in a Two-Phase Slug-Churn Flow,

Flow Mixing between Two Subchannels (1st Report, Fluctuating Pressure Model and its Experimental Verification), *Trans. JSME*, *Ser. B*, 61, pp. 2662-2668 (in

of Two-Phase Flow Mixing between Two Subchannels (2nd Report, Verification of Fluctuating Pressure Model without Steady Pressure), *Trans. JSME*, *Ser. B*, 61, pp.

Polynomial Interpolation I. One-Dimensional Solver, *Comput.Phys.Commun*., 66, pp.

Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional

*Reactor*, American Nuclear Society, La Grange Park, Illinois USA.

In this study, the way to evaluate the cross-section averaged pressure distribution in a single subchannel has been developed. If we assume that cross flow has minor effect on the pressure distribution in each subchannel, we can evaluate the pressure differences between subchannels by axial pressure distribution for each subchannel. In this way, the prediction of differential pressure by the model is compared to that obtained from the numerical simulation as shown in Fig. 32. It can be seen that the prediction of this model may reproduce the results of numerical simulation generally. For the time of 0.22 or 0.27, cross flow may have not negligible effect on inter-subchannel differential pressures and thus predictions deviate from the simulation results.
